LMFDB - Embedded newform 819.2.n.d.172.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.6
Root			$0.217953 + 0.377506i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.d.100.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929081 - 1.60921i) q^{2} +(-0.726381 - 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} +(1.58836 - 2.11592i) q^{7} +1.01686 q^{8} +O(q^{10})$	\(q+(0.929081 - 1.60921i) q^{2} +(-0.726381 - 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} +(1.58836 - 2.11592i) q^{7} +1.01686 q^{8} -0.366731 q^{10} +4.18274 q^{11} +(-2.72221 + 2.36423i) q^{13} +(-1.92926 - 4.52187i) q^{14} +(2.39750 - 4.15260i) q^{16} +(0.420653 + 0.728592i) q^{17} +1.35175 q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +(-2.05760 + 3.56386i) q^{23} +(2.48052 - 4.29639i) q^{25} +(1.27540 + 6.57718i) q^{26} +(-3.81585 - 0.461395i) q^{28} +(-4.11931 - 7.13485i) q^{29} +(0.640350 - 1.10912i) q^{31} +(-3.43809 - 5.95495i) q^{32} +1.56328 q^{34} +(-0.518396 - 0.0626819i) q^{35} +(-1.52242 + 2.63692i) q^{37} +(1.25589 - 2.17526i) q^{38} +(-0.100344 - 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(-3.03826 - 5.26242i) q^{44} +(3.82334 + 6.62223i) q^{46} +(-5.83204 - 10.1014i) q^{47} +(-1.95424 - 6.72168i) q^{49} +(-4.60921 - 7.98339i) q^{50} +(4.95187 + 1.70756i) q^{52} +(2.32398 - 4.02525i) q^{53} +(-0.412757 - 0.714916i) q^{55} +(1.61513 - 2.15159i) q^{56} -15.3087 q^{58} +(3.02905 + 5.24648i) q^{59} -11.3657 q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(0.672726 + 0.231978i) q^{65} +13.3970 q^{67} +(0.611109 - 1.05847i) q^{68} +(-0.582500 + 0.775973i) q^{70} +(-2.98520 + 5.17051i) q^{71} +(-1.94273 + 3.36491i) q^{73} +(2.82891 + 4.89982i) q^{74} +(-0.981887 - 1.70068i) q^{76} +(6.64368 - 8.85034i) q^{77} +(5.36669 + 9.29537i) q^{79} -0.946353 q^{80} +10.0284 q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(4.94994 + 8.57354i) q^{86} +4.25324 q^{88} +(-5.99207 + 10.3786i) q^{89} +(0.678673 + 9.51522i) q^{91} +5.97840 q^{92} -21.6737 q^{94} +(-0.133392 - 0.231042i) q^{95} +(-9.73637 + 16.8639i) q^{97} +(-12.6323 - 3.10019i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29} + 16 q^{31} - 8 q^{32} + 32 q^{34} - 8 q^{35} - 13 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} + 16 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} - 25 q^{52} + 2 q^{53} + 9 q^{55} + 18 q^{56} + 16 q^{58} - 13 q^{59} + 10 q^{61} - 5 q^{62} - 30 q^{64} - 19 q^{65} + 22 q^{67} - 29 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} + 3 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} - 14 q^{80} - 2 q^{82} + 54 q^{83} - q^{85} + 7 q^{86} - 4 q^{89} - 20 q^{91} - 54 q^{92} - 90 q^{94} + 6 q^{95} - 35 q^{97} - 62 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.929081	−	1.60921i	0.656959	−	1.13789i	−0.324440	−	0.945906i	$-0.605176\pi$
$2$	0.929081	−	1.60921i	0.656959	−	1.13789i	0.981399	−	0.191980i	$-0.0614909\pi$
$3$		0			0
$3$		0			0
$4$	−0.726381	−	1.25813i	−0.363191	−	0.629065i
$5$	−0.0986811	−	0.170921i	−0.0441315	−	0.0764381i	0.843116	−	0.537732i	$-0.180719\pi$
$5$	−0.0986811	−	0.170921i	−0.0441315	−	0.0764381i	−0.887247	+	0.461294i	$0.847385\pi$
$6$		0			0
$7$	1.58836	−	2.11592i	0.600343	−	0.799743i
$7$	1.58836	−	2.11592i	0.600343	−	0.799743i
$8$	1.01686			0.359513
$9$		0			0
$10$	−0.366731			−0.115970
$11$	4.18274			1.26114			0.630571	−	0.776131i	$-0.282821\pi$
$11$	4.18274			1.26114			0.630571	+	0.776131i	$0.282821\pi$
$12$		0			0
$13$	−2.72221	+	2.36423i	−0.755005	+	0.655719i
$13$	−2.72221	+	2.36423i	−0.755005	+	0.655719i
$14$	−1.92926	−	4.52187i	−0.515616	−	1.20852i
$15$		0			0
$16$	2.39750	−	4.15260i	0.599376	−	1.03815i
$17$	0.420653	+	0.728592i	0.102023	+	0.176709i	0.912518	−	0.409036i	$-0.134135\pi$
$17$	0.420653	+	0.728592i	0.102023	+	0.176709i	−0.810495	+	0.585746i	$0.800802\pi$
$18$		0			0
$19$	1.35175			0.310113			0.155057	−	0.987906i	$-0.450444\pi$
$19$	1.35175			0.310113			0.155057	+	0.987906i	$0.450444\pi$
$20$	−0.143360	+	0.248307i	−0.0320563	+	0.0555232i
$21$		0			0
$22$	3.88610	−	6.73092i	0.828519	−	1.43504i
$23$	−2.05760	+	3.56386i	−0.429038	+	0.743116i	−0.996788	−	0.0800850i	$-0.974481\pi$
$23$	−2.05760	+	3.56386i	−0.429038	+	0.743116i	0.567750	+	0.823201i	$0.307814\pi$
$24$		0			0
$25$	2.48052	−	4.29639i	0.496105	−	0.859279i
$26$	1.27540	+	6.57718i	0.250126	+	1.28989i
$27$		0			0
$28$	−3.81585	−	0.461395i	−0.721129	−	0.0871954i
$29$	−4.11931	−	7.13485i	−0.764936	−	1.32491i	−0.940280	−	0.340401i	$-0.889437\pi$
$29$	−4.11931	−	7.13485i	−0.764936	−	1.32491i	0.175344	−	0.984507i	$-0.443896\pi$
$30$		0			0
$31$	0.640350	−	1.10912i	0.115010	−	0.199203i	−0.802774	−	0.596284i	$-0.796643\pi$
$31$	0.640350	−	1.10912i	0.115010	−	0.199203i	0.917784	+	0.397080i	$0.129977\pi$
$32$	−3.43809	−	5.95495i	−0.607774	−	1.05270i
$33$		0			0
$34$	1.56328			0.268100
$35$	−0.518396	−	0.0626819i	−0.0876249	−	0.0105952i
$36$		0			0
$37$	−1.52242	+	2.63692i	−0.250285	+	0.433506i	−0.963604	−	0.267333i	$-0.913858\pi$
$37$	−1.52242	+	2.63692i	−0.250285	+	0.433506i	0.713319	+	0.700839i	$0.247191\pi$
$38$	1.25589	−	2.17526i	0.203732	−	0.352874i
$39$		0			0
$40$	−0.100344	−	0.173802i	−0.0158659	−	0.0274805i
$41$	2.69848	+	4.67390i	0.421431	+	0.729941i	0.996080	−	0.0884599i	$-0.0281945\pi$
$41$	2.69848	+	4.67390i	0.421431	+	0.729941i	−0.574648	+	0.818400i	$0.694861\pi$
$42$		0			0
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	−0.994465	−	0.105070i	$-0.966493\pi$
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	0.588226	+	0.808697i	$0.299827\pi$
$44$	−3.03826	−	5.26242i	−0.458035	−	0.793340i
$45$		0			0
$46$	3.82334	+	6.62223i	0.563721	+	0.976394i
$47$	−5.83204	−	10.1014i	−0.850690	−	1.47344i	−0.880587	−	0.473885i	$-0.842851\pi$
$47$	−5.83204	−	10.1014i	−0.850690	−	1.47344i	0.0298969	−	0.999553i	$-0.490482\pi$
$48$		0			0
$49$	−1.95424	−	6.72168i	−0.279177	−	0.960240i
$50$	−4.60921	−	7.98339i	−0.651841	−	1.12902i
$51$		0			0
$52$	4.95187	+	1.70756i	0.686700	+	0.236796i
$53$	2.32398	−	4.02525i	0.319223	−	0.552911i	−0.661103	−	0.750295i	$-0.729911\pi$
$53$	2.32398	−	4.02525i	0.319223	−	0.552911i	0.980326	+	0.197384i	$0.0632446\pi$
$54$		0			0
$55$	−0.412757	−	0.714916i	−0.0556562	−	0.0963993i
$56$	1.61513	−	2.15159i	0.215831	−	0.287518i
$57$		0			0
$58$	−15.3087			−2.01013
$59$	3.02905	+	5.24648i	0.394349	+	0.683033i	0.993018	−	0.117964i	$-0.0376367\pi$
$59$	3.02905	+	5.24648i	0.394349	+	0.683033i	−0.598669	+	0.800997i	$0.704303\pi$
$60$		0			0
$61$	−11.3657			−1.45523			−0.727614	−	0.685986i	$-0.759371\pi$
$61$	−11.3657			−1.45523			−0.727614	+	0.685986i	$0.759371\pi$
$62$	−1.18987	−	2.06092i	−0.151114	−	0.261737i
$63$		0			0
$64$	−3.18704			−0.398380
$65$	0.672726	+	0.231978i	0.0834414	+	0.0287733i
$66$		0			0
$67$	13.3970			1.63671			0.818354	−	0.574715i	$-0.194887\pi$
$67$	13.3970			1.63671			0.818354	+	0.574715i	$0.194887\pi$
$68$	0.611109	−	1.05847i	0.0741078	−	0.128358i
$69$		0			0
$70$	−0.582500	+	0.775973i	−0.0696221	+	0.0927465i
$71$	−2.98520	+	5.17051i	−0.354278	+	0.613627i	−0.986994	−	0.160757i	$-0.948607\pi$
$71$	−2.98520	+	5.17051i	−0.354278	+	0.613627i	0.632716	+	0.774384i	$0.281940\pi$
$72$		0			0
$73$	−1.94273	+	3.36491i	−0.227380	+	0.393833i	−0.957031	−	0.289986i	$-0.906349\pi$
$73$	−1.94273	+	3.36491i	−0.227380	+	0.393833i	0.729651	+	0.683820i	$0.239683\pi$
$74$	2.82891	+	4.89982i	0.328854	+	0.569592i
$75$		0			0
$76$	−0.981887	−	1.70068i	−0.112630	−	0.195081i
$77$	6.64368	−	8.85034i	0.757118	−	1.00859i
$78$		0			0
$79$	5.36669	+	9.29537i	0.603799	+	1.04581i	0.992240	+	0.124337i	$0.0396805\pi$
$79$	5.36669	+	9.29537i	0.603799	+	1.04581i	−0.388441	+	0.921474i	$0.626986\pi$
$80$	−0.946353			−0.105806
$81$		0			0
$82$	10.0284			1.10745
$83$	−3.07390			−0.337404			−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390			−0.337404			−0.168702	+	0.985667i	$0.553958\pi$
$84$		0			0
$85$	0.0830210	−	0.143797i	0.00900489	−	0.0155969i
$86$	4.94994	+	8.57354i	0.533765	+	0.924509i
$87$		0			0
$88$	4.25324			0.453397
$89$	−5.99207	+	10.3786i	−0.635159	+	1.10013i	0.351323	+	0.936254i	$0.385732\pi$
$89$	−5.99207	+	10.3786i	−0.635159	+	1.10013i	−0.986482	+	0.163873i	$0.947601\pi$
$90$		0			0
$91$	0.678673	+	9.51522i	0.0711442	+	0.997466i
$92$	5.97840			0.623291
$93$		0			0
$94$	−21.6737			−2.23547
$95$	−0.133392	−	0.231042i	−0.0136858	−	0.0237045i
$96$		0			0
$97$	−9.73637	+	16.8639i	−0.988578	+	1.71227i	−0.363771	+	0.931488i	$0.618511\pi$
$97$	−9.73637	+	16.8639i	−0.988578	+	1.71227i	−0.624807	+	0.780779i	$0.714822\pi$
$98$	−12.6323	−	3.10019i	−1.27605	−	0.313167i
$99$		0			0
$100$	−7.20722			−0.720722
$101$	16.9339			1.68499			0.842495	−	0.538704i	$-0.181086\pi$
$101$	16.9339			1.68499			0.842495	+	0.538704i	$0.181086\pi$
$102$		0			0
$103$	3.61712	+	6.26504i	0.356406	+	0.617313i	0.987357	−	0.158509i	$-0.0506688\pi$
$103$	3.61712	+	6.26504i	0.356406	+	0.617313i	−0.630952	+	0.775822i	$0.717335\pi$
$104$	−2.76809	+	2.40408i	−0.271434	+	0.235739i
$105$		0			0
$106$	−4.31833	−	7.47957i	−0.419434	−	0.726480i
$107$	−4.92625	+	8.53251i	−0.476238	+	0.824869i	−0.999629	−	0.0272237i	$-0.991333\pi$
$107$	−4.92625	+	8.53251i	−0.476238	+	0.824869i	0.523391	+	0.852093i	$0.324667\pi$
$108$		0			0
$109$	6.90796	−	11.9649i	0.661662	−	1.14603i	−0.318516	−	0.947917i	$-0.603185\pi$
$109$	6.90796	−	11.9649i	0.661662	−	1.14603i	0.980179	−	0.198115i	$-0.0634821\pi$
$110$	−1.53394			−0.146255
$111$		0			0
$112$	−4.97847	−	11.6687i	−0.470421	−	1.10259i
$113$	−2.13432	+	3.69675i	−0.200780	+	0.347761i	−0.948780	−	0.315938i	$-0.897681\pi$
$113$	−2.13432	+	3.69675i	−0.200780	+	0.347761i	0.748000	+	0.663699i	$0.231014\pi$
$114$		0			0
$115$	0.812183			0.0757365
$116$	−5.98437	+	10.3652i	−0.555635	+	0.962388i
$117$		0			0
$118$	11.2569			1.03629
$119$	2.20979	+	0.267197i	0.202571	+	0.0244939i
$120$		0			0
$121$	6.49529			0.590481
$122$	−10.5596	+	18.2898i	−0.956026	+	1.65589i
$123$		0			0
$124$	−1.86055			−0.167082
$125$	−1.96593			−0.175839
$126$		0			0
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	0.910515	−	0.413477i	$-0.135686\pi$
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	−0.813339	+	0.581791i	$0.802352\pi$
$128$	3.91516	−	6.78126i	0.346055	−	0.599385i
$129$		0			0
$130$	0.998318	−	0.867035i	0.0875583	−	0.0760440i
$131$	1.13806	+	1.97117i	0.0994326	+	0.172222i	0.911450	−	0.411411i	$-0.134964\pi$
$131$	1.13806	+	1.97117i	0.0994326	+	0.172222i	−0.812017	+	0.583633i	$0.801631\pi$
$132$		0			0
$133$	2.14707	−	2.86020i	0.186174	−	0.248011i
$134$	12.4469	−	21.5587i	1.07525	−	1.86239i
$135$		0			0
$136$	0.427743	+	0.740873i	0.0366787	+	0.0635293i
$137$	6.72399	+	11.6463i	0.574469	+	0.995010i	0.996099	+	0.0882417i	$0.0281248\pi$
$137$	6.72399	+	11.6463i	0.574469	+	0.995010i	−0.421630	+	0.906768i	$0.638542\pi$
$138$		0			0
$139$	−2.02270	+	3.50342i	−0.171563	+	0.297156i	−0.938966	−	0.344009i	$-0.888215\pi$
$139$	−2.02270	+	3.50342i	−0.171563	+	0.297156i	0.767403	+	0.641165i	$0.221548\pi$
$140$	0.297691	+	0.697740i	0.0251595	+	0.0589698i
$141$		0			0
$142$	5.54698	+	9.60765i	0.465492	+	0.806256i
$143$	−11.3863	+	9.88894i	−0.952169	+	0.826955i
$144$		0			0
$145$	−0.812996	+	1.40815i	−0.0675156	+	0.116940i
$146$	3.60991	+	6.25255i	0.298758	+	0.517465i
$147$		0			0
$148$	4.42344			0.363605
$149$	−15.3519			−1.25768			−0.628840	−	0.777535i	$-0.716470\pi$
$149$	−15.3519			−1.25768			−0.628840	+	0.777535i	$0.716470\pi$
$150$		0			0
$151$	−3.06054	+	5.30101i	−0.249063	+	0.431390i	−0.963266	−	0.268548i	$-0.913456\pi$
$151$	−3.06054	+	5.30101i	−0.249063	+	0.431390i	0.714203	+	0.699939i	$0.246789\pi$
$152$	1.37454			0.111490
$153$		0			0
$154$	−8.06958	−	18.9138i	−0.650265	−	1.52412i
$155$	−0.252762			−0.0203023
$156$		0			0
$157$	−2.26834	+	3.92888i	−0.181033	+	0.313559i	−0.942233	−	0.334959i	$-0.891278\pi$
$157$	−2.26834	+	3.92888i	−0.181033	+	0.313559i	0.761199	+	0.648518i	$0.224611\pi$
$158$	19.9443			1.58669
$159$		0			0
$160$	−0.678549	+	1.17528i	−0.0536440	+	0.0929142i
$161$	4.27265	+	10.0144i	0.336732	+	0.789245i
$162$		0			0
$163$	1.82254			0.142752			0.0713762	−	0.997449i	$-0.477261\pi$
$163$	1.82254			0.142752			0.0713762	+	0.997449i	$0.477261\pi$
$164$	3.92025	−	6.79007i	0.306120	−	0.530215i
$165$		0			0
$166$	−2.85590	+	4.94656i	−0.221661	+	0.383928i
$167$	−5.35397	−	9.27336i	−0.414303	−	0.717594i	0.581052	−	0.813866i	$-0.302641\pi$
$167$	−5.35397	−	9.27336i	−0.414303	−	0.717594i	−0.995355	+	0.0962726i	$0.969308\pi$
$168$		0			0
$169$	1.82086	−	12.8718i	0.140066	−	0.990142i
$170$	−0.154266	−	0.267197i	−0.0118317	−	0.0204931i
$171$		0			0
$172$	7.74000			0.590169
$173$	13.4927			1.02583			0.512915	−	0.858439i	$-0.328566\pi$
$173$	13.4927			1.02583			0.512915	+	0.858439i	$0.328566\pi$
$174$		0			0
$175$	−5.15087	−	12.0728i	−0.389369	−	0.912618i
$176$	10.0281	−	17.3692i	0.755898	−	1.30925i
$177$		0			0
$178$	11.1342	+	19.2851i	0.834547	+	1.44548i
$179$	−10.4692			−0.782502			−0.391251	−	0.920284i	$-0.627958\pi$
$179$	−10.4692			−0.782502			−0.391251	+	0.920284i	$0.627958\pi$
$180$		0			0
$181$	12.5209			0.930674			0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209			0.930674			0.465337	+	0.885133i	$0.345933\pi$
$182$	15.9426	+	7.74828i	1.18174	+	0.574340i
$183$		0			0
$184$	−2.09228	+	3.62393i	−0.154245	+	0.267160i
$185$	0.600938			0.0441819
$186$		0			0
$187$	1.75948	+	3.04751i	0.128666	+	0.222856i
$188$	−8.47256	+	14.6749i	−0.617925	+	1.07028i
$189$		0			0
$190$	−0.495729			−0.0359640
$191$	−13.1137			−0.948874			−0.474437	−	0.880290i	$-0.657348\pi$
$191$	−13.1137			−0.948874			−0.474437	+	0.880290i	$0.657348\pi$
$192$		0			0
$193$	1.04157			0.0749740			0.0374870	−	0.999297i	$-0.488065\pi$
$193$	1.04157			0.0749740			0.0374870	+	0.999297i	$0.488065\pi$
$194$	18.0917	+	31.3358i	1.29891	+	2.24978i
$195$		0			0
$196$	−7.03722	+	7.34118i	−0.502658	+	0.524370i
$197$	0.739167	+	1.28027i	0.0526635	+	0.0912158i	0.891155	−	0.453698i	$-0.149896\pi$
$197$	0.739167	+	1.28027i	0.0526635	+	0.0912158i	−0.838492	+	0.544914i	$0.816562\pi$
$198$		0			0
$199$	−7.04993	−	12.2108i	−0.499756	−	0.865603i	0.500244	−	0.865885i	$-0.333244\pi$
$199$	−7.04993	−	12.2108i	−0.499756	−	0.865603i	−1.00000		0.000281618i	$0.999910\pi$
$200$	2.52233	−	4.36881i	0.178356	−	0.308922i
$201$		0			0
$202$	15.7330	−	27.2503i	1.10697	−	1.91733i
$203$	−21.6397	−	2.61657i	−1.51881	−	0.183647i
$204$		0			0
$205$	0.532578	−	0.922451i	0.0371968	−	0.0644268i
$206$	13.4424			0.936576
$207$		0			0
$208$	3.29118	+	16.9725i	0.228202	+	1.17683i
$209$	5.65402			0.391097
$210$		0			0
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.812501	−	0.582959i	$-0.801895\pi$
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.0986067	−	0.995126i	$-0.531439\pi$
$212$	−6.75239			−0.463756
$213$		0			0
$214$	9.15376	+	15.8548i	0.625738	+	1.08381i
$215$	1.05150			0.0717119
$216$		0			0
$217$	−1.32970	−	3.11661i	−0.0902660	−	0.211569i
$218$	−12.8361	−	22.2328i	−0.869370	−	1.50579i
$219$		0			0
$220$	−0.599638	+	1.03860i	−0.0404276	+	0.0700227i
$221$	−2.86766	−	0.988862i	−0.192900	−	0.0665180i
$222$		0			0
$223$	0.364024	+	0.630508i	0.0243769	+	0.0422219i	0.877956	−	0.478740i	$-0.158907\pi$
$223$	0.364024	+	0.630508i	0.0243769	+	0.0422219i	−0.853580	+	0.520962i	$0.825573\pi$
$224$	−18.0611	−	2.18386i	−1.20676	−	0.145916i
$225$		0			0
$226$	3.96591	+	6.86916i	0.263808	+	0.456929i
$227$	−1.42598	−	2.46986i	−0.0946454	−	0.163931i	0.814815	−	0.579721i	$-0.196838\pi$
$227$	−1.42598	−	2.46986i	−0.0946454	−	0.163931i	−0.909461	+	0.415790i	$0.863505\pi$
$228$		0			0
$229$	−1.58676	−	2.74835i	−0.104856	−	0.181616i	0.808823	−	0.588052i	$-0.200105\pi$
$229$	−1.58676	−	2.74835i	−0.104856	−	0.181616i	−0.913679	+	0.406436i	$0.866772\pi$
$230$	0.754584	−	1.30698i	0.0497558	−	0.0861795i
$231$		0			0
$232$	−4.18874	−	7.25511i	−0.275004	−	0.476321i
$233$	6.70354	+	11.6109i	0.439163	+	0.760653i	0.997625	−	0.0688769i	$-0.0219416\pi$
$233$	6.70354	+	11.6109i	0.439163	+	0.760653i	−0.558462	+	0.829530i	$0.688608\pi$
$234$		0			0
$235$	−1.15102	+	1.99363i	−0.0750845	+	0.130050i
$236$	4.40050	−	7.62188i	0.286448	−	0.496142i
$237$		0			0
$238$	2.48305	−	3.30778i	0.160952	−	0.214411i
$239$	15.5538			1.00609			0.503046	−	0.864259i	$-0.332212\pi$
$239$	15.5538			1.00609			0.503046	+	0.864259i	$0.332212\pi$
$240$		0			0
$241$	3.78787	+	6.56078i	0.243998	+	0.422617i	0.961849	−	0.273579i	$-0.0882076\pi$
$241$	3.78787	+	6.56078i	0.243998	+	0.422617i	−0.717851	+	0.696196i	$0.754874\pi$
$242$	6.03465	−	10.4523i	0.387922	−	0.671900i
$243$		0			0
$244$	8.25583	+	14.2995i	0.528525	+	0.915433i
$245$	−0.956028	+	0.997322i	−0.0610784	+	0.0637166i
$246$		0			0
$247$	−3.67975	+	3.19585i	−0.234137	+	0.203347i
$248$	0.651143	−	1.12781i	0.0413476	−	0.0716162i
$249$		0			0
$250$	−1.82651	+	3.16361i	−0.115519	+	0.200084i
$251$	0.637382	−	1.10398i	0.0402312	−	0.0696825i	−0.845209	−	0.534436i	$-0.820524\pi$
$251$	0.637382	−	1.10398i	0.0402312	−	0.0696825i	0.885440	+	0.464754i	$0.153857\pi$
$252$		0			0
$253$	−8.60638	+	14.9067i	−0.541079	+	0.937176i
$254$	4.06982			0.255363
$255$		0			0
$256$	−10.4620	−	18.1208i	−0.653878	−	1.13255i
$257$	−4.24010	+	7.34406i	−0.264490	+	0.458110i	−0.967430	−	0.253139i	$-0.918537\pi$
$257$	−4.24010	+	7.34406i	−0.264490	+	0.458110i	0.702940	+	0.711249i	$0.251870\pi$
$258$		0			0
$259$	3.16135	+	7.40970i	0.196437	+	0.460416i
$260$	−0.196798	−	1.01488i	−0.0122049	−	0.0629402i
$261$		0			0
$262$	4.22939			0.261293
$263$	−12.7883			−0.788560			−0.394280	−	0.918990i	$-0.629006\pi$
$263$	−12.7883			−0.788560			−0.394280	+	0.918990i	$0.629006\pi$
$264$		0			0
$265$	−0.917333			−0.0563513
$266$	−2.60788	−	6.11245i	−0.159899	−	0.374778i
$267$		0			0
$268$	−9.73135	−	16.8552i	−0.594437	−	1.02959i
$269$	−2.35586	−	4.08047i	−0.143639	−	0.248790i	0.785225	−	0.619210i	$-0.212547\pi$
$269$	−2.35586	−	4.08047i	−0.143639	−	0.248790i	−0.928864	+	0.370420i	$0.879214\pi$
$270$		0			0
$271$	9.00562	−	15.5982i	0.547052	−	0.947522i	−0.451422	−	0.892310i	$-0.649083\pi$
$271$	9.00562	−	15.5982i	0.547052	−	0.947522i	0.998475	−	0.0552119i	$-0.0175834\pi$
$272$	4.03407			0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	10.3754	−	17.9707i	0.625659	−	1.08367i
$276$		0			0
$277$	13.0604	+	22.6213i	0.784725	+	1.35918i	0.929163	+	0.369670i	$0.120529\pi$
$277$	13.0604	+	22.6213i	0.784725	+	1.35918i	−0.144438	+	0.989514i	$0.546137\pi$
$278$	3.75850	+	6.50991i	0.225420	+	0.390439i
$279$		0			0
$280$	−0.527133	−	0.0637384i	−0.0315022	−	0.00380910i
$281$	3.66197			0.218455			0.109227	−	0.994017i	$-0.465162\pi$
$281$	3.66197			0.218455			0.109227	+	0.994017i	$0.465162\pi$
$282$		0			0
$283$	7.64527			0.454464			0.227232	−	0.973841i	$-0.427032\pi$
$283$	7.64527			0.454464			0.227232	+	0.973841i	$0.427032\pi$
$284$	8.67357			0.514682
$285$		0			0
$286$	5.33465	+	27.5106i	0.315445	+	1.62674i
$287$	14.1757	+	1.71406i	0.836768	+	0.101178i
$288$		0			0
$289$	8.14610	−	14.1095i	0.479183	−	0.829968i
$290$	1.51068	+	2.61657i	0.0887100	+	0.153650i
$291$		0			0
$292$	5.64466			0.330329
$293$	−8.57670	+	14.8553i	−0.501056	+	0.867855i	0.498943	+	0.866635i	$0.333722\pi$
$293$	−8.57670	+	14.8553i	−0.501056	+	0.867855i	−0.999999	+	0.00122001i	$0.999612\pi$
$294$		0			0
$295$	0.597821	−	1.03546i	0.0348065	−	0.0602866i
$296$	−1.54809	+	2.68136i	−0.0899807	+	0.155851i
$297$		0			0
$298$	−14.2632	+	24.7045i	−0.826244	+	1.43110i
$299$	−2.82457	−	14.5662i	−0.163349	−	0.842385i
$300$		0			0
$301$	5.53163	+	12.9652i	0.318838	+	0.747305i
$302$	5.68698	+	9.85014i	0.327249	+	0.566812i
$303$		0			0
$304$	3.24083	−	5.61328i	0.185874	−	0.321944i
$305$	1.12158	+	1.94263i	0.0642215	+	0.111235i
$306$		0			0
$307$	−28.0696			−1.60201			−0.801007	−	0.598655i	$-0.795702\pi$
$307$	−28.0696			−1.60201			−0.801007	+	0.598655i	$0.795702\pi$
$308$	−15.9607	−	1.92989i	−0.909446	−	0.109966i
$309$		0			0
$310$	−0.234836	+	0.406748i	−0.0133378	+	0.0231017i
$311$	−11.7670	+	20.3811i	−0.667248	+	1.15571i	0.311423	+	0.950271i	$0.399194\pi$
$311$	−11.7670	+	20.3811i	−0.667248	+	1.15571i	−0.978671	+	0.205436i	$0.934139\pi$
$312$		0			0
$313$	1.67430	+	2.89997i	0.0946370	+	0.163916i	0.909457	−	0.415798i	$-0.136498\pi$
$313$	1.67430	+	2.89997i	0.0946370	+	0.163916i	−0.814820	+	0.579714i	$0.803164\pi$
$314$	4.21494	+	7.30050i	0.237863	+	0.411991i
$315$		0			0
$316$	7.79652	−	13.5040i	0.438588	−	0.759658i
$317$	−3.63917	−	6.30323i	−0.204396	−	0.354025i	0.745544	−	0.666456i	$-0.232190\pi$
$317$	−3.63917	−	6.30323i	−0.204396	−	0.354025i	−0.949940	+	0.312432i	$0.898856\pi$
$318$		0			0
$319$	−17.2300	−	29.8432i	−0.964694	−	1.67090i
$320$	0.314501	+	0.544732i	0.0175811	+	0.0304514i
$321$		0			0
$322$	20.0849	+	2.42857i	1.11929	+	0.135339i
$323$	0.568618	+	0.984875i	0.0316388	+	0.0547999i
$324$		0			0
$325$	3.40514	+	17.5602i	0.188883	+	0.974065i
$326$	1.69329	−	2.93286i	0.0937826	−	0.162436i
$327$		0			0
$328$	2.74396	+	4.75268i	0.151510	+	0.262423i
$329$	−30.6371	−	3.70449i	−1.68908	−	0.204235i
$330$		0			0
$331$	−14.3234			−0.787283			−0.393642	−	0.919264i	$-0.628785\pi$
$331$	−14.3234			−0.787283			−0.393642	+	0.919264i	$0.628785\pi$
$332$	2.23282	+	3.86736i	0.122542	+	0.212249i
$333$		0			0
$334$	−19.8971			−1.08872
$335$	−1.32203	−	2.28983i	−0.0722304	−	0.125107i
$336$		0			0
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	−19.0218	−	14.8891i	−1.03465	−	0.809862i
$339$		0			0
$340$	−0.241220			−0.0130820
$341$	2.67841	−	4.63915i	0.145044	−	0.251224i
$342$		0			0
$343$	−17.3266	−	6.54142i	−0.935547	−	0.353203i
$344$	−2.70879	+	4.69176i	−0.146048	+	0.252963i
$345$		0			0
$346$	12.5358	−	21.7126i	0.673928	−	1.16728i
$347$	−3.85139	−	6.67080i	−0.206753	−	0.358107i	0.743937	−	0.668250i	$-0.232956\pi$
$347$	−3.85139	−	6.67080i	−0.206753	−	0.358107i	−0.950690	+	0.310143i	$0.899623\pi$
$348$		0			0
$349$	−11.1850	−	19.3730i	−0.598721	−	1.03702i	−0.993010	−	0.118029i	$-0.962343\pi$
$349$	−11.1850	−	19.3730i	−0.598721	−	1.03702i	0.394289	−	0.918986i	$-0.370991\pi$
$350$	−24.2133	−	2.92776i	−1.29426	−	0.156495i
$351$		0			0
$352$	−14.3806	−	24.9080i	−0.766490	−	1.32760i
$353$	22.2623			1.18490			0.592451	−	0.805606i	$-0.298160\pi$
$353$	22.2623			1.18490			0.592451	+	0.805606i	$0.298160\pi$
$354$		0			0
$355$	1.17833			0.0625393
$356$	17.4101			0.922735
$357$		0			0
$358$	−9.72670	+	16.8471i	−0.514072	+	0.890399i
$359$	−1.37921	−	2.38887i	−0.0727920	−	0.126079i	0.827332	−	0.561713i	$-0.189858\pi$
$359$	−1.37921	−	2.38887i	−0.0727920	−	0.126079i	−0.900124	+	0.435634i	$0.856524\pi$
$360$		0			0
$361$	−17.1728			−0.903830
$362$	11.6330	−	20.1489i	0.611415	−	1.05900i
$363$		0			0
$364$	11.4784	−	7.76553i	0.601632	−	0.407025i
$365$	0.766844			0.0401385
$366$		0			0
$367$	−14.1497			−0.738609			−0.369304	−	0.929308i	$-0.620404\pi$
$367$	−14.1497			−0.738609			−0.369304	+	0.929308i	$0.620404\pi$
$368$	9.86618	+	17.0887i	0.514310	+	0.890812i
$369$		0			0
$370$	0.558320	−	0.967039i	0.0290257	−	0.0502740i
$371$	−4.82580	−	11.3109i	−0.250543	−	0.587233i
$372$		0			0
$373$	−5.04284			−0.261109			−0.130554	−	0.991441i	$-0.541676\pi$
$373$	−5.04284			−0.261109			−0.130554	+	0.991441i	$0.541676\pi$
$374$	6.53879			0.338113
$375$		0			0
$376$	−5.93034	−	10.2716i	−0.305834	−	0.529720i
$377$	28.0820	+	9.68358i	1.44630	+	0.498730i
$378$		0			0
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	0.933289	−	0.359127i	$-0.116925\pi$
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	−0.777657	+	0.628688i	$0.783592\pi$
$380$	−0.193787	+	0.335650i	−0.00994109	+	0.0172185i
$381$		0			0
$382$	−12.1837	+	21.1028i	−0.623371	+	1.07971i
$383$	4.54105			0.232037			0.116018	−	0.993247i	$-0.462987\pi$
$383$	4.54105			0.232037			0.116018	+	0.993247i	$0.462987\pi$
$384$		0			0
$385$	−2.16831	−	0.262182i	−0.110507	−	0.0133620i
$386$	0.967705	−	1.67611i	0.0492549	−	0.0853120i
$387$		0			0
$388$	28.2893			1.43617
$389$	2.25383	−	3.90374i	0.114273	−	0.197927i	−0.803216	−	0.595688i	$-0.796879\pi$
$389$	2.25383	−	3.90374i	0.114273	−	0.197927i	0.917489	+	0.397761i	$0.130213\pi$
$390$		0			0
$391$	−3.46213			−0.175088
$392$	−1.98718	−	6.83498i	−0.100368	−	0.345218i
$393$		0			0
$394$	2.74698			0.138391
$395$	1.05918	−	1.83456i	0.0532932	−	0.0923065i
$396$		0			0
$397$	4.00349			0.200929			0.100465	−	0.994941i	$-0.467967\pi$
$397$	4.00349			0.200929			0.100465	+	0.994941i	$0.467967\pi$
$398$	−26.1998			−1.31328
$399$		0			0
$400$	−11.8941	−	20.6012i	−0.594706	−	1.03006i
$401$	6.30674	−	10.9236i	0.314944	−	0.545498i	−0.664482	−	0.747304i	$-0.731348\pi$
$401$	6.30674	−	10.9236i	0.314944	−	0.545498i	0.979426	+	0.201806i	$0.0646810\pi$
$402$		0			0
$403$	0.879041	+	4.53318i	0.0437882	+	0.225814i
$404$	−12.3005	−	21.3051i	−0.611972	−	1.05997i
$405$		0			0
$406$	−24.3157	+	32.3919i	−1.20677	+	1.60758i
$407$	−6.36790	+	11.0295i	−0.315645	+	0.546713i
$408$		0			0
$409$	−10.3476	−	17.9226i	−0.511657	−	0.886216i	−0.999909	−	0.0135128i	$-0.995699\pi$
$409$	−10.3476	−	17.9226i	−0.511657	−	0.886216i	0.488252	−	0.872703i	$-0.337635\pi$
$410$	−0.989615	−	1.71406i	−0.0488736	−	0.0846516i
$411$		0			0
$412$	5.25482	−	9.10162i	0.258886	−	0.448404i
$413$	15.9123	+	1.92404i	0.782995	+	0.0946760i
$414$		0			0
$415$	0.303336	+	0.525393i	0.0148902	+	0.0257905i
$416$	23.4381	+	8.08219i	1.14915	+	0.396262i
$417$		0			0
$418$	5.25304	−	9.09854i	0.256935	−	0.445024i
$419$	−10.9088	−	18.8945i	−0.532928	−	0.923058i	−0.999261	−	0.0384484i	$-0.987758\pi$
$419$	−10.9088	−	18.8945i	−0.532928	−	0.923058i	0.466333	−	0.884609i	$-0.345575\pi$
$420$		0			0
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	−49.1841			−2.39424
$423$		0			0
$424$	2.36315	−	4.09310i	0.114765	−	0.198779i
$425$	4.17376			0.202457
$426$		0			0
$427$	−18.0528	+	24.0489i	−0.873636	+	1.16381i
$428$	14.3133			0.691861
$429$		0			0
$430$	0.976930	−	1.69209i	0.0471118	−	0.0816000i
$431$	−20.4275			−0.983960			−0.491980	−	0.870607i	$-0.663727\pi$
$431$	−20.4275			−0.983960			−0.491980	+	0.870607i	$0.663727\pi$
$432$		0			0
$433$	−13.1743	+	22.8186i	−0.633117	+	1.09659i	0.353794	+	0.935323i	$0.384891\pi$
$433$	−13.1743	+	22.8186i	−0.633117	+	1.09659i	−0.986911	+	0.161267i	$0.948442\pi$
$434$	−6.25069	−	0.755803i	−0.300043	−	0.0362797i
$435$		0			0
$436$	−20.0712			−0.961238
$437$	−2.78136	+	4.81745i	−0.133050	+	0.230450i
$438$		0			0
$439$	−12.5655	+	21.7641i	−0.599720	+	1.03875i	0.393142	+	0.919478i	$0.371388\pi$
$439$	−12.5655	+	21.7641i	−0.599720	+	1.03875i	−0.992862	+	0.119267i	$0.961945\pi$
$440$	−0.419714	−	0.726967i	−0.0200091	−	0.0346568i
$441$		0			0
$442$	−4.25558	+	3.69595i	−0.202417	+	0.175799i
$443$	9.25995	+	16.0387i	0.439953	+	0.762022i	0.997685	−	0.0679994i	$-0.0216616\pi$
$443$	9.25995	+	16.0387i	0.439953	+	0.762022i	−0.557732	+	0.830021i	$0.688328\pi$
$444$		0			0
$445$	2.36522			0.112122
$446$	1.35283			0.0640584
$447$		0			0
$448$	−5.06216	+	6.74353i	−0.239165	+	0.318602i
$449$	5.82155	−	10.0832i	0.274736	−	0.475856i	−0.695333	−	0.718688i	$-0.744743\pi$
$449$	5.82155	−	10.0832i	0.274736	−	0.475856i	0.970068	+	0.242832i	$0.0780763\pi$
$450$		0			0
$451$	11.2870	+	19.5497i	0.531485	+	0.920559i
$452$	6.20132			0.291685
$453$		0			0
$454$	−5.29939			−0.248713
$455$	1.55938	−	1.05497i	0.0731047	−	0.0494578i
$456$		0			0
$457$	−10.2592	+	17.7695i	−0.479906	+	0.831222i	−0.999734	−	0.0230490i	$-0.992663\pi$
$457$	−10.2592	+	17.7695i	−0.479906	+	0.831222i	0.519828	+	0.854271i	$0.325996\pi$
$458$	−5.89691			−0.275544
$459$		0			0
$460$	−0.589955	−	1.02183i	−0.0275068	−	0.0476431i
$461$	1.02038	−	1.76734i	0.0475236	−	0.0823134i	−0.841285	−	0.540592i	$-0.818200\pi$
$461$	1.02038	−	1.76734i	0.0475236	−	0.0823134i	0.888809	+	0.458278i	$0.151534\pi$
$462$		0			0
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	−39.5042			−1.83394
$465$		0			0
$466$	24.9125			1.15405
$467$	−6.46371	−	11.1955i	−0.299105	−	0.518065i	0.676827	−	0.736142i	$-0.263355\pi$
$467$	−6.46371	−	11.1955i	−0.299105	−	0.518065i	−0.975931	+	0.218078i	$0.930021\pi$
$468$		0			0
$469$	21.2793	−	28.3470i	0.982585	−	1.30894i
$470$	2.13879	+	3.70449i	0.0986549	+	0.170875i
$471$		0			0
$472$	3.08011	+	5.33491i	0.141774	+	0.245559i
$473$	−11.1423	+	19.2991i	−0.512326	+	0.887374i
$474$		0			0
$475$	3.35305	−	5.80766i	0.153849	−	0.266474i
$476$	−1.26898	−	2.97429i	−0.0581637	−	0.136326i
$477$		0			0
$478$	14.4507	−	25.0294i	0.660962	−	1.14482i
$479$	−36.5821			−1.67148			−0.835740	−	0.549126i	$-0.814961\pi$
$479$	−36.5821			−1.67148			−0.835740	+	0.549126i	$0.814961\pi$
$480$		0			0
$481$	−2.08991	−	10.7776i	−0.0952918	−	0.491416i
$482$	14.0769			0.641187
$483$		0			0
$484$	−4.71806	−	8.17191i	−0.214457	−	0.371451i
$485$	3.84318			0.174510
$486$		0			0
$487$	−18.3748	−	31.8261i	−0.832642	−	1.44218i	−0.895936	−	0.444183i	$-0.853494\pi$
$487$	−18.3748	−	31.8261i	−0.832642	−	1.44218i	0.0632939	−	0.997995i	$-0.479839\pi$
$488$	−11.5573			−0.523173
$489$		0			0
$490$	0.716679	+	2.46505i	0.0323763	+	0.111359i
$491$	−4.09899	−	7.09965i	−0.184985	−	0.320403i	0.758587	−	0.651572i	$-0.225890\pi$
$491$	−4.09899	−	7.09965i	−0.184985	−	0.320403i	−0.943571	+	0.331169i	$0.892557\pi$
$492$		0			0
$493$	3.46560	−	6.00259i	0.156083	−	0.270343i
$494$	1.72402	+	8.89071i	0.0775673	+	0.400012i
$495$		0			0
$496$	−3.07048	−	5.31823i	−0.137869	−	0.238795i
$497$	6.19883	+	14.5291i	0.278056	+	0.651718i
$498$		0			0
$499$	21.6266	+	37.4584i	0.968141	+	1.67687i	0.700929	+	0.713231i	$0.252769\pi$
$499$	21.6266	+	37.4584i	0.968141	+	1.67687i	0.267211	+	0.963638i	$0.413898\pi$
$500$	1.42802	+	2.47340i	0.0638629	+	0.110614i
$501$		0			0
$502$	−1.18436	−	2.05137i	−0.0528605	−	0.0915571i
$503$	0.00909609	−	0.0157549i	0.000405575	−	0.000702476i	−0.865823	−	0.500351i	$-0.833204\pi$
$503$	0.00909609	−	0.0157549i	0.000405575	−	0.000702476i	0.866228	+	0.499649i	$0.166538\pi$
$504$		0			0
$505$	−1.67106	−	2.89436i	−0.0743612	−	0.128797i
$506$	15.9920	+	27.6990i	0.710933	+	1.23137i
$507$		0			0
$508$	1.59095	−	2.75560i	0.0705869	−	0.122260i
$509$	21.5503	−	37.3262i	0.955200	−	1.65446i	0.221292	−	0.975208i	$-0.428973\pi$
$509$	21.5503	−	37.3262i	0.955200	−	1.65446i	0.733909	−	0.679248i	$-0.237694\pi$
$510$		0			0
$511$	4.03413	+	9.45535i	0.178459	+	0.418280i
$512$	−23.2197			−1.02617
$513$		0			0
$514$	7.87878	+	13.6464i	0.347518	+	0.601919i
$515$	0.713884	−	1.23648i	0.0314575	−	0.0544859i
$516$		0			0
$517$	−24.3939	−	42.2514i	−1.07284	−	1.85822i
$518$	14.8609	+	1.79691i	0.652952	+	0.0789519i
$519$		0			0
$520$	0.684065	+	0.235888i	0.0299983	+	0.0103444i
$521$	10.4770	−	18.1467i	0.459006	−	0.795022i	−0.539903	−	0.841727i	$-0.681539\pi$
$521$	10.4770	−	18.1467i	0.459006	−	0.795022i	0.998909	+	0.0467056i	$0.0148723\pi$
$522$		0			0
$523$	17.3701	−	30.0860i	0.759543	−	1.31557i	−0.183541	−	0.983012i	$-0.558756\pi$
$523$	17.3701	−	30.0860i	0.759543	−	1.31557i	0.943084	−	0.332555i	$-0.107911\pi$
$524$	1.65333	−	2.86365i	0.0722260	−	0.125099i
$525$		0			0
$526$	−11.8814	+	20.5791i	−0.518052	+	0.897292i
$527$	1.07746			0.0469349
$528$		0			0
$529$	3.03260	+	5.25262i	0.131852	+	0.228375i
$530$	−0.852276	+	1.47619i	−0.0370205	+	0.0641214i
$531$		0			0
$532$	−5.15809	−	0.623691i	−0.223631	−	0.0270404i
$533$	−18.3960	−	6.34352i	−0.796819	−	0.274769i
$534$		0			0
$535$	1.94451			0.0840685
$536$	13.6228			0.588417
$537$		0			0
$538$	−8.75513			−0.377460
$539$	−8.17406	−	28.1150i	−0.352082	−	1.21100i
$540$		0			0
$541$	1.64923	+	2.85655i	0.0709059	+	0.122813i	0.899299	−	0.437335i	$-0.144078\pi$
$541$	1.64923	+	2.85655i	0.0709059	+	0.122813i	−0.828393	+	0.560148i	$0.810744\pi$
$542$	−16.7339	−	28.9839i	−0.718782	−	1.24497i
$543$		0			0
$544$	2.89249	−	5.00993i	0.124014	−	0.214799i
$545$	−2.72674			−0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	9.76836	−	16.9193i	0.417284	−	0.722756i
$549$		0			0
$550$	−19.2791	−	33.3924i	−0.822065	−	1.42386i
$551$	−5.56828	−	9.64455i	−0.237217	−	0.410871i
$552$		0			0
$553$	28.1925	+	3.40890i	1.19887	+	0.144961i
$554$	48.5368			2.06213
$555$		0			0
$556$	5.87700			0.249240
$557$	14.2866			0.605342			0.302671	−	0.953095i	$-0.402122\pi$
$557$	14.2866			0.605342			0.302671	+	0.953095i	$0.402122\pi$
$558$		0			0
$559$	−3.65686	−	18.8583i	−0.154669	−	0.797621i
$560$	−1.50315	+	2.00241i	−0.0635196	+	0.0846172i
$561$		0			0
$562$	3.40226	−	5.89289i	0.143516	−	0.248577i
$563$	3.39392	+	5.87844i	0.143037	+	0.247747i	0.928639	−	0.370985i	$-0.120980\pi$
$563$	3.39392	+	5.87844i	0.143037	+	0.247747i	−0.785602	+	0.618732i	$0.787647\pi$
$564$		0			0
$565$	0.842468			0.0354429
$566$	7.10307	−	12.3029i	0.298564	−	0.517128i
$567$		0			0
$568$	−3.03552	+	5.25767i	−0.127367	+	0.220607i
$569$	−8.66061	+	15.0006i	−0.363072	+	0.628859i	−0.988465	−	0.151451i	$-0.951605\pi$
$569$	−8.66061	+	15.0006i	−0.363072	+	0.628859i	0.625393	+	0.780310i	$0.284939\pi$
$570$		0			0
$571$	6.50581	−	11.2684i	0.272260	−	0.471568i	−0.697180	−	0.716896i	$-0.745562\pi$
$571$	6.50581	−	11.2684i	0.272260	−	0.471568i	0.969440	+	0.245328i	$0.0788957\pi$
$572$	20.7124	+	7.14228i	0.866027	+	0.298634i
$573$		0			0
$574$	15.9287	−	21.2193i	0.664851	−	0.885677i
$575$	10.2078	+	17.6805i	0.425696	+	0.737327i
$576$		0			0
$577$	0.365767	−	0.633528i	0.0152271	−	0.0263741i	−0.858311	−	0.513129i	$-0.828486\pi$
$577$	0.365767	−	0.633528i	0.0152271	−	0.0263741i	0.873539	+	0.486755i	$0.161820\pi$
$578$	−15.1368	−	26.2177i	−0.629607	−	1.09051i
$579$		0			0
$580$	2.36218			0.0980842
$581$	−4.88245	+	6.50412i	−0.202558	+	0.269837i
$582$		0			0
$583$	9.72061	−	16.8366i	0.402586	−	0.697300i
$584$	−1.97548	+	3.42163i	−0.0817459	+	0.141588i
$585$		0			0
$586$	15.9369	+	27.6035i	0.658347	+	1.14029i
$587$	−4.26142	−	7.38099i	−0.175888	−	0.304646i	0.764581	−	0.644528i	$-0.222946\pi$
$587$	−4.26142	−	7.38099i	−0.175888	−	0.304646i	−0.940468	+	0.339882i	$0.889613\pi$
$588$		0			0
$589$	0.865594	−	1.49925i	0.0356662	−	0.0617756i
$590$	−1.11085	−	1.92404i	−0.0457329	−	0.0792117i
$591$		0			0
$592$	7.30004	+	12.6440i	0.300030	+	0.519667i
$593$	−15.6547	−	27.1147i	−0.642860	−	1.11347i	−0.984791	−	0.173741i	$-0.944415\pi$
$593$	−15.6547	−	27.1147i	−0.642860	−	1.11347i	0.341932	−	0.939725i	$-0.388919\pi$
$594$		0			0
$595$	−0.172395	−	0.404066i	−0.00706751	−	0.0165651i
$596$	11.1514	+	19.3147i	0.456777	+	0.791161i
$597$		0			0
$598$	−26.0644	−	8.98784i	−1.06585	−	0.367540i
$599$	−0.375116	+	0.649720i	−0.0153268	+	0.0265468i	−0.873587	−	0.486668i	$-0.838212\pi$
$599$	−0.375116	+	0.649720i	−0.0153268	+	0.0265468i	0.858260	+	0.513215i	$0.171546\pi$
$600$		0			0
$601$	4.77652	+	8.27318i	0.194838	+	0.337470i	0.946848	−	0.321683i	$-0.104248\pi$
$601$	4.77652	+	8.27318i	0.194838	+	0.337470i	−0.752009	+	0.659153i	$0.770915\pi$
$602$	26.0032	+	3.14418i	1.05981	+	0.128147i
$603$		0			0
$604$	8.89248			0.361830
$605$	−0.640963	−	1.11018i	−0.0260588	−	0.0451352i
$606$		0			0
$607$	22.2395			0.902672			0.451336	−	0.892354i	$-0.350948\pi$
$607$	22.2395			0.902672			0.451336	+	0.892354i	$0.350948\pi$
$608$	−4.64745	−	8.04961i	−0.188479	−	0.326455i
$609$		0			0
$610$	4.16815			0.168764
$611$	39.7580	+	13.7098i	1.60844	+	0.554640i
$612$		0			0
$613$	−8.27987			−0.334421			−0.167210	−	0.985921i	$-0.553476\pi$
$613$	−8.27987			−0.334421			−0.167210	+	0.985921i	$0.553476\pi$
$614$	−26.0789	+	45.1699i	−1.05246	+	1.82291i
$615$		0			0
$616$	6.75567	−	8.99952i	0.272194	−	0.362601i
$617$	10.1656	−	17.6073i	0.409252	−	0.708845i	−0.585554	−	0.810633i	$-0.699123\pi$
$617$	10.1656	−	17.6073i	0.409252	−	0.708845i	0.994806	+	0.101789i	$0.0324565\pi$
$618$		0			0
$619$	−2.67049	+	4.62542i	−0.107336	+	0.185911i	−0.914690	−	0.404156i	$-0.867565\pi$
$619$	−2.67049	+	4.62542i	−0.107336	+	0.185911i	0.807354	+	0.590067i	$0.200899\pi$
$620$	0.183601	+	0.318007i	0.00737361	+	0.0127715i
$621$		0			0
$622$	21.8651	+	37.8714i	0.876709	+	1.51850i
$623$	12.4427	+	29.1636i	0.498506	+	1.16842i
$624$		0			0
$625$	−12.2086	−	21.1459i	−0.488345	−	0.845838i
$626$	6.22224			0.248691
$627$		0			0
$628$	6.59072			0.262998
$629$	−2.56165			−0.102140
$630$		0			0
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	−0.923179	−	0.384369i	$-0.874419\pi$
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	0.794463	+	0.607312i	$0.207752\pi$
$632$	5.45714	+	9.45205i	0.217074	+	0.375982i
$633$		0			0
$634$	−13.5243			−0.537120
$635$	0.216135	−	0.374357i	0.00857707	−	0.0148559i
$636$		0			0
$637$	21.2114	+	13.6776i	0.840427	+	0.541925i
$638$	−64.0322			−2.53506
$639$		0			0
$640$	−1.54541			−0.0610877
$641$	11.6644	+	20.2034i	0.460717	+	0.797985i	0.998997	−	0.0447808i	$-0.0142589\pi$
$641$	11.6644	+	20.2034i	0.460717	+	0.797985i	−0.538280	+	0.842766i	$0.680926\pi$
$642$		0			0
$643$	1.79439	−	3.10797i	0.0707637	−	0.122566i	−0.828472	−	0.560030i	$-0.810790\pi$
$643$	1.79439	−	3.10797i	0.0707637	−	0.122566i	0.899236	+	0.437463i	$0.144123\pi$
$644$	9.49583	−	12.6498i	0.374188	−	0.498472i
$645$		0			0
$646$	2.11317			0.0831415
$647$	39.6524			1.55890			0.779448	−	0.626467i	$-0.215500\pi$
$647$	39.6524			1.55890			0.779448	+	0.626467i	$0.215500\pi$
$648$		0			0
$649$	12.6697	+	21.9446i	0.497331	+	0.861402i
$650$	31.4218	+	10.8352i	1.23246	+	0.424993i
$651$		0			0
$652$	−1.32386	−	2.29299i	−0.0518464	−	0.0898005i
$653$	9.06777	−	15.7058i	0.354849	−	0.614617i	−0.632243	−	0.774770i	$-0.717865\pi$
$653$	9.06777	−	15.7058i	0.354849	−	0.614617i	0.987092	+	0.160153i	$0.0511988\pi$
$654$		0			0
$655$	0.224610	−	0.389035i	0.00877623	−	0.0152009i
$656$	25.8784			1.01038
$657$		0			0
$658$	−34.4256	+	45.8599i	−1.34205	+	1.78780i
$659$	6.74052	−	11.6749i	0.262573	−	0.454791i	−0.704352	−	0.709851i	$-0.748762\pi$
$659$	6.74052	−	11.6749i	0.262573	−	0.454791i	0.966925	+	0.255061i	$0.0820955\pi$
$660$		0			0
$661$	10.3122			0.401099			0.200549	−	0.979684i	$-0.435727\pi$
$661$	10.3122			0.401099			0.200549	+	0.979684i	$0.435727\pi$
$662$	−13.3076	+	23.0494i	−0.517213	+	0.895839i
$663$		0			0
$664$	−3.12571			−0.121301
$665$	−0.700742	−	0.0847304i	−0.0271736	−	0.00328570i
$666$		0			0
$667$	33.9035			1.31275
$668$	−7.77805	+	13.4720i	−0.300942	+	0.521247i
$669$		0			0
$670$	−4.91310			−0.189810
$671$	−47.5397			−1.83525
$672$		0			0
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	0.941163	−	0.337953i	$-0.109734\pi$
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	−0.763257	+	0.646095i	$0.776401\pi$
$674$	15.9618	−	27.6467i	0.614827	−	1.06491i
$675$		0			0
$676$	−17.5171	+	7.05900i	−0.673734	+	0.271500i
$677$	−10.5467	−	18.2674i	−0.405343	−	0.702075i	0.589018	−	0.808120i	$-0.299515\pi$
$677$	−10.5467	−	18.2674i	−0.405343	−	0.702075i	−0.994361	+	0.106045i	$0.966181\pi$
$678$		0			0
$679$	20.2178	+	47.3873i	0.775888	+	1.81856i
$680$	0.0844203	−	0.146220i	0.00323737	−	0.00560729i
$681$		0			0
$682$	−4.97693	−	8.62029i	−0.190576	−	0.330088i
$683$	−19.1106	−	33.1005i	−0.731246	−	1.26656i	−0.956351	−	0.292221i	$-0.905606\pi$
$683$	−19.1106	−	33.1005i	−0.731246	−	1.26656i	0.225104	−	0.974335i	$-0.427728\pi$
$684$		0			0
$685$	1.32706	−	2.29854i	0.0507044	−	0.0878226i
$686$	−26.6243	+	21.8047i	−1.01652	+	0.832506i
$687$		0			0
$688$	12.7734	+	22.1241i	0.486980	+	0.843474i
$689$	3.19025	+	16.4520i	0.121539	+	0.626772i
$690$		0			0
$691$	13.1161	−	22.7178i	0.498960	−	0.864224i	−0.501039	−	0.865425i	$-0.667049\pi$
$691$	13.1161	−	22.7178i	0.498960	−	0.864224i	0.999999	+	0.00120019i	$0.000382034\pi$
$692$	−9.80084	−	16.9755i	−0.372572	−	0.645313i
$693$		0			0
$694$	−14.3130			−0.543314
$695$	0.798409			0.0302854
$696$		0			0
$697$	−2.27024	+	3.93218i	−0.0859916	+	0.148942i
$698$	−41.5672			−1.57334
$699$		0			0
$700$	−11.4477	+	15.2499i	−0.432681	+	0.576393i
$701$	46.7346			1.76514			0.882570	−	0.470180i	$-0.155811\pi$
$701$	46.7346			1.76514			0.882570	+	0.470180i	$0.155811\pi$
$702$		0			0
$703$	−2.05794	+	3.56446i	−0.0776167	+	0.134436i
$704$	−13.3306			−0.502414
$705$		0			0
$706$	20.6835	−	35.8248i	0.778433	−	1.34828i
$707$	26.8972	−	35.8309i	1.01157	−	1.34756i
$708$		0			0
$709$	−47.4464			−1.78189			−0.890944	−	0.454113i	$-0.849956\pi$
$709$	−47.4464			−1.78189			−0.890944	+	0.454113i	$0.849956\pi$
$710$	1.09476	−	1.89619i	0.0410858	−	0.0711626i
$711$		0			0
$712$	−6.09307	+	10.5535i	−0.228348	+	0.395510i
$713$	2.63516	+	4.56423i	0.0986876	+	0.170932i
$714$		0			0
$715$	2.81384	+	0.970301i	0.105232	+	0.0362872i
$716$	7.60461	+	13.1716i	0.284197	+	0.492244i
$717$		0			0
$718$	−5.12560			−0.191286
$719$	49.2380			1.83627			0.918133	−	0.396273i	$-0.129696\pi$
$719$	49.2380			1.83627			0.918133	+	0.396273i	$0.129696\pi$
$720$		0			0
$721$	19.0016	+	2.29758i	0.707657	+	0.0855665i
$722$	−15.9549	+	27.6347i	−0.593779	+	1.02846i
$723$		0			0
$724$	−9.09498	−	15.7530i	−0.338012	−	0.585454i
$725$	−40.8722			−1.51795
$726$		0			0
$727$	−32.0495			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$728$	0.690112	+	9.67560i	0.0255773	+	0.358602i
$729$		0			0
$730$	0.712460	−	1.23402i	0.0263693	−	0.0456730i
$731$	−4.48229			−0.165783
$732$		0			0
$733$	−14.1005	−	24.4228i	−0.520813	−	0.902075i	−0.999707	−	0.0242025i	$-0.992295\pi$
$733$	−14.1005	−	24.4228i	−0.520813	−	0.902075i	0.478894	−	0.877873i	$-0.341038\pi$
$734$	−13.1462	+	22.7699i	−0.485236	+	0.840453i
$735$		0			0
$736$	28.2968			1.04303
$737$	56.0362			2.06412
$738$		0			0
$739$	−42.5370			−1.56475			−0.782375	−	0.622808i	$-0.785992\pi$
$739$	−42.5370			−1.56475			−0.782375	+	0.622808i	$0.785992\pi$
$740$	−0.436510	−	0.756058i	−0.0160464	−	0.0277932i
$741$		0			0
$742$	−22.6852	−	2.74299i	−0.832801	−	0.100698i
$743$	7.95711	+	13.7821i	0.291918	+	0.505617i	0.974263	−	0.225413i	$-0.0723732\pi$
$743$	7.95711	+	13.7821i	0.291918	+	0.505617i	−0.682345	+	0.731030i	$0.739040\pi$
$744$		0			0
$745$	1.51495	+	2.62396i	0.0555033	+	0.0961346i
$746$	−4.68521	+	8.11502i	−0.171538	+	0.297112i
$747$		0			0
$748$	2.55611	−	4.42731i	0.0934605	−	0.161878i
$749$	10.2295	+	23.9762i	0.373777	+	0.876072i
$750$		0			0
$751$	−9.09981	+	15.7613i	−0.332057	+	0.575139i	−0.982915	−	0.184060i	$-0.941076\pi$
$751$	−9.09981	+	15.7613i	−0.332057	+	0.575139i	0.650858	+	0.759199i	$0.274409\pi$
$752$	−55.9293			−2.03953
$753$		0			0
$754$	41.6734	−	36.1932i	1.51766	−	1.31808i
$755$	1.20807			0.0439662
$756$		0			0
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	0.908632	+	0.417598i	$0.137128\pi$
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	−0.0926649	+	0.995697i	$0.529539\pi$
$758$	11.2598			0.408974
$759$		0			0
$760$	−0.135641	−	0.234937i	−0.00492021	−	0.00852205i
$761$	26.4888			0.960217			0.480108	−	0.877209i	$-0.340597\pi$
$761$	26.4888			0.960217			0.480108	+	0.877209i	$0.340597\pi$
$762$		0			0
$763$	−14.3445	−	33.6213i	−0.519307	−	1.21717i
$764$	9.52554	+	16.4987i	0.344622	+	0.596903i
$765$		0			0
$766$	4.21900	−	7.30752i	0.152439	−	0.264031i
$767$	−20.6496	−	7.12064i	−0.745613	−	0.257111i
$768$		0			0
$769$	−6.98127	−	12.0919i	−0.251751	−	0.436045i	0.712257	−	0.701919i	$-0.247673\pi$
$769$	−6.98127	−	12.0919i	−0.251751	−	0.436045i	−0.964008	+	0.265873i	$0.914340\pi$
$770$	−2.43644	+	3.24569i	−0.0878033	+	0.116967i
$771$		0			0
$772$	−0.756579	−	1.31043i	−0.0272299	−	0.0471635i
$773$	6.40564	+	11.0949i	0.230395	+	0.399056i	0.957924	−	0.287021i	$-0.0926648\pi$
$773$	6.40564	+	11.0949i	0.230395	+	0.399056i	−0.727529	+	0.686077i	$0.759332\pi$
$774$		0			0
$775$	−3.17681	−	5.50239i	−0.114114	−	0.197652i
$776$	−9.90048	+	17.1481i	−0.355406	+	0.615582i
$777$		0			0
$778$	−4.18797	−	7.25378i	−0.150146	−	0.260061i
$779$	3.64767	+	6.31795i	0.130691	+	0.226364i
$780$		0			0
$781$	−12.4863	+	21.6269i	−0.446795	+	0.773871i
$782$	−3.21660	+	5.57132i	−0.115025	+	0.199230i
$783$		0			0
$784$	−32.5977	−	8.00008i	−1.16420	−	0.285717i
$785$	0.895370			0.0319571
$786$		0			0
$787$	13.6599	+	23.6597i	0.486924	+	0.843377i	0.999887	−	0.0150334i	$-0.00478545\pi$
$787$	13.6599	+	23.6597i	0.486924	+	0.843377i	−0.512963	+	0.858411i	$0.671452\pi$
$788$	1.07383	−	1.85993i	0.0382537	−	0.0662574i
$789$		0			0
$790$	−1.96813	−	3.40890i	−0.0700229	−	0.121283i
$791$	4.43196	+	10.3878i	0.157583	+	0.369348i
$792$		0			0
$793$	30.9398	−	26.8711i	1.09871	−	0.954221i
$794$	3.71956	−	6.44247i	0.132002	−	0.228635i
$795$		0			0
$796$	−10.2419	+	17.7394i	−0.363013	+	0.628758i
$797$	−14.7002	+	25.4614i	−0.520707	+	0.901891i	0.479003	+	0.877813i	$0.340998\pi$
$797$	−14.7002	+	25.4614i	−0.520707	+	0.901891i	−0.999710	+	0.0240775i	$0.992335\pi$
$798$		0			0
$799$	4.90652	−	8.49835i	0.173580	−	0.300650i
$800$	−34.1131			−1.20608
$801$		0			0
$802$	−11.7189	−	20.2978i	−0.413810	−	0.716740i
$803$	−8.12594	+	14.0745i	−0.286758	+	0.496680i
$804$		0			0
$805$	1.29004	−	1.71852i	0.0454679	−	0.0605697i
$806$	8.11157	+	2.79713i	0.285718	+	0.0985246i
$807$		0			0
$808$	17.2194			0.605775
$809$	6.01233			0.211382			0.105691	−	0.994399i	$-0.466294\pi$
$809$	6.01233			0.211382			0.105691	+	0.994399i	$0.466294\pi$
$810$		0			0
$811$	8.44807			0.296652			0.148326	−	0.988939i	$-0.452612\pi$
$811$	8.44807			0.296652			0.148326	+	0.988939i	$0.452612\pi$
$812$	12.4267	+	29.1262i	0.436091	+	1.02213i
$813$		0			0
$814$	11.8326	+	20.4946i	0.414732	+	0.718337i
$815$	−0.179850	−	0.311510i	−0.00629989	−	0.0109117i
$816$		0			0
$817$	−3.60092	+	6.23697i	−0.125980	+	0.218204i
$818$	−38.4551			−1.34455
$819$		0			0
$820$	−1.54742			−0.0540382
$821$	−17.1318	+	29.6731i	−0.597903	+	1.03560i	0.395228	+	0.918583i	$0.370666\pi$
$821$	−17.1318	+	29.6731i	−0.597903	+	1.03560i	−0.993130	+	0.117014i	$0.962668\pi$
$822$		0			0
$823$	3.11866	+	5.40168i	0.108710	+	0.188291i	0.915248	−	0.402891i	$-0.131995\pi$
$823$	3.11866	+	5.40168i	0.108710	+	0.188291i	−0.806538	+	0.591182i	$0.798661\pi$
$824$	3.67809	+	6.37064i	0.128132	+	0.221932i
$825$		0			0
$826$	17.8801	−	23.8188i	0.622127	−	0.828762i
$827$	−19.5232			−0.678889			−0.339445	−	0.940626i	$-0.610239\pi$
$827$	−19.5232			−0.678889			−0.339445	+	0.940626i	$0.610239\pi$
$828$		0			0
$829$	32.6766			1.13491			0.567453	−	0.823406i	$-0.307929\pi$
$829$	32.6766			1.13491			0.567453	+	0.823406i	$0.307929\pi$
$830$	1.12729			0.0391289
$831$		0			0
$832$	8.67580	−	7.53489i	0.300779	−	0.261225i
$833$	4.07530	−	4.25133i	0.141201	−	0.147300i
$834$		0			0
$835$	−1.05667	+	1.83021i	−0.0365677	+	0.0633370i
$836$	−4.10698	−	7.11349i	−0.142043	−	0.246025i
$837$		0			0
$838$	−40.5405			−1.40045
$839$	12.3713	−	21.4278i	0.427106	−	0.739769i	−0.569508	−	0.821985i	$-0.692866\pi$
$839$	12.3713	−	21.4278i	0.427106	−	0.739769i	0.996615	+	0.0822161i	$0.0261998\pi$
$840$		0			0
$841$	−19.4374	+	33.6665i	−0.670255	+	1.16092i
$842$	8.75869	−	15.1705i	0.301844	−	0.522810i
$843$		0			0
$844$	−19.2267	+	33.3017i	−0.661812	+	1.14629i
$845$	−2.37975	+	0.958986i	−0.0818659	+	0.0329901i
$846$		0			0
$847$	10.3168	−	13.7435i	0.354491	−	0.472233i
$848$	−11.1435	−	19.3011i	−0.382670	−	0.662803i
$849$		0			0
$850$	3.87776	−	6.71647i	0.133006	−	0.230373i
$851$	−6.26507	−	10.8514i	−0.214764	−	0.371982i
$852$		0			0
$853$	18.2245			0.623994			0.311997	−	0.950083i	$-0.399002\pi$
$853$	18.2245			0.623994			0.311997	+	0.950083i	$0.399002\pi$
$854$	21.9274	+	51.3942i	0.750339	+	1.75867i
$855$		0			0
$856$	−5.00928	+	8.67633i	−0.171214	+	0.296551i
$857$	1.27340	−	2.20559i	0.0434984	−	0.0753414i	−0.843457	−	0.537197i	$-0.819483\pi$
$857$	1.27340	−	2.20559i	0.0434984	−	0.0753414i	0.886955	+	0.461856i	$0.152816\pi$
$858$		0			0
$859$	−27.0045	−	46.7732i	−0.921382	−	1.59588i	−0.797278	−	0.603612i	$-0.793728\pi$
$859$	−27.0045	−	46.7732i	−0.921382	−	1.59588i	−0.124104	−	0.992269i	$-0.539606\pi$
$860$	−0.763792	−	1.32293i	−0.0260451	−	0.0451114i
$861$		0			0
$862$	−18.9788	+	32.8723i	−0.646421	+	1.11963i
$863$	0.621545	+	1.07655i	0.0211576	+	0.0366461i	0.876410	−	0.481565i	$-0.159931\pi$
$863$	0.621545	+	1.07655i	0.0211576	+	0.0366461i	−0.855253	+	0.518211i	$0.826598\pi$
$864$		0			0
$865$	−1.33147	−	2.30618i	−0.0452715	−	0.0784125i
$866$	24.4800	+	42.4006i	0.831864	+	1.44083i
$867$		0			0
$868$	−2.95522	+	3.93678i	−0.100307	+	0.133623i
$869$	22.4474	+	38.8801i	0.761477	+	1.31892i
$870$		0			0
$871$	−36.4695	+	31.6736i	−1.23572	+	1.07322i
$872$	7.02440	−	12.1666i	0.237876	−	0.412013i
$873$		0			0
$874$	5.16821	+	8.95161i	0.174817	+	0.302793i
$875$	−3.12261	+	4.15976i	−0.105563	+	0.140626i
$876$		0			0
$877$	0.802661			0.0271039			0.0135520	−	0.999908i	$-0.495686\pi$
$877$	0.802661			0.0271039			0.0135520	+	0.999908i	$0.495686\pi$
$878$	23.3488	+	40.4412i	0.787983	+	1.36483i
$879$		0			0
$880$	−3.95835			−0.133436
$881$	−18.5318	−	32.0980i	−0.624352	−	1.08141i	−0.988666	−	0.150133i	$-0.952030\pi$
$881$	−18.5318	−	32.0980i	−0.624352	−	1.08141i	0.364314	−	0.931276i	$-0.381304\pi$
$882$		0			0
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$	0.838900	+	4.32618i	0.0282153	+	0.145505i
$885$		0			0
$886$	34.4130			1.15613
$887$	−24.6287	+	42.6581i	−0.826950	+	1.43232i	0.0734699	+	0.997297i	$0.476593\pi$
$887$	−24.6287	+	42.6581i	−0.826950	+	1.43232i	−0.900420	+	0.435022i	$0.856741\pi$
$888$		0			0
$889$	5.75292	+	0.695616i	0.192947	+	0.0233302i
$890$	2.19748	−	3.80614i	0.0736597	−	0.127582i
$891$		0			0
$892$	0.528840	−	0.915978i	0.0177069	−	0.0306692i
$893$	−7.88347	−	13.6546i	−0.263810	−	0.456932i
$894$		0			0
$895$	1.03311	+	1.78940i	0.0345330	+	0.0598130i
$896$	−8.12993	−	19.0552i	−0.271602	−	0.636591i
$897$		0			0
$898$	−10.8174	−	18.7362i	−0.360980	−	0.625236i
$899$	−10.5512			−0.351902
$900$		0			0
$901$	3.91036			0.130273
$902$	41.9462			1.39666
$903$		0			0
$904$	−2.17029	+	3.75906i	−0.0721829	+	0.125024i
$905$	−1.23558	−	2.14009i	−0.0410721	−	0.0711390i
$906$		0			0
$907$	−5.00455			−0.166173			−0.0830867	−	0.996542i	$-0.526478\pi$
$907$	−5.00455			−0.166173			−0.0830867	+	0.996542i	$0.526478\pi$
$908$	−2.07161	+	3.58813i	−0.0687487	+	0.119076i
$909$		0			0
$910$	−0.248890	−	3.48952i	−0.00825063	−	0.115677i
$911$	−49.0582			−1.62537			−0.812685	−	0.582703i	$-0.801995\pi$
$911$	−49.0582			−1.62537			−0.812685	+	0.582703i	$0.801995\pi$
$912$		0			0
$913$	−12.8573			−0.425515
$914$	19.0633	+	33.0186i	0.630557	+	1.09216i
$915$		0			0
$916$	−2.30518	+	3.99270i	−0.0761654	+	0.131922i
$917$	5.97849	+	0.722891i	0.197427	+	0.0238719i
$918$		0			0
$919$	29.6056			0.976598			0.488299	−	0.872676i	$-0.337618\pi$
$919$	29.6056			0.976598			0.488299	+	0.872676i	$0.337618\pi$
$920$	0.825873			0.0272282
$921$		0			0
$922$	−1.89602	−	3.28401i	−0.0624422	−	0.108153i
$923$	−4.09794	−	21.1329i	−0.134885	−	0.695598i
$924$		0			0
$925$	7.55282	+	13.0819i	0.248335	+	0.430129i
$926$	2.81656	−	4.87842i	0.0925578	−	0.160315i
$927$		0			0
$928$	−28.3251	+	49.0605i	−0.929817	+	1.61049i
$929$	−16.8305			−0.552191			−0.276095	−	0.961130i	$-0.589041\pi$
$929$	−16.8305			−0.552191			−0.276095	+	0.961130i	$0.589041\pi$
$930$		0			0
$931$	−2.64164	−	9.08604i	−0.0865764	−	0.297783i
$932$	9.73865	−	16.8678i	0.319000	−	0.552524i
$933$		0			0
$934$	−24.0212			−0.785998
$935$	0.347255	−	0.601463i	0.0113565	−	0.0196699i
$936$		0			0
$937$	44.0131			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$938$	−25.8463	−	60.5796i	−0.843912	−	1.97799i
$939$		0			0
$940$	3.34433			0.109080
$941$	26.5338	−	45.9578i	0.864976	−	1.49818i	−0.00209573	−	0.999998i	$-0.500667\pi$
$941$	26.5338	−	45.9578i	0.864976	−	1.49818i	0.867071	−	0.498184i	$-0.166000\pi$
$942$		0			0
$943$	−22.2095			−0.723241
$944$	29.0487			0.945453
$945$		0			0
$946$	20.7043	+	35.8609i	0.673154	+	1.16594i
$947$	−13.9409	+	24.1463i	−0.453017	+	0.784649i	−0.998572	−	0.0534265i	$-0.982986\pi$
$947$	−13.9409	+	24.1463i	−0.453017	+	0.784649i	0.545555	+	0.838075i	$0.316319\pi$
$948$		0			0
$949$	−2.66689	−	13.7531i	−0.0865709	−	0.446443i
$950$	−6.23051	−	10.7916i	−0.202145	−	0.350125i
$951$		0			0
$952$	2.24704	+	0.271701i	0.0728269	+	0.00880588i
$953$	−18.1784	+	31.4859i	−0.588856	+	1.01993i	0.405527	+	0.914083i	$0.367088\pi$
$953$	−18.1784	+	31.4859i	−0.588856	+	1.01993i	−0.994383	+	0.105845i	$0.966245\pi$
$954$		0			0
$955$	1.29407	+	2.24140i	0.0418753	+	0.0725301i
$956$	−11.2980	−	19.5687i	−0.365403	−	0.632897i
$957$		0			0
$958$	−33.9877	+	58.8685i	−1.09809	+	1.90195i
$959$	35.3227	+	4.27105i	1.14063	+	0.137920i
$960$		0			0
$961$	14.6799	+	25.4263i	0.473545	+	0.820205i
$962$	−19.2852	−	6.65014i	−0.621779	−	0.214409i
$963$		0			0
$964$	5.50287	−	9.53126i	0.177236	−	0.306981i
$965$	−0.102784	−	0.178026i	−0.00330872	−	0.00573087i
$966$		0			0
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	6.60477			0.212285
$969$		0			0
$970$	3.57063	−	6.18450i	0.114646	−	0.198572i
$971$	36.8920			1.18392			0.591961	−	0.805967i	$-0.298354\pi$
$971$	36.8920			1.18392			0.591961	+	0.805967i	$0.298354\pi$
$972$		0			0
$973$	4.20018	+	9.84455i	0.134652	+	0.315602i
$974$	−68.2867			−2.18805
$975$		0			0
$976$	−27.2493	+	47.1972i	−0.872229	+	1.51074i
$977$	0.443914			0.0142021			0.00710104	−	0.999975i	$-0.497740\pi$
$977$	0.443914			0.0142021			0.00710104	+	0.999975i	$0.497740\pi$
$978$		0			0
$979$	−25.0633	+	43.4109i	−0.801026	+	1.38742i
$980$	1.94920	+	0.478370i	0.0622649	+	0.0152810i
$981$		0			0
$982$	−15.2332			−0.486109
$983$	22.7802	−	39.4564i	0.726575	−	1.25846i	−0.231748	−	0.972776i	$-0.574444\pi$
$983$	22.7802	−	39.4564i	0.726575	−	1.25846i	0.958323	−	0.285688i	$-0.0922222\pi$
$984$		0			0
$985$	0.145884	−	0.252678i	0.00464824	−	0.00805099i
$986$	−6.43964	−	11.1538i	−0.205080	−	0.355209i
$987$		0			0
$988$	6.69369	+	2.30820i	0.212955	+	0.0734336i
$989$	−10.9624	−	18.9875i	−0.348585	−	0.603766i
$990$		0			0
$991$	53.6295			1.70360			0.851799	−	0.523869i	$-0.175512\pi$
$991$	53.6295			1.70360			0.851799	+	0.523869i	$0.175512\pi$
$992$	−8.80632			−0.279601
$993$		0			0
$994$	29.1396	+	3.52342i	0.924252	+	0.111756i
$995$	−1.39139	+	2.40996i	−0.0441100	+	0.0764008i
$996$		0			0
$997$	−14.5426	−	25.1886i	−0.460569	−	0.797730i	0.538420	−	0.842677i	$-0.319021\pi$
$997$	−14.5426	−	25.1886i	−0.460569	−	0.797730i	−0.998989	+	0.0449470i	$0.985688\pi$
$998$	80.3715			2.54412
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.d.172.6		12
3.2	odd	2		91.2.g.b.81.1	yes	12
7.2	even	3		819.2.s.d.289.1		12
13.9	even	3		819.2.s.d.802.1		12
21.2	odd	6		91.2.h.b.16.6	yes	12
21.5	even	6		637.2.h.l.471.6		12
21.11	odd	6		637.2.f.k.393.1		12
21.17	even	6		637.2.f.j.393.1		12
21.20	even	2		637.2.g.l.263.1		12
39.23	odd	6		1183.2.e.g.508.6		12
39.29	odd	6		1183.2.e.h.508.1		12
39.35	odd	6		91.2.h.b.74.6	yes	12
91.9	even	3	inner	819.2.n.d.100.6		12
273.23	odd	6		1183.2.e.g.170.6		12
273.74	odd	6		637.2.f.k.295.1		12
273.101	even	6		8281.2.a.cf.1.1		6
273.107	odd	6		1183.2.e.h.170.1		12
273.152	even	6		637.2.g.l.373.1		12
273.179	odd	6		8281.2.a.ce.1.1		6
273.185	even	6		8281.2.a.ca.1.6		6
273.191	odd	6		91.2.g.b.9.1	✓	12
273.230	even	6		637.2.h.l.165.6		12
273.263	odd	6		8281.2.a.bz.1.6		6
273.269	even	6		637.2.f.j.295.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	273.191	odd	6
91.2.g.b.81.1	yes	12	3.2	odd	2
91.2.h.b.16.6	yes	12	21.2	odd	6
91.2.h.b.74.6	yes	12	39.35	odd	6
637.2.f.j.295.1		12	273.269	even	6
637.2.f.j.393.1		12	21.17	even	6
637.2.f.k.295.1		12	273.74	odd	6
637.2.f.k.393.1		12	21.11	odd	6
637.2.g.l.263.1		12	21.20	even	2
637.2.g.l.373.1		12	273.152	even	6
637.2.h.l.165.6		12	273.230	even	6
637.2.h.l.471.6		12	21.5	even	6
819.2.n.d.100.6		12	91.9	even	3	inner
819.2.n.d.172.6		12	1.1	even	1	trivial
819.2.s.d.289.1		12	7.2	even	3
819.2.s.d.802.1		12	13.9	even	3
1183.2.e.g.170.6		12	273.23	odd	6
1183.2.e.g.508.6		12	39.23	odd	6
1183.2.e.h.170.1		12	273.107	odd	6
1183.2.e.h.508.1		12	39.29	odd	6
8281.2.a.bz.1.6		6	273.263	odd	6
8281.2.a.ca.1.6		6	273.185	even	6
8281.2.a.ce.1.1		6	273.179	odd	6
8281.2.a.cf.1.1		6	273.101	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929081 - 1.60921i) q^{2} +(-0.726381 - 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} +(1.58836 - 2.11592i) q^{7} +1.01686 q^{8} +O(q^{10})\)	\(q+(0.929081 - 1.60921i) q^{2} +(-0.726381 - 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} +(1.58836 - 2.11592i) q^{7} +1.01686 q^{8} -0.366731 q^{10} +4.18274 q^{11} +(-2.72221 + 2.36423i) q^{13} +(-1.92926 - 4.52187i) q^{14} +(2.39750 - 4.15260i) q^{16} +(0.420653 + 0.728592i) q^{17} +1.35175 q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +(-2.05760 + 3.56386i) q^{23} +(2.48052 - 4.29639i) q^{25} +(1.27540 + 6.57718i) q^{26} +(-3.81585 - 0.461395i) q^{28} +(-4.11931 - 7.13485i) q^{29} +(0.640350 - 1.10912i) q^{31} +(-3.43809 - 5.95495i) q^{32} +1.56328 q^{34} +(-0.518396 - 0.0626819i) q^{35} +(-1.52242 + 2.63692i) q^{37} +(1.25589 - 2.17526i) q^{38} +(-0.100344 - 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(-3.03826 - 5.26242i) q^{44} +(3.82334 + 6.62223i) q^{46} +(-5.83204 - 10.1014i) q^{47} +(-1.95424 - 6.72168i) q^{49} +(-4.60921 - 7.98339i) q^{50} +(4.95187 + 1.70756i) q^{52} +(2.32398 - 4.02525i) q^{53} +(-0.412757 - 0.714916i) q^{55} +(1.61513 - 2.15159i) q^{56} -15.3087 q^{58} +(3.02905 + 5.24648i) q^{59} -11.3657 q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(0.672726 + 0.231978i) q^{65} +13.3970 q^{67} +(0.611109 - 1.05847i) q^{68} +(-0.582500 + 0.775973i) q^{70} +(-2.98520 + 5.17051i) q^{71} +(-1.94273 + 3.36491i) q^{73} +(2.82891 + 4.89982i) q^{74} +(-0.981887 - 1.70068i) q^{76} +(6.64368 - 8.85034i) q^{77} +(5.36669 + 9.29537i) q^{79} -0.946353 q^{80} +10.0284 q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(4.94994 + 8.57354i) q^{86} +4.25324 q^{88} +(-5.99207 + 10.3786i) q^{89} +(0.678673 + 9.51522i) q^{91} +5.97840 q^{92} -21.6737 q^{94} +(-0.133392 - 0.231042i) q^{95} +(-9.73637 + 16.8639i) q^{97} +(-12.6323 - 3.10019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29} + 16 q^{31} - 8 q^{32} + 32 q^{34} - 8 q^{35} - 13 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} + 16 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} - 25 q^{52} + 2 q^{53} + 9 q^{55} + 18 q^{56} + 16 q^{58} - 13 q^{59} + 10 q^{61} - 5 q^{62} - 30 q^{64} - 19 q^{65} + 22 q^{67} - 29 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} + 3 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} - 14 q^{80} - 2 q^{82} + 54 q^{83} - q^{85} + 7 q^{86} - 4 q^{89} - 20 q^{91} - 54 q^{92} - 90 q^{94} + 6 q^{95} - 35 q^{97} - 62 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

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