LMFDB - Embedded newform 819.2.n.d.100.6

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			100.6
Root			$0.217953 - 0.377506i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.d.172.6

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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	0.981399	+	0.191980i	$0.0614909\pi$
$2$	0.929081	+	1.60921i	0.656959	+	1.13789i	−0.324440	+	0.945906i	$0.605176\pi$
$3$		0			0
$3$		0			0
$4$	−0.726381	+	1.25813i	−0.363191	+	0.629065i
$5$	−0.0986811	+	0.170921i	−0.0441315	+	0.0764381i	−0.887247	−	0.461294i	$-0.847385\pi$
$5$	−0.0986811	+	0.170921i	−0.0441315	+	0.0764381i	0.843116	+	0.537732i	$0.180719\pi$
$6$		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	−0.810495	−	0.585746i	$-0.800802\pi$
$17$	0.420653	−	0.728592i	0.102023	−	0.176709i	0.912518	+	0.409036i	$0.134135\pi$
$18$		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	0.567750	−	0.823201i	$-0.307814\pi$
$23$	−2.05760	−	3.56386i	−0.429038	−	0.743116i	−0.996788	+	0.0800850i	$0.974481\pi$
$24$		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	0.175344	+	0.984507i	$0.443896\pi$
$29$	−4.11931	+	7.13485i	−0.764936	+	1.32491i	−0.940280	+	0.340401i	$0.889437\pi$
$30$		0			0
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	0.917784	−	0.397080i	$-0.129977\pi$
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	−0.802774	+	0.596284i	$0.796643\pi$
$32$	−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	0.713319	−	0.700839i	$-0.247191\pi$
$37$	−1.52242	−	2.63692i	−0.250285	−	0.433506i	−0.963604	+	0.267333i	$0.913858\pi$
$38$	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	−0.574648	−	0.818400i	$-0.694861\pi$
$41$	2.69848	−	4.67390i	0.421431	−	0.729941i	0.996080	+	0.0884599i	$0.0281945\pi$
$42$		0			0
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	0.588226	−	0.808697i	$-0.299827\pi$
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	−0.994465	+	0.105070i	$0.966493\pi$
$44$	−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	0.0298969	+	0.999553i	$0.490482\pi$
$47$	−5.83204	+	10.1014i	−0.850690	+	1.47344i	−0.880587	+	0.473885i	$0.842851\pi$
$48$		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	0.980326	−	0.197384i	$-0.0632446\pi$
$53$	2.32398	+	4.02525i	0.319223	+	0.552911i	−0.661103	+	0.750295i	$0.729911\pi$
$54$		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	−0.598669	−	0.800997i	$-0.704303\pi$
$59$	3.02905	−	5.24648i	0.394349	−	0.683033i	0.993018	+	0.117964i	$0.0376367\pi$
$60$		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	0.632716	−	0.774384i	$-0.281940\pi$
$71$	−2.98520	−	5.17051i	−0.354278	−	0.613627i	−0.986994	+	0.160757i	$0.948607\pi$
$72$		0			0
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	0.729651	−	0.683820i	$-0.239683\pi$
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	−0.957031	+	0.289986i	$0.906349\pi$
$74$	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	−0.388441	−	0.921474i	$-0.626986\pi$
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	0.992240	−	0.124337i	$-0.0396805\pi$
$80$	−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	−0.986482	−	0.163873i	$-0.947601\pi$
$89$	−5.99207	−	10.3786i	−0.635159	−	1.10013i	0.351323	−	0.936254i	$-0.385732\pi$
$90$		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	−0.624807	−	0.780779i	$-0.714822\pi$
$97$	−9.73637	−	16.8639i	−0.988578	−	1.71227i	−0.363771	−	0.931488i	$-0.618511\pi$
$98$	−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	−0.630952	−	0.775822i	$-0.717335\pi$
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	0.987357	+	0.158509i	$0.0506688\pi$
$104$	−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	0.523391	−	0.852093i	$-0.324667\pi$
$107$	−4.92625	−	8.53251i	−0.476238	−	0.824869i	−0.999629	+	0.0272237i	$0.991333\pi$
$108$		0			0
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	0.980179	+	0.198115i	$0.0634821\pi$
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	−0.318516	+	0.947917i	$0.603185\pi$
$110$	−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	0.748000	−	0.663699i	$-0.231014\pi$
$113$	−2.13432	−	3.69675i	−0.200780	−	0.347761i	−0.948780	+	0.315938i	$0.897681\pi$
$114$		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	−0.813339	−	0.581791i	$-0.802352\pi$
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	0.910515	+	0.413477i	$0.135686\pi$
$128$	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	−0.812017	−	0.583633i	$-0.801631\pi$
$131$	1.13806	−	1.97117i	0.0994326	−	0.172222i	0.911450	+	0.411411i	$0.134964\pi$
$132$		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	−0.421630	−	0.906768i	$-0.638542\pi$
$137$	6.72399	−	11.6463i	0.574469	−	0.995010i	0.996099	−	0.0882417i	$-0.0281248\pi$
$138$		0			0
$139$	−2.02270	−	3.50342i	−0.171563	−	0.297156i	0.767403	−	0.641165i	$-0.221548\pi$
$139$	−2.02270	−	3.50342i	−0.171563	−	0.297156i	−0.938966	+	0.344009i	$0.888215\pi$
$140$	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	0.714203	−	0.699939i	$-0.246789\pi$
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	−0.963266	+	0.268548i	$0.913456\pi$
$152$	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	0.761199	−	0.648518i	$-0.224611\pi$
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	−0.942233	+	0.334959i	$0.891278\pi$
$158$	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	−0.995355	−	0.0962726i	$-0.969308\pi$
$167$	−5.35397	+	9.27336i	−0.414303	+	0.717594i	0.581052	+	0.813866i	$0.302641\pi$
$168$		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	−0.838492	−	0.544914i	$-0.816562\pi$
$197$	0.739167	−	1.28027i	0.0526635	−	0.0912158i	0.891155	+	0.453698i	$0.149896\pi$
$198$		0			0
$199$	−7.04993	+	12.2108i	−0.499756	+	0.865603i	−1.00000		0.000281618i	$-0.999910\pi$
$199$	−7.04993	+	12.2108i	−0.499756	+	0.865603i	0.500244	+	0.865885i	$0.333244\pi$
$200$	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	−0.0986067	+	0.995126i	$0.531439\pi$
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.812501	+	0.582959i	$0.801895\pi$
$212$	−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	−0.853580	−	0.520962i	$-0.825573\pi$
$223$	0.364024	−	0.630508i	0.0243769	−	0.0422219i	0.877956	+	0.478740i	$0.158907\pi$
$224$	−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	−0.909461	−	0.415790i	$-0.863505\pi$
$227$	−1.42598	+	2.46986i	−0.0946454	+	0.163931i	0.814815	+	0.579721i	$0.196838\pi$
$228$		0			0
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	−0.913679	−	0.406436i	$-0.866772\pi$
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	0.808823	+	0.588052i	$0.200105\pi$
$230$	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	−0.558462	−	0.829530i	$-0.688608\pi$
$233$	6.70354	−	11.6109i	0.439163	−	0.760653i	0.997625	+	0.0688769i	$0.0219416\pi$
$234$		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	−0.717851	−	0.696196i	$-0.754874\pi$
$241$	3.78787	−	6.56078i	0.243998	−	0.422617i	0.961849	+	0.273579i	$0.0882076\pi$
$242$	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	0.885440	−	0.464754i	$-0.153857\pi$
$251$	0.637382	+	1.10398i	0.0402312	+	0.0696825i	−0.845209	+	0.534436i	$0.820524\pi$
$252$		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	0.702940	−	0.711249i	$-0.251870\pi$
$257$	−4.24010	−	7.34406i	−0.264490	−	0.458110i	−0.967430	+	0.253139i	$0.918537\pi$
$258$		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	−0.928864	−	0.370420i	$-0.879214\pi$
$269$	−2.35586	+	4.08047i	−0.143639	+	0.248790i	0.785225	+	0.619210i	$0.212547\pi$
$270$		0			0
$271$	9.00562	+	15.5982i	0.547052	+	0.947522i	0.998475	+	0.0552119i	$0.0175834\pi$
$271$	9.00562	+	15.5982i	0.547052	+	0.947522i	−0.451422	+	0.892310i	$0.649083\pi$
$272$	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	−0.144438	−	0.989514i	$-0.546137\pi$
$277$	13.0604	−	22.6213i	0.784725	−	1.35918i	0.929163	−	0.369670i	$-0.120529\pi$
$278$	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	−0.999999	−	0.00122001i	$-0.999612\pi$
$293$	−8.57670	−	14.8553i	−0.501056	−	0.867855i	0.498943	−	0.866635i	$-0.333722\pi$
$294$		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	−0.978671	−	0.205436i	$-0.934139\pi$
$311$	−11.7670	−	20.3811i	−0.667248	−	1.15571i	0.311423	−	0.950271i	$-0.399194\pi$
$312$		0			0
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	−0.814820	−	0.579714i	$-0.803164\pi$
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	0.909457	+	0.415798i	$0.136498\pi$
$314$	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	−0.949940	−	0.312432i	$-0.898856\pi$
$317$	−3.63917	+	6.30323i	−0.204396	+	0.354025i	0.745544	+	0.666456i	$0.232190\pi$
$318$		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	−0.950690	−	0.310143i	$-0.899623\pi$
$347$	−3.85139	+	6.67080i	−0.206753	+	0.358107i	0.743937	+	0.668250i	$0.232956\pi$
$348$		0			0
$349$	−11.1850	+	19.3730i	−0.598721	+	1.03702i	0.394289	+	0.918986i	$0.370991\pi$
$349$	−11.1850	+	19.3730i	−0.598721	+	1.03702i	−0.993010	+	0.118029i	$0.962343\pi$
$350$	−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	−0.900124	−	0.435634i	$-0.856524\pi$
$359$	−1.37921	+	2.38887i	−0.0727920	+	0.126079i	0.827332	+	0.561713i	$0.189858\pi$
$360$		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	−0.777657	−	0.628688i	$-0.783592\pi$
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	0.933289	+	0.359127i	$0.116925\pi$
$380$	−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	0.917489	−	0.397761i	$-0.130213\pi$
$389$	2.25383	+	3.90374i	0.114273	+	0.197927i	−0.803216	+	0.595688i	$0.796879\pi$
$390$		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	0.979426	−	0.201806i	$-0.0646810\pi$
$401$	6.30674	+	10.9236i	0.314944	+	0.545498i	−0.664482	+	0.747304i	$0.731348\pi$
$402$		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	0.488252	+	0.872703i	$0.337635\pi$
$409$	−10.3476	+	17.9226i	−0.511657	+	0.886216i	−0.999909	+	0.0135128i	$0.995699\pi$
$410$	−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	0.466333	+	0.884609i	$0.345575\pi$
$419$	−10.9088	+	18.8945i	−0.532928	+	0.923058i	−0.999261	+	0.0384484i	$0.987758\pi$
$420$		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	−0.986911	−	0.161267i	$-0.948442\pi$
$433$	−13.1743	−	22.8186i	−0.633117	−	1.09659i	0.353794	−	0.935323i	$-0.384891\pi$
$434$	−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	−0.992862	−	0.119267i	$-0.961945\pi$
$439$	−12.5655	−	21.7641i	−0.599720	−	1.03875i	0.393142	−	0.919478i	$-0.371388\pi$
$440$	−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	−0.557732	−	0.830021i	$-0.688328\pi$
$443$	9.25995	−	16.0387i	0.439953	−	0.762022i	0.997685	+	0.0679994i	$0.0216616\pi$
$444$		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	0.970068	−	0.242832i	$-0.0780763\pi$
$449$	5.82155	+	10.0832i	0.274736	+	0.475856i	−0.695333	+	0.718688i	$0.744743\pi$
$450$		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	0.519828	−	0.854271i	$-0.325996\pi$
$457$	−10.2592	−	17.7695i	−0.479906	−	0.831222i	−0.999734	+	0.0230490i	$0.992663\pi$
$458$	−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	0.888809	−	0.458278i	$-0.151534\pi$
$461$	1.02038	+	1.76734i	0.0475236	+	0.0823134i	−0.841285	+	0.540592i	$0.818200\pi$
$462$		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	−0.975931	−	0.218078i	$-0.930021\pi$
$467$	−6.46371	+	11.1955i	−0.299105	+	0.518065i	0.676827	+	0.736142i	$0.263355\pi$
$468$		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	0.0632939	+	0.997995i	$0.479839\pi$
$487$	−18.3748	+	31.8261i	−0.832642	+	1.44218i	−0.895936	+	0.444183i	$0.853494\pi$
$488$	−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	−0.943571	−	0.331169i	$-0.892557\pi$
$491$	−4.09899	+	7.09965i	−0.184985	+	0.320403i	0.758587	+	0.651572i	$0.225890\pi$
$492$		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	0.267211	−	0.963638i	$-0.413898\pi$
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.700929	−	0.713231i	$-0.252769\pi$
$500$	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	0.866228	−	0.499649i	$-0.166538\pi$
$503$	0.00909609	+	0.0157549i	0.000405575	+	0.000702476i	−0.865823	+	0.500351i	$0.833204\pi$
$504$		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	0.733909	+	0.679248i	$0.237694\pi$
$509$	21.5503	+	37.3262i	0.955200	+	1.65446i	0.221292	+	0.975208i	$0.428973\pi$
$510$		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	0.998909	−	0.0467056i	$-0.0148723\pi$
$521$	10.4770	+	18.1467i	0.459006	+	0.795022i	−0.539903	+	0.841727i	$0.681539\pi$
$522$		0			0
$523$	17.3701	+	30.0860i	0.759543	+	1.31557i	0.943084	+	0.332555i	$0.107911\pi$
$523$	17.3701	+	30.0860i	0.759543	+	1.31557i	−0.183541	+	0.983012i	$0.558756\pi$
$524$	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	−0.828393	−	0.560148i	$-0.810744\pi$
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	0.899299	+	0.437335i	$0.144078\pi$
$542$	−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	−0.785602	−	0.618732i	$-0.787647\pi$
$563$	3.39392	−	5.87844i	0.143037	−	0.247747i	0.928639	+	0.370985i	$0.120980\pi$
$564$		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	0.625393	−	0.780310i	$-0.284939\pi$
$569$	−8.66061	−	15.0006i	−0.363072	−	0.628859i	−0.988465	+	0.151451i	$0.951605\pi$
$570$		0			0
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	0.969440	−	0.245328i	$-0.0788957\pi$
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	−0.697180	+	0.716896i	$0.745562\pi$
$572$	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	0.873539	−	0.486755i	$-0.161820\pi$
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	−0.858311	+	0.513129i	$0.828486\pi$
$578$	−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	−0.940468	−	0.339882i	$-0.889613\pi$
$587$	−4.26142	+	7.38099i	−0.175888	+	0.304646i	0.764581	+	0.644528i	$0.222946\pi$
$588$		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	0.341932	+	0.939725i	$0.388919\pi$
$593$	−15.6547	+	27.1147i	−0.642860	+	1.11347i	−0.984791	+	0.173741i	$0.944415\pi$
$594$		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	0.858260	−	0.513215i	$-0.171546\pi$
$599$	−0.375116	−	0.649720i	−0.0153268	−	0.0265468i	−0.873587	+	0.486668i	$0.838212\pi$
$600$		0			0
$601$	4.77652	−	8.27318i	0.194838	−	0.337470i	−0.752009	−	0.659153i	$-0.770915\pi$
$601$	4.77652	−	8.27318i	0.194838	−	0.337470i	0.946848	+	0.321683i	$0.104248\pi$
$602$	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	0.994806	−	0.101789i	$-0.0324565\pi$
$617$	10.1656	+	17.6073i	0.409252	+	0.708845i	−0.585554	+	0.810633i	$0.699123\pi$
$618$		0			0
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	0.807354	−	0.590067i	$-0.200899\pi$
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	−0.914690	+	0.404156i	$0.867565\pi$
$620$	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	0.794463	−	0.607312i	$-0.207752\pi$
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	−0.923179	+	0.384369i	$0.874419\pi$
$632$	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	−0.538280	−	0.842766i	$-0.680926\pi$
$641$	11.6644	−	20.2034i	0.460717	−	0.797985i	0.998997	+	0.0447808i	$0.0142589\pi$
$642$		0			0
$643$	1.79439	+	3.10797i	0.0707637	+	0.122566i	0.899236	−	0.437463i	$-0.144123\pi$
$643$	1.79439	+	3.10797i	0.0707637	+	0.122566i	−0.828472	+	0.560030i	$0.810790\pi$
$644$	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	0.987092	−	0.160153i	$-0.0511988\pi$
$653$	9.06777	+	15.7058i	0.354849	+	0.614617i	−0.632243	+	0.774770i	$0.717865\pi$
$654$		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	0.966925	−	0.255061i	$-0.0820955\pi$
$659$	6.74052	+	11.6749i	0.262573	+	0.454791i	−0.704352	+	0.709851i	$0.748762\pi$
$660$		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	−0.763257	−	0.646095i	$-0.776401\pi$
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	0.941163	+	0.337953i	$0.109734\pi$
$674$	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	−0.994361	−	0.106045i	$-0.966181\pi$
$677$	−10.5467	+	18.2674i	−0.405343	+	0.702075i	0.589018	+	0.808120i	$0.299515\pi$
$678$		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	0.225104	+	0.974335i	$0.427728\pi$
$683$	−19.1106	+	33.1005i	−0.731246	+	1.26656i	−0.956351	+	0.292221i	$0.905606\pi$
$684$		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	0.999999	−	0.00120019i	$-0.000382034\pi$
$691$	13.1161	+	22.7178i	0.498960	+	0.864224i	−0.501039	+	0.865425i	$0.667049\pi$
$692$	−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	0.478894	+	0.877873i	$0.341038\pi$
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	−0.999707	+	0.0242025i	$0.992295\pi$
$734$	−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	−0.682345	−	0.731030i	$-0.739040\pi$
$743$	7.95711	−	13.7821i	0.291918	−	0.505617i	0.974263	+	0.225413i	$0.0723732\pi$
$744$		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	0.650858	−	0.759199i	$-0.274409\pi$
$751$	−9.09981	−	15.7613i	−0.332057	−	0.575139i	−0.982915	+	0.184060i	$0.941076\pi$
$752$	−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	−0.0926649	−	0.995697i	$-0.529539\pi$
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	0.908632	−	0.417598i	$-0.137128\pi$
$758$	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	−0.964008	−	0.265873i	$-0.914340\pi$
$769$	−6.98127	+	12.0919i	−0.251751	+	0.436045i	0.712257	+	0.701919i	$0.247673\pi$
$770$	−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	−0.727529	−	0.686077i	$-0.759332\pi$
$773$	6.40564	−	11.0949i	0.230395	−	0.399056i	0.957924	+	0.287021i	$0.0926648\pi$
$774$		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	−0.512963	−	0.858411i	$-0.671452\pi$
$787$	13.6599	−	23.6597i	0.486924	−	0.843377i	0.999887	+	0.0150334i	$0.00478545\pi$
$788$	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	−0.999710	−	0.0240775i	$-0.992335\pi$
$797$	−14.7002	−	25.4614i	−0.520707	−	0.901891i	0.479003	−	0.877813i	$-0.340998\pi$
$798$		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	−0.993130	−	0.117014i	$-0.962668\pi$
$821$	−17.1318	−	29.6731i	−0.597903	−	1.03560i	0.395228	−	0.918583i	$-0.370666\pi$
$822$		0			0
$823$	3.11866	−	5.40168i	0.108710	−	0.188291i	−0.806538	−	0.591182i	$-0.798661\pi$
$823$	3.11866	−	5.40168i	0.108710	−	0.188291i	0.915248	+	0.402891i	$0.131995\pi$
$824$	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	0.996615	−	0.0822161i	$-0.0261998\pi$
$839$	12.3713	+	21.4278i	0.427106	+	0.739769i	−0.569508	+	0.821985i	$0.692866\pi$
$840$		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	0.886955	−	0.461856i	$-0.152816\pi$
$857$	1.27340	+	2.20559i	0.0434984	+	0.0753414i	−0.843457	+	0.537197i	$0.819483\pi$
$858$		0			0
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.124104	+	0.992269i	$0.539606\pi$
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.797278	+	0.603612i	$0.793728\pi$
$860$	−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	−0.855253	−	0.518211i	$-0.826598\pi$
$863$	0.621545	−	1.07655i	0.0211576	−	0.0366461i	0.876410	+	0.481565i	$0.159931\pi$
$864$		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	0.364314	+	0.931276i	$0.381304\pi$
$881$	−18.5318	+	32.0980i	−0.624352	+	1.08141i	−0.988666	+	0.150133i	$0.952030\pi$
$882$		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	−0.900420	−	0.435022i	$-0.856741\pi$
$887$	−24.6287	−	42.6581i	−0.826950	−	1.43232i	0.0734699	−	0.997297i	$-0.476593\pi$
$888$		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	0.867071	+	0.498184i	$0.166000\pi$
$941$	26.5338	+	45.9578i	0.864976	+	1.49818i	−0.00209573	+	0.999998i	$0.500667\pi$
$942$		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	0.545555	−	0.838075i	$-0.316319\pi$
$947$	−13.9409	−	24.1463i	−0.453017	−	0.784649i	−0.998572	+	0.0534265i	$0.982986\pi$
$948$		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	−0.994383	−	0.105845i	$-0.966245\pi$
$953$	−18.1784	−	31.4859i	−0.588856	−	1.01993i	0.405527	−	0.914083i	$-0.367088\pi$
$954$		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	0.958323	+	0.285688i	$0.0922222\pi$
$983$	22.7802	+	39.4564i	0.726575	+	1.25846i	−0.231748	+	0.972776i	$0.574444\pi$
$984$		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	−0.998989	−	0.0449470i	$-0.985688\pi$
$997$	−14.5426	+	25.1886i	−0.460569	+	0.797730i	0.538420	+	0.842677i	$0.319021\pi$
$998$	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.100.6		12
3.2	odd	2		91.2.g.b.9.1	✓	12
7.4	even	3		819.2.s.d.802.1		12
13.3	even	3		819.2.s.d.289.1		12
21.2	odd	6		637.2.f.k.295.1		12
21.5	even	6		637.2.f.j.295.1		12
21.11	odd	6		91.2.h.b.74.6	yes	12
21.17	even	6		637.2.h.l.165.6		12
21.20	even	2		637.2.g.l.373.1		12
39.17	odd	6		1183.2.e.g.170.6		12
39.29	odd	6		91.2.h.b.16.6	yes	12
39.35	odd	6		1183.2.e.h.170.1		12
91.81	even	3	inner	819.2.n.d.172.6		12
273.68	even	6		637.2.f.j.393.1		12
273.74	odd	6		1183.2.e.h.508.1		12
273.95	odd	6		1183.2.e.g.508.6		12
273.107	odd	6		637.2.f.k.393.1		12
273.146	even	6		637.2.h.l.471.6		12
273.152	even	6		8281.2.a.ca.1.6		6
273.173	even	6		8281.2.a.cf.1.1		6
273.185	even	6		637.2.g.l.263.1		12
273.191	odd	6		8281.2.a.bz.1.6		6
273.212	odd	6		8281.2.a.ce.1.1		6
273.263	odd	6		91.2.g.b.81.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	3.2	odd	2
91.2.g.b.81.1	yes	12	273.263	odd	6
91.2.h.b.16.6	yes	12	39.29	odd	6
91.2.h.b.74.6	yes	12	21.11	odd	6
637.2.f.j.295.1		12	21.5	even	6
637.2.f.j.393.1		12	273.68	even	6
637.2.f.k.295.1		12	21.2	odd	6
637.2.f.k.393.1		12	273.107	odd	6
637.2.g.l.263.1		12	273.185	even	6
637.2.g.l.373.1		12	21.20	even	2
637.2.h.l.165.6		12	21.17	even	6
637.2.h.l.471.6		12	273.146	even	6
819.2.n.d.100.6		12	1.1	even	1	trivial
819.2.n.d.172.6		12	91.81	even	3	inner
819.2.s.d.289.1		12	13.3	even	3
819.2.s.d.802.1		12	7.4	even	3
1183.2.e.g.170.6		12	39.17	odd	6
1183.2.e.g.508.6		12	273.95	odd	6
1183.2.e.h.170.1		12	39.35	odd	6
1183.2.e.h.508.1		12	273.74	odd	6
8281.2.a.bz.1.6		6	273.191	odd	6
8281.2.a.ca.1.6		6	273.152	even	6
8281.2.a.ce.1.1		6	273.212	odd	6
8281.2.a.cf.1.1		6	273.173	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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