LMFDB - Embedded newform 990.2.n.j.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(91,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,0,-2,2,0,-1,-2,0,-8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$0.581882 - 1.79085i$ of defining polynomial
Character	$\chi$	$=$	990.361
Dual form			990.2.n.j.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-3.17926 - 2.30987i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.00000 q^{10} +(1.42705 - 2.99391i) q^{11} +(-1.80113 + 5.54330i) q^{13} +(-3.17926 + 2.30987i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.332405 - 1.02304i) q^{17} +(-1.22713 + 0.891565i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-2.40640 - 2.28238i) q^{22} -5.07230 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.71542 + 3.42595i) q^{26} +(1.21437 + 3.73745i) q^{28} +(0.306281 + 0.222526i) q^{29} +(-2.02891 + 6.24434i) q^{31} +1.00000 q^{32} -1.07569 q^{34} +(-1.21437 + 3.73745i) q^{35} +(0.832405 + 0.604778i) q^{37} +(0.468724 + 1.44258i) q^{38} +(0.809017 + 0.587785i) q^{40} +(3.19992 - 2.32488i) q^{41} -0.446609 q^{43} +(-2.91429 + 1.58333i) q^{44} +(-1.56743 + 4.82405i) q^{46} +(-6.14416 + 4.46399i) q^{47} +(2.60910 + 8.02999i) q^{49} +(0.309017 + 0.951057i) q^{50} +(4.71542 - 3.42595i) q^{52} +(-1.93362 + 5.95106i) q^{53} +(-3.28837 - 0.432036i) q^{55} +3.92979 q^{56} +(0.306281 - 0.222526i) q^{58} +(-8.89194 - 6.46038i) q^{59} +(-3.10121 - 9.54455i) q^{61} +(5.31175 + 3.85921i) q^{62} +(0.309017 - 0.951057i) q^{64} +5.82857 q^{65} -5.98422 q^{67} +(-0.332405 + 1.02304i) q^{68} +(3.17926 + 2.30987i) q^{70} +(-1.55548 - 4.78728i) q^{71} +(-2.86236 - 2.07963i) q^{73} +(0.832405 - 0.604778i) q^{74} +1.51682 q^{76} +(-11.4525 + 6.22214i) q^{77} +(0.218201 - 0.671554i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-1.22226 - 3.76173i) q^{82} +(-3.62801 - 11.1659i) q^{83} +(-0.870248 + 0.632272i) q^{85} +(-0.138010 + 0.424750i) q^{86} +(0.605270 + 3.26093i) q^{88} -0.0446858 q^{89} +(18.5306 - 13.4633i) q^{91} +(4.10358 + 2.98142i) q^{92} +(2.34686 + 7.22289i) q^{94} +(1.22713 + 0.891565i) q^{95} +(-5.05466 + 15.5567i) q^{97} +8.44323 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8} - 8 q^{10} - 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} - 26 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 22 q^{29}+ \cdots + 22 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8 - 8 * q^10 - 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 - 26 * q^23 - 2 * q^25 + 6 * q^26 + 4 * q^28 + 22 * q^29 - 26 * q^31 + 8 * q^32 + 2 * q^34 - 4 * q^35 - 8 * q^37 + 3 * q^38 + 2 * q^40 + 15 * q^41 + 38 * q^43 - 7 * q^44 - 6 * q^46 - 6 * q^47 + 27 * q^49 - 2 * q^50 + 6 * q^52 + 4 * q^53 - 8 * q^55 - 6 * q^56 + 22 * q^58 - 39 * q^59 - 20 * q^61 + 14 * q^62 - 2 * q^64 + 14 * q^65 - 26 * q^67 + 12 * q^68 + q^70 - 2 * q^71 + 8 * q^73 - 8 * q^74 + 8 * q^76 - 16 * q^77 + 14 * q^79 + 2 * q^80 - 15 * q^82 + 21 * q^83 + 13 * q^85 - 17 * q^86 - 7 * q^88 - 32 * q^89 + 53 * q^91 + 19 * q^92 + 9 * q^94 + 7 * q^95 - 31 * q^97 + 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	−3.17926	−	2.30987i	−1.20165	−	0.873049i	−0.207203	−	0.978298i	$-0.566436\pi$
$7$	−3.17926	−	2.30987i	−1.20165	−	0.873049i	−0.994446	+	0.105249i	$0.966436\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	1.42705	−	2.99391i	0.430272	−	0.902699i
$11$	1.42705	−	2.99391i	0.430272	−	0.902699i
$12$		0			0
$13$	−1.80113	+	5.54330i	−0.499543	+	1.53744i	0.310212	+	0.950668i	$0.399600\pi$
$13$	−1.80113	+	5.54330i	−0.499543	+	1.53744i	−0.809755	+	0.586768i	$0.800400\pi$
$14$	−3.17926	+	2.30987i	−0.849694	+	0.617339i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.332405	−	1.02304i	−0.0806201	−	0.248123i	0.902620	−	0.430438i	$-0.141641\pi$
$17$	−0.332405	−	1.02304i	−0.0806201	−	0.248123i	−0.983240	+	0.182315i	$0.941641\pi$
$18$		0			0
$19$	−1.22713	+	0.891565i	−0.281524	+	0.204539i	−0.719582	−	0.694408i	$-0.755666\pi$
$19$	−1.22713	+	0.891565i	−0.281524	+	0.204539i	0.438058	+	0.898947i	$0.355666\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$		0			0
$22$	−2.40640	−	2.28238i	−0.513046	−	0.486604i
$23$	−5.07230			−1.05765			−0.528824	−	0.848731i	$-0.677367\pi$
$23$	−5.07230			−1.05765			−0.528824	+	0.848731i	$0.677367\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	4.71542	+	3.42595i	0.924769	+	0.671884i
$27$		0			0
$28$	1.21437	+	3.73745i	0.229495	+	0.706312i
$29$	0.306281	+	0.222526i	0.0568749	+	0.0413221i	0.615859	−	0.787856i	$-0.288809\pi$
$29$	0.306281	+	0.222526i	0.0568749	+	0.0413221i	−0.558985	+	0.829178i	$0.688809\pi$
$30$		0			0
$31$	−2.02891	+	6.24434i	−0.364403	+	1.12152i	0.585951	+	0.810346i	$0.300721\pi$
$31$	−2.02891	+	6.24434i	−0.364403	+	1.12152i	−0.950354	+	0.311170i	$0.899279\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.07569			−0.184478
$35$	−1.21437	+	3.73745i	−0.205266	+	0.631744i
$36$		0			0
$37$	0.832405	+	0.604778i	0.136847	+	0.0994248i	0.654103	−	0.756406i	$-0.273046\pi$
$37$	0.832405	+	0.604778i	0.136847	+	0.0994248i	−0.517256	+	0.855831i	$0.673046\pi$
$38$	0.468724	+	1.44258i	0.0760370	+	0.234018i
$39$		0			0
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	3.19992	−	2.32488i	0.499743	−	0.363085i	−0.309176	−	0.951005i	$-0.600053\pi$
$41$	3.19992	−	2.32488i	0.499743	−	0.363085i	0.808919	+	0.587920i	$0.200053\pi$
$42$		0			0
$43$	−0.446609			−0.0681072			−0.0340536	−	0.999420i	$-0.510842\pi$
$43$	−0.446609			−0.0681072			−0.0340536	+	0.999420i	$0.510842\pi$
$44$	−2.91429	+	1.58333i	−0.439345	+	0.238696i
$45$		0			0
$46$	−1.56743	+	4.82405i	−0.231105	+	0.711267i
$47$	−6.14416	+	4.46399i	−0.896218	+	0.651140i	−0.937492	−	0.348008i	$-0.886858\pi$
$47$	−6.14416	+	4.46399i	−0.896218	+	0.651140i	0.0412741	+	0.999148i	$0.486858\pi$
$48$		0			0
$49$	2.60910	+	8.02999i	0.372729	+	1.14714i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$		0			0
$52$	4.71542	−	3.42595i	0.653911	−	0.475094i
$53$	−1.93362	+	5.95106i	−0.265603	+	0.817441i	0.725951	+	0.687746i	$0.241400\pi$
$53$	−1.93362	+	5.95106i	−0.265603	+	0.817441i	−0.991554	+	0.129695i	$0.958600\pi$
$54$		0			0
$55$	−3.28837	−	0.432036i	−0.443403	−	0.0582557i
$56$	3.92979			0.525140
$57$		0			0
$58$	0.306281	−	0.222526i	0.0402166	−	0.0292191i
$59$	−8.89194	−	6.46038i	−1.15763	−	0.841069i	−0.168156	−	0.985760i	$-0.553781\pi$
$59$	−8.89194	−	6.46038i	−1.15763	−	0.841069i	−0.989477	+	0.144691i	$0.953781\pi$
$60$		0			0
$61$	−3.10121	−	9.54455i	−0.397070	−	1.22205i	−0.927338	−	0.374225i	$-0.877909\pi$
$61$	−3.10121	−	9.54455i	−0.397070	−	1.22205i	0.530269	−	0.847830i	$-0.322091\pi$
$62$	5.31175	+	3.85921i	0.674593	+	0.490121i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	5.82857			0.722946
$66$		0			0
$67$	−5.98422			−0.731089			−0.365545	−	0.930794i	$-0.619117\pi$
$67$	−5.98422			−0.731089			−0.365545	+	0.930794i	$0.619117\pi$
$68$	−0.332405	+	1.02304i	−0.0403100	+	0.124062i
$69$		0			0
$70$	3.17926	+	2.30987i	0.379995	+	0.276082i
$71$	−1.55548	−	4.78728i	−0.184602	−	0.568146i	0.815340	−	0.578983i	$-0.196550\pi$
$71$	−1.55548	−	4.78728i	−0.184602	−	0.568146i	−0.999941	+	0.0108375i	$0.996550\pi$
$72$		0			0
$73$	−2.86236	−	2.07963i	−0.335014	−	0.243402i	0.407541	−	0.913187i	$-0.366386\pi$
$73$	−2.86236	−	2.07963i	−0.335014	−	0.243402i	−0.742555	+	0.669785i	$0.766386\pi$
$74$	0.832405	−	0.604778i	0.0967651	−	0.0703040i
$75$		0			0
$76$	1.51682			0.173991
$77$	−11.4525	+	6.22214i	−1.30514	+	0.709079i
$78$		0			0
$79$	0.218201	−	0.671554i	0.0245495	−	0.0755557i	−0.938031	−	0.346551i	$-0.887353\pi$
$79$	0.218201	−	0.671554i	0.0245495	−	0.0755557i	0.962581	+	0.270995i	$0.0873528\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$		0			0
$82$	−1.22226	−	3.76173i	−0.134976	−	0.415413i
$83$	−3.62801	−	11.1659i	−0.398226	−	1.22561i	−0.926420	−	0.376490i	$-0.877131\pi$
$83$	−3.62801	−	11.1659i	−0.398226	−	1.22561i	0.528194	−	0.849123i	$-0.322869\pi$
$84$		0			0
$85$	−0.870248	+	0.632272i	−0.0943916	+	0.0685795i
$86$	−0.138010	+	0.424750i	−0.0148820	+	0.0458020i
$87$		0			0
$88$	0.605270	+	3.26093i	0.0645220	+	0.347616i
$89$	−0.0446858			−0.00473668			−0.00236834	−	0.999997i	$-0.500754\pi$
$89$	−0.0446858			−0.00473668			−0.00236834	+	0.999997i	$0.500754\pi$
$90$		0			0
$91$	18.5306	−	13.4633i	1.94253	−	1.41133i
$92$	4.10358	+	2.98142i	0.427828	+	0.310835i
$93$		0			0
$94$	2.34686	+	7.22289i	0.242060	+	0.744984i
$95$	1.22713	+	0.891565i	0.125901	+	0.0914727i
$96$		0			0
$97$	−5.05466	+	15.5567i	−0.513223	+	1.57954i	0.273268	+	0.961938i	$0.411895\pi$
$97$	−5.05466	+	15.5567i	−0.513223	+	1.57954i	−0.786491	+	0.617601i	$0.788105\pi$
$98$	8.44323			0.852895
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.00000	+	3.07768i	−0.0995037	+	0.306241i	−0.988401	−	0.151865i	$-0.951472\pi$
$101$	−1.00000	+	3.07768i	−0.0995037	+	0.306241i	0.888897	+	0.458106i	$0.151472\pi$
$102$		0			0
$103$	9.26324	+	6.73014i	0.912734	+	0.663140i	0.941705	−	0.336440i	$-0.109223\pi$
$103$	9.26324	+	6.73014i	0.912734	+	0.663140i	−0.0289709	+	0.999580i	$0.509223\pi$
$104$	−1.80113	−	5.54330i	−0.176615	−	0.543566i
$105$		0			0
$106$	5.06228	+	3.67796i	0.491692	+	0.357235i
$107$	5.83345	−	4.23825i	0.563941	−	0.409727i	−0.268958	−	0.963152i	$-0.586679\pi$
$107$	5.83345	−	4.23825i	0.563941	−	0.409727i	0.832899	+	0.553425i	$0.186679\pi$
$108$		0			0
$109$	1.56360			0.149766			0.0748828	−	0.997192i	$-0.476142\pi$
$109$	1.56360			0.149766			0.0748828	+	0.997192i	$0.476142\pi$
$110$	−1.42705	+	2.99391i	−0.136064	+	0.285459i
$111$		0			0
$112$	1.21437	−	3.73745i	0.114747	−	0.353156i
$113$	5.05954	−	3.67597i	0.475961	−	0.345806i	−0.323799	−	0.946126i	$-0.604960\pi$
$113$	5.05954	−	3.67597i	0.475961	−	0.345806i	0.799760	+	0.600320i	$0.204960\pi$
$114$		0			0
$115$	1.56743	+	4.82405i	0.146163	+	0.449845i
$116$	−0.116989	−	0.360055i	−0.0108621	−	0.0334302i
$117$		0			0
$118$	−8.89194	+	6.46038i	−0.818570	+	0.594726i
$119$	−1.30628	+	4.02032i	−0.119747	+	0.368542i
$120$		0			0
$121$	−6.92705	−	8.54494i	−0.629732	−	0.776813i
$122$	−10.0357			−0.908593
$123$		0			0
$124$	5.31175	−	3.85921i	0.477010	−	0.346568i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	−5.86577	−	18.0530i	−0.520503	−	1.60194i	−0.773041	−	0.634357i	$-0.781265\pi$
$127$	−5.86577	−	18.0530i	−0.520503	−	1.60194i	0.252538	−	0.967587i	$-0.418735\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	1.80113	−	5.54330i	0.157969	−	0.486180i
$131$	6.34749			0.554582			0.277291	−	0.960786i	$-0.410563\pi$
$131$	6.34749			0.554582			0.277291	+	0.960786i	$0.410563\pi$
$132$		0			0
$133$	5.96079			0.516866
$134$	−1.84923	+	5.69133i	−0.159749	+	0.491656i
$135$		0			0
$136$	0.870248	+	0.632272i	0.0746231	+	0.0542169i
$137$	1.44767	+	4.45548i	0.123683	+	0.380657i	0.993659	−	0.112437i	$-0.0358657\pi$
$137$	1.44767	+	4.45548i	0.123683	+	0.380657i	−0.869976	+	0.493094i	$0.835866\pi$
$138$		0			0
$139$	−6.79392	−	4.93607i	−0.576252	−	0.418672i	0.261119	−	0.965307i	$-0.415909\pi$
$139$	−6.79392	−	4.93607i	−0.576252	−	0.418672i	−0.837371	+	0.546635i	$0.815909\pi$
$140$	3.17926	−	2.30987i	0.268697	−	0.195220i
$141$		0			0
$142$	−5.03364			−0.422414
$143$	14.0259	+	13.3030i	1.17290	+	1.11245i
$144$		0			0
$145$	0.116989	−	0.360055i	0.00971540	−	0.0299009i
$146$	−2.86236	+	2.07963i	−0.236891	+	0.172111i
$147$		0			0
$148$	−0.317950	−	0.978551i	−0.0261354	−	0.0804364i
$149$	−7.13695	−	21.9653i	−0.584681	−	1.79946i	−0.600546	−	0.799590i	$-0.705050\pi$
$149$	−7.13695	−	21.9653i	−0.584681	−	1.79946i	0.0158647	−	0.999874i	$-0.494950\pi$
$150$		0			0
$151$	4.67028	−	3.39316i	0.380062	−	0.276131i	−0.381309	−	0.924448i	$-0.624527\pi$
$151$	4.67028	−	3.39316i	0.380062	−	0.276131i	0.761371	+	0.648316i	$0.224527\pi$
$152$	0.468724	−	1.44258i	0.0380185	−	0.117009i
$153$		0			0
$154$	2.37858	+	12.8148i	0.191672	+	1.03264i
$155$	6.56569			0.527369
$156$		0			0
$157$	−8.73047	+	6.34306i	−0.696767	+	0.506231i	−0.878878	−	0.477047i	$-0.841707\pi$
$157$	−8.73047	+	6.34306i	−0.696767	+	0.506231i	0.182111	+	0.983278i	$0.441707\pi$
$158$	−0.571258	−	0.415043i	−0.0454468	−	0.0330191i
$159$		0			0
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	16.1262	+	11.7164i	1.27092	+	0.923379i
$162$		0			0
$163$	5.14311	−	15.8289i	0.402840	−	1.23981i	−0.519846	−	0.854260i	$-0.674011\pi$
$163$	5.14311	−	15.8289i	0.402840	−	1.23981i	0.922686	−	0.385553i	$-0.125989\pi$
$164$	−3.95531			−0.308858
$165$		0			0
$166$	−11.7405			−0.911239
$167$	2.67439	−	8.23092i	0.206950	−	0.636928i	−0.792677	−	0.609642i	$-0.791313\pi$
$167$	2.67439	−	8.23092i	0.206950	−	0.636928i	0.999628	−	0.0272864i	$-0.00868662\pi$
$168$		0			0
$169$	−16.9669	−	12.3272i	−1.30515	−	0.948246i
$170$	0.332405	+	1.02304i	0.0254943	+	0.0784634i
$171$		0			0
$172$	0.361314	+	0.262510i	0.0275499	+	0.0200162i
$173$	−10.3196	+	7.49762i	−0.784584	+	0.570034i	−0.906351	−	0.422525i	$-0.861144\pi$
$173$	−10.3196	+	7.49762i	−0.784584	+	0.570034i	0.121767	+	0.992559i	$0.461144\pi$
$174$		0			0
$175$	3.92979			0.297064
$176$	3.28837	+	0.432036i	0.247870	+	0.0325659i
$177$		0			0
$178$	−0.0138087	+	0.0424987i	−0.00103500	+	0.00318541i
$179$	15.2533	−	11.0822i	1.14008	−	0.828320i	0.152953	−	0.988233i	$-0.451122\pi$
$179$	15.2533	−	11.0822i	1.14008	−	0.828320i	0.987131	+	0.159914i	$0.0511216\pi$
$180$		0			0
$181$	7.34066	+	22.5922i	0.545627	+	1.67927i	0.719494	+	0.694498i	$0.244374\pi$
$181$	7.34066	+	22.5922i	0.545627	+	1.67927i	−0.173867	+	0.984769i	$0.555626\pi$
$182$	−7.07805	−	21.7840i	−0.524660	−	1.61474i
$183$		0			0
$184$	4.10358	−	2.98142i	0.302520	−	0.219794i
$185$	0.317950	−	0.978551i	0.0233762	−	0.0719445i
$186$		0			0
$187$	−3.53725	−	0.464734i	−0.258669	−	0.0339847i
$188$	7.59460			0.553893
$189$		0			0
$190$	1.22713	−	0.891565i	0.0890257	−	0.0646810i
$191$	−5.97109	−	4.33825i	−0.432053	−	0.313905i	0.350416	−	0.936594i	$-0.386040\pi$
$191$	−5.97109	−	4.33825i	−0.432053	−	0.313905i	−0.782469	+	0.622689i	$0.786040\pi$
$192$		0			0
$193$	2.14590	+	6.60440i	0.154465	+	0.475395i	0.998106	−	0.0615126i	$-0.0195924\pi$
$193$	2.14590	+	6.60440i	0.154465	+	0.475395i	−0.843641	+	0.536907i	$0.819592\pi$
$194$	13.2333	+	9.61454i	0.950094	+	0.690284i
$195$		0			0
$196$	2.60910	−	8.02999i	0.186364	−	0.573570i
$197$	−2.58485			−0.184163			−0.0920813	−	0.995751i	$-0.529352\pi$
$197$	−2.58485			−0.184163			−0.0920813	+	0.995751i	$0.529352\pi$
$198$		0			0
$199$	−4.44587			−0.315159			−0.157580	−	0.987506i	$-0.550369\pi$
$199$	−4.44587			−0.315159			−0.157580	+	0.987506i	$0.550369\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$		0			0
$202$	2.61803	+	1.90211i	0.184204	+	0.133832i
$203$	−0.459741	−	1.41494i	−0.0322675	−	0.0993092i
$204$		0			0
$205$	−3.19992	−	2.32488i	−0.223492	−	0.162376i
$206$	9.26324	−	6.73014i	0.645400	−	0.468911i
$207$		0			0
$208$	−5.82857			−0.404139
$209$	0.918087	+	4.94625i	0.0635054	+	0.342139i
$210$		0			0
$211$	3.39194	−	10.4393i	0.233511	−	0.718673i	−0.763804	−	0.645448i	$-0.776671\pi$
$211$	3.39194	−	10.4393i	0.233511	−	0.718673i	0.997315	−	0.0732254i	$-0.0233292\pi$
$212$	5.06228	−	3.67796i	0.347679	−	0.252603i
$213$		0			0
$214$	−2.22818	−	6.85763i	−0.152315	−	0.468778i
$215$	0.138010	+	0.424750i	0.00941219	+	0.0289677i
$216$		0			0
$217$	20.8741	−	15.1659i	1.41702	−	1.02953i
$218$	0.483178	−	1.48707i	0.0327250	−	0.100717i
$219$		0			0
$220$	2.40640	+	2.28238i	0.162239	+	0.153878i
$221$	6.26971			0.421746
$222$		0			0
$223$	21.6246	−	15.7112i	1.44809	−	1.05210i	0.461816	−	0.886976i	$-0.347198\pi$
$223$	21.6246	−	15.7112i	1.44809	−	1.05210i	0.986273	−	0.165123i	$-0.0528020\pi$
$224$	−3.17926	−	2.30987i	−0.212424	−	0.154335i
$225$		0			0
$226$	−1.93257	−	5.94785i	−0.128553	−	0.395645i
$227$	−14.4359	−	10.4883i	−0.958147	−	0.696134i	−0.00542711	−	0.999985i	$-0.501728\pi$
$227$	−14.4359	−	10.4883i	−0.958147	−	0.696134i	−0.952720	+	0.303851i	$0.901728\pi$
$228$		0			0
$229$	4.83833	−	14.8908i	0.319726	−	0.984014i	−0.654040	−	0.756460i	$-0.726927\pi$
$229$	4.83833	−	14.8908i	0.319726	−	0.984014i	0.973765	−	0.227554i	$-0.0730728\pi$
$230$	5.07230			0.334458
$231$		0			0
$232$	−0.378584			−0.0248553
$233$	5.16692	−	15.9021i	0.338496	−	1.04178i	−0.626478	−	0.779439i	$-0.715504\pi$
$233$	5.16692	−	15.9021i	0.338496	−	1.04178i	0.964974	−	0.262345i	$-0.0844958\pi$
$234$		0			0
$235$	6.14416	+	4.46399i	0.400801	+	0.291199i
$236$	3.39642	+	10.4531i	0.221088	+	0.680439i
$237$		0			0
$238$	3.41989	+	2.48469i	0.221678	+	0.161059i
$239$	−15.4900	+	11.2541i	−1.00196	+	0.727970i	−0.962509	−	0.271251i	$-0.912563\pi$
$239$	−15.4900	+	11.2541i	−1.00196	+	0.727970i	−0.0394564	+	0.999221i	$0.512563\pi$
$240$		0			0
$241$	−6.59386			−0.424748			−0.212374	−	0.977188i	$-0.568119\pi$
$241$	−6.59386			−0.424748			−0.212374	+	0.977188i	$0.568119\pi$
$242$	−10.2673	+	3.94749i	−0.660007	+	0.253754i
$243$		0			0
$244$	−3.10121	+	9.54455i	−0.198535	+	0.611027i
$245$	6.83071	−	4.96280i	0.436398	−	0.317062i
$246$		0			0
$247$	−2.73199	−	8.40820i	−0.173832	−	0.535001i
$248$	−2.02891	−	6.24434i	−0.128836	−	0.396516i
$249$		0			0
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−6.30583	+	19.4074i	−0.398021	+	1.22498i	0.528563	+	0.848894i	$0.322731\pi$
$251$	−6.30583	+	19.4074i	−0.398021	+	1.22498i	−0.926584	+	0.376088i	$0.877269\pi$
$252$		0			0
$253$	−7.23844	+	15.1860i	−0.455077	+	0.954738i
$254$	−18.9820			−1.19104
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.0516	−	15.2948i	−1.31316	−	0.954066i	−0.999990	−	0.00436917i	$-0.998609\pi$
$257$	−21.0516	−	15.2948i	−1.31316	−	0.954066i	−0.313169	−	0.949697i	$-0.601391\pi$
$258$		0			0
$259$	−1.24948	−	3.84550i	−0.0776388	−	0.238948i
$260$	−4.71542	−	3.42595i	−0.292438	−	0.212468i
$261$		0			0
$262$	1.96148	−	6.03682i	0.121181	−	0.372956i
$263$	−21.5368			−1.32801			−0.664007	−	0.747726i	$-0.731146\pi$
$263$	−21.5368			−1.32801			−0.664007	+	0.747726i	$0.731146\pi$
$264$		0			0
$265$	6.25732			0.384384
$266$	1.84198	−	5.66904i	0.112939	−	0.347591i
$267$		0			0
$268$	4.84134	+	3.51744i	0.295732	+	0.214862i
$269$	5.16112	+	15.8843i	0.314679	+	0.968483i	0.975886	+	0.218279i	$0.0700444\pi$
$269$	5.16112	+	15.8843i	0.314679	+	0.968483i	−0.661207	+	0.750203i	$0.729956\pi$
$270$		0			0
$271$	10.0233	+	7.28238i	0.608874	+	0.442373i	0.849018	−	0.528364i	$-0.177194\pi$
$271$	10.0233	+	7.28238i	0.608874	+	0.442373i	−0.240143	+	0.970737i	$0.577194\pi$
$272$	0.870248	−	0.632272i	0.0527665	−	0.0383371i
$273$		0			0
$274$	4.68477			0.283017
$275$	0.605270	+	3.26093i	0.0364992	+	0.196641i
$276$		0			0
$277$	−6.63207	+	20.4114i	−0.398483	+	1.22640i	0.527734	+	0.849410i	$0.323042\pi$
$277$	−6.63207	+	20.4114i	−0.398483	+	1.22640i	−0.926216	+	0.376993i	$0.876958\pi$
$278$	−6.79392	+	4.93607i	−0.407472	+	0.296046i
$279$		0			0
$280$	−1.21437	−	3.73745i	−0.0725725	−	0.223355i
$281$	−0.0891435	−	0.274356i	−0.00531786	−	0.0163667i	0.948362	−	0.317189i	$-0.102739\pi$
$281$	−0.0891435	−	0.274356i	−0.00531786	−	0.0163667i	−0.953680	+	0.300822i	$0.902739\pi$
$282$		0			0
$283$	−21.8829	+	15.8989i	−1.30080	+	0.945090i	−0.999963	−	0.00858475i	$-0.997267\pi$
$283$	−21.8829	+	15.8989i	−1.30080	+	0.945090i	−0.300841	+	0.953674i	$0.597267\pi$
$284$	−1.55548	+	4.78728i	−0.0923008	+	0.284073i
$285$		0			0
$286$	16.9861	−	9.22855i	1.00441	−	0.545695i
$287$	−15.5435			−0.917506
$288$		0			0
$289$	12.8172	−	9.31222i	0.753952	−	0.547778i
$290$	−0.306281	−	0.222526i	−0.0179854	−	0.0130672i
$291$		0			0
$292$	1.09332	+	3.36491i	0.0639819	+	0.196916i
$293$	−9.88747	−	7.18367i	−0.577632	−	0.419674i	0.260238	−	0.965545i	$-0.416199\pi$
$293$	−9.88747	−	7.18367i	−0.577632	−	0.419674i	−0.837870	+	0.545870i	$0.816199\pi$
$294$		0			0
$295$	−3.39642	+	10.4531i	−0.197747	+	0.608603i
$296$	−1.02891			−0.0598041
$297$		0			0
$298$	−23.0956			−1.33789
$299$	9.13587	−	28.1173i	0.528341	−	1.62607i
$300$		0			0
$301$	1.41989	+	1.03161i	0.0818410	+	0.0594609i
$302$	−1.78389	−	5.49025i	−0.102651	−	0.315928i
$303$		0			0
$304$	−1.22713	−	0.891565i	−0.0703810	−	0.0511348i
$305$	−8.11908	+	5.89886i	−0.464897	+	0.337768i
$306$		0			0
$307$	−28.6957			−1.63775			−0.818875	−	0.573971i	$-0.805402\pi$
$307$	−28.6957			−1.63775			−0.818875	+	0.573971i	$0.805402\pi$
$308$	12.9226	+	1.69781i	0.736332	+	0.0967416i
$309$		0			0
$310$	2.02891	−	6.24434i	0.115234	−	0.354655i
$311$	21.6936	−	15.7613i	1.23013	−	0.893744i	0.233232	−	0.972421i	$-0.425070\pi$
$311$	21.6936	−	15.7613i	1.23013	−	0.893744i	0.996900	+	0.0786775i	$0.0250697\pi$
$312$		0			0
$313$	−7.92965	−	24.4049i	−0.448210	−	1.37945i	−0.878925	−	0.476961i	$-0.841738\pi$
$313$	−7.92965	−	24.4049i	−0.448210	−	1.37945i	0.430715	−	0.902488i	$-0.358262\pi$
$314$	3.33474	+	10.2633i	0.188190	+	0.579190i
$315$		0			0
$316$	−0.571258	+	0.415043i	−0.0321358	+	0.0233480i
$317$	−4.45573	+	13.7133i	−0.250259	+	0.770218i	0.744468	+	0.667658i	$0.232703\pi$
$317$	−4.45573	+	13.7133i	−0.250259	+	0.770218i	−0.994727	+	0.102559i	$0.967297\pi$
$318$		0			0
$319$	1.10330	−	0.599423i	0.0617731	−	0.0335612i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	16.1262	−	11.7164i	0.898678	−	0.652928i
$323$	1.32001	+	0.959044i	0.0734473	+	0.0533626i
$324$		0			0
$325$	−1.80113	−	5.54330i	−0.0999086	−	0.307487i
$326$	−13.4648	−	9.78278i	−0.745749	−	0.541818i
$327$		0			0
$328$	−1.22226	+	3.76173i	−0.0674880	+	0.207707i
$329$	29.8451			1.64542
$330$		0			0
$331$	19.0365			1.04634			0.523171	−	0.852228i	$-0.324749\pi$
$331$	19.0365			1.04634			0.523171	+	0.852228i	$0.324749\pi$
$332$	−3.62801	+	11.1659i	−0.199113	+	0.612807i
$333$		0			0
$334$	−7.00164	−	5.08699i	−0.383113	−	0.278348i
$335$	1.84923	+	5.69133i	0.101034	+	0.310951i
$336$		0			0
$337$	2.45390	+	1.78286i	0.133672	+	0.0971187i	0.652612	−	0.757692i	$-0.273673\pi$
$337$	2.45390	+	1.78286i	0.133672	+	0.0971187i	−0.518940	+	0.854811i	$0.673673\pi$
$338$	−16.9669	+	12.3272i	−0.922880	+	0.670511i
$339$		0			0
$340$	1.07569			0.0583372
$341$	15.7997	+	14.9854i	0.855600	+	0.811503i
$342$		0			0
$343$	1.75261	−	5.39399i	0.0946322	−	0.291248i
$344$	0.361314	−	0.262510i	0.0194808	−	0.0141536i
$345$		0			0
$346$	3.94173	+	12.1314i	0.211909	+	0.652189i
$347$	1.08056	+	3.32562i	0.0580075	+	0.178529i	0.975862	−	0.218388i	$-0.0700800\pi$
$347$	1.08056	+	3.32562i	0.0580075	+	0.178529i	−0.917854	+	0.396917i	$0.870080\pi$
$348$		0			0
$349$	13.7784	−	10.0106i	0.737542	−	0.535855i	−0.154399	−	0.988009i	$-0.549344\pi$
$349$	13.7784	−	10.0106i	0.737542	−	0.535855i	0.891940	+	0.452153i	$0.149344\pi$
$350$	1.21437	−	3.73745i	0.0649109	−	0.199775i
$351$		0			0
$352$	1.42705	−	2.99391i	0.0760621	−	0.159576i
$353$	−17.3965			−0.925920			−0.462960	−	0.886379i	$-0.653213\pi$
$353$	−17.3965			−0.925920			−0.462960	+	0.886379i	$0.653213\pi$
$354$		0			0
$355$	−4.07230	+	2.95870i	−0.216135	+	0.157032i
$356$	0.0361516	+	0.0262656i	0.00191603	+	0.00139208i
$357$		0			0
$358$	−5.82624	−	17.9313i	−0.307926	−	0.947700i
$359$	0.789459	+	0.573576i	0.0416661	+	0.0302722i	0.608423	−	0.793613i	$-0.291802\pi$
$359$	0.789459	+	0.573576i	0.0416661	+	0.0302722i	−0.566757	+	0.823885i	$0.691802\pi$
$360$		0			0
$361$	−5.16035	+	15.8819i	−0.271598	+	0.835891i
$362$	23.7549			1.24853
$363$		0			0
$364$	−22.9051			−1.20055
$365$	−1.09332	+	3.36491i	−0.0572272	+	0.176127i
$366$		0			0
$367$	28.1390	+	20.4442i	1.46885	+	1.06718i	0.980946	+	0.194279i	$0.0622367\pi$
$367$	28.1390	+	20.4442i	1.46885	+	1.06718i	0.487899	+	0.872900i	$0.337763\pi$
$368$	−1.56743	−	4.82405i	−0.0817078	−	0.251471i
$369$		0			0
$370$	−0.832405	−	0.604778i	−0.0432747	−	0.0314409i
$371$	19.8937	−	14.4536i	1.03283	−	0.750393i
$372$		0			0
$373$	29.2364			1.51380			0.756902	−	0.653528i	$-0.226712\pi$
$373$	29.2364			1.51380			0.756902	+	0.653528i	$0.226712\pi$
$374$	−1.53506	+	3.22051i	−0.0793759	+	0.166529i
$375$		0			0
$376$	2.34686	−	7.22289i	0.121030	−	0.372492i
$377$	−1.78518	+	1.29701i	−0.0919415	+	0.0667994i
$378$		0			0
$379$	3.90786	+	12.0272i	0.200733	+	0.617794i	0.999862	+	0.0166333i	$0.00529479\pi$
$379$	3.90786	+	12.0272i	0.200733	+	0.617794i	−0.799128	+	0.601161i	$0.794705\pi$
$380$	−0.468724	−	1.44258i	−0.0240450	−	0.0740030i
$381$		0			0
$382$	−5.97109	+	4.33825i	−0.305508	+	0.221964i
$383$	0.468306	−	1.44130i	0.0239293	−	0.0736468i	−0.938379	−	0.345609i	$-0.887672\pi$
$383$	0.468306	−	1.44130i	0.0239293	−	0.0736468i	0.962308	+	0.271962i	$0.0876725\pi$
$384$		0			0
$385$	9.45664	+	8.96925i	0.481955	+	0.457116i
$386$	6.94427			0.353454
$387$		0			0
$388$	13.2333	−	9.61454i	0.671818	−	0.488104i
$389$	5.53897	+	4.02429i	0.280837	+	0.204040i	0.719282	−	0.694718i	$-0.244471\pi$
$389$	5.53897	+	4.02429i	0.280837	+	0.204040i	−0.438446	+	0.898758i	$0.644471\pi$
$390$		0			0
$391$	1.68606	+	5.18916i	0.0852677	+	0.262427i
$392$	−6.83071	−	4.96280i	−0.345003	−	0.250659i
$393$		0			0
$394$	−0.798762	+	2.45834i	−0.0402410	+	0.123849i
$395$	−0.706114			−0.0355284
$396$		0			0
$397$	−4.56861			−0.229292			−0.114646	−	0.993406i	$-0.536573\pi$
$397$	−4.56861			−0.229292			−0.114646	+	0.993406i	$0.536573\pi$
$398$	−1.37385	+	4.22827i	−0.0688649	+	0.211944i
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	0.155249	+	0.477808i	0.00775278	+	0.0238606i	0.954858	−	0.297062i	$-0.0960069\pi$
$401$	0.155249	+	0.477808i	0.00775278	+	0.0238606i	−0.947105	+	0.320923i	$0.896007\pi$
$402$		0			0
$403$	−30.9600	−	22.4937i	−1.54222	−	1.12049i
$404$	2.61803	−	1.90211i	0.130252	−	0.0946337i
$405$		0			0
$406$	−1.48775			−0.0738360
$407$	2.99854	−	1.62910i	0.148632	−	0.0807515i
$408$		0			0
$409$	4.07979	−	12.5563i	0.201733	−	0.620870i	−0.798099	−	0.602526i	$-0.794161\pi$
$409$	4.07979	−	12.5563i	0.201733	−	0.620870i	0.999832	−	0.0183432i	$-0.00583915\pi$
$410$	−3.19992	+	2.32488i	−0.158033	+	0.114817i
$411$		0			0
$412$	−3.53824	−	10.8896i	−0.174317	−	0.536492i
$413$	13.3472	+	41.0785i	0.656773	+	2.02134i
$414$		0			0
$415$	−9.49826	+	6.90089i	−0.466251	+	0.338751i
$416$	−1.80113	+	5.54330i	−0.0883076	+	0.271783i
$417$		0			0
$418$	4.98786	+	0.655321i	0.243964	+	0.0320528i
$419$	−12.6691			−0.618925			−0.309463	−	0.950912i	$-0.600149\pi$
$419$	−12.6691			−0.618925			−0.309463	+	0.950912i	$0.600149\pi$
$420$		0			0
$421$	−15.4576	+	11.2306i	−0.753355	+	0.547344i	−0.896865	−	0.442304i	$-0.854161\pi$
$421$	−15.4576	+	11.2306i	−0.753355	+	0.547344i	0.143510	+	0.989649i	$0.454161\pi$
$422$	−8.88023	−	6.45186i	−0.432283	−	0.314072i
$423$		0			0
$424$	−1.93362	−	5.95106i	−0.0939048	−	0.289009i
$425$	0.870248	+	0.632272i	0.0422132	+	0.0306697i
$426$		0			0
$427$	−12.1871	+	37.5080i	−0.589775	+	1.81514i
$428$	−7.21054			−0.348535
$429$		0			0
$430$	0.446609			0.0215374
$431$	−4.12720	+	12.7022i	−0.198800	+	0.611844i	0.801111	+	0.598516i	$0.204243\pi$
$431$	−4.12720	+	12.7022i	−0.198800	+	0.611844i	−0.999911	+	0.0133279i	$0.995757\pi$
$432$		0			0
$433$	6.96927	+	5.06347i	0.334922	+	0.243335i	0.742516	−	0.669828i	$-0.233632\pi$
$433$	6.96927	+	5.06347i	0.334922	+	0.243335i	−0.407594	+	0.913163i	$0.633632\pi$
$434$	−7.97318	−	24.5389i	−0.382725	−	1.17791i
$435$		0			0
$436$	−1.26498	−	0.919060i	−0.0605814	−	0.0440150i
$437$	6.22440	−	4.52229i	0.297753	−	0.216330i
$438$		0			0
$439$	−11.3874			−0.543493			−0.271746	−	0.962369i	$-0.587601\pi$
$439$	−11.3874			−0.543493			−0.271746	+	0.962369i	$0.587601\pi$
$440$	2.91429	−	1.58333i	0.138933	−	0.0754822i
$441$		0			0
$442$	1.93745	−	5.96285i	0.0921550	−	0.283624i
$443$	22.5127	−	16.3565i	1.06961	−	0.777119i	0.0937702	−	0.995594i	$-0.470108\pi$
$443$	22.5127	−	16.3565i	1.06961	−	0.777119i	0.975843	+	0.218475i	$0.0701081\pi$
$444$		0			0
$445$	0.0138087	+	0.0424987i	0.000654593	+	0.00201463i
$446$	−8.25986	−	25.4212i	−0.391115	−	1.20373i
$447$		0			0
$448$	−3.17926	+	2.30987i	−0.150206	+	0.109131i
$449$	−6.64270	+	20.4441i	−0.313488	+	0.964817i	0.662884	+	0.748722i	$0.269332\pi$
$449$	−6.64270	+	20.4441i	−0.313488	+	0.964817i	−0.976372	+	0.216095i	$0.930668\pi$
$450$		0			0
$451$	−2.39403	−	12.8980i	−0.112731	−	0.607343i
$452$	−6.25393			−0.294160
$453$		0			0
$454$	−14.4359	+	10.4883i	−0.677512	+	0.492241i
$455$	−18.5306	−	13.4633i	−0.868727	−	0.631167i
$456$		0			0
$457$	4.29411	+	13.2159i	0.200870	+	0.618215i	0.999858	+	0.0168673i	$0.00536929\pi$
$457$	4.29411	+	13.2159i	0.200870	+	0.618215i	−0.798988	+	0.601348i	$0.794631\pi$
$458$	−12.6669	−	9.20304i	−0.591885	−	0.430030i
$459$		0			0
$460$	1.56743	−	4.82405i	0.0730817	−	0.224922i
$461$	14.9375			0.695709			0.347855	−	0.937549i	$-0.386910\pi$
$461$	14.9375			0.695709			0.347855	+	0.937549i	$0.386910\pi$
$462$		0			0
$463$	−38.5141			−1.78990			−0.894951	−	0.446165i	$-0.852789\pi$
$463$	−38.5141			−1.78990			−0.894951	+	0.446165i	$0.852789\pi$
$464$	−0.116989	+	0.360055i	−0.00543107	+	0.0167151i
$465$		0			0
$466$	−13.5272	−	9.82806i	−0.626634	−	0.455276i
$467$	4.86514	+	14.9734i	0.225132	+	0.692885i	0.998278	+	0.0586572i	$0.0186819\pi$
$467$	4.86514	+	14.9734i	0.225132	+	0.692885i	−0.773146	+	0.634228i	$0.781318\pi$
$468$		0			0
$469$	19.0254	+	13.8228i	0.878513	+	0.638277i
$470$	6.14416	−	4.46399i	0.283409	−	0.205909i
$471$		0			0
$472$	10.9910			0.505904
$473$	−0.637334	+	1.33711i	−0.0293046	+	0.0614803i
$474$		0			0
$475$	0.468724	−	1.44258i	0.0215065	−	0.0661903i
$476$	3.41989	−	2.48469i	0.156750	−	0.113886i
$477$		0			0
$478$	5.91665	+	18.2096i	0.270621	+	0.832887i
$479$	5.01996	+	15.4498i	0.229368	+	0.705921i	0.997819	+	0.0660126i	$0.0210278\pi$
$479$	5.01996	+	15.4498i	0.229368	+	0.705921i	−0.768451	+	0.639909i	$0.778972\pi$
$480$		0			0
$481$	−4.85173	+	3.52499i	−0.221220	+	0.160726i
$482$	−2.03761	+	6.27113i	−0.0928108	+	0.285642i
$483$		0			0
$484$	0.581513	+	10.9846i	0.0264324	+	0.499301i
$485$	16.3572			0.742744
$486$		0			0
$487$	8.51344	−	6.18538i	0.385781	−	0.280286i	−0.377944	−	0.925829i	$-0.623369\pi$
$487$	8.51344	−	6.18538i	0.385781	−	0.280286i	0.763724	+	0.645542i	$0.223369\pi$
$488$	8.11908	+	5.89886i	0.367533	+	0.267029i
$489$		0			0
$490$	−2.60910	−	8.02999i	−0.117867	−	0.362758i
$491$	−3.44984	−	2.50646i	−0.155689	−	0.113115i	0.507213	−	0.861821i	$-0.330676\pi$
$491$	−3.44984	−	2.50646i	−0.155689	−	0.113115i	−0.662903	+	0.748706i	$0.730676\pi$
$492$		0			0
$493$	0.125843	−	0.387306i	0.00566769	−	0.0174434i
$494$	−8.84091			−0.397771
$495$		0			0
$496$	−6.56569			−0.294808
$497$	−6.11271	+	18.8130i	−0.274193	+	0.843878i
$498$		0			0
$499$	−0.884781	−	0.642831i	−0.0396082	−	0.0287771i	0.567805	−	0.823163i	$-0.307793\pi$
$499$	−0.884781	−	0.642831i	−0.0396082	−	0.0287771i	−0.607413	+	0.794386i	$0.707793\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$		0			0
$502$	16.5089	+	11.9944i	0.736828	+	0.535337i
$503$	13.7746	−	10.0078i	0.614178	−	0.446227i	−0.236705	−	0.971582i	$-0.576067\pi$
$503$	13.7746	−	10.0078i	0.614178	−	0.446227i	0.850883	+	0.525355i	$0.176067\pi$
$504$		0			0
$505$	3.23607			0.144003
$506$	12.2060	+	11.5769i	0.542622	+	0.514656i
$507$		0			0
$508$	−5.86577	+	18.0530i	−0.260252	+	0.800972i
$509$	−19.9574	+	14.4999i	−0.884596	+	0.642697i	−0.934463	−	0.356059i	$-0.884120\pi$
$509$	−19.9574	+	14.4999i	−0.884596	+	0.642697i	0.0498671	+	0.998756i	$0.484120\pi$
$510$		0			0
$511$	4.29653	+	13.2234i	0.190067	+	0.584967i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−21.0516	+	15.2948i	−0.928544	+	0.674627i
$515$	3.53824	−	10.8896i	0.155914	−	0.479853i
$516$		0			0
$517$	4.59679	+	24.7654i	0.202166	+	1.08918i
$518$	−4.04339			−0.177657
$519$		0			0
$520$	−4.71542	+	3.42595i	−0.206785	+	0.150238i
$521$	10.7212	+	7.78944i	0.469706	+	0.341262i	0.797327	−	0.603548i	$-0.206247\pi$
$521$	10.7212	+	7.78944i	0.469706	+	0.341262i	−0.327621	+	0.944809i	$0.606247\pi$
$522$		0			0
$523$	0.300114	+	0.923655i	0.0131231	+	0.0403886i	0.957404	−	0.288753i	$-0.0932406\pi$
$523$	0.300114	+	0.923655i	0.0131231	+	0.0403886i	−0.944281	+	0.329142i	$0.893241\pi$
$524$	−5.13522	−	3.73096i	−0.224333	−	0.162988i
$525$		0			0
$526$	−6.65523	+	20.4827i	−0.290182	+	0.893088i
$527$	7.06261			0.307652
$528$		0			0
$529$	2.72826			0.118620
$530$	1.93362	−	5.95106i	0.0839910	−	0.258498i
$531$		0			0
$532$	−4.82238	−	3.50366i	−0.209077	−	0.151903i
$533$	7.12403	+	21.9255i	0.308576	+	0.949699i
$534$		0			0
$535$	−5.83345	−	4.23825i	−0.252202	−	0.183236i
$536$	4.84134	−	3.51744i	0.209114	−	0.151930i
$537$		0			0
$538$	16.7017			0.720063
$539$	27.7644	+	3.64777i	1.19590	+	0.157121i
$540$		0			0
$541$	−11.1569	+	34.3374i	−0.479673	+	1.47628i	0.359878	+	0.932999i	$0.382818\pi$
$541$	−11.1569	+	34.3374i	−0.479673	+	1.47628i	−0.839551	+	0.543281i	$0.817182\pi$
$542$	10.0233	−	7.28238i	0.430539	−	0.312805i
$543$		0			0
$544$	−0.332405	−	1.02304i	−0.0142517	−	0.0438624i
$545$	−0.483178	−	1.48707i	−0.0206971	−	0.0636991i
$546$		0			0
$547$	−15.7856	+	11.4689i	−0.674944	+	0.490375i	−0.871677	−	0.490082i	$-0.836967\pi$
$547$	−15.7856	+	11.4689i	−0.674944	+	0.490375i	0.196733	+	0.980457i	$0.436967\pi$
$548$	1.44767	−	4.45548i	0.0618415	−	0.190329i
$549$		0			0
$550$	3.28837	+	0.432036i	0.140216	+	0.0184221i
$551$	−0.574244			−0.0244636
$552$		0			0
$553$	−2.24492	+	1.63103i	−0.0954638	+	0.0693585i
$554$	17.3630	+	12.6149i	0.737683	+	0.535958i
$555$		0			0
$556$	2.59505	+	7.98673i	0.110054	+	0.338713i
$557$	−16.9694	−	12.3290i	−0.719014	−	0.522395i	0.167055	−	0.985948i	$-0.446574\pi$
$557$	−16.9694	−	12.3290i	−0.719014	−	0.522395i	−0.886069	+	0.463553i	$0.846574\pi$
$558$		0			0
$559$	0.804400	−	2.47569i	0.0340225	−	0.104710i
$560$	−3.92979			−0.166064
$561$		0			0
$562$	−0.288474			−0.0121686
$563$	6.88278	−	21.1830i	0.290075	−	0.892758i	−0.694757	−	0.719245i	$-0.744488\pi$
$563$	6.88278	−	21.1830i	0.290075	−	0.892758i	0.984832	−	0.173513i	$-0.0555120\pi$
$564$		0			0
$565$	−5.05954	−	3.67597i	−0.212856	−	0.154649i
$566$	8.35853	+	25.7249i	0.351335	+	1.08130i
$567$		0			0
$568$	4.07230	+	2.95870i	0.170870	+	0.124144i
$569$	−0.161029	+	0.116994i	−0.00675068	+	0.00490465i	−0.591155	−	0.806558i	$-0.701328\pi$
$569$	−0.161029	+	0.116994i	−0.00675068	+	0.00490465i	0.584405	+	0.811462i	$0.301328\pi$
$570$		0			0
$571$	32.7720			1.37146			0.685732	−	0.727854i	$-0.259482\pi$
$571$	32.7720			1.37146			0.685732	+	0.727854i	$0.259482\pi$
$572$	−3.52786	−	19.0066i	−0.147507	−	0.794704i
$573$		0			0
$574$	−4.80322	+	14.7828i	−0.200482	+	0.617022i
$575$	4.10358	−	2.98142i	0.171131	−	0.124334i
$576$		0			0
$577$	2.15889	+	6.64438i	0.0898758	+	0.276609i	0.985884	−	0.167427i	$-0.0535460\pi$
$577$	2.15889	+	6.64438i	0.0898758	+	0.276609i	−0.896009	+	0.444037i	$0.853546\pi$
$578$	−4.89573	−	15.0675i	−0.203635	−	0.626725i
$579$		0			0
$580$	−0.306281	+	0.222526i	−0.0127176	+	0.00923989i
$581$	−14.2573	+	43.8795i	−0.591493	+	1.82043i
$582$		0			0
$583$	15.0576	+	14.2816i	0.623622	+	0.591482i
$584$	3.53807			0.146406
$585$		0			0
$586$	−9.88747	+	7.18367i	−0.408448	+	0.296755i
$587$	18.9135	+	13.7415i	0.780645	+	0.567172i	0.905173	−	0.425044i	$-0.139741\pi$
$587$	18.9135	+	13.7415i	0.780645	+	0.567172i	−0.124527	+	0.992216i	$0.539741\pi$
$588$		0			0
$589$	−3.07749	−	9.47155i	−0.126806	−	0.390268i
$590$	8.89194	+	6.46038i	0.366076	+	0.265969i
$591$		0			0
$592$	−0.317950	+	0.978551i	−0.0130677	+	0.0402182i
$593$	30.7990			1.26476			0.632382	−	0.774657i	$-0.282077\pi$
$593$	30.7990			1.26476			0.632382	+	0.774657i	$0.282077\pi$
$594$		0			0
$595$	4.22721			0.173299
$596$	−7.13695	+	21.9653i	−0.292341	+	0.899732i
$597$		0			0
$598$	−23.9180	−	17.3775i	−0.978081	−	0.710617i
$599$	−7.32833	−	22.5543i	−0.299427	−	0.921543i	−0.981698	−	0.190443i	$-0.939008\pi$
$599$	−7.32833	−	22.5543i	−0.299427	−	0.921543i	0.682271	−	0.731100i	$-0.260992\pi$
$600$		0			0
$601$	−6.68382	−	4.85608i	−0.272639	−	0.198084i	0.443062	−	0.896491i	$-0.353892\pi$
$601$	−6.68382	−	4.85608i	−0.272639	−	0.198084i	−0.715700	+	0.698408i	$0.753892\pi$
$602$	1.41989	−	1.03161i	0.0578703	−	0.0420452i
$603$		0			0
$604$	−5.77279			−0.234891
$605$	−5.98614	+	9.22855i	−0.243371	+	0.375194i
$606$		0			0
$607$	12.8809	−	39.6433i	0.522819	−	1.60907i	−0.245770	−	0.969328i	$-0.579041\pi$
$607$	12.8809	−	39.6433i	0.522819	−	1.60907i	0.768589	−	0.639743i	$-0.220959\pi$
$608$	−1.22713	+	0.891565i	−0.0497669	+	0.0361578i
$609$		0			0
$610$	3.10121	+	9.54455i	0.125564	+	0.386448i
$611$	−13.6788	−	42.0992i	−0.553387	−	1.70315i
$612$		0			0
$613$	26.7817	−	19.4580i	1.08170	−	0.785903i	0.103724	−	0.994606i	$-0.466924\pi$
$613$	26.7817	−	19.4580i	1.08170	−	0.785903i	0.977979	+	0.208703i	$0.0669242\pi$
$614$	−8.86746	+	27.2912i	−0.357862	+	1.10138i
$615$		0			0
$616$	5.60801	−	11.7654i	0.225953	−	0.474043i
$617$	−30.3874			−1.22335			−0.611675	−	0.791109i	$-0.709504\pi$
$617$	−30.3874			−1.22335			−0.611675	+	0.791109i	$0.709504\pi$
$618$		0			0
$619$	−32.8059	+	23.8349i	−1.31858	+	0.958004i	−0.318630	+	0.947879i	$0.603223\pi$
$619$	−32.8059	+	23.8349i	−1.31858	+	0.958004i	−0.999949	+	0.0101243i	$0.996777\pi$
$620$	−5.31175	−	3.85921i	−0.213325	−	0.154990i
$621$		0			0
$622$	−8.28623	−	25.5024i	−0.332247	−	1.02255i
$623$	0.142068	+	0.103218i	0.00569183	+	0.00413536i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−25.6609			−1.02561
$627$		0			0
$628$	10.7915			0.430626
$629$	0.342015	−	1.05261i	0.0136370	−	0.0419704i
$630$		0			0
$631$	−13.1880	−	9.58164i	−0.525006	−	0.381439i	0.293480	−	0.955965i	$-0.405186\pi$
$631$	−13.1880	−	9.58164i	−0.525006	−	0.381439i	−0.818486	+	0.574526i	$0.805186\pi$
$632$	0.218201	+	0.671554i	0.00867958	+	0.0267130i
$633$		0			0
$634$	11.6653	+	8.47531i	0.463287	+	0.336597i
$635$	−15.3568	+	11.1574i	−0.609416	+	0.442766i
$636$		0			0
$637$	−49.2120			−1.94985
$638$	−0.229146	−	1.23453i	−0.00907196	−	0.0488757i
$639$		0			0
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−18.1070	+	13.1555i	−0.715183	+	0.519611i	−0.884842	−	0.465892i	$-0.845734\pi$
$641$	−18.1070	+	13.1555i	−0.715183	+	0.519611i	0.169658	+	0.985503i	$0.445734\pi$
$642$		0			0
$643$	−0.722400	−	2.22332i	−0.0284887	−	0.0876792i	0.935801	−	0.352528i	$-0.114678\pi$
$643$	−0.722400	−	2.22332i	−0.0284887	−	0.0876792i	−0.964290	+	0.264849i	$0.914678\pi$
$644$	−6.15966	−	18.9575i	−0.242725	−	0.747029i
$645$		0			0
$646$	1.32001	−	0.959044i	0.0519351	−	0.0377331i
$647$	−2.18034	+	6.71040i	−0.0857180	+	0.263813i	−0.984724	−	0.174124i	$-0.944291\pi$
$647$	−2.18034	+	6.71040i	−0.0857180	+	0.263813i	0.899006	+	0.437937i	$0.144291\pi$
$648$		0			0
$649$	−32.0311	+	17.4024i	−1.25733	+	0.683105i
$650$	−5.82857			−0.228616
$651$		0			0
$652$	−13.4648	+	9.78278i	−0.527324	+	0.383123i
$653$	11.7511	+	8.53771i	0.459858	+	0.334106i	0.793476	−	0.608602i	$-0.208269\pi$
$653$	11.7511	+	8.53771i	0.459858	+	0.334106i	−0.333618	+	0.942709i	$0.608269\pi$
$654$		0			0
$655$	−1.96148	−	6.03682i	−0.0766414	−	0.235878i
$656$	3.19992	+	2.32488i	0.124936	+	0.0907711i
$657$		0			0
$658$	9.22266	−	28.3844i	0.359537	−	1.10654i
$659$	−28.5069			−1.11047			−0.555235	−	0.831693i	$-0.687372\pi$
$659$	−28.5069			−1.11047			−0.555235	+	0.831693i	$0.687372\pi$
$660$		0			0
$661$	2.00856			0.0781238			0.0390619	−	0.999237i	$-0.487563\pi$
$661$	2.00856			0.0781238			0.0390619	+	0.999237i	$0.487563\pi$
$662$	5.88261	−	18.1048i	0.228634	−	0.703664i
$663$		0			0
$664$	9.49826	+	6.90089i	0.368604	+	0.267806i
$665$	−1.84198	−	5.66904i	−0.0714291	−	0.219836i
$666$		0			0
$667$	−1.55355	−	1.12872i	−0.0601537	−	0.0437042i
$668$	−7.00164	+	5.08699i	−0.270902	+	0.196822i
$669$		0			0
$670$	5.98422			0.231191
$671$	−33.0012	−	4.33579i	−1.27400	−	0.167381i
$672$		0			0
$673$	5.28692	−	16.2715i	0.203796	−	0.627219i	−0.795965	−	0.605343i	$-0.793036\pi$
$673$	5.28692	−	16.2715i	0.203796	−	0.627219i	0.999761	−	0.0218762i	$-0.00696397\pi$
$674$	2.45390	−	1.78286i	0.0945207	−	0.0686733i
$675$		0			0
$676$	6.48079	+	19.9458i	0.249261	+	0.767147i
$677$	7.28887	+	22.4328i	0.280134	+	0.862164i	0.987815	+	0.155632i	$0.0497414\pi$
$677$	7.28887	+	22.4328i	0.280134	+	0.862164i	−0.707681	+	0.706532i	$0.750259\pi$
$678$		0			0
$679$	52.0040	−	37.7831i	1.99573	−	1.44998i
$680$	0.332405	−	1.02304i	0.0127471	−	0.0392317i
$681$		0			0
$682$	19.1343	−	10.3956i	0.732690	−	0.398070i
$683$	−31.7728			−1.21575			−0.607876	−	0.794032i	$-0.707978\pi$
$683$	−31.7728			−1.21575			−0.607876	+	0.794032i	$0.707978\pi$
$684$		0			0
$685$	3.79006	−	2.75364i	0.144811	−	0.105211i
$686$	−4.58840	−	3.33367i	−0.175186	−	0.127280i
$687$		0			0
$688$	−0.138010	−	0.424750i	−0.00526157	−	0.0161935i
$689$	−29.5059	−	21.4373i	−1.12408	−	0.816694i
$690$		0			0
$691$	−6.50338	+	20.0154i	−0.247400	+	0.761420i	0.747832	+	0.663888i	$0.231095\pi$
$691$	−6.50338	+	20.0154i	−0.247400	+	0.761420i	−0.995232	+	0.0975319i	$0.968905\pi$
$692$	12.7557			0.484900
$693$		0			0
$694$	3.49677			0.132735
$695$	−2.59505	+	7.98673i	−0.0984357	+	0.302954i
$696$		0			0
$697$	−3.44210	−	2.50083i	−0.130379	−	0.0947258i
$698$	−5.26289	−	16.1975i	−0.199203	−	0.613084i
$699$		0			0
$700$	−3.17926	−	2.30987i	−0.120165	−	0.0873049i
$701$	−7.98896	+	5.80432i	−0.301739	+	0.219226i	−0.728344	−	0.685212i	$-0.759710\pi$
$701$	−7.98896	+	5.80432i	−0.301739	+	0.219226i	0.426605	+	0.904438i	$0.359710\pi$
$702$		0			0
$703$	−1.56067			−0.0588619
$704$	−2.40640	−	2.28238i	−0.0906946	−	0.0860203i
$705$		0			0
$706$	−5.37580	+	16.5450i	−0.202321	+	0.622680i
$707$	10.2883	−	7.47490i	0.386932	−	0.281123i
$708$		0			0
$709$	2.09620	+	6.45143i	0.0787243	+	0.242288i	0.982672	−	0.185356i	$-0.0593437\pi$
$709$	2.09620	+	6.45143i	0.0787243	+	0.242288i	−0.903947	+	0.427644i	$0.859344\pi$
$710$	1.55548	+	4.78728i	0.0583762	+	0.179663i
$711$		0			0
$712$	0.0361516	−	0.0262656i	0.00135484	−	0.000984346i
$713$	10.2912	−	31.6732i	0.385410	−	1.18617i
$714$		0			0
$715$	8.31767	−	17.4503i	0.311063	−	0.652603i
$716$	−18.8541			−0.704611
$717$		0			0
$718$	0.789459	−	0.573576i	0.0294624	−	0.0214057i
$719$	37.9662	+	27.5840i	1.41590	+	1.02871i	0.992432	+	0.122799i	$0.0391872\pi$
$719$	37.9662	+	27.5840i	1.41590	+	1.02871i	0.423467	+	0.905911i	$0.360813\pi$
$720$		0			0
$721$	−13.9045	−	42.7938i	−0.517832	−	1.59372i
$722$	13.5100	+	9.81557i	0.502789	+	0.365298i
$723$		0			0
$724$	7.34066	−	22.5922i	0.272814	−	0.839634i
$725$	−0.378584			−0.0140603
$726$		0			0
$727$	1.32849			0.0492708			0.0246354	−	0.999697i	$-0.492158\pi$
$727$	1.32849			0.0492708			0.0246354	+	0.999697i	$0.492158\pi$
$728$	−7.07805	+	21.7840i	−0.262330	+	0.807369i
$729$		0			0
$730$	2.86236	+	2.07963i	0.105941	+	0.0769704i
$731$	0.148455	+	0.456898i	0.00549081	+	0.0168990i
$732$		0			0
$733$	−14.9732	−	10.8787i	−0.553047	−	0.401812i	0.275861	−	0.961198i	$-0.411037\pi$
$733$	−14.9732	−	10.8787i	−0.553047	−	0.401812i	−0.828908	+	0.559385i	$0.811037\pi$
$734$	28.1390	−	20.4442i	1.03863	−	0.754609i
$735$		0			0
$736$	−5.07230			−0.186968
$737$	−8.53979	+	17.9163i	−0.314567	+	0.659954i
$738$		0			0
$739$	7.54121	−	23.2094i	0.277408	−	0.853773i	−0.711165	−	0.703026i	$-0.751832\pi$
$739$	7.54121	−	23.2094i	0.277408	−	0.853773i	0.988572	−	0.150748i	$-0.0481681\pi$
$740$	−0.832405	+	0.604778i	−0.0305998	+	0.0222321i
$741$		0			0
$742$	−7.59870	−	23.3864i	−0.278957	−	0.858542i
$743$	−5.92122	−	18.2236i	−0.217229	−	0.668561i	−0.998988	−	0.0449805i	$-0.985677\pi$
$743$	−5.92122	−	18.2236i	−0.217229	−	0.668561i	0.781759	−	0.623580i	$-0.214323\pi$
$744$		0			0
$745$	−18.6848	+	13.5753i	−0.684557	+	0.497360i
$746$	9.03455	−	27.8055i	0.330778	−	1.01803i
$747$		0			0
$748$	2.58853	+	2.45512i	0.0946460	+	0.0897680i
$749$	−28.3359			−1.03537
$750$		0			0
$751$	−0.131474	+	0.0955212i	−0.00479754	+	0.00348562i	−0.590181	−	0.807271i	$-0.700944\pi$
$751$	−0.131474	+	0.0955212i	−0.00479754	+	0.00348562i	0.585384	+	0.810756i	$0.300944\pi$
$752$	−6.14416	−	4.46399i	−0.224054	−	0.162785i
$753$		0			0
$754$	0.681878	+	2.09861i	0.0248325	+	0.0764267i
$755$	−4.67028	−	3.39316i	−0.169969	−	0.123490i
$756$		0			0
$757$	0.747984	−	2.30206i	0.0271860	−	0.0836698i	−0.936543	−	0.350553i	$-0.885994\pi$
$757$	0.747984	−	2.30206i	0.0271860	−	0.0836698i	0.963729	+	0.266883i	$0.0859937\pi$
$758$	12.6461			0.459327
$759$		0			0
$760$	−1.51682			−0.0550209
$761$	1.83739	−	5.65489i	0.0666052	−	0.204990i	−0.912215	−	0.409712i	$-0.865629\pi$
$761$	1.83739	−	5.65489i	0.0666052	−	0.204990i	0.978820	+	0.204722i	$0.0656292\pi$
$762$		0			0
$763$	−4.97109	−	3.61171i	−0.179966	−	0.130753i
$764$	2.28075	+	7.01944i	0.0825148	+	0.253954i
$765$		0			0
$766$	−1.22604	−	0.890771i	−0.0442986	−	0.0321849i
$767$	51.8274	−	37.6548i	1.87138	−	1.35964i
$768$		0			0
$769$	46.4619			1.67546			0.837730	−	0.546085i	$-0.183882\pi$
$769$	46.4619			1.67546			0.837730	+	0.546085i	$0.183882\pi$
$770$	11.4525	−	6.22214i	0.412721	−	0.224230i
$771$		0			0
$772$	2.14590	−	6.60440i	0.0772326	−	0.237697i
$773$	24.5256	−	17.8189i	0.882123	−	0.640900i	−0.0516893	−	0.998663i	$-0.516461\pi$
$773$	24.5256	−	17.8189i	0.882123	−	0.640900i	0.933812	+	0.357763i	$0.116461\pi$
$774$		0			0
$775$	−2.02891	−	6.24434i	−0.0728806	−	0.224303i
$776$	−5.05466	−	15.5567i	−0.181452	−	0.558451i
$777$		0			0
$778$	5.53897	−	4.02429i	0.198582	−	0.144278i
$779$	−1.85395	+	5.70587i	−0.0664246	+	0.204434i
$780$		0			0
$781$	−16.5525	−	2.17471i	−0.592294	−	0.0778174i
$782$	5.45620			0.195113
$783$		0			0
$784$	−6.83071	+	4.96280i	−0.243954	+	0.177243i
$785$	8.73047	+	6.34306i	0.311604	+	0.226393i
$786$		0			0
$787$	14.0130	+	43.1276i	0.499509	+	1.53733i	0.809810	+	0.586693i	$0.199570\pi$
$787$	14.0130	+	43.1276i	0.499509	+	1.53733i	−0.310300	+	0.950639i	$0.600430\pi$
$788$	2.09118	+	1.51933i	0.0744954	+	0.0541241i
$789$		0			0
$790$	−0.218201	+	0.671554i	−0.00776325	+	0.0238928i
$791$	−24.5766			−0.873844
$792$		0			0
$793$	58.4940			2.07718
$794$	−1.41178	+	4.34501i	−0.0501022	+	0.154199i
$795$		0			0
$796$	3.59679	+	2.61322i	0.127485	+	0.0926230i
$797$	13.3783	+	41.1742i	0.473884	+	1.45847i	0.847457	+	0.530865i	$0.178133\pi$
$797$	13.3783	+	41.1742i	0.473884	+	1.45847i	−0.373572	+	0.927601i	$0.621867\pi$
$798$		0			0
$799$	6.60918	+	4.80185i	0.233816	+	0.169877i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$		0			0
$802$	0.502397			0.0177403
$803$	−10.3110	+	5.60193i	−0.363866	+	0.197688i
$804$		0			0
$805$	6.15966	−	18.9575i	0.217099	−	0.668163i
$806$	−30.9600	+	22.4937i	−1.09052	+	0.792308i
$807$		0			0
$808$	−1.00000	−	3.07768i	−0.0351799	−	0.108273i
$809$	−15.2113	−	46.8156i	−0.534801	−	1.64595i	−0.744078	−	0.668092i	$-0.767111\pi$
$809$	−15.2113	−	46.8156i	−0.534801	−	1.64595i	0.209277	−	0.977856i	$-0.432889\pi$
$810$		0			0
$811$	1.47255	−	1.06987i	0.0517084	−	0.0375683i	−0.561631	−	0.827388i	$-0.689826\pi$
$811$	1.47255	−	1.06987i	0.0517084	−	0.0375683i	0.613339	+	0.789820i	$0.289826\pi$
$812$	−0.459741	+	1.41494i	−0.0161338	+	0.0496546i
$813$		0			0
$814$	−0.622768	−	3.35520i	−0.0218280	−	0.117600i
$815$	−16.6435			−0.582995
$816$		0			0
$817$	0.548049	−	0.398181i	0.0191738	−	0.0139306i
$818$	−10.6810	−	7.76023i	−0.373454	−	0.271330i
$819$		0			0
$820$	1.22226	+	3.76173i	0.0426831	+	0.131365i
$821$	−22.5912	−	16.4135i	−0.788439	−	0.572834i	0.119061	−	0.992887i	$-0.462012\pi$
$821$	−22.5912	−	16.4135i	−0.788439	−	0.572834i	−0.907500	+	0.420053i	$0.862012\pi$
$822$		0			0
$823$	−5.48381	+	16.8774i	−0.191153	+	0.588310i	0.808847	+	0.588020i	$0.200092\pi$
$823$	−5.48381	+	16.8774i	−0.191153	+	0.588310i	−1.00000		0.000289980i	$0.999908\pi$
$824$	−11.4500			−0.398879
$825$		0			0
$826$	43.1925			1.50286
$827$	−10.4642	+	32.2054i	−0.363875	+	1.11989i	0.586808	+	0.809726i	$0.300384\pi$
$827$	−10.4642	+	32.2054i	−0.363875	+	1.11989i	−0.950683	+	0.310165i	$0.899616\pi$
$828$		0			0
$829$	−20.3888	−	14.8133i	−0.708132	−	0.514488i	0.174439	−	0.984668i	$-0.444189\pi$
$829$	−20.3888	−	14.8133i	−0.708132	−	0.514488i	−0.882571	+	0.470180i	$0.844189\pi$
$830$	3.62801	+	11.1659i	0.125930	+	0.387573i
$831$		0			0
$832$	4.71542	+	3.42595i	0.163478	+	0.118773i
$833$	7.34770	−	5.33841i	0.254583	−	0.184965i
$834$		0			0
$835$	−8.65451			−0.299502
$836$	2.16458	−	4.54123i	0.0748636	−	0.157062i
$837$		0			0
$838$	−3.91496	+	12.0490i	−0.135240	+	0.416226i
$839$	−6.84982	+	4.97669i	−0.236482	+	0.171814i	−0.699715	−	0.714422i	$-0.746690\pi$
$839$	−6.84982	+	4.97669i	−0.236482	+	0.171814i	0.463232	+	0.886237i	$0.346690\pi$
$840$		0			0
$841$	−8.91720	−	27.4443i	−0.307490	−	0.946356i
$842$	5.90426	+	18.1714i	0.203474	+	0.626229i
$843$		0			0
$844$	−8.88023	+	6.45186i	−0.305670	+	0.222082i
$845$	−6.48079	+	19.9458i	−0.222946	+	0.686157i
$846$		0			0
$847$	2.28522	+	43.1672i	0.0785212	+	1.48324i
$848$	−6.25732			−0.214877
$849$		0			0
$850$	0.870248	−	0.632272i	0.0298492	−	0.0216867i
$851$	−4.22221	−	3.06762i	−0.144736	−	0.105157i
$852$		0			0
$853$	−1.53299	−	4.71805i	−0.0524884	−	0.161543i	0.921376	−	0.388672i	$-0.127066\pi$
$853$	−1.53299	−	4.71805i	−0.0524884	−	0.161543i	−0.973865	+	0.227129i	$0.927066\pi$
$854$	31.9063	+	23.1812i	1.09181	+	0.793246i
$855$		0			0
$856$	−2.22818	+	6.85763i	−0.0761576	+	0.234389i
$857$	49.4733			1.68998			0.844988	−	0.534786i	$-0.179608\pi$
$857$	49.4733			1.68998			0.844988	+	0.534786i	$0.179608\pi$
$858$		0			0
$859$	21.9002			0.747224			0.373612	−	0.927585i	$-0.378119\pi$
$859$	21.9002			0.747224			0.373612	+	0.927585i	$0.378119\pi$
$860$	0.138010	−	0.424750i	0.00470609	−	0.0144839i
$861$		0			0
$862$	10.8051	+	7.85039i	0.368024	+	0.267385i
$863$	−7.22276	−	22.2294i	−0.245866	−	0.756697i	−0.995493	−	0.0948366i	$-0.969767\pi$
$863$	−7.22276	−	22.2294i	−0.245866	−	0.756697i	0.749627	−	0.661860i	$-0.230233\pi$
$864$		0			0
$865$	10.3196	+	7.49762i	0.350877	+	0.254927i
$866$	6.96927	−	5.06347i	0.236825	−	0.172064i
$867$		0			0
$868$	−25.8018			−0.875769
$869$	−1.69919	−	1.61162i	−0.0576411	−	0.0546704i
$870$		0			0
$871$	10.7784	−	33.1724i	0.365211	−	1.12400i
$872$	−1.26498	+	0.919060i	−0.0428375	+	0.0311233i
$873$		0			0
$874$	−2.37751	−	7.31722i	−0.0804204	−	0.247509i
$875$	−1.21437	−	3.73745i	−0.0410532	−	0.126349i
$876$		0			0
$877$	34.6618	−	25.1833i	1.17045	−	0.850378i	0.179383	−	0.983779i	$-0.442590\pi$
$877$	34.6618	−	25.1833i	1.17045	−	0.850378i	0.991062	+	0.133401i	$0.0425899\pi$
$878$	−3.51891	+	10.8301i	−0.118758	+	0.365498i
$879$		0			0
$880$	−0.605270	−	3.26093i	−0.0204037	−	0.109926i
$881$	5.99014			0.201813			0.100906	−	0.994896i	$-0.467826\pi$
$881$	5.99014			0.201813			0.100906	+	0.994896i	$0.467826\pi$
$882$		0			0
$883$	−7.45841	+	5.41885i	−0.250995	+	0.182359i	−0.706168	−	0.708044i	$-0.749578\pi$
$883$	−7.45841	+	5.41885i	−0.250995	+	0.182359i	0.455172	+	0.890403i	$0.349578\pi$
$884$	−5.07230	−	3.68524i	−0.170600	−	0.123948i
$885$		0			0
$886$	−8.59910	−	26.4653i	−0.288893	−	0.889120i
$887$	9.95768	+	7.23468i	0.334346	+	0.242917i	0.742273	−	0.670098i	$-0.233748\pi$
$887$	9.95768	+	7.23468i	0.334346	+	0.242917i	−0.407926	+	0.913015i	$0.633748\pi$
$888$		0			0
$889$	−23.0512	+	70.9444i	−0.773114	+	2.37940i
$890$	0.0446858			0.00149787
$891$		0			0
$892$	−26.7295			−0.894968
$893$	3.55977	−	10.9558i	0.119123	−	0.366623i
$894$		0			0
$895$	−15.2533	−	11.0822i	−0.509861	−	0.370436i
$896$	1.21437	+	3.73745i	0.0405693	+	0.124859i
$897$		0			0
$898$	17.3908	+	12.6352i	0.580339	+	0.421641i
$899$	−2.01094	+	1.46104i	−0.0670688	+	0.0487283i
$900$		0			0
$901$	6.73090			0.224239
$902$	−13.0065	−	1.70884i	−0.433070	−	0.0568980i
$903$		0			0
$904$	−1.93257	+	5.94785i	−0.0642764	+	0.197822i
$905$	19.2181	−	13.9628i	0.638831	−	0.464138i
$906$		0			0
$907$	−7.98882	−	24.5870i	−0.265264	−	0.816400i	−0.991632	−	0.129094i	$-0.958793\pi$
$907$	−7.98882	−	24.5870i	−0.265264	−	0.816400i	0.726368	−	0.687306i	$-0.241207\pi$
$908$	5.51404	+	16.9705i	0.182990	+	0.563184i
$909$		0			0
$910$	−18.5306	+	13.4633i	−0.614283	+	0.446303i
$911$	−2.70009	+	8.31002i	−0.0894579	+	0.275323i	−0.985770	−	0.168101i	$-0.946236\pi$
$911$	−2.70009	+	8.31002i	−0.0894579	+	0.275323i	0.896312	+	0.443424i	$0.146236\pi$
$912$		0			0
$913$	−38.6070	−	5.07231i	−1.27771	−	0.167869i
$914$	13.8960			0.459640
$915$		0			0
$916$	−12.6669	+	9.20304i	−0.418526	+	0.304077i
$917$	−20.1803	−	14.6619i	−0.666414	−	0.484178i
$918$		0			0
$919$	−2.39854	−	7.38195i	−0.0791206	−	0.243508i	0.903671	−	0.428228i	$-0.140862\pi$
$919$	−2.39854	−	7.38195i	−0.0791206	−	0.243508i	−0.982791	+	0.184720i	$0.940862\pi$
$920$	−4.10358	−	2.98142i	−0.135291	−	0.0982947i
$921$		0			0
$922$	4.61594	−	14.2064i	0.152018	−	0.467863i
$923$	29.3390			0.965704
$924$		0			0
$925$	−1.02891			−0.0338303
$926$	−11.9015	+	36.6291i	−0.391108	+	1.20371i
$927$		0			0
$928$	0.306281	+	0.222526i	0.0100542	+	0.00730478i
$929$	−7.01463	−	21.5888i	−0.230143	−	0.708306i	−0.997729	−	0.0673604i	$-0.978542\pi$
$929$	−7.01463	−	21.5888i	−0.230143	−	0.708306i	0.767586	−	0.640946i	$-0.221458\pi$
$930$		0			0
$931$	−10.3610	−	7.52769i	−0.339567	−	0.246710i
$932$	−13.5272	+	9.82806i	−0.443097	+	0.321929i
$933$		0			0
$934$	15.7439			0.515157
$935$	0.651080	+	3.50773i	0.0212926	+	0.114715i
$936$		0			0
$937$	9.35316	−	28.7861i	0.305554	−	0.940400i	−0.673915	−	0.738809i	$-0.735389\pi$
$937$	9.35316	−	28.7861i	0.305554	−	0.940400i	0.979470	−	0.201591i	$-0.0646113\pi$
$938$	19.0254	−	13.8228i	0.621202	−	0.451330i
$939$		0			0
$940$	−2.34686	−	7.22289i	−0.0765461	−	0.235585i
$941$	−5.67714	−	17.4725i	−0.185070	−	0.569586i	0.814880	−	0.579630i	$-0.196803\pi$
$941$	−5.67714	−	17.4725i	−0.185070	−	0.569586i	−0.999950	+	0.0100441i	$0.996803\pi$
$942$		0			0
$943$	−16.2309	+	11.7925i	−0.528552	+	0.384016i
$944$	3.39642	−	10.4531i	0.110544	−	0.340220i
$945$		0			0
$946$	1.07472	+	1.01933i	0.0349421	+	0.0331413i
$947$	34.5692			1.12335			0.561674	−	0.827358i	$-0.310157\pi$
$947$	34.5692			1.12335			0.561674	+	0.827358i	$0.310157\pi$
$948$		0			0
$949$	16.6835	−	12.1213i	0.541569	−	0.393473i
$950$	−1.22713	−	0.891565i	−0.0398135	−	0.0289262i
$951$		0			0
$952$	−1.30628	−	4.02032i	−0.0423368	−	0.130299i
$953$	−14.2979	−	10.3881i	−0.463155	−	0.336502i	0.331612	−	0.943416i	$-0.392407\pi$
$953$	−14.2979	−	10.3881i	−0.463155	−	0.336502i	−0.794768	+	0.606914i	$0.792407\pi$
$954$		0			0
$955$	−2.28075	+	7.01944i	−0.0738035	+	0.227144i
$956$	19.1467			0.619248
$957$		0			0
$958$	16.2449			0.524850
$959$	5.68905	−	17.5091i	0.183709	−	0.565398i
$960$		0			0
$961$	−9.79579	−	7.11706i	−0.315993	−	0.229582i
$962$	1.85320	+	5.70356i	0.0597495	+	0.183890i
$963$		0			0
$964$	5.33454	+	3.87577i	0.171814	+	0.124830i
$965$	5.61803	−	4.08174i	0.180851	−	0.131396i
$966$		0			0
$967$	17.1334			0.550973			0.275487	−	0.961305i	$-0.411161\pi$
$967$	17.1334			0.550973			0.275487	+	0.961305i	$0.411161\pi$
$968$	10.6267	+	2.84138i	0.341555	+	0.0913255i
$969$		0			0
$970$	5.05466	−	15.5567i	0.162295	−	0.499494i
$971$	44.0566	−	32.0090i	1.41384	−	1.02722i	0.421094	−	0.907017i	$-0.361646\pi$
$971$	44.0566	−	32.0090i	1.41384	−	1.02722i	0.992750	−	0.120201i	$-0.0383538\pi$
$972$		0			0
$973$	10.1980	+	31.3861i	0.326932	+	1.00619i
$974$	−3.25184	−	10.0081i	−0.104196	−	0.320682i
$975$		0			0
$976$	8.11908	−	5.89886i	0.259885	−	0.188818i
$977$	17.3469	−	53.3884i	0.554978	−	1.70805i	−0.141025	−	0.990006i	$-0.545040\pi$
$977$	17.3469	−	53.3884i	0.554978	−	1.70805i	0.696003	−	0.718039i	$-0.254960\pi$
$978$		0			0
$979$	−0.0637689	+	0.133785i	−0.00203806	+	0.00427580i
$980$	−8.44323			−0.269709
$981$		0			0
$982$	−3.44984	+	2.50646i	−0.110089	+	0.0799843i
$983$	−26.5241	−	19.2709i	−0.845988	−	0.614646i	0.0780492	−	0.996950i	$-0.475131\pi$
$983$	−26.5241	−	19.2709i	−0.845988	−	0.614646i	−0.924037	+	0.382304i	$0.875131\pi$
$984$		0			0
$985$	0.798762	+	2.45834i	0.0254507	+	0.0783291i
$986$	−0.329462	−	0.239368i	−0.0104922	−	0.00762303i
$987$		0			0
$988$	−2.73199	+	8.40820i	−0.0869162	+	0.267501i
$989$	2.26534			0.0720335
$990$		0			0
$991$	−9.43591			−0.299742			−0.149871	−	0.988706i	$-0.547886\pi$
$991$	−9.43591			−0.299742			−0.149871	+	0.988706i	$0.547886\pi$
$992$	−2.02891	+	6.24434i	−0.0644179	+	0.198258i
$993$		0			0
$994$	16.0033	+	11.6271i	0.507593	+	0.368788i
$995$	1.37385	+	4.22827i	0.0435540	+	0.134045i
$996$		0			0
$997$	−27.1877	−	19.7531i	−0.861044	−	0.625585i	0.0671244	−	0.997745i	$-0.478618\pi$
$997$	−27.1877	−	19.7531i	−0.861044	−	0.625585i	−0.928169	+	0.372159i	$0.878618\pi$
$998$	−0.884781	+	0.642831i	−0.0280073	+	0.0203485i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.j.361.1		8
3.2	odd	2		110.2.g.c.31.1	✓	8
11.5	even	5	inner	990.2.n.j.181.1		8
12.11	even	2		880.2.bo.g.801.2		8
15.2	even	4		550.2.ba.f.449.2		16
15.8	even	4		550.2.ba.f.449.3		16
15.14	odd	2		550.2.h.l.251.2		8
33.5	odd	10		110.2.g.c.71.1	yes	8
33.26	odd	10		1210.2.a.u.1.4		4
33.29	even	10		1210.2.a.v.1.4		4
132.59	even	10		9680.2.a.cj.1.1		4
132.71	even	10		880.2.bo.g.401.2		8
132.95	odd	10		9680.2.a.ci.1.1		4
165.29	even	10		6050.2.a.cy.1.1		4
165.38	even	20		550.2.ba.f.49.2		16
165.59	odd	10		6050.2.a.dh.1.1		4
165.104	odd	10		550.2.h.l.401.2		8
165.137	even	20		550.2.ba.f.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.1	✓	8	3.2	odd	2
110.2.g.c.71.1	yes	8	33.5	odd	10
550.2.h.l.251.2		8	15.14	odd	2
550.2.h.l.401.2		8	165.104	odd	10
550.2.ba.f.49.2		16	165.38	even	20
550.2.ba.f.49.3		16	165.137	even	20
550.2.ba.f.449.2		16	15.2	even	4
550.2.ba.f.449.3		16	15.8	even	4
880.2.bo.g.401.2		8	132.71	even	10
880.2.bo.g.801.2		8	12.11	even	2
990.2.n.j.181.1		8	11.5	even	5	inner
990.2.n.j.361.1		8	1.1	even	1	trivial
1210.2.a.u.1.4		4	33.26	odd	10
1210.2.a.v.1.4		4	33.29	even	10
6050.2.a.cy.1.1		4	165.29	even	10
6050.2.a.dh.1.1		4	165.59	odd	10
9680.2.a.ci.1.1		4	132.95	odd	10
9680.2.a.cj.1.1		4	132.59	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-3.17926 - 2.30987i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.00000 q^{10} +(1.42705 - 2.99391i) q^{11} +(-1.80113 + 5.54330i) q^{13} +(-3.17926 + 2.30987i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.332405 - 1.02304i) q^{17} +(-1.22713 + 0.891565i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-2.40640 - 2.28238i) q^{22} -5.07230 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.71542 + 3.42595i) q^{26} +(1.21437 + 3.73745i) q^{28} +(0.306281 + 0.222526i) q^{29} +(-2.02891 + 6.24434i) q^{31} +1.00000 q^{32} -1.07569 q^{34} +(-1.21437 + 3.73745i) q^{35} +(0.832405 + 0.604778i) q^{37} +(0.468724 + 1.44258i) q^{38} +(0.809017 + 0.587785i) q^{40} +(3.19992 - 2.32488i) q^{41} -0.446609 q^{43} +(-2.91429 + 1.58333i) q^{44} +(-1.56743 + 4.82405i) q^{46} +(-6.14416 + 4.46399i) q^{47} +(2.60910 + 8.02999i) q^{49} +(0.309017 + 0.951057i) q^{50} +(4.71542 - 3.42595i) q^{52} +(-1.93362 + 5.95106i) q^{53} +(-3.28837 - 0.432036i) q^{55} +3.92979 q^{56} +(0.306281 - 0.222526i) q^{58} +(-8.89194 - 6.46038i) q^{59} +(-3.10121 - 9.54455i) q^{61} +(5.31175 + 3.85921i) q^{62} +(0.309017 - 0.951057i) q^{64} +5.82857 q^{65} -5.98422 q^{67} +(-0.332405 + 1.02304i) q^{68} +(3.17926 + 2.30987i) q^{70} +(-1.55548 - 4.78728i) q^{71} +(-2.86236 - 2.07963i) q^{73} +(0.832405 - 0.604778i) q^{74} +1.51682 q^{76} +(-11.4525 + 6.22214i) q^{77} +(0.218201 - 0.671554i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-1.22226 - 3.76173i) q^{82} +(-3.62801 - 11.1659i) q^{83} +(-0.870248 + 0.632272i) q^{85} +(-0.138010 + 0.424750i) q^{86} +(0.605270 + 3.26093i) q^{88} -0.0446858 q^{89} +(18.5306 - 13.4633i) q^{91} +(4.10358 + 2.98142i) q^{92} +(2.34686 + 7.22289i) q^{94} +(1.22713 + 0.891565i) q^{95} +(-5.05466 + 15.5567i) q^{97} +8.44323 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8} - 8 q^{10} - 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} - 26 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 22 q^{29}+ \cdots + 22 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8 - 8 * q^10 - 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 - 26 * q^23 - 2 * q^25 + 6 * q^26 + 4 * q^28 + 22 * q^29 - 26 * q^31 + 8 * q^32 + 2 * q^34 - 4 * q^35 - 8 * q^37 + 3 * q^38 + 2 * q^40 + 15 * q^41 + 38 * q^43 - 7 * q^44 - 6 * q^46 - 6 * q^47 + 27 * q^49 - 2 * q^50 + 6 * q^52 + 4 * q^53 - 8 * q^55 - 6 * q^56 + 22 * q^58 - 39 * q^59 - 20 * q^61 + 14 * q^62 - 2 * q^64 + 14 * q^65 - 26 * q^67 + 12 * q^68 + q^70 - 2 * q^71 + 8 * q^73 - 8 * q^74 + 8 * q^76 - 16 * q^77 + 14 * q^79 + 2 * q^80 - 15 * q^82 + 21 * q^83 + 13 * q^85 - 17 * q^86 - 7 * q^88 - 32 * q^89 + 53 * q^91 + 19 * q^92 + 9 * q^94 + 7 * q^95 - 31 * q^97 + 22 * q^98

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