LMFDB - Embedded newform 1170.2.bj.d.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$-1.44229 - 0.433312i$ of defining polynomial
Character	$\chi$	$=$	1170.199
Dual form			1170.2.bj.d.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230377 + 2.22417i) q^{5} +(0.432713 + 0.749482i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230377 + 2.22417i) q^{5} +(0.432713 + 0.749482i) q^{7} -1.00000 q^{8} +(2.04138 + 0.912572i) q^{10} +(-0.151430 - 0.0874279i) q^{11} +(1.35486 + 3.34131i) q^{13} +0.865427 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-7.08339 + 4.08960i) q^{17} +(5.20843 - 3.00709i) q^{19} +(1.81100 - 1.31160i) q^{20} +(-0.151430 + 0.0874279i) q^{22} +(-2.52211 - 1.45614i) q^{23} +(-4.89385 + 1.02479i) q^{25} +(3.57109 + 0.497314i) q^{26} +(0.432713 - 0.749482i) q^{28} +(-3.24491 + 5.62035i) q^{29} +6.95057i q^{31} +(0.500000 + 0.866025i) q^{32} +8.17919i q^{34} +(-1.56729 + 1.13509i) q^{35} +(-0.879573 + 1.52347i) q^{37} -6.01418i q^{38} +(-0.230377 - 2.22417i) q^{40} +(7.08339 + 4.08960i) q^{41} +(-7.94476 + 4.58691i) q^{43} +0.174856i q^{44} +(-2.52211 + 1.45614i) q^{46} +11.9021 q^{47} +(3.12552 - 5.41356i) q^{49} +(-1.55943 + 4.75060i) q^{50} +(2.21623 - 2.84400i) q^{52} -2.48735i q^{53} +(0.159569 - 0.356946i) q^{55} +(-0.432713 - 0.749482i) q^{56} +(3.24491 + 5.62035i) q^{58} +(6.09393 - 3.51833i) q^{59} +(3.98695 + 6.90559i) q^{61} +(6.01937 + 3.47529i) q^{62} +1.00000 q^{64} +(-7.11951 + 3.78319i) q^{65} +(1.36766 - 2.36886i) q^{67} +(7.08339 + 4.08960i) q^{68} +(0.199374 + 1.92486i) q^{70} +(-12.2677 + 7.08275i) q^{71} -12.8706 q^{73} +(0.879573 + 1.52347i) q^{74} +(-5.20843 - 3.00709i) q^{76} -0.151325i q^{77} +9.48961 q^{79} +(-2.04138 - 0.912572i) q^{80} +(7.08339 - 4.08960i) q^{82} -0.139544 q^{83} +(-10.7278 - 14.8125i) q^{85} +9.17382i q^{86} +(0.151430 + 0.0874279i) q^{88} +(11.3790 + 6.56966i) q^{89} +(-1.91799 + 2.46127i) q^{91} +2.91228i q^{92} +(5.95105 - 10.3075i) q^{94} +(7.88817 + 10.8917i) q^{95} +(-4.32411 - 7.48957i) q^{97} +(-3.12552 - 5.41356i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^7 - 12 * q^8	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29} + 6 q^{32} - 26 q^{35} - 12 q^{37} - 2 q^{40} + 18 q^{41} - 36 q^{43} - 6 q^{46} - 16 q^{47} + 8 q^{49} + 10 q^{50} + 10 q^{52} - 28 q^{55} + 2 q^{56} + 14 q^{58} + 36 q^{59} + 10 q^{61} - 6 q^{62} + 12 q^{64} - 6 q^{65} + 4 q^{67} + 18 q^{68} - 4 q^{70} + 12 q^{71} + 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 2 q^{80} + 18 q^{82} - 72 q^{83} + 18 q^{85} + 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} + 42 q^{95} - 48 q^{97} - 8 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 6 * q^11 - 8 * q^13 - 4 * q^14 - 6 * q^16 - 18 * q^17 - 6 * q^19 - 4 * q^20 - 6 * q^22 - 6 * q^23 - 10 * q^25 + 2 * q^26 - 2 * q^28 - 14 * q^29 + 6 * q^32 - 26 * q^35 - 12 * q^37 - 2 * q^40 + 18 * q^41 - 36 * q^43 - 6 * q^46 - 16 * q^47 + 8 * q^49 + 10 * q^50 + 10 * q^52 - 28 * q^55 + 2 * q^56 + 14 * q^58 + 36 * q^59 + 10 * q^61 - 6 * q^62 + 12 * q^64 - 6 * q^65 + 4 * q^67 + 18 * q^68 - 4 * q^70 + 12 * q^71 + 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 2 * q^80 + 18 * q^82 - 72 * q^83 + 18 * q^85 + 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 + 42 * q^95 - 48 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.230377	+	2.22417i	0.103028	+	0.994678i
$5$	0.230377	+	2.22417i	0.103028	+	0.994678i
$6$		0			0
$7$	0.432713	+	0.749482i	0.163550	+	0.283277i	0.936140	−	0.351629i	$-0.114372\pi$
$7$	0.432713	+	0.749482i	0.163550	+	0.283277i	−0.772589	+	0.634906i	$0.781039\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.04138	+	0.912572i	0.645539	+	0.288581i
$11$	−0.151430	−	0.0874279i	−0.0456577	−	0.0263605i	0.476997	−	0.878905i	$-0.341725\pi$
$11$	−0.151430	−	0.0874279i	−0.0456577	−	0.0263605i	−0.522655	+	0.852544i	$0.675058\pi$
$12$		0			0
$13$	1.35486	+	3.34131i	0.375770	+	0.926713i
$13$	1.35486	+	3.34131i	0.375770	+	0.926713i
$14$	0.865427			0.231295
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−7.08339	+	4.08960i	−1.71797	+	0.991873i	−0.795370	+	0.606125i	$0.792723\pi$
$17$	−7.08339	+	4.08960i	−1.71797	+	0.991873i	−0.922604	+	0.385748i	$0.873943\pi$
$18$		0			0
$19$	5.20843	−	3.00709i	1.19490	−	0.689873i	0.235483	−	0.971879i	$-0.424333\pi$
$19$	5.20843	−	3.00709i	1.19490	−	0.689873i	0.959413	+	0.282005i	$0.0909996\pi$
$20$	1.81100	−	1.31160i	0.404951	−	0.293282i
$21$		0			0
$22$	−0.151430	+	0.0874279i	−0.0322849	+	0.0186397i
$23$	−2.52211	−	1.45614i	−0.525896	−	0.303626i	0.213448	−	0.976954i	$-0.431531\pi$
$23$	−2.52211	−	1.45614i	−0.525896	−	0.303626i	−0.739344	+	0.673328i	$0.764864\pi$
$24$		0			0
$25$	−4.89385	+	1.02479i	−0.978771	+	0.204959i
$26$	3.57109	+	0.497314i	0.700348	+	0.0975312i
$27$		0			0
$28$	0.432713	−	0.749482i	0.0817752	−	0.141639i
$29$	−3.24491	+	5.62035i	−0.602564	+	1.04367i	0.389867	+	0.920871i	$0.372521\pi$
$29$	−3.24491	+	5.62035i	−0.602564	+	1.04367i	−0.992431	+	0.122801i	$0.960812\pi$
$30$		0			0
$31$			6.95057i			1.24836i	0.781281	+	0.624180i	$0.214567\pi$
$31$			6.95057i			1.24836i	−0.781281	+	0.624180i	$0.785433\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$			8.17919i			1.40272i
$35$	−1.56729	+	1.13509i	−0.264920	+	0.191865i
$36$		0			0
$37$	−0.879573	+	1.52347i	−0.144601	+	0.250456i	−0.929224	−	0.369517i	$-0.879523\pi$
$37$	−0.879573	+	1.52347i	−0.144601	+	0.250456i	0.784623	+	0.619973i	$0.212856\pi$
$38$		−	6.01418i		−	0.975628i
$39$		0			0
$40$	−0.230377	−	2.22417i	−0.0364258	−	0.351672i
$41$	7.08339	+	4.08960i	1.10624	+	0.638688i	0.937853	−	0.347034i	$-0.112811\pi$
$41$	7.08339	+	4.08960i	1.10624	+	0.638688i	0.168387	+	0.985721i	$0.446144\pi$
$42$		0			0
$43$	−7.94476	+	4.58691i	−1.21156	+	0.699497i	−0.963100	−	0.269144i	$-0.913259\pi$
$43$	−7.94476	+	4.58691i	−1.21156	+	0.699497i	−0.248465	+	0.968641i	$0.579926\pi$
$44$			0.174856i			0.0263605i
$45$		0			0
$46$	−2.52211	+	1.45614i	−0.371865	+	0.214696i
$47$	11.9021			1.73610			0.868050	−	0.496478i	$-0.165373\pi$
$47$	11.9021			1.73610			0.868050	+	0.496478i	$0.165373\pi$
$48$		0			0
$49$	3.12552	−	5.41356i	0.446503	−	0.773365i
$50$	−1.55943	+	4.75060i	−0.220537	+	0.671836i
$51$		0			0
$52$	2.21623	−	2.84400i	0.307336	−	0.394391i
$53$		−	2.48735i		−	0.341663i	−0.985300	−	0.170832i	$-0.945355\pi$
$53$		−	2.48735i		−	0.341663i	0.985300	−	0.170832i	$-0.0546454\pi$
$54$		0			0
$55$	0.159569	−	0.356946i	0.0215162	−	0.0481306i
$56$	−0.432713	−	0.749482i	−0.0578238	−	0.100154i
$57$		0			0
$58$	3.24491	+	5.62035i	0.426077	+	0.737988i
$59$	6.09393	−	3.51833i	0.793363	−	0.458048i	−0.0477824	−	0.998858i	$-0.515215\pi$
$59$	6.09393	−	3.51833i	0.793363	−	0.458048i	0.841145	+	0.540810i	$0.181882\pi$
$60$		0			0
$61$	3.98695	+	6.90559i	0.510476	+	0.884171i	0.999926	+	0.0121394i	$0.00386418\pi$
$61$	3.98695	+	6.90559i	0.510476	+	0.884171i	−0.489450	+	0.872031i	$0.662802\pi$
$62$	6.01937	+	3.47529i	0.764461	+	0.441362i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.11951	+	3.78319i	−0.883067	+	0.469248i
$66$		0			0
$67$	1.36766	−	2.36886i	0.167086	−	0.289402i	−0.770308	−	0.637672i	$-0.779897\pi$
$67$	1.36766	−	2.36886i	0.167086	−	0.289402i	0.937394	+	0.348270i	$0.113231\pi$
$68$	7.08339	+	4.08960i	0.858987	+	0.495936i
$69$		0			0
$70$	0.199374	+	1.92486i	0.0238298	+	0.230064i
$71$	−12.2677	+	7.08275i	−1.45591	+	0.840568i	−0.998806	−	0.0488476i	$-0.984445\pi$
$71$	−12.2677	+	7.08275i	−1.45591	+	0.840568i	−0.457100	+	0.889415i	$0.651112\pi$
$72$		0			0
$73$	−12.8706			−1.50639			−0.753193	−	0.657800i	$-0.771487\pi$
$73$	−12.8706			−1.50639			−0.753193	+	0.657800i	$0.771487\pi$
$74$	0.879573	+	1.52347i	0.102248	+	0.177099i
$75$		0			0
$76$	−5.20843	−	3.00709i	−0.597448	−	0.344937i
$77$		−	0.151325i		−	0.0172451i
$78$		0			0
$79$	9.48961			1.06766			0.533832	−	0.845590i	$-0.320751\pi$
$79$	9.48961			1.06766			0.533832	+	0.845590i	$0.320751\pi$
$80$	−2.04138	−	0.912572i	−0.228233	−	0.102029i
$81$		0			0
$82$	7.08339	−	4.08960i	0.782229	−	0.451620i
$83$	−0.139544			−0.0153169			−0.00765845	−	0.999971i	$-0.502438\pi$
$83$	−0.139544			−0.0153169			−0.00765845	+	0.999971i	$0.502438\pi$
$84$		0			0
$85$	−10.7278	−	14.8125i	−1.16359	−	1.60664i
$86$			9.17382i			0.989238i
$87$		0			0
$88$	0.151430	+	0.0874279i	0.0161424	+	0.00931985i
$89$	11.3790	+	6.56966i	1.20617	+	0.696382i	0.961920	−	0.273330i	$-0.0881253\pi$
$89$	11.3790	+	6.56966i	1.20617	+	0.696382i	0.244249	+	0.969713i	$0.421459\pi$
$90$		0			0
$91$	−1.91799	+	2.46127i	−0.201060	+	0.258011i
$92$			2.91228i			0.303626i
$93$		0			0
$94$	5.95105	−	10.3075i	0.613804	−	1.06314i
$95$	7.88817	+	10.8917i	0.809309	+	1.11746i
$96$		0			0
$97$	−4.32411	−	7.48957i	−0.439047	−	0.760451i	0.558570	−	0.829458i	$-0.311350\pi$
$97$	−4.32411	−	7.48957i	−0.439047	−	0.760451i	−0.997616	+	0.0690066i	$0.978017\pi$
$98$	−3.12552	−	5.41356i	−0.315725	−	0.546852i
$99$		0			0
$100$	3.33442	+	3.72580i	0.333442	+	0.372580i
$101$	5.28276	−	9.15001i	0.525654	−	0.910460i	−0.473899	−	0.880579i	$-0.657154\pi$
$101$	5.28276	−	9.15001i	0.525654	−	0.910460i	0.999553	−	0.0298810i	$-0.00951284\pi$
$102$		0			0
$103$			8.93568i			0.880459i	0.897885	+	0.440230i	$0.145103\pi$
$103$			8.93568i			0.880459i	−0.897885	+	0.440230i	$0.854897\pi$
$104$	−1.35486	−	3.34131i	−0.132855	−	0.327642i
$105$		0			0
$106$	−2.15410	−	1.24367i	−0.209225	−	0.120796i
$107$	0.745455	+	0.430389i	0.0720658	+	0.0416072i	0.535600	−	0.844472i	$-0.320086\pi$
$107$	0.745455	+	0.430389i	0.0720658	+	0.0416072i	−0.463534	+	0.886079i	$0.653419\pi$
$108$		0			0
$109$		−	5.45336i		−	0.522337i	−0.965293	−	0.261168i	$-0.915892\pi$
$109$		−	5.45336i		−	0.522337i	0.965293	−	0.261168i	$-0.0841078\pi$
$110$	−0.229340	−	0.316664i	−0.0218667	−	0.0301927i
$111$		0			0
$112$	−0.865427			−0.0817752
$113$	10.2036	−	5.89106i	0.959876	−	0.554184i	0.0637409	−	0.997966i	$-0.479697\pi$
$113$	10.2036	−	5.89106i	0.959876	−	0.554184i	0.896135	+	0.443782i	$0.146364\pi$
$114$		0			0
$115$	2.65766	−	5.94505i	0.247829	−	0.554379i
$116$	6.48982			0.602564
$117$		0			0
$118$		−	7.03667i		−	0.647778i
$119$	−6.13015	−	3.53925i	−0.561950	−	0.324442i
$120$		0			0
$121$	−5.48471	−	9.49980i	−0.498610	−	0.863618i
$122$	7.97389			0.721922
$123$		0			0
$124$	6.01937	−	3.47529i	0.540555	−	0.312090i
$125$	−3.40675	−	10.6487i	−0.304709	−	0.952446i
$126$		0			0
$127$	6.01228	+	3.47119i	0.533503	+	0.308018i	0.742442	−	0.669911i	$-0.233668\pi$
$127$	6.01228	+	3.47119i	0.533503	+	0.308018i	−0.208939	+	0.977929i	$0.567001\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.283413	+	8.05727i	−0.0248569	+	0.706670i
$131$	−2.27133			−0.198447			−0.0992235	−	0.995065i	$-0.531636\pi$
$131$	−2.27133			−0.198447			−0.0992235	+	0.995065i	$0.531636\pi$
$132$		0			0
$133$	4.50751	+	2.60241i	0.390851	+	0.225658i
$134$	−1.36766	−	2.36886i	−0.118148	−	0.204638i
$135$		0			0
$136$	7.08339	−	4.08960i	0.607395	−	0.350680i
$137$	−3.68809	−	6.38795i	−0.315094	−	0.545760i	0.664363	−	0.747410i	$-0.268703\pi$
$137$	−3.68809	−	6.38795i	−0.315094	−	0.545760i	−0.979458	+	0.201650i	$0.935370\pi$
$138$		0			0
$139$	0.410380	+	0.710798i	0.0348079	+	0.0602891i	0.882905	−	0.469552i	$-0.155585\pi$
$139$	0.410380	+	0.710798i	0.0348079	+	0.0602891i	−0.848097	+	0.529842i	$0.822251\pi$
$140$	1.76666	+	0.789764i	0.149310	+	0.0667473i
$141$		0			0
$142$			14.1655i			1.18874i
$143$	0.0869582	−	0.624426i	0.00727181	−	0.0522171i
$144$		0			0
$145$	−13.2482	−	5.92243i	−1.10020	−	0.491831i
$146$	−6.43528	+	11.1462i	−0.532588	+	0.922469i
$147$		0			0
$148$	1.75915			0.144601
$149$	8.90766	−	5.14284i	0.729744	−	0.421318i	−0.0885845	−	0.996069i	$-0.528234\pi$
$149$	8.90766	−	5.14284i	0.729744	−	0.421318i	0.818329	+	0.574751i	$0.194901\pi$
$150$		0			0
$151$			11.7419i			0.955544i	0.878484	+	0.477772i	$0.158555\pi$
$151$			11.7419i			0.955544i	−0.878484	+	0.477772i	$0.841445\pi$
$152$	−5.20843	+	3.00709i	−0.422459	+	0.243907i
$153$		0			0
$154$	−0.131051	−	0.0756625i	−0.0105604	−	0.00609706i
$155$	−15.4592	+	1.60125i	−1.24172	+	0.128616i
$156$		0			0
$157$		−	6.76034i		−	0.539534i	−0.962926	−	0.269767i	$-0.913053\pi$
$157$		−	6.76034i		−	0.539534i	0.962926	−	0.269767i	$-0.0869467\pi$
$158$	4.74480	−	8.21824i	0.377476	−	0.653808i
$159$		0			0
$160$	−1.81100	+	1.31160i	−0.143172	+	0.103691i
$161$		−	2.52036i		−	0.198633i
$162$		0			0
$163$	−0.713746	−	1.23624i	−0.0559049	−	0.0968301i	0.836719	−	0.547633i	$-0.184471\pi$
$163$	−0.713746	−	1.23624i	−0.0559049	−	0.0968301i	−0.892623	+	0.450803i	$0.851138\pi$
$164$		−	8.17919i		−	0.638688i
$165$		0			0
$166$	−0.0697718	+	0.120848i	−0.00541534	+	0.00937964i
$167$	−2.93528	+	5.08406i	−0.227139	+	0.393416i	−0.956959	−	0.290223i	$-0.906271\pi$
$167$	−2.93528	+	5.08406i	−0.227139	+	0.393416i	0.729820	+	0.683639i	$0.239604\pi$
$168$		0			0
$169$	−9.32872	+	9.05401i	−0.717594	+	0.696462i
$170$	−18.1919	+	1.88430i	−1.39526	+	0.144519i
$171$		0			0
$172$	7.94476	+	4.58691i	0.605782	+	0.349749i
$173$	−11.8669	+	6.85138i	−0.902226	+	0.520901i	−0.877922	−	0.478804i	$-0.841070\pi$
$173$	−11.8669	+	6.85138i	−0.902226	+	0.520901i	−0.0243045	+	0.999705i	$0.507737\pi$
$174$		0			0
$175$	−2.88570	−	3.22441i	−0.218138	−	0.243743i
$176$	0.151430	−	0.0874279i	0.0114144	−	0.00659013i
$177$		0			0
$178$	11.3790	−	6.56966i	0.852890	−	0.492416i
$179$	7.09191	−	12.2835i	0.530074	−	0.918115i	−0.469310	−	0.883033i	$-0.655497\pi$
$179$	7.09191	−	12.2835i	0.530074	−	0.918115i	0.999384	−	0.0350821i	$-0.0111693\pi$
$180$		0			0
$181$	13.7728			1.02373			0.511863	−	0.859067i	$-0.328956\pi$
$181$	13.7728			1.02373			0.511863	+	0.859067i	$0.328956\pi$
$182$	1.17253	+	2.89166i	0.0869138	+	0.214344i
$183$		0			0
$184$	2.52211	+	1.45614i	0.185932	+	0.107348i
$185$	−3.59108	−	1.60535i	−0.264021	−	0.118027i
$186$		0			0
$187$	1.43018			0.104585
$188$	−5.95105	−	10.3075i	−0.434025	−	0.751753i
$189$		0			0
$190$	13.3765	−	1.38553i	0.970436	−	0.100517i
$191$	−2.78821	−	4.82932i	−0.201748	−	0.349437i	0.747344	−	0.664437i	$-0.231329\pi$
$191$	−2.78821	−	4.82932i	−0.201748	−	0.349437i	−0.949092	+	0.315000i	$0.897995\pi$
$192$		0			0
$193$	−0.110405	+	0.191227i	−0.00794712	+	0.0137648i	−0.869972	−	0.493102i	$-0.835863\pi$
$193$	−0.110405	+	0.191227i	−0.00794712	+	0.0137648i	0.862024	+	0.506867i	$0.169196\pi$
$194$	−8.64822			−0.620906
$195$		0			0
$196$	−6.25104			−0.446503
$197$	−0.861905	+	1.49286i	−0.0614082	+	0.106362i	−0.895095	−	0.445875i	$-0.852892\pi$
$197$	−0.861905	+	1.49286i	−0.0614082	+	0.106362i	0.833687	+	0.552237i	$0.186226\pi$
$198$		0			0
$199$	−3.97927	−	6.89229i	−0.282083	−	0.488581i	0.689815	−	0.723986i	$-0.257692\pi$
$199$	−3.97927	−	6.89229i	−0.282083	−	0.488581i	−0.971898	+	0.235404i	$0.924359\pi$
$200$	4.89385	−	1.02479i	0.346048	−	0.0724639i
$201$		0			0
$202$	−5.28276	−	9.15001i	−0.371694	−	0.643793i
$203$	−5.61646			−0.394198
$204$		0			0
$205$	−7.46410	+	16.6968i	−0.521315	+	1.16615i
$206$	7.73853	+	4.46784i	0.539169	+	0.311289i
$207$		0			0
$208$	−3.57109	−	0.497314i	−0.247610	−	0.0344825i
$209$	−1.05161			−0.0727416
$210$		0			0
$211$	2.10991	−	3.65448i	0.145252	−	0.251585i	−0.784215	−	0.620490i	$-0.786934\pi$
$211$	2.10991	−	3.65448i	0.145252	−	0.251585i	0.929467	+	0.368905i	$0.120267\pi$
$212$	−2.15410	+	1.24367i	−0.147945	+	0.0854158i
$213$		0			0
$214$	0.745455	−	0.430389i	0.0509582	−	0.0294208i
$215$	−12.0323	−	16.6138i	−0.820599	−	1.13305i
$216$		0			0
$217$	−5.20933	+	3.00761i	−0.353632	+	0.204170i
$218$	−4.72274	−	2.72668i	−0.319865	−	0.184674i
$219$		0			0
$220$	−0.388909	+	0.0402827i	−0.0262202	+	0.00271586i
$221$	−23.2616	−	18.1270i	−1.56474	−	1.21935i
$222$		0			0
$223$	3.47638	−	6.02126i	0.232795	−	0.403214i	−0.725834	−	0.687870i	$-0.758546\pi$
$223$	3.47638	−	6.02126i	0.232795	−	0.403214i	0.958630	+	0.284656i	$0.0918794\pi$
$224$	−0.432713	+	0.749482i	−0.0289119	+	0.0500769i
$225$		0			0
$226$		−	11.7821i		−	0.783735i
$227$	−1.44823	−	2.50840i	−0.0961221	−	0.166488i	0.813954	−	0.580929i	$-0.197311\pi$
$227$	−1.44823	−	2.50840i	−0.0961221	−	0.166488i	−0.910076	+	0.414441i	$0.863977\pi$
$228$		0			0
$229$		−	7.88800i		−	0.521254i	−0.965440	−	0.260627i	$-0.916071\pi$
$229$		−	7.88800i		−	0.521254i	0.965440	−	0.260627i	$-0.0839293\pi$
$230$	−3.81974	−	5.27413i	−0.251866	−	0.347766i
$231$		0			0
$232$	3.24491	−	5.62035i	0.213039	−	0.368994i
$233$			1.42749i			0.0935181i	0.998906	+	0.0467590i	$0.0148893\pi$
$233$			1.42749i			0.0935181i	−0.998906	+	0.0467590i	$0.985111\pi$
$234$		0			0
$235$	2.74197	+	26.4723i	0.178866	+	1.72686i
$236$	−6.09393	−	3.51833i	−0.396681	−	0.229024i
$237$		0			0
$238$	−6.13015	+	3.53925i	−0.397359	+	0.229415i
$239$		−	10.9084i		−	0.705604i	−0.935698	−	0.352802i	$-0.885229\pi$
$239$		−	10.9084i		−	0.705604i	0.935698	−	0.352802i	$-0.114771\pi$
$240$		0			0
$241$	−25.4317	+	14.6830i	−1.63820	+	0.945816i	−0.656749	+	0.754109i	$0.728069\pi$
$241$	−25.4317	+	14.6830i	−1.63820	+	0.945816i	−0.981452	+	0.191707i	$0.938598\pi$
$242$	−10.9694			−0.705141
$243$		0			0
$244$	3.98695	−	6.90559i	0.255238	−	0.442085i
$245$	12.7607	+	5.70452i	0.815252	+	0.364448i
$246$		0			0
$247$	17.1043	+	13.3288i	1.08832	+	0.848091i
$248$		−	6.95057i		−	0.441362i
$249$		0			0
$250$	−10.9254	−	2.37400i	−0.690982	−	0.150145i
$251$	−8.94708	−	15.4968i	−0.564735	−	0.978150i	−0.997074	−	0.0764387i	$-0.975645\pi$
$251$	−8.94708	−	15.4968i	−0.564735	−	0.978150i	0.432339	−	0.901711i	$-0.357688\pi$
$252$		0			0
$253$	0.254615	+	0.441005i	0.0160075	+	0.0277258i
$254$	6.01228	−	3.47119i	0.377244	−	0.217802i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5472	+	6.08945i	0.657918	+	0.379849i	0.791483	−	0.611191i	$-0.209309\pi$
$257$	10.5472	+	6.08945i	0.657918	+	0.379849i	−0.133565	+	0.991040i	$0.542642\pi$
$258$		0			0
$259$	−1.52241			−0.0945981
$260$	6.83610	+	4.27408i	0.423957	+	0.265067i
$261$		0			0
$262$	−1.13567	+	1.96703i	−0.0701616	+	0.121524i
$263$	18.3309	+	10.5834i	1.13033	+	0.652598i	0.944019	−	0.329892i	$-0.107012\pi$
$263$	18.3309	+	10.5834i	1.13033	+	0.652598i	0.186314	+	0.982490i	$0.440346\pi$
$264$		0			0
$265$	5.53228	−	0.573027i	0.339845	−	0.0352008i
$266$	4.50751	−	2.60241i	0.276373	−	0.159564i
$267$		0			0
$268$	−2.73532			−0.167086
$269$	6.04371	+	10.4680i	0.368492	+	0.638246i	0.989330	−	0.145692i	$-0.0465410\pi$
$269$	6.04371	+	10.4680i	0.368492	+	0.638246i	−0.620838	+	0.783939i	$0.713208\pi$
$270$		0			0
$271$	−12.7275	−	7.34824i	−0.773142	−	0.446374i	0.0608525	−	0.998147i	$-0.480618\pi$
$271$	−12.7275	−	7.34824i	−0.773142	−	0.446374i	−0.833994	+	0.551773i	$0.813951\pi$
$272$		−	8.17919i		−	0.495936i
$273$		0			0
$274$	−7.37617			−0.445611
$275$	0.830670	+	0.272675i	0.0500913	+	0.0164429i
$276$		0			0
$277$	−17.0717	+	9.85638i	−1.02574	+	0.592212i	−0.915762	−	0.401722i	$-0.868412\pi$
$277$	−17.0717	+	9.85638i	−1.02574	+	0.592212i	−0.109980	+	0.993934i	$0.535079\pi$
$278$	0.820759			0.0492259
$279$		0			0
$280$	1.56729	−	1.13509i	0.0936633	−	0.0678347i
$281$			9.93073i			0.592418i	0.955123	+	0.296209i	$0.0957225\pi$
$281$			9.93073i			0.592418i	−0.955123	+	0.296209i	$0.904278\pi$
$282$		0			0
$283$	10.0790	+	5.81912i	0.599135	+	0.345911i	0.768701	−	0.639608i	$-0.220903\pi$
$283$	10.0790	+	5.81912i	0.599135	+	0.345911i	−0.169566	+	0.985519i	$0.554237\pi$
$284$	12.2677	+	7.08275i	0.727953	+	0.420284i
$285$		0			0
$286$	−0.497290	−	0.387521i	−0.0294053	−	0.0229146i
$287$			7.07849i			0.417830i
$288$		0			0
$289$	24.9496	−	43.2139i	1.46762	−	2.54200i
$290$	−11.7530	+	8.51202i	−0.690163	+	0.499843i
$291$		0			0
$292$	6.43528	+	11.1462i	0.376596	+	0.652284i
$293$	−6.57636	−	11.3906i	−0.384195	−	0.665445i	0.607462	−	0.794349i	$-0.292188\pi$
$293$	−6.57636	−	11.3906i	−0.384195	−	0.665445i	−0.991657	+	0.128903i	$0.958854\pi$
$294$		0			0
$295$	9.22927	+	12.7434i	0.537349	+	0.741949i
$296$	0.879573	−	1.52347i	0.0511241	−	0.0885496i
$297$		0			0
$298$		−	10.2857i		−	0.595834i
$299$	1.44832	−	10.4000i	0.0837583	−	0.601448i
$300$		0			0
$301$	−6.87561	−	3.96963i	−0.396304	−	0.228806i
$302$	10.1688	+	5.87096i	0.585149	+	0.337836i
$303$		0			0
$304$			6.01418i			0.344937i
$305$	−14.4407	+	10.4585i	−0.826872	+	0.598854i
$306$		0			0
$307$	−14.8609			−0.848155			−0.424077	−	0.905626i	$-0.639402\pi$
$307$	−14.8609			−0.848155			−0.424077	+	0.905626i	$0.639402\pi$
$308$	−0.131051	+	0.0756625i	−0.00746734	+	0.00431127i
$309$		0			0
$310$	−6.34290	+	14.1887i	−0.360252	+	0.805865i
$311$	−9.17666			−0.520361			−0.260180	−	0.965560i	$-0.583782\pi$
$311$	−9.17666			−0.520361			−0.260180	+	0.965560i	$0.583782\pi$
$312$		0			0
$313$		−	7.43905i		−	0.420480i	−0.977650	−	0.210240i	$-0.932576\pi$
$313$		−	7.43905i		−	0.420480i	0.977650	−	0.210240i	$-0.0674245\pi$
$314$	−5.85463	−	3.38017i	−0.330396	−	0.190754i
$315$		0			0
$316$	−4.74480	−	8.21824i	−0.266916	−	0.462312i
$317$	25.7510			1.44632			0.723161	−	0.690679i	$-0.242688\pi$
$317$	25.7510			1.44632			0.723161	+	0.690679i	$0.242688\pi$
$318$		0			0
$319$	0.982750	−	0.567391i	0.0550235	−	0.0317678i
$320$	0.230377	+	2.22417i	0.0128785	+	0.124335i
$321$		0			0
$322$	−2.18270	−	1.26018i	−0.121637	−	0.0702272i
$323$	−24.5955	+	42.6007i	−1.36853	+	2.37037i
$324$		0			0
$325$	−10.0546	−	14.9634i	−0.557731	−	0.830022i
$326$	−1.42749			−0.0790614
$327$		0			0
$328$	−7.08339	−	4.08960i	−0.391115	−	0.225810i
$329$	5.15020	+	8.92040i	0.283940	+	0.491798i
$330$		0			0
$331$	5.63295	−	3.25219i	0.309615	−	0.178756i	−0.337139	−	0.941455i	$-0.609459\pi$
$331$	5.63295	−	3.25219i	0.309615	−	0.178756i	0.646754	+	0.762699i	$0.276126\pi$
$332$	0.0697718	+	0.120848i	0.00382922	+	0.00663241i
$333$		0			0
$334$	2.93528	+	5.08406i	0.160612	+	0.278187i
$335$	5.58382	+	2.49618i	0.305076	+	0.136381i
$336$		0			0
$337$		−	18.6696i		−	1.01700i	−0.861063	−	0.508498i	$-0.830201\pi$
$337$		−	18.6696i		−	1.01700i	0.861063	−	0.508498i	$-0.169799\pi$
$338$	3.17664	+	12.6059i	0.172786	+	0.685671i
$339$		0			0
$340$	−7.46410	+	16.6968i	−0.404798	+	0.905511i
$341$	0.607674	−	1.05252i	0.0329074	−	0.0569973i
$342$		0			0
$343$	11.4678			0.619203
$344$	7.94476	−	4.58691i	0.428353	−	0.247310i
$345$		0			0
$346$			13.7028i			0.736665i
$347$	24.6009	−	14.2033i	1.32064	−	0.762474i	0.336813	−	0.941572i	$-0.390651\pi$
$347$	24.6009	−	14.2033i	1.32064	−	0.762474i	0.983831	+	0.179098i	$0.0573178\pi$
$348$		0			0
$349$	1.93797	+	1.11889i	0.103737	+	0.0598926i	0.550971	−	0.834524i	$-0.314258\pi$
$349$	1.93797	+	1.11889i	0.103737	+	0.0598926i	−0.447234	+	0.894417i	$0.647591\pi$
$350$	−4.23527	+	0.886885i	−0.226385	+	0.0474060i
$351$		0			0
$352$		−	0.174856i		−	0.00931985i
$353$	−0.813287	+	1.40866i	−0.0432869	+	0.0749751i	−0.886857	−	0.462044i	$-0.847116\pi$
$353$	−0.813287	+	1.40866i	−0.0432869	+	0.0749751i	0.843570	+	0.537019i	$0.180450\pi$
$354$		0			0
$355$	−18.5794	−	25.6537i	−0.986093	−	1.36156i
$356$		−	13.1393i		−	0.696382i
$357$		0			0
$358$	−7.09191	−	12.2835i	−0.374819	−	0.649206i
$359$		−	34.4613i		−	1.81880i	−0.415923	−	0.909400i	$-0.636541\pi$
$359$		−	34.4613i		−	1.81880i	0.415923	−	0.909400i	$-0.363459\pi$
$360$		0			0
$361$	8.58515	−	14.8699i	0.451850	−	0.782627i
$362$	6.88641	−	11.9276i	0.361942	−	0.626901i
$363$		0			0
$364$	3.09052	+	0.430389i	0.161987	+	0.0225585i
$365$	−2.96508	−	28.6263i	−0.155199	−	1.49837i
$366$		0			0
$367$	12.6735	+	7.31703i	0.661550	+	0.381946i	0.792867	−	0.609394i	$-0.208587\pi$
$367$	12.6735	+	7.31703i	0.661550	+	0.381946i	−0.131317	+	0.991340i	$0.541921\pi$
$368$	2.52211	−	1.45614i	0.131474	−	0.0759065i
$369$		0			0
$370$	−3.18581	+	2.30729i	−0.165622	+	0.119950i
$371$	1.86422	−	1.07631i	0.0967855	−	0.0558791i
$372$		0			0
$373$	−19.1166	+	11.0370i	−0.989819	+	0.571472i	−0.905220	−	0.424943i	$-0.860294\pi$
$373$	−19.1166	+	11.0370i	−0.989819	+	0.571472i	−0.0845988	+	0.996415i	$0.526961\pi$
$374$	0.715090	−	1.23857i	0.0369764	−	0.0640450i
$375$		0			0
$376$	−11.9021			−0.613804
$377$	−23.1757	−	3.22747i	−1.19361	−	0.166223i
$378$		0			0
$379$	12.0573	+	6.96127i	0.619341	+	0.357577i	0.776612	−	0.629979i	$-0.216936\pi$
$379$	12.0573	+	6.96127i	0.619341	+	0.357577i	−0.157272	+	0.987555i	$0.550270\pi$
$380$	5.48837	−	12.2772i	0.281547	−	0.629806i
$381$		0			0
$382$	−5.57642			−0.285314
$383$	12.3044	+	21.3119i	0.628728	+	1.08899i	0.987807	+	0.155681i	$0.0497573\pi$
$383$	12.3044	+	21.3119i	0.628728	+	1.08899i	−0.359080	+	0.933307i	$0.616909\pi$
$384$		0			0
$385$	0.336572	−	0.0348618i	0.0171533	−	0.00177672i
$386$	0.110405	+	0.191227i	0.00561946	+	0.00973319i
$387$		0			0
$388$	−4.32411	+	7.48957i	−0.219523	+	0.380226i
$389$	−5.60980			−0.284428			−0.142214	−	0.989836i	$-0.545422\pi$
$389$	−5.60980			−0.284428			−0.142214	+	0.989836i	$0.545422\pi$
$390$		0			0
$391$	23.8201			1.20463
$392$	−3.12552	+	5.41356i	−0.157863	+	0.273426i
$393$		0			0
$394$	0.861905	+	1.49286i	0.0434222	+	0.0752094i
$395$	2.18619	+	21.1065i	0.109999	+	1.06198i
$396$		0			0
$397$	−1.18438	−	2.05141i	−0.0594424	−	0.102957i	0.834773	−	0.550595i	$-0.185599\pi$
$397$	−1.18438	−	2.05141i	−0.0594424	−	0.102957i	−0.894215	+	0.447637i	$0.852266\pi$
$398$	−7.95853			−0.398925
$399$		0			0
$400$	1.55943	−	4.75060i	0.0779714	−	0.237530i
$401$	−14.2942	−	8.25276i	−0.713818	−	0.412123i	0.0986548	−	0.995122i	$-0.468546\pi$
$401$	−14.2942	−	8.25276i	−0.713818	−	0.412123i	−0.812473	+	0.582998i	$0.801879\pi$
$402$		0			0
$403$	−23.2240	+	9.41704i	−1.15687	+	0.469096i
$404$	−10.5655			−0.525654
$405$		0			0
$406$	−2.80823	+	4.86400i	−0.139370	+	0.241396i
$407$	0.266387	−	0.153798i	0.0132043	−	0.00762351i
$408$		0			0
$409$	28.8448	−	16.6535i	1.42628	−	0.823464i	0.429457	−	0.903087i	$-0.358705\pi$
$409$	28.8448	−	16.6535i	1.42628	−	0.823464i	0.996825	+	0.0796230i	$0.0253717\pi$
$410$	10.7278	+	14.8125i	0.529808	+	0.731537i
$411$		0			0
$412$	7.73853	−	4.46784i	0.381250	−	0.220115i
$413$	5.27385	+	3.04486i	0.259509	+	0.149828i
$414$		0			0
$415$	−0.0321476	−	0.310368i	−0.00157806	−	0.0152354i
$416$	−2.21623	+	2.84400i	−0.108660	+	0.139438i
$417$		0			0
$418$	−0.525807	+	0.910724i	−0.0257181	+	0.0445450i
$419$	−15.1303	+	26.2065i	−0.739164	+	1.28027i	0.213708	+	0.976898i	$0.431446\pi$
$419$	−15.1303	+	26.2065i	−0.739164	+	1.28027i	−0.952872	+	0.303372i	$0.901887\pi$
$420$		0			0
$421$			40.2235i			1.96038i	0.198070	+	0.980188i	$0.436533\pi$
$421$			40.2235i			1.96038i	−0.198070	+	0.980188i	$0.563467\pi$
$422$	−2.10991	−	3.65448i	−0.102709	−	0.177897i
$423$		0			0
$424$			2.48735i			0.120796i
$425$	30.4741	−	27.2729i	1.47821	−	1.32293i
$426$		0			0
$427$	−3.45041	+	5.97629i	−0.166977	+	0.289213i
$428$		−	0.860777i		−	0.0416072i
$429$		0			0
$430$	−20.4041	+	2.11344i	−0.983974	+	0.101919i
$431$	28.1980	+	16.2801i	1.35825	+	0.784185i	0.989388	−	0.145300i	$-0.0464147\pi$
$431$	28.1980	+	16.2801i	1.35825	+	0.784185i	0.368860	+	0.929485i	$0.379748\pi$
$432$		0			0
$433$	26.6153	−	15.3663i	1.27905	−	0.738460i	0.302376	−	0.953189i	$-0.402220\pi$
$433$	26.6153	−	15.3663i	1.27905	−	0.738460i	0.976674	+	0.214729i	$0.0688869\pi$
$434$			6.01521i			0.288739i
$435$		0			0
$436$	−4.72274	+	2.72668i	−0.226178	+	0.130584i
$437$	−17.5150			−0.837854
$438$		0			0
$439$	3.26422	−	5.65380i	0.155793	−	0.269841i	−0.777555	−	0.628815i	$-0.783540\pi$
$439$	3.26422	−	5.65380i	0.155793	−	0.269841i	0.933347	+	0.358974i	$0.116873\pi$
$440$	−0.159569	+	0.356946i	−0.00760713	+	0.0170167i
$441$		0			0
$442$	−27.3292	+	11.0816i	−1.29992	+	0.527100i
$443$			30.3111i			1.44012i	0.693911	+	0.720061i	$0.255886\pi$
$443$			30.3111i			1.44012i	−0.693911	+	0.720061i	$0.744114\pi$
$444$		0			0
$445$	−11.9906	+	26.8223i	−0.568407	+	1.27150i
$446$	−3.47638	−	6.02126i	−0.164611	−	0.285115i
$447$		0			0
$448$	0.432713	+	0.749482i	0.0204438	+	0.0354097i
$449$	−13.8034	+	7.96938i	−0.651421	+	0.376098i	−0.789001	−	0.614392i	$-0.789401\pi$
$449$	−13.8034	+	7.96938i	−0.651421	+	0.376098i	0.137579	+	0.990491i	$0.456068\pi$
$450$		0			0
$451$	−0.715090	−	1.23857i	−0.0336723	−	0.0583221i
$452$	−10.2036	−	5.89106i	−0.479938	−	0.277092i
$453$		0			0
$454$	−2.89645			−0.135937
$455$	−5.91614	−	3.69890i	−0.277353	−	0.173407i
$456$		0			0
$457$	9.90436	−	17.1548i	0.463306	−	0.802470i	−0.535817	−	0.844334i	$-0.679996\pi$
$457$	9.90436	−	17.1548i	0.463306	−	0.802470i	0.999123	+	0.0418642i	$0.0133297\pi$
$458$	−6.83121	−	3.94400i	−0.319202	−	0.184291i
$459$		0			0
$460$	−6.47740	+	0.670922i	−0.302010	+	0.0312819i
$461$	11.5898	−	6.69139i	0.539792	−	0.311649i	−0.205202	−	0.978720i	$-0.565785\pi$
$461$	11.5898	−	6.69139i	0.539792	−	0.311649i	0.744995	+	0.667070i	$0.232452\pi$
$462$		0			0
$463$	42.3599			1.96863			0.984316	−	0.176412i	$-0.0564493\pi$
$463$	42.3599			1.96863			0.984316	+	0.176412i	$0.0564493\pi$
$464$	−3.24491	−	5.62035i	−0.150641	−	0.260918i
$465$		0			0
$466$	1.23624	+	0.713746i	0.0572679	+	0.0330636i
$467$		−	33.4593i		−	1.54831i	−0.632996	−	0.774155i	$-0.718175\pi$
$467$		−	33.4593i		−	1.54831i	0.632996	−	0.774155i	$-0.281825\pi$
$468$		0			0
$469$	2.36722			0.109308
$470$	24.2966	+	10.8615i	1.12072	+	0.501005i
$471$		0			0
$472$	−6.09393	+	3.51833i	−0.280496	+	0.161944i
$473$	1.60410			0.0737564
$474$		0			0
$475$	−22.4076	+	20.0538i	−1.02813	+	0.920132i
$476$			7.07849i			0.324442i
$477$		0			0
$478$	−9.44692	−	5.45418i	−0.432092	−	0.249469i
$479$	19.3387	+	11.1652i	0.883606	+	0.510150i	0.871846	−	0.489781i	$-0.162923\pi$
$479$	19.3387	+	11.1652i	0.883606	+	0.510150i	0.0117600	+	0.999931i	$0.496257\pi$
$480$		0			0
$481$	−6.28207	−	0.874847i	−0.286438	−	0.0398896i
$482$			29.3660i			1.33759i
$483$		0			0
$484$	−5.48471	+	9.49980i	−0.249305	+	0.431809i
$485$	15.6619	−	11.3430i	0.711170	−	0.515058i
$486$		0			0
$487$	−14.3750	−	24.8982i	−0.651392	−	1.12824i	−0.982785	−	0.184751i	$-0.940852\pi$
$487$	−14.3750	−	24.8982i	−0.651392	−	1.12824i	0.331393	−	0.943493i	$-0.392481\pi$
$488$	−3.98695	−	6.90559i	−0.180481	−	0.312602i
$489$		0			0
$490$	11.3206	−	8.19884i	0.511413	−	0.370386i
$491$	−8.02546	+	13.9005i	−0.362184	+	0.627321i	−0.988320	−	0.152393i	$-0.951302\pi$
$491$	−8.02546	+	13.9005i	−0.362184	+	0.627321i	0.626136	+	0.779714i	$0.284636\pi$
$492$		0			0
$493$		−	53.0815i		−	2.39067i
$494$	20.0952	−	8.14836i	0.904127	−	0.366612i
$495$		0			0
$496$	−6.01937	−	3.47529i	−0.270278	−	0.156045i
$497$	−10.6168	−	6.12960i	−0.476228	−	0.274950i
$498$		0			0
$499$			33.2509i			1.48851i	0.667894	+	0.744256i	$0.267196\pi$
$499$			33.2509i			1.48851i	−0.667894	+	0.744256i	$0.732804\pi$
$500$	−7.51864	+	8.27466i	−0.336244	+	0.370054i
$501$		0			0
$502$	−17.8942			−0.798656
$503$	21.7736	−	12.5710i	0.970838	−	0.560514i	0.0713466	−	0.997452i	$-0.477270\pi$
$503$	21.7736	−	12.5710i	0.970838	−	0.560514i	0.899492	+	0.436938i	$0.143937\pi$
$504$		0			0
$505$	21.5682	+	9.64180i	0.959772	+	0.429055i
$506$	0.509229			0.0226380
$507$		0			0
$508$		−	6.94238i		−	0.308018i
$509$	−22.8809	−	13.2103i	−1.01418	−	0.585536i	−0.101766	−	0.994808i	$-0.532449\pi$
$509$	−22.8809	−	13.2103i	−1.01418	−	0.585536i	−0.912412	+	0.409272i	$0.865783\pi$
$510$		0			0
$511$	−5.56927	−	9.64625i	−0.246370	−	0.426725i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.5472	−	6.08945i	0.465219	−	0.268594i
$515$	−19.8745	+	2.05858i	−0.875774	+	0.0907117i
$516$		0			0
$517$	−1.80233	−	1.04058i	−0.0792664	−	0.0457645i
$518$	−0.761206	+	1.31845i	−0.0334455	+	0.0579293i
$519$		0			0
$520$	7.11951	−	3.78319i	0.312211	−	0.165904i
$521$	22.4462			0.983384			0.491692	−	0.870769i	$-0.336379\pi$
$521$	22.4462			0.983384			0.491692	+	0.870769i	$0.336379\pi$
$522$		0			0
$523$	25.1815	+	14.5385i	1.10111	+	0.635726i	0.936512	−	0.350635i	$-0.114034\pi$
$523$	25.1815	+	14.5385i	1.10111	+	0.635726i	0.164598	+	0.986361i	$0.447367\pi$
$524$	1.13567	+	1.96703i	0.0496118	+	0.0859301i
$525$		0			0
$526$	18.3309	−	10.5834i	0.799266	−	0.461456i
$527$	−28.4250	−	49.2336i	−1.23821	−	2.14465i
$528$		0			0
$529$	−7.25931	−	12.5735i	−0.315622	−	0.546674i
$530$	2.26988	−	5.07761i	0.0985974	−	0.220557i
$531$		0			0
$532$		−	5.20483i		−	0.225658i
$533$	−4.06762	+	29.2086i	−0.176188	+	1.26517i
$534$		0			0
$535$	−0.785521	+	1.75717i	−0.0339610	+	0.0759690i
$536$	−1.36766	+	2.36886i	−0.0590739	+	0.102319i
$537$		0			0
$538$	12.0874			0.521126
$539$	−0.946592	+	0.546515i	−0.0407726	+	0.0235401i
$540$		0			0
$541$		−	8.17282i		−	0.351377i	−0.984446	−	0.175688i	$-0.943785\pi$
$541$		−	8.17282i		−	0.351377i	0.984446	−	0.175688i	$-0.0562151\pi$
$542$	−12.7275	+	7.34824i	−0.546694	+	0.315634i
$543$		0			0
$544$	−7.08339	−	4.08960i	−0.303698	−	0.175340i
$545$	12.1292	−	1.25633i	0.519557	−	0.0538152i
$546$		0			0
$547$			40.7393i			1.74188i	0.491385	+	0.870942i	$0.336491\pi$
$547$			40.7393i			1.74188i	−0.491385	+	0.870942i	$0.663509\pi$
$548$	−3.68809	+	6.38795i	−0.157547	+	0.272880i
$549$		0			0
$550$	0.651479	−	0.583044i	0.0277791	−	0.0248611i
$551$			39.0309i			1.66277i
$552$		0			0
$553$	4.10628	+	7.11229i	0.174617	+	0.302445i
$554$			19.7128i			0.837515i
$555$		0			0
$556$	0.410380	−	0.710798i	0.0174040	−	0.0301446i
$557$	0.458421	−	0.794008i	0.0194239	−	0.0336432i	−0.856150	−	0.516727i	$-0.827150\pi$
$557$	0.458421	−	0.794008i	0.0194239	−	0.0336432i	0.875574	+	0.483084i	$0.160483\pi$
$558$		0			0
$559$	−26.0903	−	20.3313i	−1.10350	−	0.859922i
$560$	−0.199374	−	1.92486i	−0.00842511	−	0.0813400i
$561$		0			0
$562$	8.60027	+	4.96537i	0.362780	+	0.209451i
$563$	10.9632	−	6.32961i	0.462044	−	0.266761i	−0.250859	−	0.968024i	$-0.580713\pi$
$563$	10.9632	−	6.32961i	0.462044	−	0.266761i	0.712903	+	0.701262i	$0.247380\pi$
$564$		0			0
$565$	15.4534	+	21.3374i	0.650129	+	0.897671i
$566$	10.0790	−	5.81912i	0.423652	−	0.244596i
$567$		0			0
$568$	12.2677	−	7.08275i	0.514741	−	0.297186i
$569$	−12.2559	+	21.2279i	−0.513795	+	0.889918i	0.486077	+	0.873916i	$0.338427\pi$
$569$	−12.2559	+	21.2279i	−0.513795	+	0.889918i	−0.999872	+	0.0160026i	$0.994906\pi$
$570$		0			0
$571$	−11.1443			−0.466376			−0.233188	−	0.972432i	$-0.574916\pi$
$571$	−11.1443			−0.466376			−0.233188	+	0.972432i	$0.574916\pi$
$572$	−0.584248	+	0.236905i	−0.0244286	+	0.00990549i
$573$		0			0
$574$	6.13015	+	3.53925i	0.255868	+	0.147725i
$575$	13.8351	+	4.54149i	0.576962	+	0.189393i
$576$		0			0
$577$	23.8325			0.992161			0.496081	−	0.868276i	$-0.334772\pi$
$577$	23.8325			0.992161			0.496081	+	0.868276i	$0.334772\pi$
$578$	−24.9496	−	43.2139i	−1.03777	−	1.79746i
$579$		0			0
$580$	1.49510	+	14.4344i	0.0620808	+	0.599358i
$581$	−0.0603824	−	0.104585i	−0.00250508	−	0.00433893i
$582$		0			0
$583$	−0.217463	+	0.376658i	−0.00900642	+	0.0155996i
$584$	12.8706			0.532588
$585$		0			0
$586$	−13.1527			−0.543334
$587$	−18.6811	+	32.3566i	−0.771051	+	1.33550i	0.165937	+	0.986136i	$0.446935\pi$
$587$	−18.6811	+	32.3566i	−0.771051	+	1.33550i	−0.936988	+	0.349362i	$0.886398\pi$
$588$		0			0
$589$	20.9010	+	36.2016i	0.861210	+	1.49166i
$590$	15.6507	−	1.62109i	0.644331	−	0.0667391i
$591$		0			0
$592$	−0.879573	−	1.52347i	−0.0361502	−	0.0626140i
$593$	−6.46136			−0.265336			−0.132668	−	0.991161i	$-0.542354\pi$
$593$	−6.46136			−0.265336			−0.132668	+	0.991161i	$0.542354\pi$
$594$		0			0
$595$	6.45963	−	14.4499i	0.264819	−	0.592386i
$596$	−8.90766	−	5.14284i	−0.364872	−	0.210659i
$597$		0			0
$598$	−8.28251	−	6.45428i	−0.338697	−	0.263935i
$599$	38.5057			1.57330			0.786651	−	0.617398i	$-0.211813\pi$
$599$	38.5057			1.57330			0.786651	+	0.617398i	$0.211813\pi$
$600$		0			0
$601$	−0.371169	+	0.642883i	−0.0151403	+	0.0262237i	−0.873496	−	0.486831i	$-0.838153\pi$
$601$	−0.371169	+	0.642883i	−0.0151403	+	0.0262237i	0.858356	+	0.513055i	$0.171486\pi$
$602$	−6.87561	+	3.96963i	−0.280229	+	0.161790i
$603$		0			0
$604$	10.1688	−	5.87096i	0.413763	−	0.238886i
$605$	19.8656	−	14.3875i	0.807652	−	0.584933i
$606$		0			0
$607$	25.5500	−	14.7513i	1.03704	−	0.598736i	0.118047	−	0.993008i	$-0.462337\pi$
$607$	25.5500	−	14.7513i	1.03704	−	0.598736i	0.918994	+	0.394272i	$0.129003\pi$
$608$	5.20843	+	3.00709i	0.211230	+	0.121954i
$609$		0			0
$610$	1.83700	+	17.7353i	0.0743780	+	0.718081i
$611$	16.1257	+	39.7686i	0.652374	+	1.60887i
$612$		0			0
$613$	−6.86720	+	11.8943i	−0.277364	+	0.480408i	−0.970729	−	0.240178i	$-0.922794\pi$
$613$	−6.86720	+	11.8943i	−0.277364	+	0.480408i	0.693365	+	0.720587i	$0.256127\pi$
$614$	−7.43044	+	12.8699i	−0.299868	+	0.519387i
$615$		0			0
$616$			0.151325i			0.00609706i
$617$	−21.4394	−	37.1342i	−0.863119	−	1.49497i	−0.868902	−	0.494983i	$-0.835174\pi$
$617$	−21.4394	−	37.1342i	−0.863119	−	1.49497i	0.00578297	−	0.999983i	$-0.498159\pi$
$618$		0			0
$619$			30.0054i			1.20602i	0.797734	+	0.603010i	$0.206032\pi$
$619$			30.0054i			1.20602i	−0.797734	+	0.603010i	$0.793968\pi$
$620$	9.11635	+	12.5875i	0.366121	+	0.505525i
$621$		0			0
$622$	−4.58833	+	7.94722i	−0.183975	+	0.318655i
$623$			11.3711i			0.455574i
$624$		0			0
$625$	22.8996	−	10.0304i	0.915984	−	0.401215i
$626$	−6.44240	−	3.71952i	−0.257490	−	0.148662i
$627$		0			0
$628$	−5.85463	+	3.38017i	−0.233625	+	0.134884i
$629$		−	14.3884i		−	0.573703i
$630$		0			0
$631$	7.73137	−	4.46371i	0.307781	−	0.177697i	−0.338152	−	0.941091i	$-0.609802\pi$
$631$	7.73137	−	4.46371i	0.307781	−	0.177697i	0.645933	+	0.763394i	$0.276468\pi$
$632$	−9.48961			−0.377476
$633$		0			0
$634$	12.8755	−	22.3011i	0.511352	−	0.885688i
$635$	−6.33542	+	14.1720i	−0.251414	+	0.562399i
$636$		0			0
$637$	22.3230	+	3.10873i	0.884470	+	0.123172i
$638$		−	1.13478i		−	0.0449265i
$639$		0			0
$640$	2.04138	+	0.912572i	0.0806924	+	0.0360726i
$641$	11.9079	+	20.6250i	0.470332	+	0.814639i	0.999424	−	0.0339254i	$-0.0108008\pi$
$641$	11.9079	+	20.6250i	0.470332	+	0.814639i	−0.529092	+	0.848564i	$0.677468\pi$
$642$		0			0
$643$	−4.79374	−	8.30300i	−0.189047	−	0.327439i	0.755886	−	0.654703i	$-0.227206\pi$
$643$	−4.79374	−	8.30300i	−0.189047	−	0.327439i	−0.944933	+	0.327265i	$0.893873\pi$
$644$	−2.18270	+	1.26018i	−0.0860104	+	0.0496581i
$645$		0			0
$646$	24.5955	+	42.6007i	0.967699	+	1.67610i
$647$	39.2219	+	22.6448i	1.54197	+	0.890259i	0.998714	+	0.0506940i	$0.0161433\pi$
$647$	39.2219	+	22.6448i	1.54197	+	0.890259i	0.543259	+	0.839565i	$0.317190\pi$
$648$		0			0
$649$	−1.23040			−0.0482975
$650$	−17.9860	+	1.22585i	−0.705470	+	0.0480819i
$651$		0			0
$652$	−0.713746	+	1.23624i	−0.0279524	+	0.0484150i
$653$	−8.00988	−	4.62451i	−0.313451	−	0.180971i	0.335019	−	0.942211i	$-0.391257\pi$
$653$	−8.00988	−	4.62451i	−0.313451	−	0.180971i	−0.648470	+	0.761241i	$0.724591\pi$
$654$		0			0
$655$	−0.523262	−	5.05182i	−0.0204455	−	0.197391i
$656$	−7.08339	+	4.08960i	−0.276560	+	0.159672i
$657$		0			0
$658$	10.3004			0.401551
$659$	11.0666	+	19.1679i	0.431093	+	0.746676i	0.996968	−	0.0778159i	$-0.0247946\pi$
$659$	11.0666	+	19.1679i	0.431093	+	0.746676i	−0.565874	+	0.824491i	$0.691461\pi$
$660$		0			0
$661$	8.75083	+	5.05229i	0.340368	+	0.196511i	0.660435	−	0.750884i	$-0.270372\pi$
$661$	8.75083	+	5.05229i	0.340368	+	0.196511i	−0.320067	+	0.947395i	$0.603705\pi$
$662$		−	6.50437i		−	0.252800i
$663$		0			0
$664$	0.139544			0.00541534
$665$	−4.74978	+	10.6250i	−0.184189	+	0.412020i
$666$		0			0
$667$	16.3680	−	9.45008i	0.633772	−	0.365909i
$668$	5.87057			0.227139
$669$		0			0
$670$	4.95366	−	3.58764i	0.191377	−	0.138603i
$671$		−	1.39428i		−	0.0538256i
$672$		0			0
$673$	11.6594	+	6.73157i	0.449437	+	0.259483i	0.707593	−	0.706621i	$-0.249781\pi$
$673$	11.6594	+	6.73157i	0.449437	+	0.259483i	−0.258155	+	0.966103i	$0.583115\pi$
$674$	−16.1683	−	9.33479i	−0.622781	−	0.359562i
$675$		0			0
$676$	12.5054	+	3.55190i	0.480975	+	0.136612i
$677$			7.86444i			0.302255i	0.988514	+	0.151127i	$0.0482904\pi$
$677$			7.86444i			0.302255i	−0.988514	+	0.151127i	$0.951710\pi$
$678$		0			0
$679$	3.74220	−	6.48168i	0.143612	−	0.248744i
$680$	10.7278	+	14.8125i	0.411392	+	0.568033i
$681$		0			0
$682$	−0.607674	−	1.05252i	−0.0232690	−	0.0403032i
$683$	−9.21246	−	15.9565i	−0.352505	−	0.610557i	0.634183	−	0.773183i	$-0.281337\pi$
$683$	−9.21246	−	15.9565i	−0.352505	−	0.610557i	−0.986688	+	0.162627i	$0.948003\pi$
$684$		0			0
$685$	13.3582	−	9.67456i	0.510392	−	0.369646i
$686$	5.73390	−	9.93141i	0.218921	−	0.379183i
$687$		0			0
$688$		−	9.17382i		−	0.349749i
$689$	8.31100	−	3.37000i	0.316624	−	0.128387i
$690$		0			0
$691$	−20.5618	−	11.8714i	−0.782208	−	0.451608i	0.0550042	−	0.998486i	$-0.482483\pi$
$691$	−20.5618	−	11.8714i	−0.782208	−	0.451608i	−0.837212	+	0.546878i	$0.815816\pi$
$692$	11.8669	+	6.85138i	0.451113	+	0.260450i
$693$		0			0
$694$		−	28.4066i		−	1.07830i
$695$	−1.48639	+	1.07650i	−0.0563821	+	0.0408342i
$696$		0			0
$697$	−66.8992			−2.53399
$698$	1.93797	−	1.11889i	0.0733532	−	0.0423505i
$699$		0			0
$700$	−1.34957	+	4.11130i	−0.0510090	+	0.155392i
$701$	6.52189			0.246328			0.123164	−	0.992386i	$-0.460696\pi$
$701$	6.52189			0.246328			0.123164	+	0.992386i	$0.460696\pi$
$702$		0			0
$703$			10.5798i			0.399025i
$704$	−0.151430	−	0.0874279i	−0.00570722	−	0.00329506i
$705$		0			0
$706$	0.813287	+	1.40866i	0.0306085	+	0.0530154i
$707$	9.14369			0.343884
$708$		0			0
$709$	27.5565	−	15.9098i	1.03491	−	0.597504i	0.116521	−	0.993188i	$-0.462826\pi$
$709$	27.5565	−	15.9098i	1.03491	−	0.597504i	0.918387	+	0.395684i	$0.129493\pi$
$710$	−31.5065	+	3.26340i	−1.18242	+	0.122473i
$711$		0			0
$712$	−11.3790	−	6.56966i	−0.426445	−	0.246208i
$713$	10.1210	−	17.5301i	0.379035	−	0.656507i
$714$		0			0
$715$	1.40886	+	0.0495564i	0.0526884	+	0.00185330i
$716$	−14.1838			−0.530074
$717$		0			0
$718$	−29.8444	−	17.2307i	−1.11378	−	0.643043i
$719$	−11.6970	−	20.2597i	−0.436223	−	0.755560i	0.561172	−	0.827699i	$-0.310351\pi$
$719$	−11.6970	−	20.2597i	−0.436223	−	0.755560i	−0.997395	+	0.0721392i	$0.977017\pi$
$720$		0			0
$721$	−6.69713	+	3.86659i	−0.249414	+	0.143999i
$722$	−8.58515	−	14.8699i	−0.319506	−	0.553401i
$723$		0			0
$724$	−6.88641	−	11.9276i	−0.255931	−	0.443286i
$725$	10.1204	−	30.8305i	0.375862	−	1.14502i
$726$		0			0
$727$		−	36.0471i		−	1.33691i	−0.743750	−	0.668457i	$-0.766955\pi$
$727$		−	36.0471i		−	1.33691i	0.743750	−	0.668457i	$-0.233045\pi$
$728$	1.91799	−	2.46127i	0.0710853	−	0.0912208i
$729$		0			0
$730$	−26.2737	−	11.7453i	−0.972432	−	0.434714i
$731$	37.5172	−	64.9817i	1.38762	−	2.40344i
$732$		0			0
$733$	−17.0888			−0.631189			−0.315594	−	0.948894i	$-0.602204\pi$
$733$	−17.0888			−0.631189			−0.315594	+	0.948894i	$0.602204\pi$
$734$	12.6735	−	7.31703i	0.467787	−	0.270077i
$735$		0			0
$736$		−	2.91228i		−	0.107348i
$737$	−0.414209	+	0.239143i	−0.0152576	+	0.00880896i
$738$		0			0
$739$	33.4931	+	19.3373i	1.23206	+	0.711333i	0.967460	−	0.253024i	$-0.0814253\pi$
$739$	33.4931	+	19.3373i	1.23206	+	0.711333i	0.264604	+	0.964357i	$0.414759\pi$
$740$	0.405267	+	3.91264i	0.0148979	+	0.143831i
$741$		0			0
$742$		−	2.15262i		−	0.0790250i
$743$	−0.225532	+	0.390632i	−0.00827395	+	0.0143309i	−0.870133	−	0.492817i	$-0.835967\pi$
$743$	−0.225532	+	0.390632i	−0.00827395	+	0.0143309i	0.861859	+	0.507148i	$0.169300\pi$
$744$		0			0
$745$	13.4907	+	18.6274i	0.494260	+	0.682453i
$746$			22.0739i			0.808184i
$747$		0			0
$748$	−0.715090	−	1.23857i	−0.0261463	−	0.0452867i
$749$			0.744940i			0.0272195i
$750$		0			0
$751$	−11.1206	+	19.2614i	−0.405795	+	0.702858i	−0.994414	−	0.105553i	$-0.966339\pi$
$751$	−11.1206	+	19.2614i	−0.405795	+	0.702858i	0.588618	+	0.808411i	$0.299672\pi$
$752$	−5.95105	+	10.3075i	−0.217012	+	0.375876i
$753$		0			0
$754$	−14.3829	+	18.4570i	−0.523796	+	0.672165i
$755$	−26.1160	+	2.70507i	−0.950459	+	0.0984475i
$756$		0			0
$757$	7.30326	+	4.21654i	0.265442	+	0.153253i	0.626814	−	0.779169i	$-0.284358\pi$
$757$	7.30326	+	4.21654i	0.265442	+	0.153253i	−0.361373	+	0.932421i	$0.617692\pi$
$758$	12.0573	−	6.96127i	0.437940	−	0.252845i
$759$		0			0
$760$	−7.88817	−	10.8917i	−0.286134	−	0.395082i
$761$	−18.3585	+	10.5993i	−0.665496	+	0.384224i	−0.794368	−	0.607437i	$-0.792198\pi$
$761$	−18.3585	+	10.5993i	−0.665496	+	0.384224i	0.128872	+	0.991661i	$0.458864\pi$
$762$		0			0
$763$	4.08719	−	2.35974i	0.147966	−	0.0854283i
$764$	−2.78821	+	4.82932i	−0.100874	+	0.174719i
$765$		0			0
$766$	24.6089			0.889155
$767$	20.0123	+	15.5949i	0.722601	+	0.563099i
$768$		0			0
$769$	3.34820	+	1.93308i	0.120739	+	0.0697088i	0.559153	−	0.829064i	$-0.311126\pi$
$769$	3.34820	+	1.93308i	0.120739	+	0.0697088i	−0.438414	+	0.898773i	$0.644460\pi$
$770$	0.138095	−	0.308911i	0.00497660	−	0.0111324i
$771$		0			0
$772$	0.220810			0.00794712
$773$	16.6218	+	28.7898i	0.597845	+	1.03550i	0.993139	+	0.116944i	$0.0373097\pi$
$773$	16.6218	+	28.7898i	0.597845	+	1.03550i	−0.395293	+	0.918555i	$0.629357\pi$
$774$		0			0
$775$	−7.12291	−	34.0151i	−0.255862	−	1.22186i
$776$	4.32411	+	7.48957i	0.155226	+	0.268860i
$777$		0			0
$778$	−2.80490	+	4.85823i	−0.100561	+	0.174176i
$779$	49.1911			1.76245
$780$		0			0
$781$	2.47692			0.0886312
$782$	11.9100	−	20.6288i	0.425902	−	0.737684i
$783$		0			0
$784$	3.12552	+	5.41356i	0.111626	+	0.193341i
$785$	15.0361	−	1.55743i	0.536663	−	0.0555870i
$786$		0			0
$787$	15.9873	+	27.6908i	0.569886	+	0.987071i	0.996577	+	0.0826737i	$0.0263459\pi$
$787$	15.9873	+	27.6908i	0.569886	+	0.987071i	−0.426691	+	0.904398i	$0.640321\pi$
$788$	1.72381			0.0614082
$789$		0			0
$790$	19.3718	+	8.65995i	0.689219	+	0.308107i
$791$	8.83049	+	5.09828i	0.313976	+	0.181274i
$792$		0			0
$793$	−17.6720	+	22.6777i	−0.627551	+	0.805310i
$794$	−2.36876			−0.0840643
$795$		0			0
$796$	−3.97927	+	6.89229i	−0.141041	+	0.244291i
$797$	−31.2464	+	18.0401i	−1.10680	+	0.639014i	−0.938000	−	0.346635i	$-0.887324\pi$
$797$	−31.2464	+	18.0401i	−1.10680	+	0.639014i	−0.168805	+	0.985649i	$0.553991\pi$
$798$		0			0
$799$	−84.3072	+	48.6748i	−2.98257	+	1.72199i
$800$	−3.33442	−	3.72580i	−0.117890	−	0.131727i
$801$		0			0
$802$	−14.2942	+	8.25276i	−0.504746	+	0.291415i
$803$	1.94898	+	1.12525i	0.0687782	+	0.0397091i
$804$		0			0
$805$	5.60572	−	0.580634i	0.197576	−	0.0204647i
$806$	−3.45661	+	24.8211i	−0.121754	+	0.874286i
$807$		0			0
$808$	−5.28276	+	9.15001i	−0.185847	+	0.321896i
$809$	−12.4162	+	21.5054i	−0.436529	+	0.756090i	−0.997419	−	0.0718003i	$-0.977126\pi$
$809$	−12.4162	+	21.5054i	−0.436529	+	0.756090i	0.560890	+	0.827890i	$0.310459\pi$
$810$		0			0
$811$		−	21.3899i		−	0.751102i	−0.926802	−	0.375551i	$-0.877453\pi$
$811$		−	21.3899i		−	0.751102i	0.926802	−	0.375551i	$-0.122547\pi$
$812$	2.80823	+	4.86400i	0.0985496	+	0.170693i
$813$		0			0
$814$		−	0.307597i		−	0.0107813i
$815$	2.58518	−	1.87229i	0.0905551	−	0.0655836i
$816$		0			0
$817$	−27.5865	+	47.7812i	−0.965129	+	1.67165i
$818$		−	33.3071i		−	1.16455i
$819$		0			0
$820$	18.1919	−	1.88430i	0.635289	−	0.0658025i
$821$	−28.4938	−	16.4509i	−0.994441	−	0.574141i	−0.0878420	−	0.996134i	$-0.527997\pi$
$821$	−28.4938	−	16.4509i	−0.994441	−	0.574141i	−0.906599	+	0.421994i	$0.861330\pi$
$822$		0			0
$823$	−27.5779	+	15.9221i	−0.961306	+	0.555010i	−0.896575	−	0.442893i	$-0.853952\pi$
$823$	−27.5779	+	15.9221i	−0.961306	+	0.555010i	−0.0647309	+	0.997903i	$0.520619\pi$
$824$		−	8.93568i		−	0.311289i
$825$		0			0
$826$	5.27385	−	3.04486i	0.183501	−	0.105944i
$827$	1.91814			0.0667004			0.0333502	−	0.999444i	$-0.489382\pi$
$827$	1.91814			0.0667004			0.0333502	+	0.999444i	$0.489382\pi$
$828$		0			0
$829$	−13.2223	+	22.9016i	−0.459228	+	0.795407i	−0.998920	−	0.0464558i	$-0.985207\pi$
$829$	−13.2223	+	22.9016i	−0.459228	+	0.795407i	0.539692	+	0.841863i	$0.318541\pi$
$830$	−0.284861	−	0.127344i	−0.00988766	−	0.00442016i
$831$		0			0
$832$	1.35486	+	3.34131i	0.0469713	+	0.115839i
$833$			51.1284i			1.77149i
$834$		0			0
$835$	−11.9840	−	5.35732i	−0.414724	−	0.185398i
$836$	0.525807	+	0.910724i	0.0181854	+	0.0314981i
$837$		0			0
$838$	15.1303	+	26.2065i	0.522668	+	0.905288i
$839$	−25.9126	+	14.9607i	−0.894604	+	0.516500i	−0.875446	−	0.483317i	$-0.839432\pi$
$839$	−25.9126	+	14.9607i	−0.894604	+	0.516500i	−0.0191582	+	0.999816i	$0.506099\pi$
$840$		0			0
$841$	−6.55886	−	11.3603i	−0.226168	−	0.391734i
$842$	34.8346	+	20.1118i	1.20048	+	0.693098i
$843$		0			0
$844$	−4.21983			−0.145252
$845$	−22.2868	−	18.6628i	−0.766688	−	0.642020i
$846$		0			0
$847$	4.74662	−	8.22138i	0.163096	−	0.282490i
$848$	2.15410	+	1.24367i	0.0739723	+	0.0427079i
$849$		0			0
$850$	−8.38199	−	40.0278i	−0.287500	−	1.37294i
$851$	4.43676	−	2.56156i	0.152090	−	0.0878092i
$852$		0			0
$853$	9.19805			0.314935			0.157468	−	0.987524i	$-0.449667\pi$
$853$	9.19805			0.314935			0.157468	+	0.987524i	$0.449667\pi$
$854$	3.45041	+	5.97629i	0.118071	+	0.204504i
$855$		0			0
$856$	−0.745455	−	0.430389i	−0.0254791	−	0.0147104i
$857$			13.1946i			0.450720i	0.974276	+	0.225360i	$0.0723559\pi$
$857$			13.1946i			0.450720i	−0.974276	+	0.225360i	$0.927644\pi$
$858$		0			0
$859$	−52.7575			−1.80006			−0.900032	−	0.435824i	$-0.856457\pi$
$859$	−52.7575			−1.80006			−0.900032	+	0.435824i	$0.856457\pi$
$860$	−8.37177	+	18.7272i	−0.285475	+	0.638592i
$861$		0			0
$862$	28.1980	−	16.2801i	0.960426	−	0.554502i
$863$	18.6411			0.634551			0.317276	−	0.948333i	$-0.397232\pi$
$863$	18.6411			0.634551			0.317276	+	0.948333i	$0.397232\pi$
$864$		0			0
$865$	−17.9725	−	24.8157i	−0.611083	−	0.843758i
$866$		−	30.7327i		−	1.04434i
$867$		0			0
$868$	5.20933	+	3.00761i	0.176816	+	0.102085i
$869$	−1.43701	−	0.829657i	−0.0487471	−	0.0281442i
$870$		0			0
$871$	9.76808	+	1.36031i	0.330979	+	0.0460924i
$872$			5.45336i			0.184674i
$873$		0			0
$874$	−8.75748	+	15.1684i	−0.296226	+	0.513079i
$875$	6.50684	−	7.16111i	0.219971	−	0.242090i
$876$		0			0
$877$	−22.7268	−	39.3640i	−0.767429	−	1.32923i	−0.938953	−	0.344047i	$-0.888202\pi$
$877$	−22.7268	−	39.3640i	−0.767429	−	1.32923i	0.171523	−	0.985180i	$-0.445131\pi$
$878$	−3.26422	−	5.65380i	−0.110162	−	0.190807i
$879$		0			0
$880$	0.229340	+	0.316664i	0.00773106	+	0.0106747i
$881$	−10.0027	+	17.3252i	−0.337000	+	0.583701i	−0.983867	−	0.178902i	$-0.942745\pi$
$881$	−10.0027	+	17.3252i	−0.337000	+	0.583701i	0.646867	+	0.762603i	$0.276079\pi$
$882$		0			0
$883$			29.0388i			0.977233i	0.872499	+	0.488617i	$0.162498\pi$
$883$			29.0388i			0.977233i	−0.872499	+	0.488617i	$0.837502\pi$
$884$	−4.06762	+	29.2086i	−0.136809	+	0.982392i
$885$		0			0
$886$	26.2501	+	15.1555i	0.881891	+	0.509160i
$887$	−2.48763	−	1.43623i	−0.0835264	−	0.0482240i	0.457655	−	0.889130i	$-0.348689\pi$
$887$	−2.48763	−	1.43623i	−0.0835264	−	0.0482240i	−0.541181	+	0.840906i	$0.682023\pi$
$888$		0			0
$889$			6.00812i			0.201506i
$890$	17.2335	+	23.7953i	0.577667	+	0.797619i
$891$		0			0
$892$	−6.95276			−0.232795
$893$	61.9912	−	35.7906i	2.07446	−	1.19769i
$894$		0			0
$895$	28.9545	+	12.9438i	0.967842	+	0.432662i
$896$	0.865427			0.0289119
$897$		0			0
$898$			15.9388i			0.531883i
$899$	−39.0646	−	22.5540i	−1.30288	−	0.752217i
$900$		0			0
$901$	10.1722	+	17.6188i	0.338886	+	0.586968i
$902$	−1.43018			−0.0476198
$903$		0			0
$904$	−10.2036	+	5.89106i	−0.339367	+	0.195934i
$905$	3.17294	+	30.6331i	0.105472	+	1.01828i
$906$		0			0
$907$	−28.9860	−	16.7351i	−0.962464	−	0.555679i	−0.0655336	−	0.997850i	$-0.520875\pi$
$907$	−28.9860	−	16.7351i	−0.962464	−	0.555679i	−0.896931	+	0.442171i	$0.854208\pi$
$908$	−1.44823	+	2.50840i	−0.0480611	+	0.0832442i
$909$		0			0
$910$	−6.16142	+	3.27408i	−0.204249	+	0.108535i
$911$	−20.7528			−0.687570			−0.343785	−	0.939048i	$-0.611709\pi$
$911$	−20.7528			−0.687570			−0.343785	+	0.939048i	$0.611709\pi$
$912$		0			0
$913$	0.0211310	+	0.0122000i	0.000699335	+	0.000403761i
$914$	−9.90436	−	17.1548i	−0.327607	−	0.567432i
$915$		0			0
$916$	−6.83121	+	3.94400i	−0.225710	+	0.130313i
$917$	−0.982835	−	1.70232i	−0.0324561	−	0.0562156i
$918$		0			0
$919$	−13.7419	−	23.8017i	−0.453304	−	0.785146i	0.545285	−	0.838251i	$-0.316421\pi$
$919$	−13.7419	−	23.8017i	−0.453304	−	0.785146i	−0.998589	+	0.0531051i	$0.983088\pi$
$920$	−2.65766	+	5.94505i	−0.0876206	+	0.196003i
$921$		0			0
$922$		−	13.3828i		−	0.440739i
$923$	−40.2866	−	31.3940i	−1.32605	−	1.03335i
$924$		0			0
$925$	2.74326	−	8.35700i	0.0901979	−	0.274776i
$926$	21.1800	−	36.6848i	0.696017	−	1.20554i
$927$		0			0
$928$	−6.48982			−0.213039
$929$	−8.03305	+	4.63788i	−0.263556	+	0.152164i	−0.625956	−	0.779859i	$-0.715291\pi$
$929$	−8.03305	+	4.63788i	−0.263556	+	0.152164i	0.362400	+	0.932023i	$0.381958\pi$
$930$		0			0
$931$		−	37.5948i		−	1.23212i
$932$	1.23624	−	0.713746i	0.0404945	−	0.0233795i
$933$		0			0
$934$	−28.9766	−	16.7296i	−0.948143	−	0.547410i
$935$	0.329480	+	3.18096i	0.0107752	+	0.104029i
$936$		0			0
$937$		−	15.0600i		−	0.491989i	−0.969271	−	0.245995i	$-0.920885\pi$
$937$		−	15.0600i		−	0.491989i	0.969271	−	0.245995i	$-0.0791146\pi$
$938$	1.18361	−	2.05007i	0.0386462	−	0.0669373i
$939$		0			0
$940$	21.5547	−	15.6107i	0.703036	−	0.509166i
$941$			19.4194i			0.633055i	0.948583	+	0.316528i	$0.102517\pi$
$941$			19.4194i			0.633055i	−0.948583	+	0.316528i	$0.897483\pi$
$942$		0			0
$943$	−11.9100	−	20.6288i	−0.387844	−	0.671766i
$944$			7.03667i			0.229024i
$945$		0			0
$946$	0.802048	−	1.38919i	0.0260768	−	0.0451664i
$947$	2.72224	−	4.71506i	0.0884610	−	0.153219i	−0.818400	−	0.574649i	$-0.805138\pi$
$947$	2.72224	−	4.71506i	0.0884610	−	0.153219i	0.906861	+	0.421430i	$0.138472\pi$
$948$		0			0
$949$	−17.4378	−	43.0046i	−0.566055	−	1.39599i
$950$	6.16329	+	29.4325i	0.199964	+	0.954916i
$951$		0			0
$952$	6.13015	+	3.53925i	0.198679	+	0.114708i
$953$	−20.2248	+	11.6768i	−0.655146	+	0.378249i	−0.790425	−	0.612559i	$-0.790140\pi$
$953$	−20.2248	+	11.6768i	−0.655146	+	0.378249i	0.135279	+	0.990808i	$0.456807\pi$
$954$		0			0
$955$	10.0989	−	7.31401i	0.326792	−	0.236676i
$956$	−9.44692	+	5.45418i	−0.305535	+	0.176401i
$957$		0			0
$958$	19.3387	−	11.1652i	0.624803	−	0.360730i
$959$	3.19177	−	5.52831i	0.103068	−	0.178518i
$960$		0			0
$961$	−17.3104			−0.558401
$962$	−3.89867	+	5.00301i	−0.125698	+	0.161303i
$963$		0			0
$964$	25.4317	+	14.6830i	0.819101	+	0.472908i
$965$	−0.450756	−	0.201505i	−0.0145103	−	0.00648667i
$966$		0			0
$967$	32.2070			1.03571			0.517854	−	0.855469i	$-0.326731\pi$
$967$	32.2070			1.03571			0.517854	+	0.855469i	$0.326731\pi$
$968$	5.48471	+	9.49980i	0.176285	+	0.305335i
$969$		0			0
$970$	−1.99235	−	19.2351i	−0.0639705	−	0.617602i
$971$	15.4181	+	26.7049i	0.494789	+	0.857000i	0.999982	−	0.00600636i	$-0.00191189\pi$
$971$	15.4181	+	26.7049i	0.494789	+	0.857000i	−0.505193	+	0.863007i	$0.668579\pi$
$972$		0			0
$973$	−0.355154	+	0.615144i	−0.0113857	+	0.0197206i
$974$	−28.7499			−0.921207
$975$		0			0
$976$	−7.97389			−0.255238
$977$	−10.6533	+	18.4521i	−0.340829	+	0.590334i	−0.984587	−	0.174896i	$-0.944041\pi$
$977$	−10.6533	+	18.4521i	−0.340829	+	0.590334i	0.643758	+	0.765230i	$0.277375\pi$
$978$		0			0
$979$	−1.14874	−	1.98968i	−0.0367140	−	0.0635905i
$980$	−1.44009	−	13.9034i	−0.0460021	−	0.444127i
$981$		0			0
$982$	8.02546	+	13.9005i	0.256103	+	0.443583i
$983$	−6.15826			−0.196418			−0.0982090	−	0.995166i	$-0.531311\pi$
$983$	−6.15826			−0.196418			−0.0982090	+	0.995166i	$0.531311\pi$
$984$		0			0
$985$	−3.51894	−	1.57310i	−0.112123	−	0.0501232i
$986$	−45.9699	−	26.5407i	−1.46398	−	0.845229i
$987$		0			0
$988$	2.99093	−	21.4772i	0.0951542	−	0.683279i
$989$	26.7167			0.849542
$990$		0			0
$991$	−2.46451	+	4.26866i	−0.0782877	+	0.135598i	−0.902511	−	0.430666i	$-0.858279\pi$
$991$	−2.46451	+	4.26866i	−0.0782877	+	0.135598i	0.824224	+	0.566265i	$0.191612\pi$
$992$	−6.01937	+	3.47529i	−0.191115	+	0.110340i
$993$		0			0
$994$	−10.6168	+	6.12960i	−0.336744	+	0.194419i
$995$	14.4129	−	10.4384i	0.456919	−	0.330919i
$996$		0			0
$997$	−20.2628	+	11.6988i	−0.641730	+	0.370503i	−0.785281	−	0.619140i	$-0.787481\pi$
$997$	−20.2628	+	11.6988i	−0.641730	+	0.370503i	0.143550	+	0.989643i	$0.454148\pi$
$998$	28.7961	+	16.6254i	0.911524	+	0.526269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.d.199.3		12
3.2	odd	2		390.2.x.a.199.5	yes	12
5.4	even	2		1170.2.bj.c.199.4		12
13.10	even	6		1170.2.bj.c.829.4		12
15.2	even	4		1950.2.bc.j.901.2		12
15.8	even	4		1950.2.bc.i.901.5		12
15.14	odd	2		390.2.x.b.199.2	yes	12
39.23	odd	6		390.2.x.b.49.2	yes	12
65.49	even	6	inner	1170.2.bj.d.829.3		12
195.23	even	12		1950.2.bc.i.751.5		12
195.62	even	12		1950.2.bc.j.751.2		12
195.179	odd	6		390.2.x.a.49.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.5	✓	12	195.179	odd	6
390.2.x.a.199.5	yes	12	3.2	odd	2
390.2.x.b.49.2	yes	12	39.23	odd	6
390.2.x.b.199.2	yes	12	15.14	odd	2
1170.2.bj.c.199.4		12	5.4	even	2
1170.2.bj.c.829.4		12	13.10	even	6
1170.2.bj.d.199.3		12	1.1	even	1	trivial
1170.2.bj.d.829.3		12	65.49	even	6	inner
1950.2.bc.i.751.5		12	195.23	even	12
1950.2.bc.i.901.5		12	15.8	even	4
1950.2.bc.j.751.2		12	195.62	even	12
1950.2.bc.j.901.2		12	15.2	even	4

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230377 + 2.22417i) q^{5} +(0.432713 + 0.749482i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230377 + 2.22417i) q^{5} +(0.432713 + 0.749482i) q^{7} -1.00000 q^{8} +(2.04138 + 0.912572i) q^{10} +(-0.151430 - 0.0874279i) q^{11} +(1.35486 + 3.34131i) q^{13} +0.865427 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-7.08339 + 4.08960i) q^{17} +(5.20843 - 3.00709i) q^{19} +(1.81100 - 1.31160i) q^{20} +(-0.151430 + 0.0874279i) q^{22} +(-2.52211 - 1.45614i) q^{23} +(-4.89385 + 1.02479i) q^{25} +(3.57109 + 0.497314i) q^{26} +(0.432713 - 0.749482i) q^{28} +(-3.24491 + 5.62035i) q^{29} +6.95057i q^{31} +(0.500000 + 0.866025i) q^{32} +8.17919i q^{34} +(-1.56729 + 1.13509i) q^{35} +(-0.879573 + 1.52347i) q^{37} -6.01418i q^{38} +(-0.230377 - 2.22417i) q^{40} +(7.08339 + 4.08960i) q^{41} +(-7.94476 + 4.58691i) q^{43} +0.174856i q^{44} +(-2.52211 + 1.45614i) q^{46} +11.9021 q^{47} +(3.12552 - 5.41356i) q^{49} +(-1.55943 + 4.75060i) q^{50} +(2.21623 - 2.84400i) q^{52} -2.48735i q^{53} +(0.159569 - 0.356946i) q^{55} +(-0.432713 - 0.749482i) q^{56} +(3.24491 + 5.62035i) q^{58} +(6.09393 - 3.51833i) q^{59} +(3.98695 + 6.90559i) q^{61} +(6.01937 + 3.47529i) q^{62} +1.00000 q^{64} +(-7.11951 + 3.78319i) q^{65} +(1.36766 - 2.36886i) q^{67} +(7.08339 + 4.08960i) q^{68} +(0.199374 + 1.92486i) q^{70} +(-12.2677 + 7.08275i) q^{71} -12.8706 q^{73} +(0.879573 + 1.52347i) q^{74} +(-5.20843 - 3.00709i) q^{76} -0.151325i q^{77} +9.48961 q^{79} +(-2.04138 - 0.912572i) q^{80} +(7.08339 - 4.08960i) q^{82} -0.139544 q^{83} +(-10.7278 - 14.8125i) q^{85} +9.17382i q^{86} +(0.151430 + 0.0874279i) q^{88} +(11.3790 + 6.56966i) q^{89} +(-1.91799 + 2.46127i) q^{91} +2.91228i q^{92} +(5.95105 - 10.3075i) q^{94} +(7.88817 + 10.8917i) q^{95} +(-4.32411 - 7.48957i) q^{97} +(-3.12552 - 5.41356i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^7 - 12 * q^8	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29} + 6 q^{32} - 26 q^{35} - 12 q^{37} - 2 q^{40} + 18 q^{41} - 36 q^{43} - 6 q^{46} - 16 q^{47} + 8 q^{49} + 10 q^{50} + 10 q^{52} - 28 q^{55} + 2 q^{56} + 14 q^{58} + 36 q^{59} + 10 q^{61} - 6 q^{62} + 12 q^{64} - 6 q^{65} + 4 q^{67} + 18 q^{68} - 4 q^{70} + 12 q^{71} + 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 2 q^{80} + 18 q^{82} - 72 q^{83} + 18 q^{85} + 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} + 42 q^{95} - 48 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 6 * q^11 - 8 * q^13 - 4 * q^14 - 6 * q^16 - 18 * q^17 - 6 * q^19 - 4 * q^20 - 6 * q^22 - 6 * q^23 - 10 * q^25 + 2 * q^26 - 2 * q^28 - 14 * q^29 + 6 * q^32 - 26 * q^35 - 12 * q^37 - 2 * q^40 + 18 * q^41 - 36 * q^43 - 6 * q^46 - 16 * q^47 + 8 * q^49 + 10 * q^50 + 10 * q^52 - 28 * q^55 + 2 * q^56 + 14 * q^58 + 36 * q^59 + 10 * q^61 - 6 * q^62 + 12 * q^64 - 6 * q^65 + 4 * q^67 + 18 * q^68 - 4 * q^70 + 12 * q^71 + 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 2 * q^80 + 18 * q^82 - 72 * q^83 + 18 * q^85 + 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 + 42 * q^95 - 48 * q^97 - 8 * q^98

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