LMFDB - Embedded newform 600.2.m.d.299.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, not 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 + 4x^12 + 12x^10 + 16x^8 + 48x^6 + 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.13
Root			$1.15595 - 0.814732i$ of defining polynomial
Character	$\chi$	$=$	600.299
Dual form			600.2.m.d.299.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15595 - 0.814732i) q^{2} +(0.887900 + 1.48716i) q^{3} +(0.672424 - 1.88357i) q^{4} +(2.23800 + 0.995672i) q^{6} +0.797253 q^{7} +(-0.757320 - 2.72515i) q^{8} +(-1.42327 + 2.64089i) q^{9} +O(q^{10})$	\(q+(1.15595 - 0.814732i) q^{2} +(0.887900 + 1.48716i) q^{3} +(0.672424 - 1.88357i) q^{4} +(2.23800 + 0.995672i) q^{6} +0.797253 q^{7} +(-0.757320 - 2.72515i) q^{8} +(-1.42327 + 2.64089i) q^{9} -0.320548i q^{11} +(3.39821 - 0.672424i) q^{12} +4.30324 q^{13} +(0.921582 - 0.649548i) q^{14} +(-3.09569 - 2.53312i) q^{16} +2.57305 q^{17} +(0.506399 + 4.21231i) q^{18} +6.10546 q^{19} +(0.707881 + 1.18564i) q^{21} +(-0.261161 - 0.370537i) q^{22} -3.13115i q^{23} +(3.38031 - 3.54592i) q^{24} +(4.97431 - 3.50598i) q^{26} +(-5.19114 + 0.228229i) q^{27} +(0.536093 - 1.50168i) q^{28} -8.79516 q^{29} +9.90557i q^{31} +(-5.64227 - 0.405993i) q^{32} +(0.476705 - 0.284615i) q^{33} +(2.97431 - 2.09635i) q^{34} +(4.01727 + 4.45663i) q^{36} -8.49593 q^{37} +(7.05758 - 4.97431i) q^{38} +(3.82085 + 6.39959i) q^{39} +5.28178i q^{41} +(1.78425 + 0.793803i) q^{42} -2.97431i q^{43} +(-0.603776 - 0.215544i) q^{44} +(-2.55105 - 3.61944i) q^{46} -6.56192i q^{47} +(1.01848 - 6.85293i) q^{48} -6.36439 q^{49} +(2.28461 + 3.82653i) q^{51} +(2.89360 - 8.10546i) q^{52} -3.94862i q^{53} +(-5.81473 + 4.49321i) q^{54} +(-0.603776 - 2.17264i) q^{56} +(5.42104 + 9.07977i) q^{57} +(-10.1667 + 7.16569i) q^{58} -12.4786i q^{59} +8.83339i q^{61} +(8.07038 + 11.4503i) q^{62} +(-1.13470 + 2.10546i) q^{63} +(-6.85293 + 4.12763i) q^{64} +(0.319161 - 0.717386i) q^{66} -4.66738i q^{67} +(1.73018 - 4.84653i) q^{68} +(4.65651 - 2.78015i) q^{69} -3.43077 q^{71} +(8.27471 + 1.87862i) q^{72} -1.43077i q^{73} +(-9.82085 + 6.92191i) q^{74} +(4.10546 - 11.5001i) q^{76} -0.255558i q^{77} +(9.63064 + 4.28461i) q^{78} +2.89360i q^{79} +(-4.94862 - 7.51739i) q^{81} +(4.30324 + 6.10546i) q^{82} -3.37031 q^{83} +(2.70924 - 0.536093i) q^{84} +(-2.42327 - 3.43815i) q^{86} +(-7.80922 - 13.0798i) q^{87} +(-0.873543 + 0.242757i) q^{88} +13.7526i q^{89} +3.43077 q^{91} +(-5.89774 - 2.10546i) q^{92} +(-14.7311 + 8.79516i) q^{93} +(-5.34620 - 7.58523i) q^{94} +(-4.40599 - 8.75141i) q^{96} +4.26230i q^{97} +(-7.35689 + 5.18527i) q^{98} +(0.846533 + 0.456225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) $ 16 * q - 2 * q^4 + 2 * q^6	$ 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	1.15595	−	0.814732i	0.817378	−	0.576102i
$2$	1.15595	−	0.814732i	0.817378	−	0.576102i
$3$	0.887900	+	1.48716i	0.512629	+	0.858610i
$3$	0.887900	+	1.48716i	0.512629	+	0.858610i
$4$	0.672424	−	1.88357i	0.336212	−	0.941786i
$5$		0			0
$5$		0			0
$6$	2.23800	+	0.995672i	0.913659	+	0.406482i
$7$	0.797253			0.301333			0.150667	−	0.988585i	$-0.451858\pi$
$7$	0.797253			0.301333			0.150667	+	0.988585i	$0.451858\pi$
$8$	−0.757320	−	2.72515i	−0.267753	−	0.963488i
$9$	−1.42327	+	2.64089i	−0.474422	+	0.880297i
$10$		0			0
$11$		−	0.320548i		−	0.0966489i	−0.998832	−	0.0483245i	$-0.984612\pi$
$11$		−	0.320548i		−	0.0966489i	0.998832	−	0.0483245i	$-0.0153881\pi$
$12$	3.39821	−	0.672424i	0.980979	−	0.194112i
$13$	4.30324			1.19350			0.596752	−	0.802426i	$-0.296458\pi$
$13$	4.30324			1.19350			0.596752	+	0.802426i	$0.296458\pi$
$14$	0.921582	−	0.649548i	0.246303	−	0.173599i
$15$		0			0
$16$	−3.09569	−	2.53312i	−0.773923	−	0.633280i
$17$	2.57305			0.624057			0.312029	−	0.950073i	$-0.398992\pi$
$17$	2.57305			0.624057			0.312029	+	0.950073i	$0.398992\pi$
$18$	0.506399	+	4.21231i	0.119359	+	0.992851i
$19$	6.10546			1.40069			0.700344	−	0.713805i	$-0.253030\pi$
$19$	6.10546			1.40069			0.700344	+	0.713805i	$0.253030\pi$
$20$		0			0
$21$	0.707881	+	1.18564i	0.154472	+	0.258728i
$22$	−0.261161	−	0.370537i	−0.0556797	−	0.0789986i
$23$		−	3.13115i		−	0.652889i	−0.945216	−	0.326445i	$-0.894149\pi$
$23$		−	3.13115i		−	0.652889i	0.945216	−	0.326445i	$-0.105851\pi$
$24$	3.38031	−	3.54592i	0.690002	−	0.723807i
$25$		0			0
$26$	4.97431	−	3.50598i	0.975543	−	0.687580i
$27$	−5.19114	+	0.228229i	−0.999035	+	0.0439227i
$28$	0.536093	−	1.50168i	0.101312	−	0.283792i
$29$	−8.79516			−1.63322			−0.816610	−	0.577190i	$-0.804149\pi$
$29$	−8.79516			−1.63322			−0.816610	+	0.577190i	$0.804149\pi$
$30$		0			0
$31$			9.90557i			1.77909i	0.456845	+	0.889546i	$0.348980\pi$
$31$			9.90557i			1.77909i	−0.456845	+	0.889546i	$0.651020\pi$
$32$	−5.64227	−	0.405993i	−0.997421	−	0.0717702i
$33$	0.476705	−	0.284615i	0.0829837	−	0.0495451i
$34$	2.97431	−	2.09635i	0.510090	−	0.359521i
$35$		0			0
$36$	4.01727	+	4.45663i	0.669546	+	0.742771i
$37$	−8.49593			−1.39672			−0.698362	−	0.715745i	$-0.746087\pi$
$37$	−8.49593			−1.39672			−0.698362	+	0.715745i	$0.746087\pi$
$38$	7.05758	−	4.97431i	1.14489	−	0.806940i
$39$	3.82085	+	6.39959i	0.611825	+	1.02475i
$40$		0			0
$41$			5.28178i			0.824876i	0.910986	+	0.412438i	$0.135323\pi$
$41$			5.28178i			0.824876i	−0.910986	+	0.412438i	$0.864677\pi$
$42$	1.78425	+	0.793803i	0.275316	+	0.122486i
$43$		−	2.97431i		−	0.453578i	−0.973944	−	0.226789i	$-0.927177\pi$
$43$		−	2.97431i		−	0.453578i	0.973944	−	0.226789i	$-0.0728228\pi$
$44$	−0.603776	−	0.215544i	−0.0910226	−	0.0324945i
$45$		0			0
$46$	−2.55105	−	3.61944i	−0.376131	−	0.533657i
$47$		−	6.56192i		−	0.957154i	−0.878046	−	0.478577i	$-0.841153\pi$
$47$		−	6.56192i		−	0.957154i	0.878046	−	0.478577i	$-0.158847\pi$
$48$	1.01848	−	6.85293i	0.147005	−	0.989136i
$49$	−6.36439			−0.909198
$50$		0			0
$51$	2.28461	+	3.82653i	0.319910	+	0.535822i
$52$	2.89360	−	8.10546i	0.401270	−	1.12403i
$53$		−	3.94862i		−	0.542385i	−0.962525	−	0.271193i	$-0.912582\pi$
$53$		−	3.94862i		−	0.542385i	0.962525	−	0.271193i	$-0.0874180\pi$
$54$	−5.81473	+	4.49321i	−0.791285	+	0.611448i
$55$		0			0
$56$	−0.603776	−	2.17264i	−0.0806829	−	0.290331i
$57$	5.42104	+	9.07977i	0.718034	+	1.20265i
$58$	−10.1667	+	7.16569i	−1.33496	+	0.940902i
$59$		−	12.4786i		−	1.62458i	−0.583255	−	0.812289i	$-0.698221\pi$
$59$		−	12.4786i		−	1.62458i	0.583255	−	0.812289i	$-0.301779\pi$
$60$		0			0
$61$			8.83339i			1.13100i	0.824749	+	0.565500i	$0.191317\pi$
$61$			8.83339i			1.13100i	−0.824749	+	0.565500i	$0.808683\pi$
$62$	8.07038	+	11.4503i	1.02494	+	1.45419i
$63$	−1.13470	+	2.10546i	−0.142959	+	0.265263i
$64$	−6.85293	+	4.12763i	−0.856617	+	0.515953i
$65$		0			0
$66$	0.319161	−	0.717386i	0.0392860	−	0.0883041i
$67$		−	4.66738i		−	0.570211i	−0.958496	−	0.285106i	$-0.907971\pi$
$67$		−	4.66738i		−	0.570211i	0.958496	−	0.285106i	$-0.0920286\pi$
$68$	1.73018	−	4.84653i	0.209816	−	0.587728i
$69$	4.65651	−	2.78015i	0.560577	−	0.334690i
$70$		0			0
$71$	−3.43077			−0.407158			−0.203579	−	0.979059i	$-0.565257\pi$
$71$	−3.43077			−0.407158			−0.203579	+	0.979059i	$0.565257\pi$
$72$	8.27471	+	1.87862i	0.975184	+	0.221398i
$73$		−	1.43077i		−	0.167459i	−0.996489	−	0.0837295i	$-0.973317\pi$
$73$		−	1.43077i		−	0.167459i	0.996489	−	0.0837295i	$-0.0266832\pi$
$74$	−9.82085	+	6.92191i	−1.14165	+	0.804655i
$75$		0			0
$76$	4.10546	−	11.5001i	0.470929	−	1.31915i
$77$		−	0.255558i		−	0.0291235i
$78$	9.63064	+	4.28461i	1.09046	+	0.485137i
$79$			2.89360i			0.325556i	0.986663	+	0.162778i	$0.0520454\pi$
$79$			2.89360i			0.325556i	−0.986663	+	0.162778i	$0.947955\pi$
$80$		0			0
$81$	−4.94862	−	7.51739i	−0.549847	−	0.835265i
$82$	4.30324	+	6.10546i	0.475213	+	0.674235i
$83$	−3.37031			−0.369939			−0.184970	−	0.982744i	$-0.559219\pi$
$83$	−3.37031			−0.369939			−0.184970	+	0.982744i	$0.559219\pi$
$84$	2.70924	−	0.536093i	0.295602	−	0.0584925i
$85$		0			0
$86$	−2.42327	−	3.43815i	−0.261308	−	0.370745i
$87$	−7.80922	−	13.0798i	−0.837236	−	1.40230i
$88$	−0.873543	+	0.242757i	−0.0931200	+	0.0258780i
$89$			13.7526i			1.45777i	0.684636	+	0.728885i	$0.259961\pi$
$89$			13.7526i			1.45777i	−0.684636	+	0.728885i	$0.740039\pi$
$90$		0			0
$91$	3.43077			0.359642
$92$	−5.89774	−	2.10546i	−0.614882	−	0.219509i
$93$	−14.7311	+	8.79516i	−1.52755	+	0.912015i
$94$	−5.34620	−	7.58523i	−0.551419	−	0.782356i
$95$		0			0
$96$	−4.40599	−	8.75141i	−0.449685	−	0.893187i
$97$			4.26230i			0.432771i	0.976308	+	0.216385i	$0.0694267\pi$
$97$			4.26230i			0.432771i	−0.976308	+	0.216385i	$0.930573\pi$
$98$	−7.35689	+	5.18527i	−0.743158	+	0.523791i
$99$	0.846533	+	0.456225i	0.0850798	+	0.0458524i
$100$		0			0
$101$	−15.3130			−1.52370			−0.761851	−	0.647753i	$-0.775709\pi$
$101$	−15.3130			−1.52370			−0.761851	+	0.647753i	$0.775709\pi$
$102$	5.75849	+	2.56192i	0.570175	+	0.253668i
$103$	7.25936			0.715286			0.357643	−	0.933858i	$-0.383581\pi$
$103$	7.25936			0.715286			0.357643	+	0.933858i	$0.383581\pi$
$104$	−3.25893	−	11.7270i	−0.319564	−	1.14993i
$105$		0			0
$106$	−3.21707	−	4.56440i	−0.312469	−	0.443334i
$107$	−13.2928			−1.28506			−0.642531	−	0.766260i	$-0.722116\pi$
$107$	−13.2928			−1.28506			−0.642531	+	0.766260i	$0.722116\pi$
$108$	−3.06076	+	9.93135i	−0.294522	+	0.955645i
$109$		−	3.41592i		−	0.327186i	−0.986528	−	0.163593i	$-0.947692\pi$
$109$		−	3.41592i		−	0.327186i	0.986528	−	0.163593i	$-0.0523084\pi$
$110$		0			0
$111$	−7.54354	−	12.6348i	−0.716001	−	1.19924i
$112$	−2.46805	−	2.01954i	−0.233209	−	0.190828i
$113$	10.2261			0.961992			0.480996	−	0.876723i	$-0.340275\pi$
$113$	10.2261			0.961992			0.480996	+	0.876723i	$0.340275\pi$
$114$	13.6640	+	6.07904i	1.27975	+	0.569354i
$115$		0			0
$116$	−5.91408	+	16.5663i	−0.549108	+	1.53814i
$117$	−6.12465	+	11.3644i	−0.566224	+	1.05064i
$118$	−10.1667	−	14.4246i	−0.935923	−	1.32789i
$119$	2.05138			0.188049
$120$		0			0
$121$	10.8972			0.990659
$122$	7.19684	+	10.2109i	0.651571	+	0.924453i
$123$	−7.85484	+	4.68970i	−0.708247	+	0.422856i
$124$	18.6579	+	6.66075i	1.67553	+	0.598153i
$125$		0			0
$126$	0.403728	+	3.35828i	0.0359670	+	0.299179i
$127$	4.98995			0.442786			0.221393	−	0.975185i	$-0.428940\pi$
$127$	4.98995			0.442786			0.221393	+	0.975185i	$0.428940\pi$
$128$	−4.55872	+	10.3546i	−0.402937	+	0.915228i
$129$	4.42327	−	2.64089i	0.389447	−	0.232518i
$130$		0			0
$131$		−	8.92702i		−	0.779958i	−0.920824	−	0.389979i	$-0.872482\pi$
$131$		−	8.92702i		−	0.779958i	0.920824	−	0.389979i	$-0.127518\pi$
$132$	−0.215544	−	1.08929i	−0.0187607	−	0.0948106i
$133$	4.86760			0.422074
$134$	−3.80266	−	5.39524i	−0.328500	−	0.466078i
$135$		0			0
$136$	−1.94862	−	7.01197i	−0.167093	−	0.601271i
$137$	−1.61964			−0.138375			−0.0691877	−	0.997604i	$-0.522041\pi$
$137$	−1.61964			−0.138375			−0.0691877	+	0.997604i	$0.522041\pi$
$138$	3.11760	−	7.00750i	0.265388	−	0.596518i
$139$	−3.58761			−0.304297			−0.152148	−	0.988358i	$-0.548619\pi$
$139$	−3.58761			−0.304297			−0.152148	+	0.988358i	$0.548619\pi$
$140$		0			0
$141$	9.75860	−	5.82633i	0.821822	−	0.490665i
$142$	−3.96579	+	2.79516i	−0.332801	+	0.234564i
$143$		−	1.37939i		−	0.115351i
$144$	11.0957	−	4.57008i	0.924641	−	0.380840i
$145$		0			0
$146$	−1.16569	−	1.65389i	−0.0964735	−	0.136877i
$147$	−5.65094	−	9.46484i	−0.466082	−	0.780647i
$148$	−5.71287	+	16.0027i	−0.469595	+	1.31541i
$149$	−2.31367			−0.189543			−0.0947717	−	0.995499i	$-0.530212\pi$
$149$	−2.31367			−0.189543			−0.0947717	+	0.995499i	$0.530212\pi$
$150$		0			0
$151$		−	3.44347i		−	0.280225i	−0.990136	−	0.140113i	$-0.955254\pi$
$151$		−	3.44347i		−	0.280225i	0.990136	−	0.140113i	$-0.0447465\pi$
$152$	−4.62379	−	16.6383i	−0.375039	−	1.34955i
$153$	−3.66214	+	6.79516i	−0.296067	+	0.549356i
$154$	−0.208211	−	0.295411i	−0.0167781	−	0.0238049i
$155$		0			0
$156$	14.6233	−	2.89360i	1.17080	−	0.231674i
$157$	9.17084			0.731912			0.365956	−	0.930632i	$-0.380742\pi$
$157$	9.17084			0.731912			0.365956	+	0.930632i	$0.380742\pi$
$158$	2.35751	+	3.34485i	0.187553	+	0.266102i
$159$	5.87222	−	3.50598i	0.465697	−	0.278043i
$160$		0			0
$161$		−	2.49632i		−	0.196737i
$162$	−11.8450	−	4.65790i	−0.930631	−	0.365959i
$163$		−	10.6160i		−	0.831510i	−0.909477	−	0.415755i	$-0.863517\pi$
$163$		−	10.6160i		−	0.831510i	0.909477	−	0.415755i	$-0.136483\pi$
$164$	9.94862	+	3.55160i	0.776857	+	0.277333i
$165$		0			0
$166$	−3.89589	+	2.74590i	−0.302380	+	0.213123i
$167$			13.3353i			1.03192i	0.856613	+	0.515959i	$0.172564\pi$
$167$			13.3353i			1.03192i	−0.856613	+	0.515959i	$0.827436\pi$
$168$	2.69496	−	2.82699i	0.207921	−	0.218107i
$169$	5.51785			0.424450
$170$		0			0
$171$	−8.68970	+	16.1239i	−0.664518	+	1.23302i
$172$	−5.60233	−	2.00000i	−0.427174	−	0.152499i
$173$			13.8972i			1.05659i	0.849061	+	0.528294i	$0.177168\pi$
$173$			13.8972i			1.05659i	−0.849061	+	0.528294i	$0.822832\pi$
$174$	−19.6835	−	8.75710i	−1.49221	−	0.663874i
$175$		0			0
$176$	−0.811987	+	0.992318i	−0.0612058	+	0.0747988i
$177$	18.5577	−	11.0798i	1.39488	−	0.832807i
$178$	11.2047	+	15.8972i	0.839825	+	1.19155i
$179$			5.18815i			0.387780i	0.981023	+	0.193890i	$0.0621105\pi$
$179$			5.18815i			0.387780i	−0.981023	+	0.193890i	$0.937889\pi$
$180$		0			0
$181$		−	2.59819i		−	0.193122i	−0.995327	−	0.0965610i	$-0.969216\pi$
$181$		−	2.59819i		−	0.193122i	0.995327	−	0.0965610i	$-0.0307843\pi$
$182$	3.96579	−	2.79516i	0.293964	−	0.207191i
$183$	−13.1366	+	7.84316i	−0.971087	+	0.579783i
$184$	−8.53286	+	2.37128i	−0.629051	+	0.174813i
$185$		0			0
$186$	−9.86270	+	22.1687i	−0.723168	+	1.62548i
$187$		−	0.824788i		−	0.0603144i
$188$	−12.3598	−	4.41239i	−0.901435	−	0.321807i
$189$	−4.13865	+	0.181956i	−0.301043	+	0.0132354i
$190$		0			0
$191$	12.2556			0.886781			0.443391	−	0.896329i	$-0.353775\pi$
$191$	12.2556			0.886781			0.443391	+	0.896329i	$0.353775\pi$
$192$	−12.2231	−	6.52646i	−0.882130	−	0.471007i
$193$			8.26230i			0.594733i	0.954763	+	0.297367i	$0.0961083\pi$
$193$			8.26230i			0.594733i	−0.954763	+	0.297367i	$0.903892\pi$
$194$	3.47263	+	4.92699i	0.249320	+	0.353737i
$195$		0			0
$196$	−4.27957	+	11.9878i	−0.305683	+	0.856270i
$197$			10.8102i			0.770192i	0.922876	+	0.385096i	$0.125832\pi$
$197$			10.8102i			0.770192i	−0.922876	+	0.385096i	$0.874168\pi$
$198$	1.35025	−	0.162325i	0.0959580	−	0.0115360i
$199$		−	5.71287i		−	0.404975i	−0.979285	−	0.202487i	$-0.935097\pi$
$199$		−	5.71287i		−	0.404975i	0.979285	−	0.202487i	$-0.0649025\pi$
$200$		0			0
$201$	6.94112	−	4.14417i	0.489589	−	0.292307i
$202$	−17.7010	+	12.4760i	−1.24544	+	0.877808i
$203$	−7.01197			−0.492144
$204$	8.74378	−	1.73018i	0.612187	−	0.121137i
$205$		0			0
$206$	8.39143	−	5.91443i	0.584659	−	0.412078i
$207$	8.26902	+	4.45646i	0.574737	+	0.309745i
$208$	−13.3215	−	10.9006i	−0.923679	−	0.755822i
$209$		−	1.95709i		−	0.135375i
$210$		0			0
$211$	−8.15684			−0.561540			−0.280770	−	0.959775i	$-0.590590\pi$
$211$	−8.15684			−0.561540			−0.280770	+	0.959775i	$0.590590\pi$
$212$	−7.43752	−	2.65515i	−0.510811	−	0.182357i
$213$	−3.04618	−	5.10209i	−0.208721	−	0.349590i
$214$	−15.3657	+	10.8300i	−1.05038	+	0.740327i
$215$		0			0
$216$	4.55331	+	13.9738i	0.309814	+	0.950797i
$217$			7.89725i			0.536100i
$218$	−2.78306	−	3.94862i	−0.188493	−	0.267435i
$219$	2.12778	−	1.27038i	0.143782	−	0.0858444i
$220$		0			0
$221$	11.0725			0.744814
$222$	−19.0139	−	8.45917i	−1.27613	−	0.567742i
$223$	20.6084			1.38004			0.690020	−	0.723790i	$-0.257602\pi$
$223$	20.6084			1.38004			0.690020	+	0.723790i	$0.257602\pi$
$224$	−4.49832	−	0.323680i	−0.300556	−	0.0216268i
$225$		0			0
$226$	11.8208	−	8.33154i	0.786311	−	0.554206i
$227$	27.0044			1.79235			0.896173	−	0.443706i	$-0.146336\pi$
$227$	27.0044			1.79235			0.896173	+	0.443706i	$0.146336\pi$
$228$	20.7476	−	4.10546i	1.37405	−	0.271891i
$229$			9.65112i			0.637764i	0.947794	+	0.318882i	$0.103307\pi$
$229$			9.65112i			0.637764i	−0.947794	+	0.318882i	$0.896693\pi$
$230$		0			0
$231$	0.380055	−	0.226910i	0.0250058	−	0.0149296i
$232$	6.66075	+	23.9682i	0.437299	+	1.57359i
$233$	1.29086			0.0845671			0.0422836	−	0.999106i	$-0.486537\pi$
$233$	1.29086			0.0845671			0.0422836	+	0.999106i	$0.486537\pi$
$234$	2.17915	+	18.1266i	0.142456	+	1.18497i
$235$		0			0
$236$	−23.5044	−	8.39093i	−1.53001	−	0.546203i
$237$	−4.30324	+	2.56923i	−0.279525	+	0.166889i
$238$	2.37128	−	1.67132i	0.153707	−	0.108336i
$239$	4.21092			0.272382			0.136191	−	0.990683i	$-0.456514\pi$
$239$	4.21092			0.272382			0.136191	+	0.990683i	$0.456514\pi$
$240$		0			0
$241$	−19.5686			−1.26052			−0.630261	−	0.776383i	$-0.717052\pi$
$241$	−19.5686			−1.26052			−0.630261	+	0.776383i	$0.717052\pi$
$242$	12.5966	−	8.87833i	0.809742	−	0.570721i
$243$	6.78564	−	14.0341i	0.435299	−	0.900286i
$244$	16.6383	+	5.93978i	1.06516	+	0.380256i
$245$		0			0
$246$	−5.25893	+	11.8206i	−0.335297	+	0.753656i
$247$	26.2732			1.67173
$248$	26.9942	−	7.50168i	1.71413	−	0.476357i
$249$	−2.99250	−	5.01217i	−0.189642	−	0.317634i
$250$		0			0
$251$		−	17.5335i		−	1.10670i	−0.832947	−	0.553352i	$-0.813348\pi$
$251$		−	17.5335i		−	1.10670i	0.832947	−	0.553352i	$-0.186652\pi$
$252$	3.20278	+	3.55306i	0.201756	+	0.223822i
$253$	−1.00368			−0.0631011
$254$	5.76812	−	4.06547i	0.361924	−	0.255090i
$255$		0			0
$256$	3.16660	+	15.6835i	0.197913	+	0.980220i
$257$	−1.16582			−0.0727221			−0.0363610	−	0.999339i	$-0.511577\pi$
$257$	−1.16582			−0.0727221			−0.0363610	+	0.999339i	$0.511577\pi$
$258$	2.96144	−	6.65651i	0.184371	−	0.414416i
$259$	−6.77341			−0.420879
$260$		0			0
$261$	12.5179	−	23.2271i	0.774836	−	1.43772i
$262$	−7.27313	−	10.3192i	−0.449335	−	0.637520i
$263$		−	15.3867i		−	0.948785i	−0.880313	−	0.474392i	$-0.842668\pi$
$263$		−	15.3867i		−	0.948785i	0.880313	−	0.474392i	$-0.157332\pi$
$264$	−1.13664	−	1.08355i	−0.0699552	−	0.0666879i
$265$		0			0
$266$	5.62668	−	3.96579i	0.344994	−	0.243158i
$267$	−20.4522	+	12.2109i	−1.25166	+	0.747296i
$268$	−8.79135	−	3.13846i	−0.537017	−	0.191712i
$269$	−2.82479			−0.172230			−0.0861152	−	0.996285i	$-0.527445\pi$
$269$	−2.82479			−0.172230			−0.0861152	+	0.996285i	$0.527445\pi$
$270$		0			0
$271$		−	3.89729i		−	0.236743i	−0.992969	−	0.118372i	$-0.962233\pi$
$271$		−	3.89729i		−	0.236743i	0.992969	−	0.118372i	$-0.0377674\pi$
$272$	−7.96538	−	6.51785i	−0.482972	−	0.395203i
$273$	3.04618	+	5.10209i	0.184363	+	0.308793i
$274$	−1.87222	+	1.31957i	−0.113105	+	0.0797184i
$275$		0			0
$276$	−2.10546	−	10.6403i	−0.126734	−	0.640471i
$277$	21.8450			1.31254			0.656269	−	0.754527i	$-0.272134\pi$
$277$	21.8450			1.31254			0.656269	+	0.754527i	$0.272134\pi$
$278$	−4.14708	+	2.92294i	−0.248725	+	0.175306i
$279$	−26.1595	−	14.0983i	−1.56613	−	0.844041i
$280$		0			0
$281$			20.7201i			1.23606i	0.786155	+	0.618029i	$0.212069\pi$
$281$			20.7201i			1.23606i	−0.786155	+	0.618029i	$0.787931\pi$
$282$	6.53352	−	14.6856i	0.389066	−	0.874513i
$283$			1.23661i			0.0735087i	0.999324	+	0.0367544i	$0.0117019\pi$
$283$			1.23661i			0.0735087i	−0.999324	+	0.0367544i	$0.988298\pi$
$284$	−2.30693	+	6.46211i	−0.136891	+	0.383455i
$285$		0			0
$286$	−1.12384	−	1.59451i	−0.0664539	−	0.0942852i
$287$			4.21092i			0.248563i
$288$	9.10263	−	14.3228i	0.536378	−	0.843978i
$289$	−10.3794			−0.610553
$290$		0			0
$291$	−6.33870	+	3.78449i	−0.371581	+	0.221851i
$292$	−2.69496	−	0.962085i	−0.157711	−	0.0563018i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	−14.2435	−	6.33684i	−0.830697	−	0.369572i
$295$		0			0
$296$	6.43414	+	23.1527i	0.373977	+	1.34573i
$297$	0.0731584	+	1.66401i	0.00424508	+	0.0965556i
$298$	−2.67448	+	1.88502i	−0.154928	+	0.109196i
$299$		−	13.4741i		−	0.779226i
$300$		0			0
$301$		−	2.37128i		−	0.136678i
$302$	−2.80550	−	3.98046i	−0.161438	−	0.229050i
$303$	−13.5964	−	22.7728i	−0.781094	−	1.30827i
$304$	−18.9006	−	15.4659i	−1.08402	−	0.887028i
$305$		0			0
$306$	1.30299	+	10.8385i	0.0744871	+	0.619596i
$307$		−	6.71875i		−	0.383460i	−0.981448	−	0.191730i	$-0.938590\pi$
$307$		−	6.71875i		−	0.383460i	0.981448	−	0.191730i	$-0.0614097\pi$
$308$	−0.481362	−	0.171843i	−0.0274282	−	0.00979169i
$309$	6.44559	+	10.7958i	0.366677	+	0.614152i
$310$		0			0
$311$	22.0568			1.25073			0.625363	−	0.780334i	$-0.284951\pi$
$311$	22.0568			1.25073			0.625363	+	0.780334i	$0.284951\pi$
$312$	14.5463	−	15.2589i	0.823520	−	0.863867i
$313$		−	11.0357i		−	0.623775i	−0.950119	−	0.311888i	$-0.899039\pi$
$313$		−	11.0357i		−	0.623775i	0.950119	−	0.311888i	$-0.100961\pi$
$314$	10.6010	−	7.47177i	0.598249	−	0.421656i
$315$		0			0
$316$	5.45031	+	1.94573i	0.306604	+	0.109456i
$317$		−	24.3705i		−	1.36878i	−0.729115	−	0.684391i	$-0.760068\pi$
$317$		−	24.3705i		−	1.36878i	0.729115	−	0.684391i	$-0.239932\pi$
$318$	3.93154	−	8.83701i	0.220470	−	0.495555i
$319$			2.81927i			0.157849i
$320$		0			0
$321$	−11.8027	−	19.7684i	−0.658760	−	1.10337i
$322$	−2.03383	−	2.88561i	−0.113341	−	0.160809i
$323$	15.7097			0.874110
$324$	−17.4871	+	4.26622i	−0.971507	+	0.237012i
$325$		0			0
$326$	−8.64919	−	12.2715i	−0.479035	−	0.679657i
$327$	5.08001	−	3.03300i	0.280925	−	0.167725i
$328$	14.3937	−	4.00000i	0.794758	−	0.220863i
$329$		−	5.23151i		−	0.288423i
$330$		0			0
$331$	13.1925			0.725128			0.362564	−	0.931959i	$-0.381901\pi$
$331$	13.1925			0.725128			0.362564	+	0.931959i	$0.381901\pi$
$332$	−2.26628	+	6.34822i	−0.124378	+	0.348404i
$333$	12.0920	−	22.4368i	0.662636	−	1.22953i
$334$	10.8647	+	15.4149i	0.594491	+	0.843467i
$335$		0			0
$336$	0.811987	−	5.46352i	0.0442975	−	0.298060i
$337$		−	27.4876i		−	1.49734i	−0.662941	−	0.748672i	$-0.730692\pi$
$337$		−	27.4876i		−	1.49734i	0.662941	−	0.748672i	$-0.269308\pi$
$338$	6.37834	−	4.49557i	0.346936	−	0.244527i
$339$	9.07977	+	15.2078i	0.493146	+	0.825976i
$340$		0			0
$341$	3.17521			0.171947
$342$	3.09180	+	25.7181i	0.167185	+	1.39068i
$343$	−10.6548			−0.575305
$344$	−8.10546	+	2.25251i	−0.437017	+	0.121447i
$345$		0			0
$346$	11.3225	+	16.0645i	0.608703	+	0.863632i
$347$	10.9731			0.589067			0.294533	−	0.955641i	$-0.404836\pi$
$347$	10.9731			0.589067			0.294533	+	0.955641i	$0.404836\pi$
$348$	−29.8878	+	5.91408i	−1.60215	+	0.317028i
$349$		−	31.6066i		−	1.69186i	−0.533291	−	0.845932i	$-0.679045\pi$
$349$		−	31.6066i		−	1.69186i	0.533291	−	0.845932i	$-0.320955\pi$
$350$		0			0
$351$	−22.3387	+	0.982124i	−1.19235	+	0.0524219i
$352$	−0.130140	+	1.80862i	−0.00693651	+	0.0963997i
$353$	−21.4646			−1.14244			−0.571222	−	0.820795i	$-0.693531\pi$
$353$	−21.4646			−1.14244			−0.571222	+	0.820795i	$0.693531\pi$
$354$	12.4246	−	27.9271i	0.660361	−	1.48431i
$355$		0			0
$356$	25.9040	+	9.24757i	1.37291	+	0.490120i
$357$	1.82142	+	3.05072i	0.0963996	+	0.161461i
$358$	4.22695	+	5.99722i	0.223401	+	0.316963i
$359$	34.3124			1.81094			0.905468	−	0.424414i	$-0.139520\pi$
$359$	34.3124			1.81094			0.905468	+	0.424414i	$0.139520\pi$
$360$		0			0
$361$	18.2766			0.961929
$362$	−2.11683	−	3.00337i	−0.111258	−	0.157854i
$363$	9.67567	+	16.2059i	0.507841	+	0.850590i
$364$	2.30693	−	6.46211i	0.120916	−	0.338706i
$365$		0			0
$366$	−8.79516	+	19.7691i	−0.459730	+	1.03335i
$367$	−27.9901			−1.46107			−0.730536	−	0.682874i	$-0.760730\pi$
$367$	−27.9901			−1.46107			−0.730536	+	0.682874i	$0.760730\pi$
$368$	−7.93157	+	9.69307i	−0.413462	+	0.505286i
$369$	−13.9486	−	7.51739i	−0.726136	−	0.391340i
$370$		0			0
$371$		−	3.14805i		−	0.163439i
$372$	6.66075	+	33.6612i	0.345344	+	1.74525i
$373$	13.9134			0.720408			0.360204	−	0.932873i	$-0.382707\pi$
$373$	13.9134			0.720408			0.360204	+	0.932873i	$0.382707\pi$
$374$	−0.671981	−	0.953410i	−0.0347473	−	0.0492997i
$375$		0			0
$376$	−17.8822	+	4.96947i	−0.922206	+	0.256281i
$377$	−37.8477			−1.94925
$378$	−4.63581	+	3.58222i	−0.238441	+	0.184250i
$379$	−7.79853			−0.400583			−0.200292	−	0.979736i	$-0.564189\pi$
$379$	−7.79853			−0.400583			−0.200292	+	0.979736i	$0.564189\pi$
$380$		0			0
$381$	4.43058	+	7.42084i	0.226985	+	0.380181i
$382$	14.1668	−	9.98499i	0.724835	−	0.510877i
$383$			27.8386i			1.42248i	0.702947	+	0.711242i	$0.251867\pi$
$383$			27.8386i			1.42248i	−0.702947	+	0.711242i	$0.748133\pi$
$384$	−19.4466	+	2.41435i	−0.992381	+	0.123207i
$385$		0			0
$386$	6.73155	+	9.55077i	0.342627	+	0.486121i
$387$	7.85484	+	4.23324i	0.399284	+	0.215188i
$388$	8.02834	+	2.86607i	0.407577	+	0.145503i
$389$	18.5246			0.939234			0.469617	−	0.882870i	$-0.344392\pi$
$389$	18.5246			0.939234			0.469617	+	0.882870i	$0.344392\pi$
$390$		0			0
$391$		−	8.05661i		−	0.407440i
$392$	4.81988	+	17.3439i	0.243441	+	0.876001i
$393$	13.2759	−	7.92631i	0.669679	−	0.399829i
$394$	8.80738	+	12.4960i	0.443710	+	0.629538i
$395$		0			0
$396$	1.42856	−	1.28773i	0.0717880	−	0.0647108i
$397$	−4.97814			−0.249846			−0.124923	−	0.992166i	$-0.539868\pi$
$397$	−4.97814			−0.249846			−0.124923	+	0.992166i	$0.539868\pi$
$398$	−4.65446	−	6.60378i	−0.233307	−	0.331017i
$399$	4.32194	+	7.23888i	0.216368	+	0.362397i
$400$		0			0
$401$			16.8094i			0.839422i	0.907658	+	0.419711i	$0.137868\pi$
$401$			16.8094i			0.839422i	−0.907658	+	0.419711i	$0.862132\pi$
$402$	4.64718	−	10.4456i	0.231780	−	0.520978i
$403$			42.6260i			2.12335i
$404$	−10.2968	+	28.8432i	−0.512287	+	1.43500i
$405$		0			0
$406$	−8.10546	+	5.71287i	−0.402267	+	0.283525i
$407$			2.72336i			0.134992i
$408$	8.69771	−	9.12384i	0.430601	−	0.451697i
$409$	17.6053			0.870527			0.435264	−	0.900303i	$-0.356655\pi$
$409$	17.6053			0.870527			0.435264	+	0.900303i	$0.356655\pi$
$410$		0			0
$411$	−1.43808	−	2.40866i	−0.0709353	−	0.118811i
$412$	4.88137	−	13.6735i	0.240488	−	0.673646i
$413$		−	9.94862i		−	0.489540i
$414$	13.1894	−	1.58561i	0.648222	−	0.0779285i
$415$		0			0
$416$	−24.2800	−	1.74709i	−1.19043	−	0.0856580i
$417$	−3.18544	−	5.33533i	−0.155991	−	0.261272i
$418$	−1.59451	−	2.26230i	−0.0779899	−	0.110653i
$419$			13.3408i			0.651741i	0.945414	+	0.325870i	$0.105657\pi$
$419$			13.3408i			0.651741i	−0.945414	+	0.325870i	$0.894343\pi$
$420$		0			0
$421$			16.7650i			0.817074i	0.912742	+	0.408537i	$0.133961\pi$
$421$			16.7650i			0.817074i	−0.912742	+	0.408537i	$0.866039\pi$
$422$	−9.42887	+	6.64563i	−0.458990	+	0.323504i
$423$	17.3293	+	9.33936i	0.842580	+	0.454095i
$424$	−10.7606	+	2.99037i	−0.522581	+	0.145225i
$425$		0			0
$426$	−7.67806	−	3.41592i	−0.372003	−	0.165502i
$427$			7.04245i			0.340808i
$428$	−8.93839	+	25.0379i	−0.432053	+	1.21025i
$429$	2.05138	−	1.22476i	0.0990413	−	0.0591322i
$430$		0			0
$431$	28.9911			1.39645			0.698225	−	0.715878i	$-0.253973\pi$
$431$	28.9911			1.39645			0.698225	+	0.715878i	$0.253973\pi$
$432$	16.6483	+	12.4432i	0.800991	+	0.598676i
$433$		−	23.6484i		−	1.13647i	−0.822866	−	0.568235i	$-0.807626\pi$
$433$		−	23.6484i		−	1.13647i	0.822866	−	0.568235i	$-0.192374\pi$
$434$	6.43414	+	9.12880i	0.308849	+	0.438196i
$435$		0			0
$436$	−6.43414	−	2.29695i	−0.308139	−	0.110004i
$437$		−	19.1171i		−	0.914495i
$438$	1.42458	−	3.20206i	0.0680690	−	0.153000i
$439$			7.85724i			0.375006i	0.982264	+	0.187503i	$0.0600394\pi$
$439$			7.85724i			0.375006i	−0.982264	+	0.187503i	$0.939961\pi$
$440$		0			0
$441$	9.05822	−	16.8077i	0.431344	−	0.800365i
$442$	12.7992	−	9.02109i	0.608795	−	0.429089i
$443$	−12.9805			−0.616721			−0.308360	−	0.951270i	$-0.599780\pi$
$443$	−12.9805			−0.616721			−0.308360	+	0.951270i	$0.599780\pi$
$444$	−28.8710	+	5.71287i	−1.37016	+	0.271121i
$445$		0			0
$446$	23.8222	−	16.7903i	1.12801	−	0.795044i
$447$	−2.05431	−	3.44079i	−0.0971655	−	0.162744i
$448$	−5.46352	+	3.29076i	−0.258127	+	0.155474i
$449$			13.4847i			0.636383i	0.948026	+	0.318191i	$0.103075\pi$
$449$			13.4847i			0.636383i	−0.948026	+	0.318191i	$0.896925\pi$
$450$		0			0
$451$	1.69307			0.0797234
$452$	6.87629	−	19.2616i	0.323434	−	0.905991i
$453$	5.12097	−	3.05745i	0.240604	−	0.143652i
$454$	31.2156	−	22.0013i	1.46502	−	1.03257i
$455$		0			0
$456$	20.6383	−	21.6495i	0.966478	−	1.01383i
$457$			28.1014i			1.31453i	0.753660	+	0.657265i	$0.228287\pi$
$457$			28.1014i			1.31453i	−0.753660	+	0.657265i	$0.771713\pi$
$458$	7.86307	+	11.1562i	0.367417	+	0.521294i
$459$	−13.3571	+	0.587246i	−0.623455	+	0.0274103i
$460$		0			0
$461$	−29.2170			−1.36077			−0.680386	−	0.732854i	$-0.738188\pi$
$461$	−29.2170			−1.36077			−0.680386	+	0.732854i	$0.738188\pi$
$462$	0.254452	−	0.571939i	0.0118382	−	0.0266090i
$463$	−14.1463			−0.657434			−0.328717	−	0.944429i	$-0.606616\pi$
$463$	−14.1463			−0.657434			−0.328717	+	0.944429i	$0.606616\pi$
$464$	27.2271	+	22.2792i	1.26399	+	1.03429i
$465$		0			0
$466$	1.49217	−	1.05171i	0.0691233	−	0.0487193i
$467$	28.9687			1.34051			0.670255	−	0.742131i	$-0.266185\pi$
$467$	28.9687			1.34051			0.670255	+	0.742131i	$0.266185\pi$
$468$	17.2873	+	19.1779i	0.799105	+	0.886500i
$469$		−	3.72108i		−	0.171824i
$470$		0			0
$471$	8.14279	+	13.6385i	0.375200	+	0.628427i
$472$	−34.0062	+	9.45031i	−1.56526	+	0.434986i
$473$	−0.953410			−0.0438379
$474$	−2.88108	+	6.47588i	−0.132332	+	0.297447i
$475$		0			0
$476$	1.37939	−	3.86391i	0.0632245	−	0.177102i
$477$	10.4279	+	5.61995i	0.477460	+	0.257320i
$478$	4.86760	−	3.43077i	0.222639	−	0.156920i
$479$	−37.9040			−1.73188			−0.865939	−	0.500150i	$-0.833278\pi$
$479$	−37.9040			−1.73188			−0.865939	+	0.500150i	$0.833278\pi$
$480$		0			0
$481$	−36.5600			−1.66699
$482$	−22.6202	+	15.9431i	−1.03032	+	0.726190i
$483$	3.71241	−	2.21648i	0.168921	−	0.100853i
$484$	7.32758	−	20.5258i	0.333072	−	0.932989i
$485$		0			0
$486$	−3.59016	−	21.7511i	−0.162853	−	0.986650i
$487$	−41.9180			−1.89949			−0.949743	−	0.313031i	$-0.898656\pi$
$487$	−41.9180			−1.89949			−0.949743	+	0.313031i	$0.898656\pi$
$488$	24.0723	−	6.68970i	1.08970	−	0.302828i
$489$	15.7877	−	9.42595i	0.713942	−	0.426256i
$490$		0			0
$491$			5.09691i			0.230020i	0.993364	+	0.115010i	$0.0366901\pi$
$491$			5.09691i			0.230020i	−0.993364	+	0.115010i	$0.963310\pi$
$492$	3.55160	+	17.9486i	0.160119	+	0.809186i
$493$	−22.6304			−1.01922
$494$	30.3705	−	21.4056i	1.36643	−	0.963086i
$495$		0			0
$496$	25.0920	−	30.6646i	1.12666	−	1.37688i
$497$	−2.73519			−0.122690
$498$	−7.54274	−	3.35572i	−0.337998	−	0.150373i
$499$	27.3821			1.22579			0.612896	−	0.790164i	$-0.290005\pi$
$499$	27.3821			1.22579			0.612896	+	0.790164i	$0.290005\pi$
$500$		0			0
$501$	−19.8317	+	11.8404i	−0.886016	+	0.528992i
$502$	−14.2851	−	20.2678i	−0.637575	−	0.904596i
$503$			21.7572i			0.970104i	0.874485	+	0.485052i	$0.161199\pi$
$503$			21.7572i			0.970104i	−0.874485	+	0.485052i	$0.838801\pi$
$504$	6.59704	+	1.49774i	0.293855	+	0.0667145i
$505$		0			0
$506$	−1.16020	+	0.817733i	−0.0515774	+	0.0363527i
$507$	4.89930	+	8.20591i	0.217586	+	0.364437i
$508$	3.35536	−	9.39893i	0.148870	−	0.417010i
$509$	25.0061			1.10837			0.554187	−	0.832392i	$-0.313029\pi$
$509$	25.0061			1.10837			0.554187	+	0.832392i	$0.313029\pi$
$510$		0			0
$511$		−	1.14069i		−	0.0504610i
$512$	16.4383	+	15.5494i	0.726476	+	0.687192i
$513$	−31.6943	+	1.39344i	−1.39934	+	0.0615220i
$514$	−1.34763	+	0.949833i	−0.0594414	+	0.0418953i
$515$		0			0
$516$	−2.00000	−	10.1073i	−0.0880451	−	0.444951i
$517$	−2.10341			−0.0925079
$518$	−7.82970	+	5.51851i	−0.344017	+	0.242470i
$519$	−20.6674	+	12.3394i	−0.907197	+	0.541638i
$520$		0			0
$521$			26.3235i			1.15325i	0.817007	+	0.576627i	$0.195631\pi$
$521$			26.3235i			1.15325i	−0.817007	+	0.576627i	$0.804369\pi$
$522$	−4.45386	−	37.0479i	−0.194940	−	1.62154i
$523$		−	23.5435i		−	1.02949i	−0.857344	−	0.514744i	$-0.827887\pi$
$523$		−	23.5435i		−	1.02949i	0.857344	−	0.514744i	$-0.172113\pi$
$524$	−16.8147	−	6.00275i	−0.734553	−	0.262231i
$525$		0			0
$526$	−12.5360	−	17.7862i	−0.546597	−	0.775516i
$527$			25.4876i			1.11026i
$528$	−2.19670	−	0.326472i	−0.0955989	−	0.0142079i
$529$	13.1959			0.573735
$530$		0			0
$531$	32.9547	+	17.7604i	1.43011	+	0.770736i
$532$	3.27309	−	9.16847i	0.141907	−	0.397504i
$533$			22.7288i			0.984492i
$534$	−13.6931	+	30.7783i	−0.592557	+	1.33191i
$535$		0			0
$536$	−12.7193	+	3.53470i	−0.549391	+	0.152676i
$537$	−7.71558	+	4.60656i	−0.332952	+	0.198788i
$538$	−3.26530	+	2.30144i	−0.140777	+	0.0992223i
$539$			2.04009i			0.0878730i
$540$		0			0
$541$		−	18.2576i		−	0.784955i	−0.919762	−	0.392478i	$-0.871618\pi$
$541$		−	18.2576i		−	0.784955i	0.919762	−	0.392478i	$-0.128382\pi$
$542$	−3.17524	−	4.50505i	−0.136388	−	0.193509i
$543$	3.86391	−	2.30693i	0.165816	−	0.0990000i
$544$	−14.5179	−	1.04464i	−0.622448	−	0.0447887i
$545$		0			0
$546$	7.67806	+	3.41592i	0.328591	+	0.146188i
$547$			6.40508i			0.273862i	0.990581	+	0.136931i	$0.0437238\pi$
$547$			6.40508i			0.273862i	−0.990581	+	0.136931i	$0.956276\pi$
$548$	−1.08909	+	3.05072i	−0.0465235	+	0.130320i
$549$	−23.3280	−	12.5723i	−0.995616	−	0.536571i
$550$		0			0
$551$	−53.6985			−2.28763
$552$	−11.1028	−	10.5842i	−0.472566	−	0.450495i
$553$			2.30693i			0.0981008i
$554$	25.2516	−	17.7978i	1.07284	−	0.756156i
$555$		0			0
$556$	−2.41239	+	6.75752i	−0.102308	+	0.286583i
$557$		−	7.79582i		−	0.330319i	−0.986267	−	0.165160i	$-0.947186\pi$
$557$		−	7.79582i		−	0.330319i	0.986267	−	0.165160i	$-0.0528140\pi$
$558$	−41.7253	+	5.01617i	−1.76637	+	0.212351i
$559$		−	12.7992i		−	0.541347i
$560$		0			0
$561$	1.22659	−	0.732329i	0.0517866	−	0.0309190i
$562$	16.8813	+	23.9513i	0.712096	+	1.01033i
$563$	−4.37399			−0.184342			−0.0921709	−	0.995743i	$-0.529381\pi$
$563$	−4.37399			−0.184342			−0.0921709	+	0.995743i	$0.529381\pi$
$564$	−4.41239	−	22.2988i	−0.185795	−	0.938948i
$565$		0			0
$566$	1.00750	+	1.42945i	0.0423485	+	0.0600844i
$567$	−3.94531	−	5.99326i	−0.165687	−	0.251693i
$568$	2.59819	+	9.34938i	0.109018	+	0.392291i
$569$		−	21.8198i		−	0.914735i	−0.889278	−	0.457368i	$-0.848792\pi$
$569$		−	21.8198i		−	0.914735i	0.889278	−	0.457368i	$-0.151208\pi$
$570$		0			0
$571$	1.42806			0.0597625			0.0298813	−	0.999553i	$-0.490487\pi$
$571$	1.42806			0.0597625			0.0298813	+	0.999553i	$0.490487\pi$
$572$	−2.59819	−	0.927539i	−0.108636	−	0.0387823i
$573$	10.8817	+	18.2259i	0.454590	+	0.761399i
$574$	3.43077	+	4.86760i	0.143198	+	0.203170i
$575$		0			0
$576$	−1.14707	−	23.9726i	−0.0477944	−	0.998857i
$577$		−	43.3548i		−	1.80488i	−0.430812	−	0.902442i	$-0.641773\pi$
$577$		−	43.3548i		−	1.80488i	0.430812	−	0.902442i	$-0.358227\pi$
$578$	−11.9980	+	8.45642i	−0.499052	+	0.351741i
$579$	−12.2873	+	7.33609i	−0.510644	+	0.304878i
$580$		0			0
$581$	−2.68699			−0.111475
$582$	−4.24385	+	9.53901i	−0.175913	+	0.395405i
$583$	−1.26572			−0.0524209
$584$	−3.89907	+	1.08355i	−0.161345	+	0.0448377i
$585$		0			0
$586$	−4.88839	−	6.93568i	−0.201938	−	0.286510i
$587$	6.88810			0.284302			0.142151	−	0.989845i	$-0.454598\pi$
$587$	6.88810			0.284302			0.142151	+	0.989845i	$0.454598\pi$
$588$	−21.6275	+	4.27957i	−0.891905	+	0.176486i
$589$			60.4781i			2.49196i
$590$		0			0
$591$	−16.0764	+	9.59835i	−0.661295	+	0.394823i
$592$	26.3008	+	21.5212i	1.08096	+	0.884517i
$593$	−0.894469			−0.0367314			−0.0183657	−	0.999831i	$-0.505846\pi$
$593$	−0.894469			−0.0367314			−0.0183657	+	0.999831i	$0.505846\pi$
$594$	1.44029	+	1.86390i	0.0590958	+	0.0764768i
$595$		0			0
$596$	−1.55577	+	4.35797i	−0.0637268	+	0.178509i
$597$	8.49593	−	5.07246i	0.347715	−	0.207602i
$598$	−10.9778	−	15.5753i	−0.448914	−	0.636922i
$599$	−11.5836			−0.473292			−0.236646	−	0.971596i	$-0.576048\pi$
$599$	−11.5836			−0.473292			−0.236646	+	0.971596i	$0.576048\pi$
$600$		0			0
$601$	24.9480			1.01765			0.508824	−	0.860870i	$-0.330080\pi$
$601$	24.9480			1.01765			0.508824	+	0.860870i	$0.330080\pi$
$602$	−1.93196	−	2.74107i	−0.0787407	−	0.111718i
$603$	12.3260	+	6.64292i	0.501955	+	0.270521i
$604$	−6.48602	−	2.31547i	−0.263912	−	0.0942151i
$605$		0			0
$606$	−34.2705	−	15.2467i	−1.39214	−	0.619357i
$607$	21.8741			0.887843			0.443922	−	0.896066i	$-0.353587\pi$
$607$	21.8741			0.887843			0.443922	+	0.896066i	$0.353587\pi$
$608$	−34.4486	−	2.47878i	−1.39708	−	0.100528i
$609$	−6.22593	−	10.4279i	−0.252287	−	0.422560i
$610$		0			0
$611$		−	28.2375i		−	1.14237i
$612$	10.3367	+	11.4671i	0.417835	+	0.463532i
$613$	−25.8339			−1.04342			−0.521711	−	0.853122i	$-0.674706\pi$
$613$	−25.8339			−1.04342			−0.521711	+	0.853122i	$0.674706\pi$
$614$	−5.47398	−	7.76652i	−0.220912	−	0.313431i
$615$		0			0
$616$	−0.696435	+	0.193539i	−0.0280602	+	0.00779792i
$617$	−27.5641			−1.10969			−0.554845	−	0.831954i	$-0.687222\pi$
$617$	−27.5641			−1.10969			−0.554845	+	0.831954i	$0.687222\pi$
$618$	16.2464	+	7.22794i	0.653527	+	0.290750i
$619$	−22.2136			−0.892841			−0.446421	−	0.894823i	$-0.647301\pi$
$619$	−22.2136			−0.892841			−0.446421	+	0.894823i	$0.647301\pi$
$620$		0			0
$621$	0.714619	+	16.2542i	0.0286767	+	0.652259i
$622$	25.4965	−	17.9704i	1.02232	−	0.720546i
$623$			10.9643i			0.439275i
$624$	4.38276	−	29.4898i	0.175451	−	1.18054i
$625$		0			0
$626$	−8.99114	−	12.7567i	−0.359358	−	0.509860i
$627$	2.91050	−	1.73770i	0.116234	−	0.0693972i
$628$	6.16669	−	17.2739i	0.246078	−	0.689305i
$629$	−21.8605			−0.871635
$630$		0			0
$631$			26.2225i			1.04390i	0.852975	+	0.521951i	$0.174796\pi$
$631$			26.2225i			1.04390i	−0.852975	+	0.521951i	$0.825204\pi$
$632$	7.88551	−	2.19138i	0.313669	−	0.0871685i
$633$	−7.24246	−	12.1305i	−0.287862	−	0.482144i
$634$	−19.8554	−	28.1710i	−0.788558	−	1.11881i
$635$		0			0
$636$	−2.65515	−	13.4183i	−0.105284	−	0.532069i
$637$	−27.3875			−1.08513
$638$	2.29695	+	3.25893i	0.0909371	+	0.129022i
$639$	4.88290	−	9.06030i	0.193165	−	0.358420i
$640$		0			0
$641$		−	47.0436i		−	1.85811i	−0.369940	−	0.929056i	$-0.620622\pi$
$641$		−	47.0436i		−	1.85811i	0.369940	−	0.929056i	$-0.379378\pi$
$642$	−29.7492	−	13.2353i	−1.17411	−	0.522354i
$643$		−	18.1696i		−	0.716538i	−0.933618	−	0.358269i	$-0.883367\pi$
$643$		−	18.1696i		−	0.716538i	0.933618	−	0.358269i	$-0.116633\pi$
$644$	−4.70200	−	1.67859i	−0.185285	−	0.0661455i
$645$		0			0
$646$	18.1595	−	12.7992i	0.714478	−	0.503577i
$647$			36.9324i			1.45196i	0.687715	+	0.725981i	$0.258614\pi$
$647$			36.9324i			1.45196i	−0.687715	+	0.725981i	$0.741386\pi$
$648$	−16.7384	+	19.1788i	−0.657545	+	0.753416i
$649$	−4.00000			−0.157014
$650$		0			0
$651$	−11.7444	+	7.01197i	−0.460301	+	0.274821i
$652$	−19.9960	−	7.13846i	−0.783104	−	0.279564i
$653$		−	1.11710i		−	0.0437155i	−0.999761	−	0.0218577i	$-0.993042\pi$
$653$		−	1.11710i		−	0.0437155i	0.999761	−	0.0218577i	$-0.00695809\pi$
$654$	3.40114	−	7.64483i	0.132995	−	0.298937i
$655$		0			0
$656$	13.3794	−	16.3508i	0.522378	−	0.638390i
$657$	3.77851	+	2.03637i	0.147414	+	0.0794463i
$658$	−4.26228	−	6.04735i	−0.166161	−	0.235750i
$659$			30.7865i			1.19927i	0.800273	+	0.599636i	$0.204688\pi$
$659$			30.7865i			1.19927i	−0.800273	+	0.599636i	$0.795312\pi$
$660$		0			0
$661$		−	11.5686i		−	0.449966i	−0.974363	−	0.224983i	$-0.927767\pi$
$661$		−	11.5686i		−	0.449966i	0.974363	−	0.224983i	$-0.0722326\pi$
$662$	15.2499	−	10.7484i	0.592703	−	0.417748i
$663$	9.83124	+	16.4665i	0.381814	+	0.639505i
$664$	2.55240	+	9.18461i	0.0990523	+	0.356432i
$665$		0			0
$666$	−4.30233	−	35.7875i	−0.166712	−	1.38674i
$667$			27.5389i			1.06631i
$668$	25.1181	+	8.96700i	0.971847	+	0.346944i
$669$	18.2982	+	30.6479i	0.707449	+	1.18492i
$670$		0			0
$671$	2.83153			0.109310
$672$	−3.51269	−	6.97709i	−0.135505	−	0.269147i
$673$			30.4072i			1.17211i	0.810271	+	0.586056i	$0.199320\pi$
$673$			30.4072i			1.17211i	−0.810271	+	0.586056i	$0.800680\pi$
$674$	−22.3950	−	31.7742i	−0.862623	−	1.22389i
$675$		0			0
$676$	3.71034	−	10.3933i	0.142705	−	0.399741i
$677$		−	29.9608i		−	1.15149i	−0.817631	−	0.575743i	$-0.804713\pi$
$677$		−	29.9608i		−	1.15149i	0.817631	−	0.575743i	$-0.195287\pi$
$678$	22.8860	+	10.1819i	0.878933	+	0.391032i
$679$			3.39813i			0.130408i
$680$		0			0
$681$	23.9772	+	40.1598i	0.918809	+	1.53893i
$682$	3.67038	−	2.58695i	0.140546	−	0.0990593i
$683$	30.8345			1.17985			0.589925	−	0.807458i	$-0.299157\pi$
$683$	30.8345			1.17985			0.589925	+	0.807458i	$0.299157\pi$
$684$	24.5273	+	27.2098i	0.937825	+	1.04039i
$685$		0			0
$686$	−12.3164	+	8.68081i	−0.470242	+	0.331435i
$687$	−14.3527	+	8.56923i	−0.547590	+	0.326936i
$688$	−7.53429	+	9.20755i	−0.287242	+	0.351035i
$689$		−	16.9919i		−	0.647339i
$690$		0			0
$691$	−19.2293			−0.731517			−0.365758	−	0.930710i	$-0.619190\pi$
$691$	−19.2293			−0.731517			−0.365758	+	0.930710i	$0.619190\pi$
$692$	26.1765	+	9.34485i	0.995080	+	0.355238i
$693$	0.674901	+	0.363727i	0.0256374	+	0.0138169i
$694$	12.6843	−	8.94013i	0.481490	−	0.339363i
$695$		0			0
$696$	−29.7303	+	31.1869i	−1.12692	+	1.18214i
$697$			13.5903i			0.514770i
$698$	−25.7509	−	36.5356i	−0.974687	−	1.38289i
$699$	1.14616	+	1.91971i	0.0433516	+	0.0726102i
$700$		0			0
$701$	−25.8972			−0.978126			−0.489063	−	0.872249i	$-0.662661\pi$
$701$	−25.8972			−0.978126			−0.489063	+	0.872249i	$0.662661\pi$
$702$	−25.0222	+	19.3353i	−0.944401	+	0.729765i
$703$	−51.8716			−1.95637
$704$	1.32310	+	2.19670i	0.0498663	+	0.0827911i
$705$		0			0
$706$	−24.8119	+	17.4879i	−0.933809	+	0.658165i
$707$	−12.2083			−0.459142
$708$	−8.39093	−	42.4050i	−0.315350	−	1.59368i
$709$			6.00828i			0.225646i	0.993615	+	0.112823i	$0.0359893\pi$
$709$			6.00828i			0.225646i	−0.993615	+	0.112823i	$0.964011\pi$
$710$		0			0
$711$	−7.64169	−	4.11837i	−0.286586	−	0.154451i
$712$	37.4779	−	10.4151i	1.40454	−	0.390322i
$713$	31.0158			1.16155
$714$	4.59098	+	2.04250i	0.171813	+	0.0764386i
$715$		0			0
$716$	9.77225	+	3.48864i	0.365206	+	0.130376i
$717$	3.73888	+	6.26230i	0.139631	+	0.233870i
$718$	39.6632	−	27.9554i	1.48022	−	1.04328i
$719$	3.34264			0.124659			0.0623297	−	0.998056i	$-0.480147\pi$
$719$	3.34264			0.124659			0.0623297	+	0.998056i	$0.480147\pi$
$720$		0			0
$721$	5.78755			0.215540
$722$	21.1268	−	14.8906i	0.786259	−	0.554169i
$723$	−17.3749	−	29.1015i	−0.646181	−	1.08230i
$724$	−4.89388	−	1.74709i	−0.181880	−	0.0649300i
$725$		0			0
$726$	24.3880	+	10.8501i	0.905124	+	0.402685i
$727$	−15.4120			−0.571600			−0.285800	−	0.958289i	$-0.592259\pi$
$727$	−15.4120			−0.571600			−0.285800	+	0.958289i	$0.592259\pi$
$728$	−2.59819	−	9.34938i	−0.0962953	−	0.346511i
$729$	26.8958	−	2.36954i	0.996142	−	0.0877607i
$730$		0			0
$731$		−	7.65306i		−	0.283059i
$732$	5.93978	+	30.0177i	0.219541	+	1.10949i
$733$	42.7008			1.57719			0.788594	−	0.614914i	$-0.210809\pi$
$733$	42.7008			1.57719			0.788594	+	0.614914i	$0.210809\pi$
$734$	−32.3551	+	22.8044i	−1.19425	+	0.841727i
$735$		0			0
$736$	−1.27123	+	17.6668i	−0.0468580	+	0.651206i
$737$	−1.49612			−0.0551103
$738$	−22.2485	+	2.67469i	−0.818979	+	0.0984567i
$739$	−30.4546			−1.12029			−0.560145	−	0.828395i	$-0.689254\pi$
$739$	−30.4546			−1.12029			−0.560145	+	0.828395i	$0.689254\pi$
$740$		0			0
$741$	23.3280	+	39.0724i	0.856976	+	1.43536i
$742$	−2.56482	−	3.63898i	−0.0941575	−	0.133591i
$743$		−	49.8954i		−	1.83048i	−0.402906	−	0.915242i	$-0.632000\pi$
$743$		−	49.8954i		−	1.83048i	0.402906	−	0.915242i	$-0.368000\pi$
$744$	35.1243	+	33.4839i	1.28772	+	1.22758i
$745$		0			0
$746$	16.0831	−	11.3357i	0.588846	−	0.415029i
$747$	4.79685	−	8.90062i	0.175507	−	0.325657i
$748$	−1.55355	−	0.554607i	−0.0568033	−	0.0202785i
$749$	−10.5977			−0.387232
$750$		0			0
$751$			3.81321i			0.139146i	0.997577	+	0.0695730i	$0.0221637\pi$
$751$			3.81321i			0.139146i	−0.997577	+	0.0695730i	$0.977836\pi$
$752$	−16.6221	+	20.3137i	−0.606147	+	0.740763i
$753$	26.0750	−	15.5680i	0.950228	−	0.567329i
$754$	−43.7499	+	30.8357i	−1.59328	+	1.12297i
$755$		0			0
$756$	−2.44020	+	7.91780i	−0.0887493	+	0.287968i
$757$	−38.1793			−1.38765			−0.693825	−	0.720144i	$-0.744076\pi$
$757$	−38.1793			−1.38765			−0.693825	+	0.720144i	$0.744076\pi$
$758$	−9.01468	+	6.35371i	−0.327428	+	0.230777i
$759$	−0.891171	−	1.49263i	−0.0323475	−	0.0541792i
$760$		0			0
$761$			10.7460i			0.389543i	0.980849	+	0.194772i	$0.0623966\pi$
$761$			10.7460i			0.389543i	−0.980849	+	0.194772i	$0.937603\pi$
$762$	11.1675	+	4.96836i	0.404556	+	0.179985i
$763$		−	2.72336i		−	0.0985921i
$764$	8.24094	−	23.0842i	0.298147	−	0.835158i
$765$		0			0
$766$	22.6810	+	32.1799i	0.819496	+	1.16271i
$767$		−	53.6985i		−	1.93894i
$768$	−20.5122	+	18.6346i	−0.740170	+	0.672419i
$769$	−1.13172			−0.0408109			−0.0204055	−	0.999792i	$-0.506496\pi$
$769$	−1.13172			−0.0408109			−0.0204055	+	0.999792i	$0.506496\pi$
$770$		0			0
$771$	−1.03513	−	1.73376i	−0.0372795	−	0.0624399i
$772$	15.5626	+	5.55577i	0.560111	+	0.199957i
$773$		−	13.7144i		−	0.493274i	−0.969108	−	0.246637i	$-0.920675\pi$
$773$		−	13.7144i		−	0.493274i	0.969108	−	0.246637i	$-0.0793255\pi$
$774$	12.5287	−	1.50619i	0.450336	−	0.0541388i
$775$		0			0
$776$	11.6154	−	3.22792i	0.416969	−	0.115876i
$777$	−6.01411	−	10.0731i	−0.215755	−	0.361371i
$778$	21.4134	−	15.0926i	0.767709	−	0.541095i
$779$			32.2477i			1.15539i
$780$		0			0
$781$			1.09973i			0.0393513i
$782$	−6.56398	−	9.31301i	−0.234727	−	0.333033i
$783$	45.6569	−	2.00731i	1.63164	−	0.0717354i
$784$	19.7022	+	16.1218i	0.703649	+	0.575777i
$785$		0			0
$786$	8.88839	−	19.9787i	0.317038	−	0.712615i
$787$			32.6374i			1.16340i	0.813405	+	0.581698i	$0.197612\pi$
$787$			32.6374i			1.16340i	−0.813405	+	0.581698i	$0.802388\pi$
$788$	20.3617	+	7.26902i	0.725357	+	0.258948i
$789$	22.8824	−	13.6619i	0.814636	−	0.486375i
$790$		0			0
$791$	8.15281			0.289880
$792$	0.602189	−	2.65244i	0.0213978	−	0.0942504i
$793$			38.0122i			1.34985i
$794$	−5.75446	+	4.05585i	−0.204218	+	0.143937i
$795$		0			0
$796$	−10.7606	−	3.84148i	−0.381400	−	0.136157i
$797$			39.1293i			1.38603i	0.720923	+	0.693015i	$0.243718\pi$
$797$			39.1293i			1.38603i	−0.720923	+	0.693015i	$0.756282\pi$
$798$	10.8937	+	4.84653i	0.385632	+	0.171565i
$799$		−	16.8842i		−	0.597319i
$800$		0			0
$801$	−36.3191	−	19.5736i	−1.28327	−	0.691599i
$802$	13.6952	+	19.4308i	0.483593	+	0.686124i
$803$	−0.458631			−0.0161847
$804$	−3.13846	−	15.8607i	−0.110685	−	0.559365i
$805$		0			0
$806$	34.7288	+	49.2734i	1.22327	+	1.73558i
$807$	−2.50813	−	4.20090i	−0.0882903	−	0.147879i
$808$	11.5968	+	41.7303i	0.407976	+	1.46807i
$809$			25.5481i			0.898222i	0.893476	+	0.449111i	$0.148259\pi$
$809$			25.5481i			0.898222i	−0.893476	+	0.449111i	$0.851741\pi$
$810$		0			0
$811$	5.63898			0.198011			0.0990057	−	0.995087i	$-0.468434\pi$
$811$	5.63898			0.198011			0.0990057	+	0.995087i	$0.468434\pi$
$812$	−4.71502	+	13.2076i	−0.165465	+	0.463494i
$813$	5.79587	−	3.46040i	0.203270	−	0.121362i
$814$	2.21880	+	3.14805i	0.0777691	+	0.110339i
$815$		0			0
$816$	2.62061	−	17.6330i	0.0917395	−	0.617277i
$817$		−	18.1595i		−	0.635322i
$818$	20.3508	−	14.3436i	0.711549	−	0.501513i
$819$	−4.88290	+	9.06030i	−0.170622	+	0.316592i
$820$		0			0
$821$	26.8248			0.936192			0.468096	−	0.883678i	$-0.344940\pi$
$821$	26.8248			0.936192			0.468096	+	0.883678i	$0.344940\pi$
$822$	−3.62476	−	1.61263i	−0.126428	−	0.0562471i
$823$	8.35909			0.291379			0.145690	−	0.989330i	$-0.453460\pi$
$823$	8.35909			0.291379			0.145690	+	0.989330i	$0.453460\pi$
$824$	−5.49766	−	19.7829i	−0.191520	−	0.689169i
$825$		0			0
$826$	−8.10546	−	11.5001i	−0.282025	−	0.400139i
$827$	6.27366			0.218156			0.109078	−	0.994033i	$-0.465210\pi$
$827$	6.27366			0.218156			0.109078	+	0.994033i	$0.465210\pi$
$828$	13.9544	−	12.5787i	0.484947	−	0.437139i
$829$			8.61230i			0.299118i	0.988753	+	0.149559i	$0.0477853\pi$
$829$			8.61230i			0.299118i	−0.988753	+	0.149559i	$0.952215\pi$
$830$		0			0
$831$	19.3962	+	32.4869i	0.672845	+	1.12696i
$832$	−29.4898	+	17.7622i	−1.02237	+	0.615792i
$833$	−16.3759			−0.567392
$834$	−8.02906	−	3.57208i	−0.278023	−	0.123691i
$835$		0			0
$836$	−3.68633	−	1.31600i	−0.127494	−	0.0455147i
$837$	−2.26074	−	51.4212i	−0.0781426	−	1.77738i
$838$	10.8692	+	15.4213i	0.375469	+	0.532718i
$839$	−2.93969			−0.101490			−0.0507448	−	0.998712i	$-0.516160\pi$
$839$	−2.93969			−0.101490			−0.0507448	+	0.998712i	$0.516160\pi$
$840$		0			0
$841$	48.3548			1.66741
$842$	13.6589	+	19.3794i	0.470718	+	0.667858i
$843$	−30.8140	+	18.3974i	−1.06129	+	0.633640i
$844$	−5.48486	+	15.3640i	−0.188796	+	0.528850i
$845$		0			0
$846$	27.6408	−	3.32295i	0.950312	−	0.114245i
$847$	8.68787			0.298519
$848$	−10.0023	+	12.2237i	−0.343482	+	0.419764i
$849$	−1.83903	+	1.09798i	−0.0631153	+	0.0376827i
$850$		0			0
$851$			26.6020i			0.911906i
$852$	−11.6585	+	2.30693i	−0.399413	+	0.0790342i
$853$	−34.2193			−1.17165			−0.585824	−	0.810439i	$-0.699229\pi$
$853$	−34.2193			−1.17165			−0.585824	+	0.810439i	$0.699229\pi$
$854$	5.73770	+	8.14069i	0.196340	+	0.278569i
$855$		0			0
$856$	10.0669	+	36.2249i	0.344079	+	1.23814i
$857$	−0.519916			−0.0177600			−0.00888000	−	0.999961i	$-0.502827\pi$
$857$	−0.519916			−0.0177600			−0.00888000	+	0.999961i	$0.502827\pi$
$858$	1.37343	−	3.08708i	0.0468880	−	0.105391i
$859$	32.9724			1.12500			0.562502	−	0.826796i	$-0.309839\pi$
$859$	32.9724			1.12500			0.562502	+	0.826796i	$0.309839\pi$
$860$		0			0
$861$	−6.26230	+	3.73888i	−0.213418	+	0.127421i
$862$	33.5121	−	23.6199i	1.14143	−	0.804499i
$863$		−	21.8453i		−	0.743623i	−0.928308	−	0.371811i	$-0.878737\pi$
$863$		−	21.8453i		−	0.743623i	0.928308	−	0.371811i	$-0.121263\pi$
$864$	29.3824	+	0.819839i	0.999611	+	0.0278915i
$865$		0			0
$866$	−19.2671	−	27.3363i	−0.654724	−	0.928926i
$867$	−9.21587	−	15.4358i	−0.312987	−	0.524227i
$868$	14.8750	+	5.31030i	0.504892	+	0.180243i
$869$	0.927539			0.0314646
$870$		0			0
$871$		−	20.0848i		−	0.680549i
$872$	−9.30892	+	2.58695i	−0.315240	+	0.0876051i
$873$	−11.2563	−	6.06638i	−0.380967	−	0.205316i
$874$	−15.5753	−	22.0983i	−0.526843	−	0.747488i
$875$		0			0
$876$	−0.962085	−	4.86206i	−0.0325058	−	0.164274i
$877$	37.2187			1.25679			0.628393	−	0.777896i	$-0.283713\pi$
$877$	37.2187			1.25679			0.628393	+	0.777896i	$0.283713\pi$
$878$	6.40155	+	9.08255i	0.216042	+	0.306521i
$879$	8.92294	−	5.32740i	0.300963	−	0.179689i
$880$		0			0
$881$			17.2984i			0.582796i	0.956602	+	0.291398i	$0.0941205\pi$
$881$			17.2984i			0.582796i	−0.956602	+	0.291398i	$0.905880\pi$
$882$	−3.22292	−	26.8088i	−0.108521	−	0.902698i
$883$			51.3234i			1.72717i	0.504203	+	0.863585i	$0.331786\pi$
$883$			51.3234i			1.72717i	−0.504203	+	0.863585i	$0.668214\pi$
$884$	7.44539	−	20.8558i	0.250416	−	0.701456i
$885$		0			0
$886$	−15.0047	+	10.5756i	−0.504094	+	0.355294i
$887$		−	15.3867i		−	0.516635i	−0.966060	−	0.258318i	$-0.916832\pi$
$887$		−	15.3867i		−	0.516635i	0.966060	−	0.258318i	$-0.0831681\pi$
$888$	−28.7189	+	30.1259i	−0.963742	+	1.01096i
$889$	3.97825			0.133426
$890$		0			0
$891$	−2.40968	+	1.58627i	−0.0807275	+	0.0531421i
$892$	13.8576	−	38.8174i	0.463986	−	1.29970i
$893$		−	40.0635i		−	1.34067i
$894$	−5.17799	−	2.30366i	−0.173178	−	0.0770459i
$895$		0			0
$896$	−3.63445	+	8.25525i	−0.121418	+	0.275789i
$897$	20.0381	−	11.9636i	0.669051	−	0.399454i
$898$	10.9864	+	15.5876i	0.366622	+	0.520165i
$899$		−	87.1211i		−	2.90565i
$900$		0			0
$901$		−	10.1600i		−	0.338479i
$902$	1.95709	−	1.37939i	0.0651641	−	0.0459288i
$903$	3.52646	−	2.10546i	0.117353	−	0.0700653i
$904$	−7.74444	−	27.8678i	−0.257576	−	0.926868i
$905$		0			0
$906$	3.42856	−	7.70647i	0.113906	−	0.256030i
$907$		−	34.3304i		−	1.13992i	−0.821671	−	0.569962i	$-0.806958\pi$
$907$		−	34.3304i		−	1.13992i	0.821671	−	0.569962i	$-0.193042\pi$
$908$	18.1584	−	50.8648i	0.602608	−	1.68801i
$909$	21.7945	−	40.4400i	0.722878	−	1.34131i
$910$		0			0
$911$	−20.7856			−0.688657			−0.344328	−	0.938849i	$-0.611893\pi$
$911$	−20.7856			−0.688657			−0.344328	+	0.938849i	$0.611893\pi$
$912$	6.21829	−	41.8403i	0.205908	−	1.38547i
$913$			1.08035i			0.0357542i
$914$	22.8951	+	32.4837i	0.757304	+	1.07447i
$915$		0			0
$916$	18.1786	+	6.48965i	0.600637	+	0.214424i
$917$		−	7.11710i		−	0.235027i
$918$	−14.9616	+	11.5613i	−0.493807	+	0.381578i
$919$		−	35.6290i		−	1.17529i	−0.809119	−	0.587645i	$-0.800055\pi$
$919$		−	35.6290i		−	1.17529i	0.809119	−	0.587645i	$-0.199945\pi$
$920$		0			0
$921$	9.99184	−	5.96558i	0.329242	−	0.196573i
$922$	−33.7733	+	23.8040i	−1.11226	+	0.783944i
$923$	−14.7634			−0.485944
$924$	−0.171843	−	0.868441i	−0.00565324	−	0.0285696i
$925$		0			0
$926$	−16.3524	+	11.5254i	−0.537372	+	0.378749i
$927$	−10.3320	+	19.1712i	−0.339347	+	0.629664i
$928$	49.6246	+	3.57078i	1.62901	+	0.117216i
$929$		−	44.9041i		−	1.47325i	−0.676299	−	0.736627i	$-0.736417\pi$
$929$		−	44.9041i		−	1.47325i	0.676299	−	0.736627i	$-0.263583\pi$
$930$		0			0
$931$	−38.8575			−1.27350
$932$	0.868006	−	2.43143i	0.0284325	−	0.0796441i
$933$	19.5842	+	32.8019i	0.641159	+	1.07389i
$934$	33.4862	−	23.6017i	1.09570	−	0.772271i
$935$		0			0
$936$	35.6080	+	8.08415i	1.16388	+	0.264239i
$937$			56.5086i			1.84606i	0.384731	+	0.923029i	$0.374294\pi$
$937$			56.5086i			1.84606i	−0.384731	+	0.923029i	$0.625706\pi$
$938$	−3.03168	−	4.30137i	−0.0989880	−	0.140445i
$939$	16.4118	−	9.79861i	0.535580	−	0.319765i
$940$		0			0
$941$	29.6334			0.966022			0.483011	−	0.875614i	$-0.339543\pi$
$941$	29.6334			0.966022			0.483011	+	0.875614i	$0.339543\pi$
$942$	20.5243	+	9.13115i	0.668718	+	0.297509i
$943$	16.5380			0.538553
$944$	−31.6099	+	38.6300i	−1.02881	+	1.25730i
$945$		0			0
$946$	−1.10209	+	0.776774i	−0.0358321	+	0.0252551i
$947$	−29.2810			−0.951504			−0.475752	−	0.879580i	$-0.657824\pi$
$947$	−29.2810			−0.951504			−0.475752	+	0.879580i	$0.657824\pi$
$948$	1.94573	+	9.83307i	0.0631943	+	0.319363i
$949$		−	6.15695i		−	0.199863i
$950$		0			0
$951$	36.2427	−	21.6385i	1.17525	−	0.701678i
$952$	−1.55355	−	5.59032i	−0.0503508	−	0.181183i
$953$	−40.2311			−1.30321			−0.651606	−	0.758557i	$-0.725905\pi$
$953$	−40.2311			−1.30321			−0.651606	+	0.758557i	$0.725905\pi$
$954$	16.6328	−	1.99958i	0.538508	−	0.0647388i
$955$		0			0
$956$	2.83153	−	7.93157i	0.0915781	−	0.256525i
$957$	−4.19270	+	2.50323i	−0.135531	+	0.0809180i
$958$	−43.8150	+	30.8816i	−1.41560	+	0.997739i
$959$	−1.29127			−0.0416972
$960$		0			0
$961$	−67.1203			−2.16517
$962$	−42.2614	+	29.7866i	−1.36256	+	0.960359i
$963$	18.9192	−	35.1048i	0.609662	−	1.13124i
$964$	−13.1584	+	36.8588i	−0.423803	+	1.18714i
$965$		0			0
$966$	2.48551	−	5.58676i	0.0799701	−	0.179751i
$967$	34.4522			1.10791			0.553954	−	0.832547i	$-0.313118\pi$
$967$	34.4522			1.10791			0.553954	+	0.832547i	$0.313118\pi$
$968$	−8.25270	−	29.6967i	−0.265252	−	0.954488i
$969$	13.9486	+	23.3627i	0.448094	+	0.750519i
$970$		0			0
$971$			26.9133i			0.863688i	0.901948	+	0.431844i	$0.142137\pi$
$971$			26.9133i			0.863688i	−0.901948	+	0.431844i	$0.857863\pi$
$972$	−21.8714	−	22.2181i	−0.701524	−	0.712646i
$973$	−2.86023			−0.0916948
$974$	−48.4550	+	34.1519i	−1.55260	+	1.09430i
$975$		0			0
$976$	22.3760	−	27.3454i	0.716239	−	0.875306i
$977$	41.9916			1.34343			0.671715	−	0.740810i	$-0.265558\pi$
$977$	41.9916			1.34343			0.671715	+	0.740810i	$0.265558\pi$
$978$	10.5701	−	23.7586i	0.337993	−	0.759716i
$979$	4.40837			0.140892
$980$		0			0
$981$	9.02109	+	4.86177i	0.288021	+	0.155224i
$982$	4.15262	+	5.89176i	0.132515	+	0.188014i
$983$			3.83856i			0.122431i	0.998125	+	0.0612156i	$0.0194977\pi$
$983$			3.83856i			0.122431i	−0.998125	+	0.0612156i	$0.980502\pi$
$984$	18.7288	+	17.8540i	0.597052	+	0.569166i
$985$		0			0
$986$	−26.1595	+	18.4377i	−0.833090	+	0.587176i
$987$	7.78007	−	4.64506i	0.247642	−	0.147854i
$988$	17.6668	−	49.4876i	0.562055	−	1.57441i
$989$	−9.31301			−0.296137
$990$		0			0
$991$		−	48.3440i		−	1.53570i	−0.640630	−	0.767850i	$-0.721327\pi$
$991$		−	48.3440i		−	1.53570i	0.640630	−	0.767850i	$-0.278673\pi$
$992$	4.02160	−	55.8899i	0.127686	−	1.77451i
$993$	11.7137	+	19.6194i	0.371722	+	0.622602i
$994$	−3.16174	+	2.22845i	−0.100284	+	0.0706821i
$995$		0			0
$996$	−11.4530	+	2.26628i	−0.362903	+	0.0718097i
$997$	23.5236			0.744998			0.372499	−	0.928032i	$-0.378501\pi$
$997$	23.5236			0.744998			0.372499	+	0.928032i	$0.378501\pi$
$998$	31.6522	−	22.3091i	1.00193	−	0.706181i
$999$	44.1036	−	1.93902i	1.39538	−	0.0613479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.m.d.299.13		16
3.2	odd	2		600.2.m.c.299.4		16
4.3	odd	2		2400.2.m.c.1199.5		16
5.2	odd	4		120.2.b.b.11.6	yes	8
5.3	odd	4		600.2.b.e.251.3		8
5.4	even	2	inner	600.2.m.d.299.4		16
8.3	odd	2		600.2.m.c.299.14		16
8.5	even	2		2400.2.m.d.1199.5		16
12.11	even	2		2400.2.m.d.1199.11		16
15.2	even	4		120.2.b.a.11.3	✓	8
15.8	even	4		600.2.b.f.251.6		8
15.14	odd	2		600.2.m.c.299.13		16
20.3	even	4		2400.2.b.e.2351.7		8
20.7	even	4		480.2.b.a.431.2		8
20.19	odd	2		2400.2.m.c.1199.12		16
24.5	odd	2		2400.2.m.c.1199.11		16
24.11	even	2	inner	600.2.m.d.299.3		16
40.3	even	4		600.2.b.f.251.5		8
40.13	odd	4		2400.2.b.f.2351.7		8
40.19	odd	2		600.2.m.c.299.3		16
40.27	even	4		120.2.b.a.11.4	yes	8
40.29	even	2		2400.2.m.d.1199.12		16
40.37	odd	4		480.2.b.b.431.2		8
60.23	odd	4		2400.2.b.f.2351.8		8
60.47	odd	4		480.2.b.b.431.1		8
60.59	even	2		2400.2.m.d.1199.6		16
120.29	odd	2		2400.2.m.c.1199.6		16
120.53	even	4		2400.2.b.e.2351.8		8
120.59	even	2	inner	600.2.m.d.299.14		16
120.77	even	4		480.2.b.a.431.1		8
120.83	odd	4		600.2.b.e.251.4		8
120.107	odd	4		120.2.b.b.11.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.3	✓	8	15.2	even	4
120.2.b.a.11.4	yes	8	40.27	even	4
120.2.b.b.11.5	yes	8	120.107	odd	4
120.2.b.b.11.6	yes	8	5.2	odd	4
480.2.b.a.431.1		8	120.77	even	4
480.2.b.a.431.2		8	20.7	even	4
480.2.b.b.431.1		8	60.47	odd	4
480.2.b.b.431.2		8	40.37	odd	4
600.2.b.e.251.3		8	5.3	odd	4
600.2.b.e.251.4		8	120.83	odd	4
600.2.b.f.251.5		8	40.3	even	4
600.2.b.f.251.6		8	15.8	even	4
600.2.m.c.299.3		16	40.19	odd	2
600.2.m.c.299.4		16	3.2	odd	2
600.2.m.c.299.13		16	15.14	odd	2
600.2.m.c.299.14		16	8.3	odd	2
600.2.m.d.299.3		16	24.11	even	2	inner
600.2.m.d.299.4		16	5.4	even	2	inner
600.2.m.d.299.13		16	1.1	even	1	trivial
600.2.m.d.299.14		16	120.59	even	2	inner
2400.2.b.e.2351.7		8	20.3	even	4
2400.2.b.e.2351.8		8	120.53	even	4
2400.2.b.f.2351.7		8	40.13	odd	4
2400.2.b.f.2351.8		8	60.23	odd	4
2400.2.m.c.1199.5		16	4.3	odd	2
2400.2.m.c.1199.6		16	120.29	odd	2
2400.2.m.c.1199.11		16	24.5	odd	2
2400.2.m.c.1199.12		16	20.19	odd	2
2400.2.m.d.1199.5		16	8.5	even	2
2400.2.m.d.1199.6		16	60.59	even	2
2400.2.m.d.1199.11		16	12.11	even	2
2400.2.m.d.1199.12		16	40.29	even	2

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.15595 - 0.814732i) q^{2} +(0.887900 + 1.48716i) q^{3} +(0.672424 - 1.88357i) q^{4} +(2.23800 + 0.995672i) q^{6} +0.797253 q^{7} +(-0.757320 - 2.72515i) q^{8} +(-1.42327 + 2.64089i) q^{9} +O(q^{10})\)	\(q+(1.15595 - 0.814732i) q^{2} +(0.887900 + 1.48716i) q^{3} +(0.672424 - 1.88357i) q^{4} +(2.23800 + 0.995672i) q^{6} +0.797253 q^{7} +(-0.757320 - 2.72515i) q^{8} +(-1.42327 + 2.64089i) q^{9} -0.320548i q^{11} +(3.39821 - 0.672424i) q^{12} +4.30324 q^{13} +(0.921582 - 0.649548i) q^{14} +(-3.09569 - 2.53312i) q^{16} +2.57305 q^{17} +(0.506399 + 4.21231i) q^{18} +6.10546 q^{19} +(0.707881 + 1.18564i) q^{21} +(-0.261161 - 0.370537i) q^{22} -3.13115i q^{23} +(3.38031 - 3.54592i) q^{24} +(4.97431 - 3.50598i) q^{26} +(-5.19114 + 0.228229i) q^{27} +(0.536093 - 1.50168i) q^{28} -8.79516 q^{29} +9.90557i q^{31} +(-5.64227 - 0.405993i) q^{32} +(0.476705 - 0.284615i) q^{33} +(2.97431 - 2.09635i) q^{34} +(4.01727 + 4.45663i) q^{36} -8.49593 q^{37} +(7.05758 - 4.97431i) q^{38} +(3.82085 + 6.39959i) q^{39} +5.28178i q^{41} +(1.78425 + 0.793803i) q^{42} -2.97431i q^{43} +(-0.603776 - 0.215544i) q^{44} +(-2.55105 - 3.61944i) q^{46} -6.56192i q^{47} +(1.01848 - 6.85293i) q^{48} -6.36439 q^{49} +(2.28461 + 3.82653i) q^{51} +(2.89360 - 8.10546i) q^{52} -3.94862i q^{53} +(-5.81473 + 4.49321i) q^{54} +(-0.603776 - 2.17264i) q^{56} +(5.42104 + 9.07977i) q^{57} +(-10.1667 + 7.16569i) q^{58} -12.4786i q^{59} +8.83339i q^{61} +(8.07038 + 11.4503i) q^{62} +(-1.13470 + 2.10546i) q^{63} +(-6.85293 + 4.12763i) q^{64} +(0.319161 - 0.717386i) q^{66} -4.66738i q^{67} +(1.73018 - 4.84653i) q^{68} +(4.65651 - 2.78015i) q^{69} -3.43077 q^{71} +(8.27471 + 1.87862i) q^{72} -1.43077i q^{73} +(-9.82085 + 6.92191i) q^{74} +(4.10546 - 11.5001i) q^{76} -0.255558i q^{77} +(9.63064 + 4.28461i) q^{78} +2.89360i q^{79} +(-4.94862 - 7.51739i) q^{81} +(4.30324 + 6.10546i) q^{82} -3.37031 q^{83} +(2.70924 - 0.536093i) q^{84} +(-2.42327 - 3.43815i) q^{86} +(-7.80922 - 13.0798i) q^{87} +(-0.873543 + 0.242757i) q^{88} +13.7526i q^{89} +3.43077 q^{91} +(-5.89774 - 2.10546i) q^{92} +(-14.7311 + 8.79516i) q^{93} +(-5.34620 - 7.58523i) q^{94} +(-4.40599 - 8.75141i) q^{96} +4.26230i q^{97} +(-7.35689 + 5.18527i) q^{98} +(0.846533 + 0.456225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) \) 16 * q - 2 * q^4 + 2 * q^6	\( 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * q^99

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