LMFDB - Embedded newform 279.2.i.a.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,2,Mod(64,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.i (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	279.163
Dual form			279.2.i.a.190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.190983 - 0.587785i) q^{2} +(1.30902 + 0.951057i) q^{4} +2.61803 q^{5} +(-2.42705 - 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.500000 - 1.53884i) q^{10} +(-0.618034 - 0.449028i) q^{11} +(1.50000 + 4.61653i) q^{13} +(-1.50000 + 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.190983 - 0.138757i) q^{17} +(1.54508 - 4.75528i) q^{19} +(3.42705 + 2.48990i) q^{20} +(-0.381966 + 0.277515i) q^{22} +(-4.42705 + 3.21644i) q^{23} +1.85410 q^{25} +3.00000 q^{26} +(-1.50000 - 4.61653i) q^{28} +(2.66312 - 8.19624i) q^{29} +(-5.54508 - 0.502029i) q^{31} +5.61803 q^{32} +(-0.0450850 - 0.138757i) q^{34} +(-6.35410 - 4.61653i) q^{35} +0.236068 q^{37} +(-2.50000 - 1.81636i) q^{38} +(4.73607 - 3.44095i) q^{40} +(-2.00000 + 6.15537i) q^{41} +(-1.42705 + 4.39201i) q^{43} +(-0.381966 - 1.17557i) q^{44} +(1.04508 + 3.21644i) q^{46} +(1.04508 + 3.21644i) q^{47} +(0.618034 + 1.90211i) q^{49} +(0.354102 - 1.08981i) q^{50} +(-2.42705 + 7.46969i) q^{52} +(-10.2812 + 7.46969i) q^{53} +(-1.61803 - 1.17557i) q^{55} -6.70820 q^{56} +(-4.30902 - 3.13068i) q^{58} +(-2.92705 - 9.00854i) q^{59} -6.94427 q^{61} +(-1.35410 + 3.16344i) q^{62} +(-0.0729490 + 0.224514i) q^{64} +(3.92705 + 12.0862i) q^{65} -4.23607 q^{67} +0.381966 q^{68} +(-3.92705 + 2.85317i) q^{70} +(0.0729490 - 0.0530006i) q^{71} +(6.92705 + 5.03280i) q^{73} +(0.0450850 - 0.138757i) q^{74} +(6.54508 - 4.75528i) q^{76} +(0.708204 + 2.17963i) q^{77} +(1.50000 + 4.61653i) q^{80} +(3.23607 + 2.35114i) q^{82} +(1.26393 - 3.88998i) q^{83} +(0.500000 - 0.363271i) q^{85} +(2.30902 + 1.67760i) q^{86} -1.70820 q^{88} +(-5.16312 - 3.75123i) q^{89} +(4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(4.04508 - 12.4495i) q^{95} +(4.28115 + 3.11044i) q^{97} +1.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 3 q^{7} + 5 q^{8} + 2 q^{10} + 2 q^{11} + 6 q^{13} - 6 q^{14} + 9 q^{16} + 3 q^{17} - 5 q^{19} + 7 q^{20} - 6 q^{22} - 11 q^{23} - 6 q^{25} + 12 q^{26} - 6 q^{28} - 5 q^{29}+ \cdots - 4 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 3 * q^7 + 5 * q^8 + 2 * q^10 + 2 * q^11 + 6 * q^13 - 6 * q^14 + 9 * q^16 + 3 * q^17 - 5 * q^19 + 7 * q^20 - 6 * q^22 - 11 * q^23 - 6 * q^25 + 12 * q^26 - 6 * q^28 - 5 * q^29 - 11 * q^31 + 18 * q^32 + 11 * q^34 - 12 * q^35 - 8 * q^37 - 10 * q^38 + 10 * q^40 - 8 * q^41 + q^43 - 6 * q^44 - 7 * q^46 - 7 * q^47 - 2 * q^49 - 12 * q^50 - 3 * q^52 - 21 * q^53 - 2 * q^55 - 15 * q^58 - 5 * q^59 + 8 * q^61 + 8 * q^62 - 7 * q^64 + 9 * q^65 - 8 * q^67 + 6 * q^68 - 9 * q^70 + 7 * q^71 + 21 * q^73 - 11 * q^74 + 15 * q^76 - 24 * q^77 + 6 * q^80 + 4 * q^82 + 14 * q^83 + 2 * q^85 + 7 * q^86 + 20 * q^88 - 5 * q^89 + 18 * q^91 - 22 * q^92 - 14 * q^94 + 5 * q^95 - 3 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	−0.860552	−	0.509363i	$-0.829881\pi$
$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	0.995597	+	0.0937362i	$0.0298810\pi$
$3$		0			0
$3$		0			0
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	2.61803			1.17082			0.585410	−	0.810737i	$-0.300933\pi$
$5$	2.61803			1.17082			0.585410	+	0.810737i	$0.300933\pi$
$6$		0			0
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	0.0255212	−	0.999674i	$-0.491875\pi$
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	−0.942860	+	0.333188i	$0.891875\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$		0			0
$10$	0.500000	−	1.53884i	0.158114	−	0.486624i
$11$	−0.618034	−	0.449028i	−0.186344	−	0.135387i	0.490702	−	0.871327i	$-0.336740\pi$
$11$	−0.618034	−	0.449028i	−0.186344	−	0.135387i	−0.677046	+	0.735940i	$0.736740\pi$
$12$		0			0
$13$	1.50000	+	4.61653i	0.416025	+	1.28039i	0.911331	+	0.411675i	$0.135056\pi$
$13$	1.50000	+	4.61653i	0.416025	+	1.28039i	−0.495306	+	0.868719i	$0.664944\pi$
$14$	−1.50000	+	1.08981i	−0.400892	+	0.291265i
$15$		0			0
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	0.190983	−	0.138757i	0.0463202	−	0.0336536i	−0.564384	−	0.825512i	$-0.690886\pi$
$17$	0.190983	−	0.138757i	0.0463202	−	0.0336536i	0.610704	+	0.791859i	$0.290886\pi$
$18$		0			0
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	−0.601851	−	0.798608i	$-0.705570\pi$
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	0.956318	−	0.292328i	$-0.0944300\pi$
$20$	3.42705	+	2.48990i	0.766312	+	0.556758i
$21$		0			0
$22$	−0.381966	+	0.277515i	−0.0814354	+	0.0591663i
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	−0.944295	−	0.329101i	$-0.893254\pi$
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	0.0211907	+	0.999775i	$0.493254\pi$
$24$		0			0
$25$	1.85410			0.370820
$26$	3.00000			0.588348
$27$		0			0
$28$	−1.50000	−	4.61653i	−0.283473	−	0.872441i
$29$	2.66312	−	8.19624i	0.494529	−	1.52200i	−0.323161	−	0.946344i	$-0.604746\pi$
$29$	2.66312	−	8.19624i	0.494529	−	1.52200i	0.817690	−	0.575659i	$-0.195254\pi$
$30$		0			0
$31$	−5.54508	−	0.502029i	−0.995927	−	0.0901670i
$31$	−5.54508	−	0.502029i	−0.995927	−	0.0901670i
$32$	5.61803			0.993137
$33$		0			0
$34$	−0.0450850	−	0.138757i	−0.00773201	−	0.0237967i
$35$	−6.35410	−	4.61653i	−1.07404	−	0.780335i
$36$		0			0
$37$	0.236068			0.0388093			0.0194047	−	0.999812i	$-0.493823\pi$
$37$	0.236068			0.0388093			0.0194047	+	0.999812i	$0.493823\pi$
$38$	−2.50000	−	1.81636i	−0.405554	−	0.294652i
$39$		0			0
$40$	4.73607	−	3.44095i	0.748838	−	0.544063i
$41$	−2.00000	+	6.15537i	−0.312348	+	0.961307i	0.664485	+	0.747302i	$0.268651\pi$
$41$	−2.00000	+	6.15537i	−0.312348	+	0.961307i	−0.976833	+	0.214005i	$0.931349\pi$
$42$		0			0
$43$	−1.42705	+	4.39201i	−0.217623	+	0.669775i	0.781334	+	0.624113i	$0.214540\pi$
$43$	−1.42705	+	4.39201i	−0.217623	+	0.669775i	−0.998957	+	0.0456620i	$0.985460\pi$
$44$	−0.381966	−	1.17557i	−0.0575835	−	0.177224i
$45$		0			0
$46$	1.04508	+	3.21644i	0.154089	+	0.474238i
$47$	1.04508	+	3.21644i	0.152441	+	0.469166i	0.997893	−	0.0648863i	$-0.0206685\pi$
$47$	1.04508	+	3.21644i	0.152441	+	0.469166i	−0.845451	+	0.534052i	$0.820668\pi$
$48$		0			0
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	0.354102	−	1.08981i	0.0500776	−	0.154123i
$51$		0			0
$52$	−2.42705	+	7.46969i	−0.336571	+	1.03586i
$53$	−10.2812	+	7.46969i	−1.41222	+	1.02604i	−0.419231	+	0.907880i	$0.637700\pi$
$53$	−10.2812	+	7.46969i	−1.41222	+	1.02604i	−0.992994	+	0.118162i	$0.962300\pi$
$54$		0			0
$55$	−1.61803	−	1.17557i	−0.218176	−	0.158514i
$56$	−6.70820			−0.896421
$57$		0			0
$58$	−4.30902	−	3.13068i	−0.565802	−	0.411079i
$59$	−2.92705	−	9.00854i	−0.381070	−	1.17281i	−0.939292	−	0.343120i	$-0.888516\pi$
$59$	−2.92705	−	9.00854i	−0.381070	−	1.17281i	0.558222	−	0.829692i	$-0.311484\pi$
$60$		0			0
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$	−1.35410	+	3.16344i	−0.171971	+	0.401757i
$63$		0			0
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	3.92705	+	12.0862i	0.487091	+	1.49911i
$66$		0			0
$67$	−4.23607			−0.517518			−0.258759	−	0.965942i	$-0.583314\pi$
$67$	−4.23607			−0.517518			−0.258759	+	0.965942i	$0.583314\pi$
$68$	0.381966			0.0463202
$69$		0			0
$70$	−3.92705	+	2.85317i	−0.469372	+	0.341019i
$71$	0.0729490	−	0.0530006i	0.00865746	−	0.00629001i	−0.583448	−	0.812150i	$-0.698297\pi$
$71$	0.0729490	−	0.0530006i	0.00865746	−	0.00629001i	0.592106	+	0.805860i	$0.298297\pi$
$72$		0			0
$73$	6.92705	+	5.03280i	0.810750	+	0.589044i	0.914048	−	0.405606i	$-0.132940\pi$
$73$	6.92705	+	5.03280i	0.810750	+	0.589044i	−0.103298	+	0.994650i	$0.532940\pi$
$74$	0.0450850	−	0.138757i	0.00524102	−	0.0161302i
$75$		0			0
$76$	6.54508	−	4.75528i	0.750773	−	0.545468i
$77$	0.708204	+	2.17963i	0.0807073	+	0.248392i
$78$		0			0
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$	1.50000	+	4.61653i	0.167705	+	0.516143i
$81$		0			0
$82$	3.23607	+	2.35114i	0.357364	+	0.259640i
$83$	1.26393	−	3.88998i	0.138735	−	0.426981i	−0.857418	−	0.514621i	$-0.827933\pi$
$83$	1.26393	−	3.88998i	0.138735	−	0.426981i	0.996152	+	0.0876401i	$0.0279326\pi$
$84$		0			0
$85$	0.500000	−	0.363271i	0.0542326	−	0.0394023i
$86$	2.30902	+	1.67760i	0.248988	+	0.180900i
$87$		0			0
$88$	−1.70820			−0.182095
$89$	−5.16312	−	3.75123i	−0.547290	−	0.397629i	0.279496	−	0.960147i	$-0.409833\pi$
$89$	−5.16312	−	3.75123i	−0.547290	−	0.397629i	−0.826785	+	0.562518i	$0.809833\pi$
$90$		0			0
$91$	4.50000	−	13.8496i	0.471728	−	1.45183i
$92$	−8.85410			−0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	4.04508	−	12.4495i	0.415017	−	1.27729i
$96$		0			0
$97$	4.28115	+	3.11044i	0.434685	+	0.315817i	0.783520	−	0.621367i	$-0.213422\pi$
$97$	4.28115	+	3.11044i	0.434685	+	0.315817i	−0.348834	+	0.937184i	$0.613422\pi$
$98$	1.23607			0.124862
$99$		0			0
$100$	2.42705	+	1.76336i	0.242705	+	0.176336i
$101$	3.85410	−	2.80017i	0.383497	−	0.278627i	−0.379288	−	0.925279i	$-0.623831\pi$
$101$	3.85410	−	2.80017i	0.383497	−	0.278627i	0.762786	+	0.646651i	$0.223831\pi$
$102$		0			0
$103$	−0.0450850	+	0.138757i	−0.00444235	+	0.0136722i	−0.953253	−	0.302173i	$-0.902288\pi$
$103$	−0.0450850	+	0.138757i	−0.00444235	+	0.0136722i	0.948811	+	0.315845i	$0.102288\pi$
$104$	8.78115	+	6.37988i	0.861063	+	0.625599i
$105$		0			0
$106$	2.42705	+	7.46969i	0.235736	+	0.725521i
$107$	0.881966	−	0.640786i	0.0852629	−	0.0619471i	−0.544337	−	0.838867i	$-0.683219\pi$
$107$	0.881966	−	0.640786i	0.0852629	−	0.0619471i	0.629600	+	0.776919i	$0.283219\pi$
$108$		0			0
$109$	−2.60081	−	8.00448i	−0.249113	−	0.766690i	−0.994933	−	0.100543i	$-0.967942\pi$
$109$	−2.60081	−	8.00448i	−0.249113	−	0.766690i	0.745820	−	0.666147i	$-0.232058\pi$
$110$	−1.00000	+	0.726543i	−0.0953463	+	0.0692731i
$111$		0			0
$112$	1.71885	−	5.29007i	0.162416	−	0.499864i
$113$	−1.50000	−	1.08981i	−0.141108	−	0.102521i	0.514992	−	0.857195i	$-0.327795\pi$
$113$	−1.50000	−	1.08981i	−0.141108	−	0.102521i	−0.656100	+	0.754674i	$0.727795\pi$
$114$		0			0
$115$	−11.5902	+	8.42075i	−1.08079	+	0.785239i
$116$	11.2812	−	8.19624i	1.04743	−	0.761002i
$117$		0			0
$118$	−5.85410			−0.538914
$119$	−0.708204			−0.0649209
$120$		0			0
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	−1.32624	+	4.08174i	−0.120072	+	0.369543i
$123$		0			0
$124$	−6.78115	−	5.93085i	−0.608966	−	0.532606i
$125$	−8.23607			−0.736656
$126$		0			0
$127$	3.16312	+	9.73508i	0.280681	+	0.863849i	0.987660	+	0.156614i	$0.0500577\pi$
$127$	3.16312	+	9.73508i	0.280681	+	0.863849i	−0.706979	+	0.707235i	$0.749942\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$		0			0
$130$	7.85410			0.688850
$131$	0.0729490	+	0.0530006i	0.00637359	+	0.00463068i	0.590967	−	0.806695i	$-0.298746\pi$
$131$	0.0729490	+	0.0530006i	0.00637359	+	0.00463068i	−0.584594	+	0.811326i	$0.698746\pi$
$132$		0			0
$133$	−12.1353	+	8.81678i	−1.05226	+	0.764512i
$134$	−0.809017	+	2.48990i	−0.0698884	+	0.215094i
$135$		0			0
$136$	0.163119	−	0.502029i	0.0139873	−	0.0430486i
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	0.999421	−	0.0340275i	$-0.0108334\pi$
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	−0.828549	+	0.559916i	$0.810833\pi$
$138$		0			0
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	0.997999	−	0.0632239i	$-0.0201382\pi$
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	−0.844561	+	0.535460i	$0.820138\pi$
$140$	−3.92705	−	12.0862i	−0.331896	−	1.02147i
$141$		0			0
$142$	−0.0172209	−	0.0530006i	−0.00144515	−	0.00444771i
$143$	1.14590	−	3.52671i	0.0958248	−	0.294918i
$144$		0			0
$145$	6.97214	−	21.4580i	0.579004	−	1.78199i
$146$	4.28115	−	3.11044i	0.354311	−	0.257422i
$147$		0			0
$148$	0.309017	+	0.224514i	0.0254010	+	0.0184549i
$149$	17.0344			1.39552			0.697758	−	0.716334i	$-0.254181\pi$
$149$	17.0344			1.39552			0.697758	+	0.716334i	$0.254181\pi$
$150$		0			0
$151$	15.7812	+	11.4657i	1.28425	+	0.933064i	0.999673	−	0.0255888i	$-0.00814604\pi$
$151$	15.7812	+	11.4657i	1.28425	+	0.933064i	0.284579	+	0.958652i	$0.408146\pi$
$152$	−3.45492	−	10.6331i	−0.280231	−	0.862461i
$153$		0			0
$154$	1.41641			0.114137
$155$	−14.5172	−	1.31433i	−1.16605	−	0.105569i
$156$		0			0
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$		0			0
$159$		0			0
$160$	14.7082			1.16279
$161$	16.4164			1.29379
$162$		0			0
$163$	10.2812	−	7.46969i	0.805282	−	0.585072i	−0.107177	−	0.994240i	$-0.534181\pi$
$163$	10.2812	−	7.46969i	0.805282	−	0.585072i	0.912459	+	0.409168i	$0.134181\pi$
$164$	−8.47214	+	6.15537i	−0.661563	+	0.480653i
$165$		0			0
$166$	−2.04508	−	1.48584i	−0.158729	−	0.115324i
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	−0.777829	−	0.628476i	$-0.783679\pi$
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	0.998686	−	0.0512518i	$-0.0163211\pi$
$168$		0			0
$169$	−8.54508	+	6.20837i	−0.657314	+	0.477567i
$170$	−0.118034	−	0.363271i	−0.00905279	−	0.0278616i
$171$		0			0
$172$	−6.04508	+	4.39201i	−0.460933	+	0.334888i
$173$	−0.281153	−	0.865300i	−0.0213757	−	0.0657875i	0.939800	−	0.341726i	$-0.111011\pi$
$173$	−0.281153	−	0.865300i	−0.0213757	−	0.0657875i	−0.961175	+	0.275938i	$0.911011\pi$
$174$		0			0
$175$	−4.50000	−	3.26944i	−0.340168	−	0.247147i
$176$	0.437694	−	1.34708i	0.0329924	−	0.101540i
$177$		0			0
$178$	−3.19098	+	2.31838i	−0.239174	+	0.173770i
$179$	16.0172	+	11.6372i	1.19718	+	0.869805i	0.994005	−	0.109337i	$-0.0348728\pi$
$179$	16.0172	+	11.6372i	1.19718	+	0.869805i	0.203179	+	0.979142i	$0.434873\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−7.28115	−	5.29007i	−0.539715	−	0.392126i
$183$		0			0
$184$	−3.78115	+	11.6372i	−0.278750	+	0.857905i
$185$	0.618034			0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	−1.69098	+	5.20431i	−0.123328	+	0.379563i
$189$		0			0
$190$	−6.54508	−	4.75528i	−0.474830	−	0.344984i
$191$	16.0902			1.16424			0.582122	−	0.813102i	$-0.302223\pi$
$191$	16.0902			1.16424			0.582122	+	0.813102i	$0.302223\pi$
$192$		0			0
$193$	1.92705	+	1.40008i	0.138712	+	0.100780i	0.654977	−	0.755648i	$-0.272678\pi$
$193$	1.92705	+	1.40008i	0.138712	+	0.100780i	−0.516265	+	0.856429i	$0.672678\pi$
$194$	2.64590	−	1.92236i	0.189964	−	0.138017i
$195$		0			0
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$	13.2812	+	9.64932i	0.946243	+	0.687486i	0.949915	−	0.312507i	$-0.101169\pi$
$197$	13.2812	+	9.64932i	0.946243	+	0.687486i	−0.00367232	+	0.999993i	$0.501169\pi$
$198$		0			0
$199$	−8.25329	−	25.4010i	−0.585060	−	1.80063i	−0.599029	−	0.800728i	$-0.704446\pi$
$199$	−8.25329	−	25.4010i	−0.585060	−	1.80063i	0.0139686	−	0.999902i	$-0.495554\pi$
$200$	3.35410	−	2.43690i	0.237171	−	0.172315i
$201$		0			0
$202$	−0.909830	−	2.80017i	−0.0640154	−	0.197019i
$203$	−20.9164	+	15.1967i	−1.46804	+	1.06660i
$204$		0			0
$205$	−5.23607	+	16.1150i	−0.365703	+	1.12552i
$206$	0.0729490	+	0.0530006i	0.00508260	+	0.00369272i
$207$		0			0
$208$	−7.28115	+	5.29007i	−0.504857	+	0.366800i
$209$	−3.09017	+	2.24514i	−0.213752	+	0.155300i
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−20.5623			−1.41222
$213$		0			0
$214$	−0.208204	−	0.640786i	−0.0142325	−	0.0438032i
$215$	−3.73607	+	11.4984i	−0.254798	+	0.784187i
$216$		0			0
$217$	12.5729	+	10.9964i	0.853507	+	0.746485i
$218$	−5.20163			−0.352299
$219$		0			0
$220$	−1.00000	−	3.07768i	−0.0674200	−	0.207497i
$221$	0.927051	+	0.673542i	0.0623602	+	0.0453073i
$222$		0			0
$223$	0.708204			0.0474248			0.0237124	−	0.999719i	$-0.492451\pi$
$223$	0.708204			0.0474248			0.0237124	+	0.999719i	$0.492451\pi$
$224$	−13.6353	−	9.90659i	−0.911044	−	0.661912i
$225$		0			0
$226$	−0.927051	+	0.673542i	−0.0616665	+	0.0448033i
$227$	6.40983	−	19.7274i	0.425435	−	1.30936i	−0.477141	−	0.878827i	$-0.658327\pi$
$227$	6.40983	−	19.7274i	0.425435	−	1.30936i	0.902577	−	0.430529i	$-0.141673\pi$
$228$		0			0
$229$	−2.23607	+	6.88191i	−0.147764	+	0.454769i	−0.997356	−	0.0726703i	$-0.976848\pi$
$229$	−2.23607	+	6.88191i	−0.147764	+	0.454769i	0.849592	+	0.527440i	$0.176848\pi$
$230$	2.73607	+	8.42075i	0.180411	+	0.555248i
$231$		0			0
$232$	−5.95492	−	18.3273i	−0.390959	−	1.20325i
$233$	−5.80902	−	17.8783i	−0.380561	−	1.17125i	−0.939649	−	0.342139i	$-0.888849\pi$
$233$	−5.80902	−	17.8783i	−0.380561	−	1.17125i	0.559088	−	0.829108i	$-0.311151\pi$
$234$		0			0
$235$	2.73607	+	8.42075i	0.178481	+	0.549309i
$236$	4.73607	−	14.5761i	0.308292	−	0.948824i
$237$		0			0
$238$	−0.135255	+	0.416272i	−0.00876727	+	0.0269829i
$239$	−10.8541	+	7.88597i	−0.702093	+	0.510101i	−0.880613	−	0.473836i	$-0.842869\pi$
$239$	−10.8541	+	7.88597i	−0.702093	+	0.510101i	0.178520	+	0.983936i	$0.442869\pi$
$240$		0			0
$241$	6.89919	+	5.01255i	0.444416	+	0.322887i	0.787387	−	0.616459i	$-0.211433\pi$
$241$	6.89919	+	5.01255i	0.444416	+	0.322887i	−0.342971	+	0.939346i	$0.611433\pi$
$242$	−6.43769			−0.413831
$243$		0			0
$244$	−9.09017	−	6.60440i	−0.581938	−	0.422803i
$245$	1.61803	+	4.97980i	0.103372	+	0.318148i
$246$		0			0
$247$	24.2705			1.54430
$248$	−10.6910	+	6.37988i	−0.678878	+	0.405123i
$249$		0			0
$250$	−1.57295	+	4.84104i	−0.0994820	+	0.306174i
$251$	−0.291796	−	0.898056i	−0.0184180	−	0.0566848i	0.941425	−	0.337222i	$-0.109487\pi$
$251$	−0.291796	−	0.898056i	−0.0184180	−	0.0566848i	−0.959843	+	0.280537i	$0.909487\pi$
$252$		0			0
$253$	4.18034			0.262816
$254$	6.32624			0.396943
$255$		0			0
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	1.14590	−	0.832544i	0.0714792	−	0.0519326i	−0.551472	−	0.834194i	$-0.685934\pi$
$257$	1.14590	−	0.832544i	0.0714792	−	0.0519326i	0.622951	+	0.782261i	$0.285934\pi$
$258$		0			0
$259$	−0.572949	−	0.416272i	−0.0356013	−	0.0258659i
$260$	−6.35410	+	19.5559i	−0.394065	+	1.21281i
$261$		0			0
$262$	0.0450850	−	0.0327561i	0.00278536	−	0.00202368i
$263$	3.33688	+	10.2699i	0.205761	+	0.633267i	0.999681	+	0.0252452i	$0.00803665\pi$
$263$	3.33688	+	10.2699i	0.205761	+	0.633267i	−0.793920	+	0.608022i	$0.791963\pi$
$264$		0			0
$265$	−26.9164	+	19.5559i	−1.65346	+	1.20131i
$266$	2.86475	+	8.81678i	0.175649	+	0.540591i
$267$		0			0
$268$	−5.54508	−	4.02874i	−0.338720	−	0.246094i
$269$	0.427051	−	1.31433i	0.0260378	−	0.0801360i	−0.937193	−	0.348811i	$-0.886586\pi$
$269$	0.427051	−	1.31433i	0.0260378	−	0.0801360i	0.963231	+	0.268675i	$0.0865856\pi$
$270$		0			0
$271$	−7.73607	+	5.62058i	−0.469933	+	0.341426i	−0.797415	−	0.603431i	$-0.793800\pi$
$271$	−7.73607	+	5.62058i	−0.469933	+	0.341426i	0.327482	+	0.944857i	$0.393800\pi$
$272$	0.354102	+	0.257270i	0.0214706	+	0.0155993i
$273$		0			0
$274$	4.00000			0.241649
$275$	−1.14590	−	0.832544i	−0.0691003	−	0.0502043i
$276$		0			0
$277$	4.11803	−	12.6740i	0.247429	−	0.761507i	−0.747799	−	0.663925i	$-0.768889\pi$
$277$	4.11803	−	12.6740i	0.247429	−	0.761507i	0.995228	−	0.0975818i	$-0.0311108\pi$
$278$	3.61803			0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	−5.88197	+	18.1028i	−0.350889	+	1.07992i	0.607466	+	0.794345i	$0.292186\pi$
$281$	−5.88197	+	18.1028i	−0.350889	+	1.07992i	−0.958355	+	0.285579i	$0.907814\pi$
$282$		0			0
$283$	−5.30902	−	3.85723i	−0.315588	−	0.229288i	0.418702	−	0.908124i	$-0.362485\pi$
$283$	−5.30902	−	3.85723i	−0.315588	−	0.229288i	−0.734291	+	0.678835i	$0.762485\pi$
$284$	0.145898			0.00865746
$285$		0			0
$286$	−1.85410	−	1.34708i	−0.109635	−	0.0796547i
$287$	15.7082	−	11.4127i	0.927226	−	0.673669i
$288$		0			0
$289$	−5.23607	+	16.1150i	−0.308004	+	0.947939i
$290$	−11.2812	−	8.19624i	−0.662452	−	0.481300i
$291$		0			0
$292$	4.28115	+	13.1760i	0.250536	+	0.771069i
$293$	−6.66312	+	4.84104i	−0.389264	+	0.282817i	−0.765154	−	0.643848i	$-0.777337\pi$
$293$	−6.66312	+	4.84104i	−0.389264	+	0.282817i	0.375890	+	0.926664i	$0.377337\pi$
$294$		0			0
$295$	−7.66312	−	23.5847i	−0.446164	−	1.37315i
$296$	0.427051	−	0.310271i	0.0248218	−	0.0180341i
$297$		0			0
$298$	3.25329	−	10.0126i	0.188458	−	0.580014i
$299$	−21.4894	−	15.6129i	−1.24276	−	0.902919i
$300$		0			0
$301$	11.2082	−	8.14324i	0.646030	−	0.469368i
$302$	9.75329	−	7.08618i	0.561239	−	0.407764i
$303$		0			0
$304$	9.27051			0.531700
$305$	−18.1803			−1.04100
$306$		0			0
$307$	1.88197	+	5.79210i	0.107409	+	0.330572i	0.990288	−	0.139028i	$-0.0443979\pi$
$307$	1.88197	+	5.79210i	0.107409	+	0.330572i	−0.882879	+	0.469601i	$0.844398\pi$
$308$	−1.14590	+	3.52671i	−0.0652936	+	0.200953i
$309$		0			0
$310$	−3.54508	+	8.28199i	−0.201347	+	0.470386i
$311$	−16.4721			−0.934049			−0.467025	−	0.884244i	$-0.654674\pi$
$311$	−16.4721			−0.934049			−0.467025	+	0.884244i	$0.654674\pi$
$312$		0			0
$313$	0.381966	+	1.17557i	0.0215900	+	0.0664472i	0.961271	−	0.275605i	$-0.0888781\pi$
$313$	0.381966	+	1.17557i	0.0215900	+	0.0664472i	−0.939681	+	0.342052i	$0.888878\pi$
$314$	−4.85410	−	3.52671i	−0.273933	−	0.199024i
$315$		0			0
$316$		0			0
$317$	20.9443	+	15.2169i	1.17635	+	0.854666i	0.991755	−	0.128149i	$-0.0409035\pi$
$317$	20.9443	+	15.2169i	1.17635	+	0.854666i	0.184593	+	0.982815i	$0.440903\pi$
$318$		0			0
$319$	−5.32624	+	3.86974i	−0.298212	+	0.216664i
$320$	−0.190983	+	0.587785i	−0.0106763	+	0.0328582i
$321$		0			0
$322$	3.13525	−	9.64932i	0.174721	−	0.537736i
$323$	−0.364745	−	1.12257i	−0.0202950	−	0.0624615i
$324$		0			0
$325$	2.78115	+	8.55951i	0.154271	+	0.474796i
$326$	−2.42705	−	7.46969i	−0.134422	−	0.413708i
$327$		0			0
$328$	4.47214	+	13.7638i	0.246932	+	0.759980i
$329$	3.13525	−	9.64932i	0.172852	−	0.531984i
$330$		0			0
$331$	3.48278	−	10.7189i	0.191431	−	0.589164i	−0.808569	−	0.588402i	$-0.799757\pi$
$331$	3.48278	−	10.7189i	0.191431	−	0.589164i	1.00000		0.000762014i	$-0.000242557\pi$
$332$	5.35410	−	3.88998i	0.293845	−	0.213491i
$333$		0			0
$334$	−4.61803	−	3.35520i	−0.252688	−	0.183588i
$335$	−11.0902			−0.605921
$336$		0			0
$337$	−15.3541	−	11.1554i	−0.836391	−	0.607674i	0.0849690	−	0.996384i	$-0.472921\pi$
$337$	−15.3541	−	11.1554i	−0.836391	−	0.607674i	−0.921360	+	0.388710i	$0.872921\pi$
$338$	2.01722	+	6.20837i	0.109722	+	0.337691i
$339$		0			0
$340$	1.00000			0.0542326
$341$	3.20163	+	2.80017i	0.173378	+	0.151638i
$342$		0			0
$343$	−4.63525	+	14.2658i	−0.250280	+	0.770283i
$344$	3.19098	+	9.82084i	0.172046	+	0.529504i
$345$		0			0
$346$	−0.562306			−0.0302298
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$		0			0
$349$	13.5172	−	9.82084i	0.723560	−	0.525697i	−0.163959	−	0.986467i	$-0.552427\pi$
$349$	13.5172	−	9.82084i	0.723560	−	0.525697i	0.887520	+	0.460770i	$0.152427\pi$
$350$	−2.78115	+	2.02063i	−0.148659	+	0.108007i
$351$		0			0
$352$	−3.47214	−	2.52265i	−0.185065	−	0.134458i
$353$	10.0066	−	30.7971i	0.532596	−	1.63916i	−0.216190	−	0.976351i	$-0.569363\pi$
$353$	10.0066	−	30.7971i	0.532596	−	1.63916i	0.748786	−	0.662812i	$-0.230637\pi$
$354$		0			0
$355$	0.190983	−	0.138757i	0.0101363	−	0.00736447i
$356$	−3.19098	−	9.82084i	−0.169122	−	0.520503i
$357$		0			0
$358$	9.89919	−	7.19218i	0.523188	−	0.380119i
$359$	7.82624	+	24.0867i	0.413053	+	1.27125i	0.913981	+	0.405757i	$0.132992\pi$
$359$	7.82624	+	24.0867i	0.413053	+	1.27125i	−0.500928	+	0.865489i	$0.667008\pi$
$360$		0			0
$361$	−4.85410	−	3.52671i	−0.255479	−	0.185616i
$362$	3.24671	−	9.99235i	0.170643	−	0.525186i
$363$		0			0
$364$	19.0623	−	13.8496i	0.999136	−	0.725915i
$365$	18.1353	+	13.1760i	0.949243	+	0.689665i
$366$		0			0
$367$	−36.2705			−1.89331			−0.946653	−	0.322256i	$-0.895559\pi$
$367$	−36.2705			−1.89331			−0.946653	+	0.322256i	$0.895559\pi$
$368$	−8.20820	−	5.96361i	−0.427882	−	0.310875i
$369$		0			0
$370$	0.118034	−	0.363271i	0.00613629	−	0.0188856i
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	−0.0344419	+	0.106001i	−0.00178095	+	0.00548119i
$375$		0			0
$376$	6.11803	+	4.44501i	0.315514	+	0.229234i
$377$	41.8328			2.15450
$378$		0			0
$379$	14.8992	+	10.8249i	0.765320	+	0.556037i	0.900537	−	0.434779i	$-0.143173\pi$
$379$	14.8992	+	10.8249i	0.765320	+	0.556037i	−0.135218	+	0.990816i	$0.543173\pi$
$380$	17.1353	−	12.4495i	0.879020	−	0.638645i
$381$		0			0
$382$	3.07295	−	9.45756i	0.157226	−	0.483891i
$383$	−13.6353	−	9.90659i	−0.696729	−	0.506203i	0.182136	−	0.983273i	$-0.441699\pi$
$383$	−13.6353	−	9.90659i	−0.696729	−	0.506203i	−0.878865	+	0.477070i	$0.841699\pi$
$384$		0			0
$385$	1.85410	+	5.70634i	0.0944938	+	0.290822i
$386$	1.19098	−	0.865300i	0.0606194	−	0.0440426i
$387$		0			0
$388$	2.64590	+	8.14324i	0.134325	+	0.413410i
$389$	−23.5172	+	17.0863i	−1.19237	+	0.866308i	−0.993513	−	0.113721i	$-0.963723\pi$
$389$	−23.5172	+	17.0863i	−1.19237	+	0.866308i	−0.198858	+	0.980028i	$0.563723\pi$
$390$		0			0
$391$	−0.399187	+	1.22857i	−0.0201878	+	0.0621315i
$392$	3.61803	+	2.62866i	0.182738	+	0.132767i
$393$		0			0
$394$	8.20820	−	5.96361i	0.413523	−	0.300442i
$395$		0			0
$396$		0			0
$397$	16.2918			0.817662			0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918			0.817662			0.408831	+	0.912610i	$0.365937\pi$
$398$	−16.5066			−0.827400
$399$		0			0
$400$	1.06231	+	3.26944i	0.0531153	+	0.163472i
$401$	9.21885	−	28.3727i	0.460367	−	1.41686i	−0.404349	−	0.914605i	$-0.632502\pi$
$401$	9.21885	−	28.3727i	0.460367	−	1.41686i	0.864717	−	0.502260i	$-0.167498\pi$
$402$		0			0
$403$	−6.00000	−	26.3521i	−0.298881	−	1.31269i
$404$	7.70820			0.383497
$405$		0			0
$406$	4.93769	+	15.1967i	0.245054	+	0.754198i
$407$	−0.145898	−	0.106001i	−0.00723190	−	0.00525428i
$408$		0			0
$409$	−6.18034			−0.305598			−0.152799	−	0.988257i	$-0.548829\pi$
$409$	−6.18034			−0.305598			−0.152799	+	0.988257i	$0.548829\pi$
$410$	8.47214	+	6.15537i	0.418409	+	0.303992i
$411$		0			0
$412$	−0.190983	+	0.138757i	−0.00940906	+	0.00683608i
$413$	−8.78115	+	27.0256i	−0.432092	+	1.32984i
$414$		0			0
$415$	3.30902	−	10.1841i	0.162433	−	0.499918i
$416$	8.42705	+	25.9358i	0.413170	+	1.27161i
$417$		0			0
$418$	0.729490	+	2.24514i	0.0356805	+	0.109813i
$419$	−1.38197	−	4.25325i	−0.0675135	−	0.207785i	0.911608	−	0.411060i	$-0.134841\pi$
$419$	−1.38197	−	4.25325i	−0.0675135	−	0.207785i	−0.979122	+	0.203275i	$0.934841\pi$
$420$		0			0
$421$	4.56231	+	14.0413i	0.222353	+	0.684333i	0.998549	+	0.0538414i	$0.0171466\pi$
$421$	4.56231	+	14.0413i	0.222353	+	0.684333i	−0.776196	+	0.630491i	$0.782853\pi$
$422$	−1.52786	+	4.70228i	−0.0743753	+	0.228904i
$423$		0			0
$424$	−8.78115	+	27.0256i	−0.426450	+	1.31248i
$425$	0.354102	−	0.257270i	0.0171765	−	0.0124794i
$426$		0			0
$427$	16.8541	+	12.2452i	0.815627	+	0.592588i
$428$	1.76393			0.0852629
$429$		0			0
$430$	6.04508	+	4.39201i	0.291520	+	0.211802i
$431$	−9.03444	−	27.8052i	−0.435174	−	1.33933i	−0.892908	−	0.450238i	$-0.851339\pi$
$431$	−9.03444	−	27.8052i	−0.435174	−	1.33933i	0.457735	−	0.889089i	$-0.348661\pi$
$432$		0			0
$433$	0.583592			0.0280456			0.0140228	−	0.999902i	$-0.495536\pi$
$433$	0.583592			0.0280456			0.0140228	+	0.999902i	$0.495536\pi$
$434$	8.86475	−	5.29007i	0.425521	−	0.253931i
$435$		0			0
$436$	4.20820	−	12.9515i	0.201536	−	0.620265i
$437$	8.45492	+	26.0216i	0.404453	+	1.24478i
$438$		0			0
$439$	41.8328			1.99657			0.998286	−	0.0585295i	$-0.0186412\pi$
$439$	41.8328			1.99657			0.998286	+	0.0585295i	$0.0186412\pi$
$440$	−4.47214			−0.213201
$441$		0			0
$442$	0.572949	−	0.416272i	0.0272524	−	0.0198000i
$443$	−33.2705	+	24.1724i	−1.58073	+	1.14847i	−0.664877	+	0.746953i	$0.731516\pi$
$443$	−33.2705	+	24.1724i	−1.58073	+	1.14847i	−0.915853	+	0.401514i	$0.868484\pi$
$444$		0			0
$445$	−13.5172	−	9.82084i	−0.640778	−	0.465552i
$446$	0.135255	−	0.416272i	0.00640451	−	0.0197110i
$447$		0			0
$448$	0.572949	−	0.416272i	0.0270693	−	0.0196670i
$449$	−7.43769	−	22.8909i	−0.351006	−	1.08029i	−0.958289	−	0.285801i	$-0.907740\pi$
$449$	−7.43769	−	22.8909i	−0.351006	−	1.08029i	0.607283	−	0.794486i	$-0.292260\pi$
$450$		0			0
$451$	4.00000	−	2.90617i	0.188353	−	0.136846i
$452$	−0.927051	−	2.85317i	−0.0436048	−	0.134202i
$453$		0			0
$454$	−10.3713	−	7.53521i	−0.486750	−	0.353645i
$455$	11.7812	−	36.2587i	0.552309	−	1.69983i
$456$		0			0
$457$	12.7361	−	9.25330i	0.595768	−	0.432851i	−0.248606	−	0.968605i	$-0.579972\pi$
$457$	12.7361	−	9.25330i	0.595768	−	0.432851i	0.844374	+	0.535754i	$0.179972\pi$
$458$	3.61803	+	2.62866i	0.169060	+	0.122829i
$459$		0			0
$460$	−23.1803			−1.08079
$461$	8.69098	+	6.31437i	0.404779	+	0.294089i	0.771485	−	0.636248i	$-0.219514\pi$
$461$	8.69098	+	6.31437i	0.404779	+	0.294089i	−0.366705	+	0.930337i	$0.619514\pi$
$462$		0			0
$463$	−9.61803	+	29.6013i	−0.446988	+	1.37569i	0.433301	+	0.901249i	$0.357349\pi$
$463$	−9.61803	+	29.6013i	−0.446988	+	1.37569i	−0.880289	+	0.474438i	$0.842651\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	10.1287	−	31.1729i	0.468699	−	1.44251i	−0.385571	−	0.922678i	$-0.625995\pi$
$467$	10.1287	−	31.1729i	0.468699	−	1.44251i	0.854270	−	0.519830i	$-0.174005\pi$
$468$		0			0
$469$	10.2812	+	7.46969i	0.474740	+	0.344918i
$470$	5.47214			0.252411
$471$		0			0
$472$	−17.1353	−	12.4495i	−0.788714	−	0.573034i
$473$	2.85410	−	2.07363i	0.131232	−	0.0953454i
$474$		0			0
$475$	2.86475	−	8.81678i	0.131444	−	0.404542i
$476$	−0.927051	−	0.673542i	−0.0424913	−	0.0308717i
$477$		0			0
$478$	2.56231	+	7.88597i	0.117197	+	0.360696i
$479$	−7.23607	+	5.25731i	−0.330624	+	0.240213i	−0.740696	−	0.671841i	$-0.765504\pi$
$479$	−7.23607	+	5.25731i	−0.330624	+	0.240213i	0.410071	+	0.912054i	$0.365504\pi$
$480$		0			0
$481$	0.354102	+	1.08981i	0.0161457	+	0.0496912i
$482$	4.26393	−	3.09793i	0.194217	−	0.141107i
$483$		0			0
$484$	5.20820	−	16.0292i	0.236737	−	0.728600i
$485$	11.2082	+	8.14324i	0.508938	+	0.369765i
$486$		0			0
$487$	−18.5451	+	13.4738i	−0.840358	+	0.610556i	−0.922471	−	0.386067i	$-0.873833\pi$
$487$	−18.5451	+	13.4738i	−0.840358	+	0.610556i	0.0821126	+	0.996623i	$0.473833\pi$
$488$	−12.5623	+	9.12705i	−0.568669	+	0.413162i
$489$		0			0
$490$	3.23607			0.146191
$491$	27.5967			1.24542			0.622712	−	0.782451i	$-0.286031\pi$
$491$	27.5967			1.24542			0.622712	+	0.782451i	$0.286031\pi$
$492$		0			0
$493$	−0.628677	−	1.93487i	−0.0283142	−	0.0871421i
$494$	4.63525	−	14.2658i	0.208550	−	0.641851i
$495$		0			0
$496$	−2.29180	−	10.0656i	−0.102905	−	0.451959i
$497$	−0.270510			−0.0121340
$498$		0			0
$499$	1.28115	+	3.94298i	0.0573523	+	0.176512i	0.975629	−	0.219427i	$-0.0704189\pi$
$499$	1.28115	+	3.94298i	0.0573523	+	0.176512i	−0.918277	+	0.395940i	$0.870419\pi$
$500$	−10.7812	−	7.83297i	−0.482148	−	0.350301i
$501$		0			0
$502$	−0.583592			−0.0260470
$503$	10.6353	+	7.72696i	0.474203	+	0.344528i	0.799077	−	0.601229i	$-0.205322\pi$
$503$	10.6353	+	7.72696i	0.474203	+	0.344528i	−0.324874	+	0.945757i	$0.605322\pi$
$504$		0			0
$505$	10.0902	−	7.33094i	0.449007	−	0.326222i
$506$	0.798374	−	2.45714i	0.0354920	−	0.109233i
$507$		0			0
$508$	−5.11803	+	15.7517i	−0.227076	+	0.698868i
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	0.963284	−	0.268486i	$-0.0865232\pi$
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	−0.937125	+	0.348994i	$0.886523\pi$
$510$		0			0
$511$	−7.93769	−	24.4297i	−0.351143	−	1.08071i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$		0			0
$514$	−0.270510	−	0.832544i	−0.0119317	−	0.0367219i
$515$	−0.118034	+	0.363271i	−0.00520120	+	0.0160076i
$516$		0			0
$517$	0.798374	−	2.45714i	0.0351124	−	0.108065i
$518$	−0.354102	+	0.257270i	−0.0155583	+	0.0113038i
$519$		0			0
$520$	22.9894	+	16.7027i	1.00815	+	0.732464i
$521$	−31.0689			−1.36115			−0.680576	−	0.732677i	$-0.738271\pi$
$521$	−31.0689			−1.36115			−0.680576	+	0.732677i	$0.738271\pi$
$522$		0			0
$523$	−27.6074	−	20.0579i	−1.20719	−	0.877073i	−0.212215	−	0.977223i	$-0.568068\pi$
$523$	−27.6074	−	20.0579i	−1.20719	−	0.877073i	−0.994972	+	0.100150i	$0.968068\pi$
$524$	0.0450850	+	0.138757i	0.00196955	+	0.00606164i
$525$		0			0
$526$	6.67376			0.290990
$527$	−1.12868	+	0.673542i	−0.0491659	+	0.0293399i
$528$		0			0
$529$	2.14590	−	6.60440i	0.0932999	−	0.287148i
$530$	6.35410	+	19.5559i	0.276005	+	0.849455i
$531$		0			0
$532$	−24.2705			−1.05226
$533$	−31.4164			−1.36080
$534$		0			0
$535$	2.30902	−	1.67760i	0.0998275	−	0.0725289i
$536$	−7.66312	+	5.56758i	−0.330996	+	0.240483i
$537$		0			0
$538$	−0.690983	−	0.502029i	−0.0297904	−	0.0216440i
$539$	0.472136	−	1.45309i	0.0203363	−	0.0625888i
$540$		0			0
$541$	−17.7984	+	12.9313i	−0.765212	+	0.555959i	−0.900504	−	0.434847i	$-0.856803\pi$
$541$	−17.7984	+	12.9313i	−0.765212	+	0.555959i	0.135293	+	0.990806i	$0.456803\pi$
$542$	1.82624	+	5.62058i	0.0784436	+	0.241425i
$543$		0			0
$544$	1.07295	−	0.779543i	0.0460023	−	0.0334226i
$545$	−6.80902	−	20.9560i	−0.291666	−	0.897656i
$546$		0			0
$547$	19.1803	+	13.9353i	0.820092	+	0.595832i	0.916739	−	0.399487i	$-0.130812\pi$
$547$	19.1803	+	13.9353i	0.820092	+	0.595832i	−0.0966468	+	0.995319i	$0.530812\pi$
$548$	−3.23607	+	9.95959i	−0.138238	+	0.425453i
$549$		0			0
$550$	−0.708204	+	0.514540i	−0.0301979	+	0.0219401i
$551$	−34.8607	−	25.3278i	−1.48511	−	1.07900i
$552$		0			0
$553$		0			0
$554$	−6.66312	−	4.84104i	−0.283089	−	0.205676i
$555$		0			0
$556$	−2.92705	+	9.00854i	−0.124135	+	0.382047i
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	4.50000	−	13.8496i	0.190160	−	0.585251i
$561$		0			0
$562$	9.51722	+	6.91467i	0.401460	+	0.291678i
$563$	8.56231			0.360858			0.180429	−	0.983588i	$-0.442251\pi$
$563$	8.56231			0.360858			0.180429	+	0.983588i	$0.442251\pi$
$564$		0			0
$565$	−3.92705	−	2.85317i	−0.165212	−	0.120034i
$566$	−3.28115	+	2.38390i	−0.137917	+	0.100203i
$567$		0			0
$568$	0.0623059	−	0.191758i	0.00261430	−	0.00804598i
$569$	12.5623	+	9.12705i	0.526639	+	0.382626i	0.819099	−	0.573652i	$-0.194474\pi$
$569$	12.5623	+	9.12705i	0.526639	+	0.382626i	−0.292460	+	0.956278i	$0.594474\pi$
$570$		0			0
$571$	2.16312	+	6.65740i	0.0905237	+	0.278603i	0.986061	−	0.166383i	$-0.0532087\pi$
$571$	2.16312	+	6.65740i	0.0905237	+	0.278603i	−0.895538	+	0.444986i	$0.853209\pi$
$572$	4.85410	−	3.52671i	0.202960	−	0.147459i
$573$		0			0
$574$	−3.70820	−	11.4127i	−0.154777	−	0.476356i
$575$	−8.20820	+	5.96361i	−0.342306	+	0.248700i
$576$		0			0
$577$	12.0451	−	37.0710i	0.501443	−	1.54328i	−0.305225	−	0.952280i	$-0.598732\pi$
$577$	12.0451	−	37.0710i	0.501443	−	1.54328i	0.806669	−	0.591004i	$-0.201268\pi$
$578$	8.47214	+	6.15537i	0.352394	+	0.256030i
$579$		0			0
$580$	29.5344	−	21.4580i	1.22635	−	0.890996i
$581$	−9.92705	+	7.21242i	−0.411843	+	0.299222i
$582$		0			0
$583$	9.70820			0.402073
$584$	19.1459			0.792263
$585$		0			0
$586$	1.57295	+	4.84104i	0.0649779	+	0.199981i
$587$	−11.1287	+	34.2505i	−0.459330	+	1.41367i	0.406646	+	0.913586i	$0.366698\pi$
$587$	−11.1287	+	34.2505i	−0.459330	+	1.41367i	−0.865976	+	0.500086i	$0.833302\pi$
$588$		0			0
$589$	−10.9549	+	25.5928i	−0.451389	+	1.05453i
$590$	−15.3262			−0.630971
$591$		0			0
$592$	0.135255	+	0.416272i	0.00555894	+	0.0171087i
$593$	4.94427	+	3.59222i	0.203037	+	0.147515i	0.684658	−	0.728865i	$-0.259952\pi$
$593$	4.94427	+	3.59222i	0.203037	+	0.147515i	−0.481621	+	0.876380i	$0.659952\pi$
$594$		0			0
$595$	−1.85410			−0.0760108
$596$	22.2984	+	16.2007i	0.913377	+	0.663607i
$597$		0			0
$598$	−13.2812	+	9.64932i	−0.543107	+	0.394590i
$599$	−9.20820	+	28.3399i	−0.376237	+	1.15794i	0.566403	+	0.824128i	$0.308334\pi$
$599$	−9.20820	+	28.3399i	−0.376237	+	1.15794i	−0.942640	+	0.333810i	$0.891666\pi$
$600$		0			0
$601$	6.79837	−	20.9232i	0.277311	−	0.853477i	−0.711287	−	0.702902i	$-0.751887\pi$
$601$	6.79837	−	20.9232i	0.277311	−	0.853477i	0.988599	−	0.150575i	$-0.0481126\pi$
$602$	−2.64590	−	8.14324i	−0.107839	−	0.331894i
$603$		0			0
$604$	9.75329	+	30.0175i	0.396856	+	1.22140i
$605$	−8.42705	−	25.9358i	−0.342608	−	1.05444i
$606$		0			0
$607$	−7.85410	−	24.1724i	−0.318788	−	0.981129i	−0.974167	−	0.225829i	$-0.927491\pi$
$607$	−7.85410	−	24.1724i	−0.318788	−	0.981129i	0.655379	−	0.755300i	$-0.272509\pi$
$608$	8.68034	−	26.7153i	0.352034	−	1.08345i
$609$		0			0
$610$	−3.47214	+	10.6861i	−0.140583	+	0.432669i
$611$	−13.2812	+	9.64932i	−0.537298	+	0.390370i
$612$		0			0
$613$	−20.2705	−	14.7274i	−0.818718	−	0.594834i	0.0976269	−	0.995223i	$-0.468875\pi$
$613$	−20.2705	−	14.7274i	−0.818718	−	0.594834i	−0.916345	+	0.400390i	$0.868875\pi$
$614$	3.76393			0.151900
$615$		0			0
$616$	4.14590	+	3.01217i	0.167043	+	0.121364i
$617$	4.39919	+	13.5393i	0.177105	+	0.545072i	0.999723	−	0.0235215i	$-0.00748780\pi$
$617$	4.39919	+	13.5393i	0.177105	+	0.545072i	−0.822619	+	0.568593i	$0.807488\pi$
$618$		0			0
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	−17.7533	−	15.5272i	−0.712989	−	0.623586i
$621$		0			0
$622$	−3.14590	+	9.68208i	−0.126139	+	0.388216i
$623$	5.91641	+	18.2088i	0.237036	+	0.729521i
$624$		0			0
$625$	−30.8328			−1.23331
$626$	0.763932			0.0305329
$627$		0			0
$628$	12.7082	−	9.23305i	0.507113	−	0.368439i
$629$	0.0450850	−	0.0327561i	0.00179766	−	0.00130607i
$630$		0			0
$631$	7.06231	+	5.13107i	0.281146	+	0.204264i	0.719417	−	0.694578i	$-0.244409\pi$
$631$	7.06231	+	5.13107i	0.281146	+	0.204264i	−0.438271	+	0.898843i	$0.644409\pi$
$632$		0			0
$633$		0			0
$634$	12.9443	−	9.40456i	0.514083	−	0.373503i
$635$	8.28115	+	25.4868i	0.328628	+	1.01141i
$636$		0			0
$637$	−7.85410	+	5.70634i	−0.311191	+	0.226093i
$638$	1.25735	+	3.86974i	0.0497791	+	0.153204i
$639$		0			0
$640$	24.1074	+	17.5150i	0.952928	+	0.692343i
$641$	12.6976	−	39.0791i	0.501523	−	1.54353i	−0.305014	−	0.952348i	$-0.598661\pi$
$641$	12.6976	−	39.0791i	0.501523	−	1.54353i	0.806538	−	0.591183i	$-0.201339\pi$
$642$		0			0
$643$	−6.59017	+	4.78804i	−0.259891	+	0.188822i	−0.710099	−	0.704102i	$-0.751350\pi$
$643$	−6.59017	+	4.78804i	−0.259891	+	0.188822i	0.450208	+	0.892924i	$0.351350\pi$
$644$	21.4894	+	15.6129i	0.846799	+	0.615236i
$645$		0			0
$646$	−0.729490			−0.0287014
$647$	−24.1803	−	17.5680i	−0.950627	−	0.690671i	0.000327889	−	1.00000i	$-0.499896\pi$
$647$	−24.1803	−	17.5680i	−0.950627	−	0.690671i	−0.950955	+	0.309329i	$0.899896\pi$
$648$		0			0
$649$	−2.23607	+	6.88191i	−0.0877733	+	0.270139i
$650$	5.56231			0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	−12.2533	+	37.7117i	−0.479508	+	1.47577i	0.360272	+	0.932847i	$0.382684\pi$
$653$	−12.2533	+	37.7117i	−0.479508	+	1.47577i	−0.839780	+	0.542927i	$0.817316\pi$
$654$		0			0
$655$	0.190983	+	0.138757i	0.00746232	+	0.00542170i
$656$	−12.0000			−0.468521
$657$		0			0
$658$	−5.07295	−	3.68571i	−0.197764	−	0.143684i
$659$	18.3541	−	13.3350i	0.714974	−	0.519459i	−0.169800	−	0.985478i	$-0.554312\pi$
$659$	18.3541	−	13.3350i	0.714974	−	0.519459i	0.884775	+	0.466019i	$0.154312\pi$
$660$		0			0
$661$	−5.13525	+	15.8047i	−0.199738	+	0.614731i	0.800150	+	0.599800i	$0.204753\pi$
$661$	−5.13525	+	15.8047i	−0.199738	+	0.614731i	−0.999889	+	0.0149316i	$0.995247\pi$
$662$	−5.63525	−	4.09425i	−0.219020	−	0.159128i
$663$		0			0
$664$	−2.82624	−	8.69827i	−0.109679	−	0.337558i
$665$	−31.7705	+	23.0826i	−1.23201	+	0.895106i
$666$		0			0
$667$	14.5729	+	44.8509i	0.564267	+	1.73663i
$668$	12.0902	−	8.78402i	0.467783	−	0.339864i
$669$		0			0
$670$	−2.11803	+	6.51864i	−0.0818268	+	0.251837i
$671$	4.29180	+	3.11817i	0.165683	+	0.120376i
$672$		0			0
$673$	3.57295	−	2.59590i	0.137727	−	0.100065i	−0.516788	−	0.856113i	$-0.672873\pi$
$673$	3.57295	−	2.59590i	0.137727	−	0.100065i	0.654516	+	0.756049i	$0.272873\pi$
$674$	−9.48936	+	6.89442i	−0.365516	+	0.265563i
$675$		0			0
$676$	−17.0902			−0.657314
$677$	−28.6525			−1.10120			−0.550602	−	0.834768i	$-0.685602\pi$
$677$	−28.6525			−1.10120			−0.550602	+	0.834768i	$0.685602\pi$
$678$		0			0
$679$	−4.90576	−	15.0984i	−0.188266	−	0.579423i
$680$	0.427051	−	1.31433i	0.0163767	−	0.0504022i
$681$		0			0
$682$	2.25735	−	1.34708i	0.0864386	−	0.0515825i
$683$	−10.0557			−0.384772			−0.192386	−	0.981319i	$-0.561623\pi$
$683$	−10.0557			−0.384772			−0.192386	+	0.981319i	$0.561623\pi$
$684$		0			0
$685$	5.23607	+	16.1150i	0.200060	+	0.615721i
$686$	7.50000	+	5.44907i	0.286351	+	0.208046i
$687$		0			0
$688$	−8.56231			−0.326435
$689$	−49.9058	−	36.2587i	−1.90126	−	1.38134i
$690$		0			0
$691$	−3.10081	+	2.25287i	−0.117960	+	0.0857033i	−0.645201	−	0.764013i	$-0.723227\pi$
$691$	−3.10081	+	2.25287i	−0.117960	+	0.0857033i	0.527241	+	0.849716i	$0.323227\pi$
$692$	0.454915	−	1.40008i	0.0172933	−	0.0532232i
$693$		0			0
$694$	−1.55166	+	4.77553i	−0.0589003	+	0.181277i
$695$	4.73607	+	14.5761i	0.179649	+	0.552904i
$696$		0			0
$697$	0.472136	+	1.45309i	0.0178834	+	0.0550395i
$698$	−3.19098	−	9.82084i	−0.120780	−	0.371724i
$699$		0			0
$700$	−2.78115	−	8.55951i	−0.105118	−	0.323519i
$701$	9.28115	−	28.5645i	0.350544	−	1.07886i	−0.608004	−	0.793934i	$-0.708030\pi$
$701$	9.28115	−	28.5645i	0.350544	−	1.07886i	0.958548	−	0.284930i	$-0.0919705\pi$
$702$		0			0
$703$	0.364745	−	1.12257i	0.0137566	−	0.0423385i
$704$	0.145898	−	0.106001i	0.00549874	−	0.00399507i
$705$		0			0
$706$	−16.1910	−	11.7634i	−0.609356	−	0.442723i
$707$	−14.2918			−0.537498
$708$		0			0
$709$	−3.35410	−	2.43690i	−0.125966	−	0.0915196i	0.523018	−	0.852321i	$-0.324806\pi$
$709$	−3.35410	−	2.43690i	−0.125966	−	0.0915196i	−0.648984	+	0.760802i	$0.724806\pi$
$710$	−0.0450850	−	0.138757i	−0.00169201	−	0.00520747i
$711$		0			0
$712$	−14.2705			−0.534810
$713$	26.1631	−	15.6129i	0.979817	−	0.584709i
$714$		0			0
$715$	3.00000	−	9.23305i	0.112194	−	0.345297i
$716$	9.89919	+	30.4666i	0.369950	+	1.13859i
$717$		0			0
$718$	15.6525			0.584145
$719$	41.3820			1.54329			0.771643	−	0.636055i	$-0.219435\pi$
$719$	41.3820			1.54329			0.771643	+	0.636055i	$0.219435\pi$
$720$		0			0
$721$	0.354102	−	0.257270i	0.0131874	−	0.00958124i
$722$	−3.00000	+	2.17963i	−0.111648	+	0.0811173i
$723$		0			0
$724$	22.2533	+	16.1680i	0.827037	+	0.600878i
$725$	4.93769	−	15.1967i	0.183381	−	0.564390i
$726$		0			0
$727$	19.2812	−	14.0086i	0.715098	−	0.519549i	−0.169716	−	0.985493i	$-0.554285\pi$
$727$	19.2812	−	14.0086i	0.715098	−	0.519549i	0.884814	+	0.465944i	$0.154285\pi$
$728$	−10.0623	−	30.9686i	−0.372934	−	1.14777i
$729$		0			0
$730$	11.2082	−	8.14324i	0.414834	−	0.301395i
$731$	0.336881	+	1.03681i	0.0124600	+	0.0383479i
$732$		0			0
$733$	−22.6074	−	16.4252i	−0.835023	−	0.606680i	0.0859529	−	0.996299i	$-0.472607\pi$
$733$	−22.6074	−	16.4252i	−0.835023	−	0.606680i	−0.920976	+	0.389619i	$0.872607\pi$
$734$	−6.92705	+	21.3193i	−0.255682	+	0.786909i
$735$		0			0
$736$	−24.8713	+	18.0701i	−0.916769	+	0.666072i
$737$	2.61803	+	1.90211i	0.0964365	+	0.0700652i
$738$		0			0
$739$	21.7082			0.798549			0.399275	−	0.916831i	$-0.369262\pi$
$739$	21.7082			0.798549			0.399275	+	0.916831i	$0.369262\pi$
$740$	0.809017	+	0.587785i	0.0297401	+	0.0216074i
$741$		0			0
$742$	7.28115	−	22.4091i	0.267300	−	0.822663i
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	−0.0663712	+	0.204270i	−0.00243002	+	0.00747884i
$747$		0			0
$748$	−0.236068	−	0.171513i	−0.00863150	−	0.00627115i
$749$	−3.27051			−0.119502
$750$		0			0
$751$	32.2254	+	23.4131i	1.17592	+	0.854358i	0.991706	−	0.128528i	$-0.0410252\pi$
$751$	32.2254	+	23.4131i	1.17592	+	0.854358i	0.184217	+	0.982886i	$0.441025\pi$
$752$	−5.07295	+	3.68571i	−0.184991	+	0.134404i
$753$		0			0
$754$	7.98936	−	24.5887i	0.290955	−	0.895468i
$755$	41.3156	+	30.0175i	1.50363	+	1.09245i
$756$		0			0
$757$	13.3262	+	41.0139i	0.484350	+	1.49068i	0.832920	+	0.553394i	$0.186668\pi$
$757$	13.3262	+	41.0139i	0.484350	+	1.49068i	−0.348569	+	0.937283i	$0.613332\pi$
$758$	9.20820	−	6.69015i	0.334457	−	0.242997i
$759$		0			0
$760$	−9.04508	−	27.8379i	−0.328100	−	1.00979i
$761$	2.83688	−	2.06111i	0.102837	−	0.0747154i	−0.535178	−	0.844739i	$-0.679756\pi$
$761$	2.83688	−	2.06111i	0.102837	−	0.0747154i	0.638015	+	0.770024i	$0.279756\pi$
$762$		0			0
$763$	−7.80244	+	24.0134i	−0.282467	+	0.869345i
$764$	21.0623	+	15.3027i	0.762007	+	0.553631i
$765$		0			0
$766$	−8.42705	+	6.12261i	−0.304482	+	0.221219i
$767$	37.1976	−	27.0256i	1.34313	−	0.975838i
$768$		0			0
$769$	−53.7426			−1.93801			−0.969005	−	0.247042i	$-0.920541\pi$
$769$	−53.7426			−1.93801			−0.969005	+	0.247042i	$0.920541\pi$
$770$	3.70820			0.133634
$771$		0			0
$772$	1.19098	+	3.66547i	0.0428644	+	0.131923i
$773$	5.89919	−	18.1558i	0.212179	−	0.653020i	−0.787163	−	0.616745i	$-0.788451\pi$
$773$	5.89919	−	18.1558i	0.212179	−	0.653020i	0.999342	−	0.0362746i	$-0.0115491\pi$
$774$		0			0
$775$	−10.2812	−	0.930812i	−0.369310	−	0.0334358i
$776$	11.8328			0.424773
$777$		0			0
$778$	5.55166	+	17.0863i	0.199037	+	0.612572i
$779$	26.1803	+	19.0211i	0.938008	+	0.681503i
$780$		0			0
$781$	−0.0688837			−0.00246485
$782$	0.645898	+	0.469272i	0.0230973	+	0.0167811i
$783$		0			0
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$	7.85410	−	24.1724i	0.280325	−	0.862751i
$786$		0			0
$787$	9.66970	−	29.7603i	0.344687	−	1.06084i	−0.617063	−	0.786913i	$-0.711678\pi$
$787$	9.66970	−	29.7603i	0.344687	−	1.06084i	0.961751	−	0.273926i	$-0.0883222\pi$
$788$	8.20820	+	25.2623i	0.292405	+	0.899931i
$789$		0			0
$790$		0			0
$791$	1.71885	+	5.29007i	0.0611152	+	0.188093i
$792$		0			0
$793$	−10.4164	−	32.0584i	−0.369897	−	1.13843i
$794$	3.11146	−	9.57608i	0.110421	−	0.339842i
$795$		0			0
$796$	13.3541	−	41.0997i	0.473324	−	1.45674i
$797$	7.32624	−	5.32282i	0.259509	−	0.188544i	−0.450422	−	0.892816i	$-0.648726\pi$
$797$	7.32624	−	5.32282i	0.259509	−	0.188544i	0.709930	+	0.704272i	$0.248726\pi$
$798$		0			0
$799$	0.645898	+	0.469272i	0.0228502	+	0.0166017i
$800$	10.4164			0.368276
$801$		0			0
$802$	−14.9164	−	10.8374i	−0.526717	−	0.382682i
$803$	−2.02129	−	6.22088i	−0.0713296	−	0.219530i
$804$		0			0
$805$	42.9787			1.51480
$806$	−16.6353	−	1.50609i	−0.585952	−	0.0530496i
$807$		0			0
$808$	3.29180	−	10.1311i	0.115805	−	0.356411i
$809$	−16.9336	−	52.1164i	−0.595355	−	1.83231i	−0.552953	−	0.833213i	$-0.686499\pi$
$809$	−16.9336	−	52.1164i	−0.595355	−	1.83231i	−0.0424020	−	0.999101i	$-0.513501\pi$
$810$		0			0
$811$	42.7771			1.50211			0.751053	−	0.660242i	$-0.229546\pi$
$811$	42.7771			1.50211			0.751053	+	0.660242i	$0.229546\pi$
$812$	−41.8328			−1.46804
$813$		0			0
$814$	−0.0901699	+	0.0655123i	−0.00316045	+	0.00229620i
$815$	26.9164	−	19.5559i	0.942841	−	0.685014i
$816$		0			0
$817$	18.6803	+	13.5721i	0.653542	+	0.474826i
$818$	−1.18034	+	3.63271i	−0.0412696	+	0.127015i
$819$		0			0
$820$	−22.1803	+	16.1150i	−0.774571	+	0.562759i
$821$	10.0344	+	30.8828i	0.350204	+	1.07782i	0.958738	+	0.284290i	$0.0917580\pi$
$821$	10.0344	+	30.8828i	0.350204	+	1.07782i	−0.608534	+	0.793528i	$0.708242\pi$
$822$		0			0
$823$	4.95492	−	3.59996i	0.172717	−	0.125487i	−0.498068	−	0.867138i	$-0.665957\pi$
$823$	4.95492	−	3.59996i	0.172717	−	0.125487i	0.670786	+	0.741651i	$0.265957\pi$
$824$	0.100813	+	0.310271i	0.00351199	+	0.0108088i
$825$		0			0
$826$	14.2082	+	10.3229i	0.494367	+	0.359178i
$827$	−0.826238	+	2.54290i	−0.0287311	+	0.0884253i	−0.964394	−	0.264470i	$-0.914803\pi$
$827$	−0.826238	+	2.54290i	−0.0287311	+	0.0884253i	0.935663	+	0.352896i	$0.114803\pi$
$828$		0			0
$829$	17.5623	−	12.7598i	0.609964	−	0.443165i	−0.239438	−	0.970912i	$-0.576963\pi$
$829$	17.5623	−	12.7598i	0.609964	−	0.443165i	0.849402	+	0.527747i	$0.176963\pi$
$830$	−5.35410	−	3.88998i	−0.185844	−	0.135023i
$831$		0			0
$832$	−1.14590			−0.0397269
$833$	0.381966	+	0.277515i	0.0132343	+	0.00961531i
$834$		0			0
$835$	7.47214	−	22.9969i	0.258584	−	0.795839i
$836$	−6.18034			−0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	−3.45492	+	10.6331i	−0.119277	+	0.367097i	−0.992815	−	0.119659i	$-0.961820\pi$
$839$	−3.45492	+	10.6331i	−0.119277	+	0.367097i	0.873538	+	0.486756i	$0.161820\pi$
$840$		0			0
$841$	−36.6246	−	26.6093i	−1.26292	−	0.917563i
$842$	9.12461			0.314455
$843$		0			0
$844$	−10.4721	−	7.60845i	−0.360466	−	0.261894i
$845$	−22.3713	+	16.2537i	−0.769597	+	0.559145i
$846$		0			0
$847$	−9.65654	+	29.7198i	−0.331803	+	1.02118i
$848$	−19.0623	−	13.8496i	−0.654602	−	0.475596i
$849$		0			0
$850$	−0.0835921	−	0.257270i	−0.00286719	−	0.00882429i
$851$	−1.04508	+	0.759299i	−0.0358251	+	0.0260284i
$852$		0			0
$853$	1.23607	+	3.80423i	0.0423222	+	0.130254i	0.969985	−	0.243164i	$-0.0781855\pi$
$853$	1.23607	+	3.80423i	0.0423222	+	0.130254i	−0.927663	+	0.373419i	$0.878185\pi$
$854$	10.4164	−	7.56796i	0.356442	−	0.258970i
$855$		0			0
$856$	0.753289	−	2.31838i	0.0257469	−	0.0792408i
$857$	−6.61803	−	4.80828i	−0.226068	−	0.164248i	0.468986	−	0.883206i	$-0.344619\pi$
$857$	−6.61803	−	4.80828i	−0.226068	−	0.164248i	−0.695054	+	0.718958i	$0.744619\pi$
$858$		0			0
$859$	−35.0238	+	25.4463i	−1.19500	+	0.868216i	−0.993783	−	0.111332i	$-0.964488\pi$
$859$	−35.0238	+	25.4463i	−1.19500	+	0.868216i	−0.201213	+	0.979547i	$0.564488\pi$
$860$	−15.8262	+	11.4984i	−0.539670	+	0.392093i
$861$		0			0
$862$	−18.0689			−0.615429
$863$	−2.49342			−0.0848771			−0.0424385	−	0.999099i	$-0.513513\pi$
$863$	−2.49342			−0.0848771			−0.0424385	+	0.999099i	$0.513513\pi$
$864$		0			0
$865$	−0.736068	−	2.26538i	−0.0250271	−	0.0770254i
$866$	0.111456	−	0.343027i	0.00378744	−	0.0116565i
$867$		0			0
$868$	6.00000	+	26.3521i	0.203653	+	0.894447i
$869$		0			0
$870$		0			0
$871$	−6.35410	−	19.5559i	−0.215301	−	0.662627i
$872$	−15.2254	−	11.0619i	−0.515598	−	0.374604i
$873$		0			0
$874$	16.9098			0.571984
$875$	19.9894	+	14.5231i	0.675764	+	0.490971i
$876$		0			0
$877$	−13.1803	+	9.57608i	−0.445068	+	0.323361i	−0.787646	−	0.616129i	$-0.788700\pi$
$877$	−13.1803	+	9.57608i	−0.445068	+	0.323361i	0.342577	+	0.939490i	$0.388700\pi$
$878$	7.98936	−	24.5887i	0.269628	−	0.829829i
$879$		0			0
$880$	1.14590	−	3.52671i	0.0386282	−	0.118885i
$881$	4.74671	+	14.6089i	0.159921	+	0.492185i	0.998626	−	0.0523999i	$-0.0166870\pi$
$881$	4.74671	+	14.6089i	0.159921	+	0.492185i	−0.838705	+	0.544585i	$0.816687\pi$
$882$		0			0
$883$	−0.309017	−	0.951057i	−0.0103992	−	0.0320056i	0.945722	−	0.324976i	$-0.105356\pi$
$883$	−0.309017	−	0.951057i	−0.0103992	−	0.0320056i	−0.956121	+	0.292970i	$0.905356\pi$
$884$	0.572949	+	1.76336i	0.0192704	+	0.0593081i
$885$		0			0
$886$	7.85410	+	24.1724i	0.263864	+	0.812089i
$887$	−12.0836	+	37.1895i	−0.405727	+	1.24870i	0.514559	+	0.857455i	$0.327956\pi$
$887$	−12.0836	+	37.1895i	−0.405727	+	1.24870i	−0.920286	+	0.391245i	$0.872044\pi$
$888$		0			0
$889$	9.48936	−	29.2052i	0.318263	−	0.979512i
$890$	−8.35410	+	6.06961i	−0.280030	+	0.203454i
$891$		0			0
$892$	0.927051	+	0.673542i	0.0310400	+	0.0225519i
$893$	16.9098			0.565866
$894$		0			0
$895$	41.9336	+	30.4666i	1.40169	+	1.01838i
$896$	−10.5517	−	32.4747i	−0.352506	−	1.08490i
$897$		0			0
$898$	−14.8754			−0.496398
$899$	−18.8820	+	44.1119i	−0.629749	+	1.47121i
$900$		0			0
$901$	−0.927051	+	2.85317i	−0.0308845	+	0.0950529i
$902$	−0.944272	−	2.90617i	−0.0314408	−	0.0967649i
$903$		0			0
$904$	−4.14590			−0.137891
$905$	44.5066			1.47945
$906$		0			0
$907$	−42.8156	+	31.1074i	−1.42167	+	1.03290i	−0.430175	+	0.902745i	$0.641548\pi$
$907$	−42.8156	+	31.1074i	−1.42167	+	1.03290i	−0.991493	+	0.130157i	$0.958452\pi$
$908$	27.1525	−	19.7274i	0.901087	−	0.654678i
$909$		0			0
$910$	−19.0623	−	13.8496i	−0.631909	−	0.459109i
$911$	−2.52786	+	7.77997i	−0.0837519	+	0.257762i	−0.984159	−	0.177286i	$-0.943268\pi$
$911$	−2.52786	+	7.77997i	−0.0837519	+	0.257762i	0.900408	+	0.435047i	$0.143268\pi$
$912$		0			0
$913$	−2.52786	+	1.83660i	−0.0836601	+	0.0607826i
$914$	−3.00658	−	9.25330i	−0.0994488	−	0.306072i
$915$		0			0
$916$	−9.47214	+	6.88191i	−0.312968	+	0.227385i
$917$	−0.0835921	−	0.257270i	−0.00276046	−	0.00849581i
$918$		0			0
$919$	−7.98936	−	5.80461i	−0.263545	−	0.191476i	0.448164	−	0.893952i	$-0.352078\pi$
$919$	−7.98936	−	5.80461i	−0.263545	−	0.191476i	−0.711708	+	0.702475i	$0.752078\pi$
$920$	−9.89919	+	30.4666i	−0.326367	+	1.00445i
$921$		0			0
$922$	5.37132	−	3.90249i	0.176895	−	0.128522i
$923$	0.354102	+	0.257270i	0.0116554	+	0.00846815i
$924$		0			0
$925$	0.437694			0.0143913
$926$	15.5623	+	11.3067i	0.511409	+	0.371560i
$927$		0			0
$928$	14.9615	−	46.0467i	0.491135	−	1.51156i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	9.39919	−	28.9277i	0.307881	−	0.947559i
$933$		0			0
$934$	−16.3885	−	11.9070i	−0.536250	−	0.389608i
$935$	−0.472136			−0.0154405
$936$		0			0
$937$	−32.7533	−	23.7967i	−1.07000	−	0.777403i	−0.0940905	−	0.995564i	$-0.529994\pi$
$937$	−32.7533	−	23.7967i	−1.07000	−	0.777403i	−0.975913	+	0.218161i	$0.929994\pi$
$938$	6.35410	−	4.61653i	0.207469	−	0.150735i
$939$		0			0
$940$	−4.42705	+	13.6251i	−0.144394	+	0.444401i
$941$	23.1246	+	16.8010i	0.753841	+	0.547697i	0.897015	−	0.442000i	$-0.145731\pi$
$941$	23.1246	+	16.8010i	0.753841	+	0.547697i	−0.143174	+	0.989698i	$0.545731\pi$
$942$		0			0
$943$	−10.9443	−	33.6830i	−0.356395	−	1.09687i
$944$	14.2082	−	10.3229i	0.462438	−	0.335981i
$945$		0			0
$946$	−0.673762	−	2.07363i	−0.0219059	−	0.0674194i
$947$	17.8541	−	12.9718i	0.580180	−	0.421526i	−0.258609	−	0.965982i	$-0.583264\pi$
$947$	17.8541	−	12.9718i	0.580180	−	0.421526i	0.838789	+	0.544456i	$0.183264\pi$
$948$		0			0
$949$	−12.8435	+	39.5281i	−0.416916	+	1.28314i
$950$	−4.63525	−	3.36771i	−0.150388	−	0.109263i
$951$		0			0
$952$	−1.28115	+	0.930812i	−0.0415224	+	0.0301678i
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.124229	−	0.992254i	$-0.460354\pi$
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.982078	+	0.188474i	$0.0603542\pi$
$954$		0			0
$955$	42.1246			1.36312
$956$	−21.7082			−0.702093
$957$		0			0
$958$	1.70820	+	5.25731i	0.0551896	+	0.169856i
$959$	6.00000	−	18.4661i	0.193750	−	0.596302i
$960$		0			0
$961$	30.4959	+	5.56758i	0.983740	+	0.179599i
$962$	0.708204			0.0228334
$963$		0			0
$964$	4.26393	+	13.1230i	0.137332	+	0.422664i
$965$	5.04508	+	3.66547i	0.162407	+	0.117996i
$966$		0			0
$967$	43.6525			1.40377			0.701884	−	0.712291i	$-0.252342\pi$
$967$	43.6525			1.40377			0.701884	+	0.712291i	$0.252342\pi$
$968$	−18.8435	−	13.6906i	−0.605652	−	0.440032i
$969$		0			0
$970$	6.92705	−	5.03280i	0.222414	−	0.161593i
$971$	6.35410	−	19.5559i	0.203913	−	0.627579i	−0.795843	−	0.605502i	$-0.792972\pi$
$971$	6.35410	−	19.5559i	0.203913	−	0.627579i	0.999756	−	0.0220767i	$-0.00702781\pi$
$972$		0			0
$973$	5.42705	−	16.7027i	0.173983	−	0.535465i
$974$	4.37790	+	13.4738i	0.140277	+	0.431728i
$975$		0			0
$976$	−3.97871	−	12.2452i	−0.127356	−	0.391960i
$977$	1.87539	+	5.77185i	0.0599990	+	0.184658i	0.976564	−	0.215228i	$-0.0690496\pi$
$977$	1.87539	+	5.77185i	0.0599990	+	0.184658i	−0.916565	+	0.399886i	$0.869050\pi$
$978$		0			0
$979$	1.50658	+	4.63677i	0.0481504	+	0.148192i
$980$	−2.61803	+	8.05748i	−0.0836300	+	0.257387i
$981$		0			0
$982$	5.27051	−	16.2210i	0.168189	−	0.517632i
$983$	17.0172	−	12.3637i	0.542765	−	0.394342i	−0.282346	−	0.959313i	$-0.591113\pi$
$983$	17.0172	−	12.3637i	0.542765	−	0.394342i	0.825111	+	0.564971i	$0.191113\pi$
$984$		0			0
$985$	34.7705	+	25.2623i	1.10788	+	0.804922i
$986$	−1.25735			−0.0400423
$987$		0			0
$988$	31.7705	+	23.0826i	1.01075	+	0.734356i
$989$	−7.80902	−	24.0337i	−0.248312	−	0.764227i
$990$		0			0
$991$	−17.2705			−0.548616			−0.274308	−	0.961642i	$-0.588449\pi$
$991$	−17.2705			−0.548616			−0.274308	+	0.961642i	$0.588449\pi$
$992$	−31.1525	−	2.82041i	−0.989092	−	0.0895482i
$993$		0			0
$994$	−0.0516628	+	0.159002i	−0.00163864	+	0.00504323i
$995$	−21.6074	−	66.5007i	−0.685000	−	2.10821i
$996$		0			0
$997$	−27.2492			−0.862992			−0.431496	−	0.902115i	$-0.642014\pi$
$997$	−27.2492			−0.862992			−0.431496	+	0.902115i	$0.642014\pi$
$998$	2.56231			0.0811084
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.i.a.163.1		4
3.2	odd	2		31.2.d.a.8.1	yes	4
12.11	even	2		496.2.n.b.225.1		4
15.2	even	4		775.2.bf.a.349.1		8
15.8	even	4		775.2.bf.a.349.2		8
15.14	odd	2		775.2.k.c.101.1		4
31.2	even	5		8649.2.a.g.1.2		2
31.4	even	5	inner	279.2.i.a.190.1		4
31.29	odd	10		8649.2.a.f.1.2		2
93.2	odd	10		961.2.a.d.1.1		2
93.5	odd	6		961.2.g.b.448.1		8
93.8	odd	10		961.2.d.f.388.1		4
93.11	even	30		961.2.g.c.844.1		8
93.14	odd	30		961.2.g.f.235.1		8
93.17	even	30		961.2.g.g.235.1		8
93.20	odd	30		961.2.g.b.844.1		8
93.23	even	10		961.2.d.e.388.1		4
93.26	even	6		961.2.g.c.448.1		8
93.29	even	10		961.2.a.e.1.1		2
93.35	odd	10		31.2.d.a.4.1	✓	4
93.38	odd	30		961.2.g.b.547.1		8
93.41	odd	30		961.2.c.f.521.1		4
93.44	even	30		961.2.g.g.732.1		8
93.47	odd	10		961.2.d.f.374.1		4
93.50	odd	30		961.2.c.f.439.1		4
93.53	even	30		961.2.g.g.338.1		8
93.56	odd	6		961.2.g.b.846.1		8
93.59	odd	30		961.2.g.f.816.1		8
93.65	even	30		961.2.g.g.816.1		8
93.68	even	6		961.2.g.c.846.1		8
93.71	odd	30		961.2.g.f.338.1		8
93.74	even	30		961.2.c.d.439.1		4
93.77	even	10		961.2.d.e.374.1		4
93.80	odd	30		961.2.g.f.732.1		8
93.83	even	30		961.2.c.d.521.1		4
93.86	even	30		961.2.g.c.547.1		8
93.89	even	10		961.2.d.b.531.1		4
93.92	even	2		961.2.d.b.628.1		4
372.35	even	10		496.2.n.b.97.1		4
465.128	even	20		775.2.bf.a.624.1		8
465.314	odd	10		775.2.k.c.376.1		4
465.407	even	20		775.2.bf.a.624.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	93.35	odd	10
31.2.d.a.8.1	yes	4	3.2	odd	2
279.2.i.a.163.1		4	1.1	even	1	trivial
279.2.i.a.190.1		4	31.4	even	5	inner
496.2.n.b.97.1		4	372.35	even	10
496.2.n.b.225.1		4	12.11	even	2
775.2.k.c.101.1		4	15.14	odd	2
775.2.k.c.376.1		4	465.314	odd	10
775.2.bf.a.349.1		8	15.2	even	4
775.2.bf.a.349.2		8	15.8	even	4
775.2.bf.a.624.1		8	465.128	even	20
775.2.bf.a.624.2		8	465.407	even	20
961.2.a.d.1.1		2	93.2	odd	10
961.2.a.e.1.1		2	93.29	even	10
961.2.c.d.439.1		4	93.74	even	30
961.2.c.d.521.1		4	93.83	even	30
961.2.c.f.439.1		4	93.50	odd	30
961.2.c.f.521.1		4	93.41	odd	30
961.2.d.b.531.1		4	93.89	even	10
961.2.d.b.628.1		4	93.92	even	2
961.2.d.e.374.1		4	93.77	even	10
961.2.d.e.388.1		4	93.23	even	10
961.2.d.f.374.1		4	93.47	odd	10
961.2.d.f.388.1		4	93.8	odd	10
961.2.g.b.448.1		8	93.5	odd	6
961.2.g.b.547.1		8	93.38	odd	30
961.2.g.b.844.1		8	93.20	odd	30
961.2.g.b.846.1		8	93.56	odd	6
961.2.g.c.448.1		8	93.26	even	6
961.2.g.c.547.1		8	93.86	even	30
961.2.g.c.844.1		8	93.11	even	30
961.2.g.c.846.1		8	93.68	even	6
961.2.g.f.235.1		8	93.14	odd	30
961.2.g.f.338.1		8	93.71	odd	30
961.2.g.f.732.1		8	93.80	odd	30
961.2.g.f.816.1		8	93.59	odd	30
961.2.g.g.235.1		8	93.17	even	30
961.2.g.g.338.1		8	93.53	even	30
961.2.g.g.732.1		8	93.44	even	30
961.2.g.g.816.1		8	93.65	even	30
8649.2.a.f.1.2		2	31.29	odd	10
8649.2.a.g.1.2		2	31.2	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(1.30902 + 0.951057i) q^{4} +2.61803 q^{5} +(-2.42705 - 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.500000 - 1.53884i) q^{10} +(-0.618034 - 0.449028i) q^{11} +(1.50000 + 4.61653i) q^{13} +(-1.50000 + 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.190983 - 0.138757i) q^{17} +(1.54508 - 4.75528i) q^{19} +(3.42705 + 2.48990i) q^{20} +(-0.381966 + 0.277515i) q^{22} +(-4.42705 + 3.21644i) q^{23} +1.85410 q^{25} +3.00000 q^{26} +(-1.50000 - 4.61653i) q^{28} +(2.66312 - 8.19624i) q^{29} +(-5.54508 - 0.502029i) q^{31} +5.61803 q^{32} +(-0.0450850 - 0.138757i) q^{34} +(-6.35410 - 4.61653i) q^{35} +0.236068 q^{37} +(-2.50000 - 1.81636i) q^{38} +(4.73607 - 3.44095i) q^{40} +(-2.00000 + 6.15537i) q^{41} +(-1.42705 + 4.39201i) q^{43} +(-0.381966 - 1.17557i) q^{44} +(1.04508 + 3.21644i) q^{46} +(1.04508 + 3.21644i) q^{47} +(0.618034 + 1.90211i) q^{49} +(0.354102 - 1.08981i) q^{50} +(-2.42705 + 7.46969i) q^{52} +(-10.2812 + 7.46969i) q^{53} +(-1.61803 - 1.17557i) q^{55} -6.70820 q^{56} +(-4.30902 - 3.13068i) q^{58} +(-2.92705 - 9.00854i) q^{59} -6.94427 q^{61} +(-1.35410 + 3.16344i) q^{62} +(-0.0729490 + 0.224514i) q^{64} +(3.92705 + 12.0862i) q^{65} -4.23607 q^{67} +0.381966 q^{68} +(-3.92705 + 2.85317i) q^{70} +(0.0729490 - 0.0530006i) q^{71} +(6.92705 + 5.03280i) q^{73} +(0.0450850 - 0.138757i) q^{74} +(6.54508 - 4.75528i) q^{76} +(0.708204 + 2.17963i) q^{77} +(1.50000 + 4.61653i) q^{80} +(3.23607 + 2.35114i) q^{82} +(1.26393 - 3.88998i) q^{83} +(0.500000 - 0.363271i) q^{85} +(2.30902 + 1.67760i) q^{86} -1.70820 q^{88} +(-5.16312 - 3.75123i) q^{89} +(4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(4.04508 - 12.4495i) q^{95} +(4.28115 + 3.11044i) q^{97} +1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 3 q^{7} + 5 q^{8} + 2 q^{10} + 2 q^{11} + 6 q^{13} - 6 q^{14} + 9 q^{16} + 3 q^{17} - 5 q^{19} + 7 q^{20} - 6 q^{22} - 11 q^{23} - 6 q^{25} + 12 q^{26} - 6 q^{28} - 5 q^{29}+ \cdots - 4 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 3 * q^7 + 5 * q^8 + 2 * q^10 + 2 * q^11 + 6 * q^13 - 6 * q^14 + 9 * q^16 + 3 * q^17 - 5 * q^19 + 7 * q^20 - 6 * q^22 - 11 * q^23 - 6 * q^25 + 12 * q^26 - 6 * q^28 - 5 * q^29 - 11 * q^31 + 18 * q^32 + 11 * q^34 - 12 * q^35 - 8 * q^37 - 10 * q^38 + 10 * q^40 - 8 * q^41 + q^43 - 6 * q^44 - 7 * q^46 - 7 * q^47 - 2 * q^49 - 12 * q^50 - 3 * q^52 - 21 * q^53 - 2 * q^55 - 15 * q^58 - 5 * q^59 + 8 * q^61 + 8 * q^62 - 7 * q^64 + 9 * q^65 - 8 * q^67 + 6 * q^68 - 9 * q^70 + 7 * q^71 + 21 * q^73 - 11 * q^74 + 15 * q^76 - 24 * q^77 + 6 * q^80 + 4 * q^82 + 14 * q^83 + 2 * q^85 + 7 * q^86 + 20 * q^88 - 5 * q^89 + 18 * q^91 - 22 * q^92 - 14 * q^94 + 5 * q^95 - 3 * q^97 - 4 * q^98

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