LMFDB - Embedded newform 405.3.l.f.28.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(28,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.28"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,0,-4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	405.28
Dual form			405.3.l.f.217.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.03906 - 0.814313i) q^{2} +(5.10867 + 2.94949i) q^{4} +(-2.32162 - 4.42833i) q^{5} +(1.98004 + 0.530550i) q^{7} +(-4.22474 - 4.22474i) q^{8} +(3.44949 + 15.3485i) q^{10} +(-1.67423 - 2.89986i) q^{11} +(14.2743 - 3.82478i) q^{13} +(-5.58542 - 3.22474i) q^{14} +(-2.39898 - 4.15515i) q^{16} +(2.65153 - 2.65153i) q^{17} +20.6969i q^{19} +(1.20093 - 29.4704i) q^{20} +(2.72670 + 10.1762i) q^{22} +(22.4704 - 6.02093i) q^{23} +(-14.2202 + 20.5618i) q^{25} -46.4949 q^{26} +(8.55051 + 8.55051i) q^{28} +(0.739215 - 0.426786i) q^{29} +(9.34847 - 16.1920i) q^{31} +(10.0925 + 37.6657i) q^{32} +(-10.2173 + 5.89898i) q^{34} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +(16.8538 - 62.8992i) q^{38} +(-8.90031 + 28.5168i) q^{40} +(-14.3485 + 24.8523i) q^{41} +(8.23370 - 30.7286i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(26.9825 + 7.22994i) q^{47} +(-38.7962 - 22.3990i) q^{49} +(59.9596 - 50.9088i) q^{50} +(84.2036 + 22.5623i) q^{52} +(-28.6969 - 28.6969i) q^{53} +(-8.95459 + 14.1464i) q^{55} +(-6.12372 - 10.6066i) q^{56} +(-2.59405 + 0.695075i) q^{58} +(-96.9378 - 55.9671i) q^{59} +(-47.0454 - 81.4850i) q^{61} +(-41.5959 + 41.5959i) q^{62} -103.495i q^{64} +(-50.0768 - 54.3315i) q^{65} +(-20.0944 - 74.9934i) q^{67} +(21.3664 - 5.72512i) q^{68} +(-1.31300 + 32.2207i) q^{70} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} +(-146.603 + 84.6413i) q^{74} +(-61.0454 + 105.734i) q^{76} +(-1.77653 - 6.63010i) q^{77} +(-21.2132 + 12.2474i) q^{79} +(-12.8309 + 20.2702i) q^{80} +(63.8434 - 63.8434i) q^{82} +(7.74013 - 28.8866i) q^{83} +(-17.8977 - 5.58600i) q^{85} +(-50.0454 + 86.6812i) q^{86} +(-5.17795 + 19.3244i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(132.553 + 35.5173i) q^{92} +(-76.1139 - 43.9444i) q^{94} +(91.6528 - 48.0504i) q^{95} +(-19.9384 - 5.34248i) q^{97} +(99.6640 + 99.6640i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{5} - 4 q^{7} - 24 q^{8} + 8 q^{10} + 16 q^{11} + 32 q^{13} + 20 q^{16} + 80 q^{17} - 36 q^{20} - 20 q^{22} + 56 q^{23} - 16 q^{25} - 176 q^{26} + 88 q^{28} + 16 q^{31} - 76 q^{32} + 80 q^{35}+ \cdots + 376 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 - 24 * q^8 + 8 * q^10 + 16 * q^11 + 32 * q^13 + 20 * q^16 + 80 * q^17 - 36 * q^20 - 20 * q^22 + 56 * q^23 - 16 * q^25 - 176 * q^26 + 88 * q^28 + 16 * q^31 - 76 * q^32 + 80 * q^35 + 128 * q^37 - 96 * q^38 - 48 * q^40 - 56 * q^41 + 8 * q^43 - 272 * q^46 + 128 * q^47 + 164 * q^50 + 80 * q^52 - 112 * q^53 - 248 * q^55 + 12 * q^58 - 200 * q^61 - 176 * q^62 - 112 * q^65 + 200 * q^67 - 104 * q^68 + 60 * q^70 + 544 * q^71 + 152 * q^73 - 312 * q^76 + 88 * q^77 - 328 * q^80 + 256 * q^82 - 16 * q^83 - 232 * q^85 - 224 * q^86 - 12 * q^88 - 32 * q^91 + 104 * q^92 + 144 * q^95 + 20 * q^97 + 376 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−3.03906	−	0.814313i	−1.51953	−	0.407157i	−0.599942	−	0.800043i	$-0.704810\pi$
$2$	−3.03906	−	0.814313i	−1.51953	−	0.407157i	−0.919587	+	0.392887i	$0.871476\pi$
$3$		0			0
$3$		0			0
$4$	5.10867	+	2.94949i	1.27717	+	0.737372i
$5$	−2.32162	−	4.42833i	−0.464324	−	0.885666i
$5$	−2.32162	−	4.42833i	−0.464324	−	0.885666i
$6$		0			0
$7$	1.98004	+	0.530550i	0.282863	+	0.0757929i	0.397461	−	0.917619i	$-0.369891\pi$
$7$	1.98004	+	0.530550i	0.282863	+	0.0757929i	−0.114598	+	0.993412i	$0.536558\pi$
$8$	−4.22474	−	4.22474i	−0.528093	−	0.528093i
$9$		0			0
$10$	3.44949	+	15.3485i	0.344949	+	1.53485i
$11$	−1.67423	−	2.89986i	−0.152203	−	0.263624i	0.779834	−	0.625986i	$-0.215303\pi$
$11$	−1.67423	−	2.89986i	−0.152203	−	0.263624i	−0.932037	+	0.362363i	$0.881970\pi$
$12$		0			0
$13$	14.2743	−	3.82478i	1.09802	−	0.294214i	0.336062	−	0.941840i	$-0.390905\pi$
$13$	14.2743	−	3.82478i	1.09802	−	0.294214i	0.761958	+	0.647626i	$0.224238\pi$
$14$	−5.58542	−	3.22474i	−0.398959	−	0.230339i
$15$		0			0
$16$	−2.39898	−	4.15515i	−0.149936	−	0.259697i
$17$	2.65153	−	2.65153i	0.155972	−	0.155972i	−0.624807	−	0.780779i	$-0.714822\pi$
$17$	2.65153	−	2.65153i	0.155972	−	0.155972i	0.780779	+	0.624807i	$0.214822\pi$
$18$		0			0
$19$			20.6969i			1.08931i	0.838659	+	0.544656i	$0.183340\pi$
$19$			20.6969i			1.08931i	−0.838659	+	0.544656i	$0.816660\pi$
$20$	1.20093	−	29.4704i	0.0600465	−	1.47352i
$21$		0			0
$22$	2.72670	+	10.1762i	0.123941	+	0.462554i
$23$	22.4704	−	6.02093i	0.976975	−	0.261780i	0.265205	−	0.964192i	$-0.414560\pi$
$23$	22.4704	−	6.02093i	0.976975	−	0.261780i	0.711770	+	0.702413i	$0.247894\pi$
$24$		0			0
$25$	−14.2202	+	20.5618i	−0.568807	+	0.822471i
$26$	−46.4949			−1.78827
$27$		0			0
$28$	8.55051	+	8.55051i	0.305375	+	0.305375i
$29$	0.739215	−	0.426786i	0.0254902	−	0.0147168i	−0.487201	−	0.873290i	$-0.661982\pi$
$29$	0.739215	−	0.426786i	0.0254902	−	0.0147168i	0.512691	+	0.858573i	$0.328649\pi$
$30$		0			0
$31$	9.34847	−	16.1920i	0.301564	−	0.522323i	−0.674927	−	0.737885i	$-0.735825\pi$
$31$	9.34847	−	16.1920i	0.301564	−	0.522323i	0.976490	+	0.215561i	$0.0691581\pi$
$32$	10.0925	+	37.6657i	0.315391	+	1.17705i
$33$		0			0
$34$	−10.2173	+	5.89898i	−0.300510	+	0.173499i
$35$	−2.24745	−	10.0000i	−0.0642128	−	0.285714i
$36$		0			0
$37$	38.0454	−	38.0454i	1.02825	−	1.02825i	0.0286652	−	0.999589i	$-0.490874\pi$
$37$	38.0454	−	38.0454i	1.02825	−	1.02825i	0.999589	−	0.0286652i	$-0.00912566\pi$
$38$	16.8538	−	62.8992i	0.443521	−	1.65524i
$39$		0			0
$40$	−8.90031	+	28.5168i	−0.222508	+	0.712920i
$41$	−14.3485	+	24.8523i	−0.349963	+	0.606153i	−0.986242	−	0.165305i	$-0.947139\pi$
$41$	−14.3485	+	24.8523i	−0.349963	+	0.606153i	0.636280	+	0.771458i	$0.280472\pi$
$42$		0			0
$43$	8.23370	−	30.7286i	0.191481	−	0.714619i	−0.801668	−	0.597769i	$-0.796054\pi$
$43$	8.23370	−	30.7286i	0.191481	−	0.714619i	0.993150	−	0.116849i	$-0.0372795\pi$
$44$		−	19.7526i		−	0.448922i
$45$		0			0
$46$	−73.1918			−1.59113
$47$	26.9825	+	7.22994i	0.574095	+	0.153828i	0.534174	−	0.845374i	$-0.320623\pi$
$47$	26.9825	+	7.22994i	0.574095	+	0.153828i	0.0399212	+	0.999203i	$0.487289\pi$
$48$		0			0
$49$	−38.7962	−	22.3990i	−0.791759	−	0.457122i
$50$	59.9596	−	50.9088i	1.19919	−	1.01818i
$51$		0			0
$52$	84.2036	+	22.5623i	1.61930	+	0.433890i
$53$	−28.6969	−	28.6969i	−0.541452	−	0.541452i	0.382503	−	0.923954i	$-0.375062\pi$
$53$	−28.6969	−	28.6969i	−0.541452	−	0.541452i	−0.923954	+	0.382503i	$0.875062\pi$
$54$		0			0
$55$	−8.95459	+	14.1464i	−0.162811	+	0.257208i
$56$	−6.12372	−	10.6066i	−0.109352	−	0.189404i
$57$		0			0
$58$	−2.59405	+	0.695075i	−0.0447251	+	0.0119840i
$59$	−96.9378	−	55.9671i	−1.64301	−	0.948595i	−0.979754	−	0.200206i	$-0.935839\pi$
$59$	−96.9378	−	55.9671i	−1.64301	−	0.948595i	−0.663261	−	0.748389i	$-0.730828\pi$
$60$		0			0
$61$	−47.0454	−	81.4850i	−0.771236	−	1.33582i	−0.936886	−	0.349636i	$-0.886305\pi$
$61$	−47.0454	−	81.4850i	−0.771236	−	1.33582i	0.165650	−	0.986185i	$-0.447028\pi$
$62$	−41.5959	+	41.5959i	−0.670902	+	0.670902i
$63$		0			0
$64$		−	103.495i		−	1.61711i
$65$	−50.0768	−	54.3315i	−0.770412	−	0.835869i
$66$		0			0
$67$	−20.0944	−	74.9934i	−0.299917	−	1.11930i	−0.937233	−	0.348703i	$-0.886622\pi$
$67$	−20.0944	−	74.9934i	−0.299917	−	1.11930i	0.637317	−	0.770602i	$-0.280044\pi$
$68$	21.3664	−	5.72512i	0.314212	−	0.0841930i
$69$		0			0
$70$	−1.31300	+	32.2207i	−0.0187572	+	0.460296i
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	−39.7878	−	39.7878i	−0.545038	−	0.545038i	0.379964	−	0.925001i	$-0.375936\pi$
$73$	−39.7878	−	39.7878i	−0.545038	−	0.545038i	−0.925001	+	0.379964i	$0.875936\pi$
$74$	−146.603	+	84.6413i	−1.98112	+	1.14380i
$75$		0			0
$76$	−61.0454	+	105.734i	−0.803229	+	1.39123i
$77$	−1.77653	−	6.63010i	−0.0230718	−	0.0861052i
$78$		0			0
$79$	−21.2132	+	12.2474i	−0.268522	+	0.155031i	−0.628216	−	0.778039i	$-0.716214\pi$
$79$	−21.2132	+	12.2474i	−0.268522	+	0.155031i	0.359694	+	0.933070i	$0.382881\pi$
$80$	−12.8309	+	20.2702i	−0.160386	+	0.253377i
$81$		0			0
$82$	63.8434	−	63.8434i	0.778578	−	0.778578i
$83$	7.74013	−	28.8866i	0.0932546	−	0.348031i	−0.903494	−	0.428600i	$-0.859007\pi$
$83$	7.74013	−	28.8866i	0.0932546	−	0.348031i	0.996749	+	0.0805689i	$0.0256737\pi$
$84$		0			0
$85$	−17.8977	−	5.58600i	−0.210561	−	0.0657177i
$86$	−50.0454	+	86.6812i	−0.581923	+	1.00792i
$87$		0			0
$88$	−5.17795	+	19.3244i	−0.0588404	+	0.219595i
$89$		−	94.1816i		−	1.05822i	−0.848553	−	0.529110i	$-0.822526\pi$
$89$		−	94.1816i		−	1.05822i	0.848553	−	0.529110i	$-0.177474\pi$
$90$		0			0
$91$	30.2929			0.332889
$92$	132.553	+	35.5173i	1.44079	+	0.386058i
$93$		0			0
$94$	−76.1139	−	43.9444i	−0.809722	−	0.467493i
$95$	91.6528	−	48.0504i	0.964767	−	0.505794i
$96$		0			0
$97$	−19.9384	−	5.34248i	−0.205550	−	0.0550771i	0.154575	−	0.987981i	$-0.450599\pi$
$97$	−19.9384	−	5.34248i	−0.205550	−	0.0550771i	−0.360125	+	0.932904i	$0.617266\pi$
$98$	99.6640	+	99.6640i	1.01698	+	1.01698i
$99$		0			0
$100$	−133.293	+	63.1010i	−1.33293	+	0.631010i
$101$	86.8105	+	150.360i	0.859509	+	1.48871i	0.872397	+	0.488797i	$0.162564\pi$
$101$	86.8105	+	150.360i	0.859509	+	1.48871i	−0.0128880	+	0.999917i	$0.504102\pi$
$102$		0			0
$103$	88.4536	−	23.7011i	0.858773	−	0.230108i	0.197546	−	0.980294i	$-0.436703\pi$
$103$	88.4536	−	23.7011i	0.858773	−	0.230108i	0.661227	+	0.750186i	$0.270036\pi$
$104$	−76.4639	−	44.1464i	−0.735229	−	0.424485i
$105$		0			0
$106$	63.8434	+	110.580i	0.602296	+	1.04321i
$107$	4.74235	−	4.74235i	0.0443210	−	0.0443210i	−0.684599	−	0.728920i	$-0.740023\pi$
$107$	4.74235	−	4.74235i	0.0443210	−	0.0443210i	0.728920	+	0.684599i	$0.240023\pi$
$108$		0			0
$109$		−	39.3031i		−	0.360579i	−0.983614	−	0.180289i	$-0.942297\pi$
$109$		−	39.3031i		−	0.360579i	0.983614	−	0.180289i	$-0.0577034\pi$
$110$	38.7331	−	35.7000i	0.352120	−	0.324545i
$111$		0			0
$112$	−2.54556	−	9.50015i	−0.0227282	−	0.0848228i
$113$	19.6143	−	5.25564i	0.173578	−	0.0465101i	−0.170983	−	0.985274i	$-0.554694\pi$
$113$	19.6143	−	5.25564i	0.173578	−	0.0465101i	0.344561	+	0.938764i	$0.388028\pi$
$114$		0			0
$115$	−78.8304	−	85.5281i	−0.685482	−	0.743722i
$116$	5.03520			0.0434069
$117$		0			0
$118$	249.025	+	249.025i	2.11038	+	2.11038i
$119$	6.65691	−	3.84337i	0.0559404	−	0.0322972i
$120$		0			0
$121$	54.8939	−	95.0790i	0.453668	−	0.785777i
$122$	76.6194	+	285.947i	0.628028	+	2.34383i
$123$		0			0
$124$	95.5164	−	55.1464i	0.770294	−	0.444729i
$125$	124.068	+	15.2350i	0.992545	+	0.121880i
$126$		0			0
$127$	−114.621	+	114.621i	−0.902527	+	0.902527i	−0.995654	−	0.0931273i	$-0.970314\pi$
$127$	−114.621	+	114.621i	−0.902527	+	0.902527i	0.0931273	+	0.995654i	$0.470314\pi$
$128$	−43.9073	+	163.864i	−0.343026	+	1.28019i
$129$		0			0
$130$	107.943	+	205.895i	0.830334	+	1.58380i
$131$	−13.0681	+	22.6346i	−0.0997566	+	0.172783i	−0.911584	−	0.411114i	$-0.865140\pi$
$131$	−13.0681	+	22.6346i	−0.0997566	+	0.172783i	0.811827	+	0.583898i	$0.198473\pi$
$132$		0			0
$133$	−10.9808	+	40.9808i	−0.0825621	+	0.308126i
$134$			244.272i			1.82293i
$135$		0			0
$136$	−22.4041			−0.164736
$137$	19.9865	+	5.35536i	0.145887	+	0.0390902i	0.331023	−	0.943623i	$-0.392606\pi$
$137$	19.9865	+	5.35536i	0.145887	+	0.0390902i	−0.185137	+	0.982713i	$0.559273\pi$
$138$		0			0
$139$	72.0286	+	41.5857i	0.518191	+	0.299178i	0.736194	−	0.676770i	$-0.236621\pi$
$139$	72.0286	+	41.5857i	0.518191	+	0.299178i	−0.218003	+	0.975948i	$0.569954\pi$
$140$	18.0134	−	57.7155i	0.128667	−	0.412253i
$141$		0			0
$142$	−206.656	−	55.3733i	−1.45532	−	0.389953i
$143$	−34.9898	−	34.9898i	−0.244684	−	0.244684i
$144$		0			0
$145$	−3.60612	−	2.28265i	−0.0248698	−	0.0157424i
$146$	88.5176	+	153.317i	0.606285	+	1.05012i
$147$		0			0
$148$	306.576	−	82.1467i	2.07146	−	0.555046i
$149$	−103.184	−	59.5732i	−0.692509	−	0.399820i	0.112042	−	0.993703i	$-0.464261\pi$
$149$	−103.184	−	59.5732i	−0.692509	−	0.399820i	−0.804551	+	0.593883i	$0.797594\pi$
$150$		0			0
$151$	72.4847	+	125.547i	0.480031	+	0.831438i	0.999738	−	0.0229066i	$-0.00729205\pi$
$151$	72.4847	+	125.547i	0.480031	+	0.831438i	−0.519707	+	0.854345i	$0.673959\pi$
$152$	87.4393	−	87.4393i	0.575258	−	0.575258i
$153$		0			0
$154$			21.5959i			0.140233i
$155$	−93.4072	−	3.80637i	−0.602627	−	0.0245572i
$156$		0			0
$157$	18.7209	+	69.8673i	0.119241	+	0.445015i	0.999569	−	0.0293510i	$-0.00934407\pi$
$157$	18.7209	+	69.8673i	0.119241	+	0.445015i	−0.880328	+	0.474366i	$0.842677\pi$
$158$	74.4414	−	19.9465i	0.471148	−	0.126244i
$159$		0			0
$160$	143.365	−	132.138i	0.896032	−	0.825864i
$161$	47.6867			0.296191
$162$		0			0
$163$	189.394	+	189.394i	1.16193	+	1.16193i	0.984054	+	0.177872i	$0.0569213\pi$
$163$	189.394	+	189.394i	1.16193	+	1.16193i	0.177872	+	0.984054i	$0.443079\pi$
$164$	−146.603	+	84.6413i	−0.893921	+	0.516106i
$165$		0			0
$166$	−47.0454	+	81.4850i	−0.283406	+	0.490874i
$167$	−35.5173	−	132.553i	−0.212679	−	0.793728i	−0.986971	−	0.160899i	$-0.948561\pi$
$167$	−35.5173	−	132.553i	−0.212679	−	0.793728i	0.774292	−	0.632828i	$-0.218106\pi$
$168$		0			0
$169$	42.7675	−	24.6918i	0.253062	−	0.146106i
$170$	49.8434	+	31.5505i	0.293196	+	0.185591i
$171$		0			0
$172$	132.697	−	132.697i	0.771494	−	0.771494i
$173$	12.6759	−	47.3070i	0.0732709	−	0.273451i	−0.919565	−	0.392938i	$-0.871459\pi$
$173$	12.6759	−	47.3070i	0.0732709	−	0.273451i	0.992836	+	0.119488i	$0.0381252\pi$
$174$		0			0
$175$	−39.0656	+	33.1686i	−0.223232	+	0.189535i
$176$	−8.03291	+	13.9134i	−0.0456415	+	0.0790534i
$177$		0			0
$178$	−76.6933	+	286.223i	−0.430861	+	1.60800i
$179$		−	183.712i		−	1.02632i	−0.858292	−	0.513161i	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		0			0
$181$	−21.7276			−0.120042			−0.0600209	−	0.998197i	$-0.519117\pi$
$181$	−21.7276			−0.120042			−0.0600209	+	0.998197i	$0.519117\pi$
$182$	−92.0617	−	24.6679i	−0.505834	−	0.135538i
$183$		0			0
$184$	−120.369	−	69.4949i	−0.654178	−	0.377690i
$185$	−256.804	−	80.1506i	−1.38813	−	0.433246i
$186$		0			0
$187$	−12.1284	−	3.24978i	−0.0648575	−	0.0173785i
$188$	116.520	+	116.520i	0.619787	+	0.619787i
$189$		0			0
$190$	−317.666	+	71.3939i	−1.67193	+	0.375757i
$191$	−20.0454	−	34.7197i	−0.104950	−	0.181778i	0.808768	−	0.588128i	$-0.200135\pi$
$191$	−20.0454	−	34.7197i	−0.104950	−	0.181778i	−0.913718	+	0.406350i	$0.866802\pi$
$192$		0			0
$193$	−105.956	+	28.3909i	−0.548996	+	0.147103i	−0.522646	−	0.852550i	$-0.675055\pi$
$193$	−105.956	+	28.3909i	−0.548996	+	0.147103i	−0.0263498	+	0.999653i	$0.508388\pi$
$194$	56.2435	+	32.4722i	0.289915	+	0.167382i
$195$		0			0
$196$	−132.131	−	228.858i	−0.674138	−	1.16764i
$197$	67.3031	−	67.3031i	0.341640	−	0.341640i	−0.515344	−	0.856984i	$-0.672336\pi$
$197$	67.3031	−	67.3031i	0.341640	−	0.341640i	0.856984	+	0.515344i	$0.172336\pi$
$198$		0			0
$199$		−	251.394i		−	1.26329i	−0.775259	−	0.631643i	$-0.782381\pi$
$199$		−	251.394i		−	1.26329i	0.775259	−	0.631643i	$-0.217619\pi$
$200$	146.945	−	26.7917i	0.734724	−	0.133958i
$201$		0			0
$202$	−141.382	−	527.644i	−0.699910	−	2.61210i
$203$	1.69011	−	0.452863i	0.00832565	−	0.00223085i
$204$		0			0
$205$	143.366	+	5.84220i	0.699345	+	0.0284985i
$206$	−288.116			−1.39862
$207$		0			0
$208$	−50.1362	−	50.1362i	−0.241040	−	0.241040i
$209$	60.0182	−	34.6515i	0.287168	−	0.165797i
$210$		0			0
$211$	−132.394	+	229.313i	−0.627459	+	1.08679i	0.360601	+	0.932720i	$0.382572\pi$
$211$	−132.394	+	229.313i	−0.627459	+	1.08679i	−0.988060	+	0.154071i	$0.950762\pi$
$212$	−61.9618	−	231.244i	−0.292272	−	1.09078i
$213$		0			0
$214$	−18.2740	+	10.5505i	−0.0853926	+	0.0493014i
$215$	−155.192	+	34.8786i	−0.721822	+	0.162226i
$216$		0			0
$217$	27.1010	−	27.1010i	0.124889	−	0.124889i
$218$	−32.0050	+	119.444i	−0.146812	+	0.547910i
$219$		0			0
$220$	−87.4708	+	45.8579i	−0.397594	+	0.208445i
$221$	27.7071	−	47.9902i	0.125372	−	0.217150i
$222$		0			0
$223$	−12.2359	+	45.6650i	−0.0548695	+	0.204776i	−0.987919	−	0.154973i	$-0.950471\pi$
$223$	−12.2359	+	45.6650i	−0.0548695	+	0.204776i	0.933049	+	0.359749i	$0.117138\pi$
$224$			79.9342i			0.356849i
$225$		0			0
$226$	−63.8888			−0.282694
$227$	−28.9207	−	7.74928i	−0.127404	−	0.0341378i	0.194554	−	0.980892i	$-0.437674\pi$
$227$	−28.9207	−	7.74928i	−0.127404	−	0.0341378i	−0.321958	+	0.946754i	$0.604341\pi$
$228$		0			0
$229$	−211.135	−	121.899i	−0.921988	−	0.532310i	−0.0377192	−	0.999288i	$-0.512009\pi$
$229$	−211.135	−	121.899i	−0.921988	−	0.532310i	−0.884269	+	0.466978i	$0.845343\pi$
$230$	169.924	+	324.117i	0.738798	+	1.40921i
$231$		0			0
$232$	−4.92606	−	1.31993i	−0.0212330	−	0.00568936i
$233$	−161.712	−	161.712i	−0.694042	−	0.694042i	0.269077	−	0.963119i	$-0.413281\pi$
$233$	−161.712	−	161.712i	−0.694042	−	0.694042i	−0.963119	+	0.269077i	$0.913281\pi$
$234$		0			0
$235$	−30.6265	−	136.272i	−0.130326	−	0.579883i
$236$	−330.149	−	571.834i	−1.39894	−	2.42303i
$237$		0			0
$238$	−23.3604	+	6.25941i	−0.0981531	+	0.0263000i
$239$	282.499	+	163.101i	1.18201	+	0.682431i	0.956478	−	0.291806i	$-0.0942561\pi$
$239$	282.499	+	163.101i	1.18201	+	0.682431i	0.225528	+	0.974237i	$0.427589\pi$
$240$		0			0
$241$	66.7878	+	115.680i	0.277128	+	0.479999i	0.970670	−	0.240417i	$-0.0772842\pi$
$241$	66.7878	+	115.680i	0.277128	+	0.479999i	−0.693542	+	0.720416i	$0.743951\pi$
$242$	−244.250	+	244.250i	−1.00930	+	1.00930i
$243$		0			0
$244$		−	555.040i		−	2.27475i
$245$	−9.12009	+	223.804i	−0.0372249	+	0.913486i
$246$		0			0
$247$	79.1612	+	295.434i	0.320491	+	1.19609i
$248$	−107.902	+	28.9123i	−0.435089	+	0.116582i
$249$		0			0
$250$	−364.644	−	147.330i	−1.45858	−	0.589321i
$251$	404.742			1.61252			0.806260	−	0.591562i	$-0.201488\pi$
$251$	404.742			1.61252			0.806260	+	0.591562i	$0.201488\pi$
$252$		0			0
$253$	−55.0806	−	55.0806i	−0.217710	−	0.217710i
$254$	441.677	−	255.002i	1.73889	−	1.00395i
$255$		0			0
$256$	59.8837	−	103.722i	0.233921	−	0.405162i
$257$	32.6631	+	121.900i	0.127094	+	0.474320i	0.999906	−	0.0137364i	$-0.00437256\pi$
$257$	32.6631	+	121.900i	0.127094	+	0.474320i	−0.872812	+	0.488057i	$0.837706\pi$
$258$		0			0
$259$	95.5164	−	55.1464i	0.368789	−	0.212921i
$260$	−95.5755	−	425.262i	−0.367598	−	1.63562i
$261$		0			0
$262$	58.1464	−	58.1464i	0.221933	−	0.221933i
$263$	125.123	−	466.967i	0.475754	−	1.77554i	−0.142751	−	0.989759i	$-0.545595\pi$
$263$	125.123	−	466.967i	0.475754	−	1.77554i	0.618506	−	0.785780i	$-0.287738\pi$
$264$		0			0
$265$	−60.4561	+	193.703i	−0.228136	+	0.730954i
$266$	66.7423	−	115.601i	0.250911	−	0.434591i
$267$		0			0
$268$	118.537	−	442.385i	0.442301	−	1.65069i
$269$		−	3.50052i		−	0.0130131i	−0.999979	−	0.00650653i	$-0.997929\pi$
$269$		−	3.50052i		−	0.0130131i	0.999979	−	0.00650653i	$-0.00207111\pi$
$270$		0			0
$271$	−103.576			−0.382197			−0.191099	−	0.981571i	$-0.561205\pi$
$271$	−103.576			−0.382197			−0.191099	+	0.981571i	$0.561205\pi$
$272$	−17.3785	−	4.65655i	−0.0638915	−	0.0171197i
$273$		0			0
$274$	−56.3791	−	32.5505i	−0.205763	−	0.118797i
$275$	83.4342	+	6.81125i	0.303397	+	0.0247682i
$276$		0			0
$277$	390.013	+	104.504i	1.40799	+	0.377270i	0.881208	−	0.472730i	$-0.156731\pi$
$277$	390.013	+	104.504i	1.40799	+	0.377270i	0.526783	+	0.850000i	$0.323398\pi$
$278$	−185.035	−	185.035i	−0.665594	−	0.665594i
$279$		0			0
$280$	−32.7526	+	51.7423i	−0.116973	+	0.184794i
$281$	186.348	+	322.765i	0.663162	+	1.14863i	0.979780	+	0.200077i	$0.0641192\pi$
$281$	186.348	+	322.765i	0.663162	+	1.14863i	−0.316618	+	0.948553i	$0.602547\pi$
$282$		0			0
$283$	105.446	−	28.2542i	0.372601	−	0.0998381i	−0.0676591	−	0.997709i	$-0.521553\pi$
$283$	105.446	−	28.2542i	0.372601	−	0.0998381i	0.440260	+	0.897870i	$0.354886\pi$
$284$	347.389	+	200.565i	1.22320	+	0.706216i
$285$		0			0
$286$	77.8434	+	134.829i	0.272180	+	0.471429i
$287$	−41.5959	+	41.5959i	−0.144934	+	0.144934i
$288$		0			0
$289$			274.939i			0.951345i
$290$	9.10042	+	9.87362i	0.0313808	+	0.0340470i
$291$		0			0
$292$	−85.9088	−	320.616i	−0.294208	−	1.09800i
$293$	−323.154	+	86.5889i	−1.10292	+	0.295525i	−0.763951	−	0.645274i	$-0.776743\pi$
$293$	−323.154	+	86.5889i	−1.10292	+	0.295525i	−0.338964	+	0.940799i	$0.610077\pi$
$294$		0			0
$295$	−22.7879	+	559.207i	−0.0772470	+	1.89562i
$296$	−321.464			−1.08603
$297$		0			0
$298$	265.070	+	265.070i	0.889498	+	0.889498i
$299$	297.720	−	171.889i	0.995719	−	0.574879i
$300$		0			0
$301$	32.6061	−	56.4755i	0.108326	−	0.187626i
$302$	−118.050	−	440.570i	−0.390896	−	1.45884i
$303$		0			0
$304$	85.9990	−	49.6515i	0.282891	−	0.163327i
$305$	−251.621	+	397.510i	−0.824987	+	1.30331i
$306$		0			0
$307$	168.969	−	168.969i	0.550389	−	0.550389i	−0.376164	−	0.926553i	$-0.622757\pi$
$307$	168.969	−	168.969i	0.550389	−	0.550389i	0.926553	+	0.376164i	$0.122757\pi$
$308$	10.4797	−	39.1108i	0.0340251	−	0.126983i
$309$		0			0
$310$	280.770	+	87.6305i	0.905710	+	0.282679i
$311$	177.151	−	306.835i	0.569617	−	0.986606i	−0.426986	−	0.904258i	$-0.640425\pi$
$311$	177.151	−	306.835i	0.569617	−	0.986606i	0.996604	−	0.0823482i	$-0.0262420\pi$
$312$		0			0
$313$	55.7726	−	208.146i	0.178187	−	0.665003i	−0.817800	−	0.575503i	$-0.804806\pi$
$313$	55.7726	−	208.146i	0.178187	−	0.665003i	0.995987	−	0.0895003i	$-0.0285270\pi$
$314$		−	227.576i		−	0.724763i
$315$		0			0
$316$	−144.495			−0.457262
$317$	−583.589	−	156.372i	−1.84097	−	0.493288i	−0.842039	−	0.539416i	$-0.818645\pi$
$317$	−583.589	−	156.372i	−1.84097	−	0.493288i	−0.998936	+	0.0461283i	$0.985312\pi$
$318$		0			0
$319$	−2.47524	−	1.42908i	−0.00775937	−	0.00447987i
$320$	−458.309	+	240.276i	−1.43222	+	0.750862i
$321$		0			0
$322$	−144.923	−	38.8319i	−0.450071	−	0.120596i
$323$	54.8786	+	54.8786i	0.169903	+	0.169903i
$324$		0			0
$325$	−124.338	+	347.893i	−0.382579	+	1.07044i
$326$	−421.353	−	729.805i	−1.29249	−	2.23867i
$327$		0			0
$328$	165.613	−	44.3759i	0.504918	−	0.135292i
$329$	49.5906	+	28.6311i	0.150731	+	0.0870247i
$330$		0			0
$331$	−244.712	−	423.853i	−0.739310	−	1.28052i	−0.952806	−	0.303579i	$-0.901818\pi$
$331$	−244.712	−	423.853i	−0.739310	−	1.28052i	0.213496	−	0.976944i	$-0.431515\pi$
$332$	124.742	−	124.742i	0.375730	−	0.375730i
$333$		0			0
$334$			431.757i			1.29269i
$335$	−285.444	+	263.091i	−0.852071	+	0.785346i
$336$		0			0
$337$	106.950	+	399.141i	0.317358	+	1.18440i	0.921774	+	0.387727i	$0.126740\pi$
$337$	106.950	+	399.141i	0.317358	+	1.18440i	−0.604416	+	0.796669i	$0.706594\pi$
$338$	−150.080	+	40.2138i	−0.444023	+	0.118976i
$339$		0			0
$340$	−74.9575	−	81.3261i	−0.220463	−	0.239194i
$341$	−62.6061			−0.183596
$342$		0			0
$343$	−135.959	−	135.959i	−0.396382	−	0.396382i
$344$	−164.606	+	95.0352i	−0.478505	+	0.276265i
$345$		0			0
$346$	−77.0454	+	133.447i	−0.222675	+	0.385684i
$347$	−117.146	−	437.196i	−0.337598	−	1.25993i	−0.901025	−	0.433767i	$-0.857184\pi$
$347$	−117.146	−	437.196i	−0.337598	−	1.25993i	0.563428	−	0.826166i	$-0.309482\pi$
$348$		0			0
$349$	−497.107	+	287.005i	−1.42437	+	0.822363i	−0.996669	−	0.0815556i	$-0.974011\pi$
$349$	−497.107	+	287.005i	−1.42437	+	0.822363i	−0.427705	+	0.903918i	$0.640678\pi$
$350$	145.732	−	68.9898i	0.416378	−	0.197114i
$351$		0			0
$352$	92.3281	−	92.3281i	0.262296	−	0.262296i
$353$	−97.5531	+	364.073i	−0.276354	+	1.03137i	0.678574	+	0.734532i	$0.262598\pi$
$353$	−97.5531	+	364.073i	−0.276354	+	1.03137i	−0.954928	+	0.296836i	$0.904068\pi$
$354$		0			0
$355$	−157.870	−	301.126i	−0.444704	−	0.848243i
$356$	277.788	−	481.143i	0.780303	−	1.35152i
$357$		0			0
$358$	−149.599	+	558.311i	−0.417874	+	1.55953i
$359$		−	216.272i		−	0.602430i	−0.953556	−	0.301215i	$-0.902608\pi$
$359$		−	216.272i		−	0.602430i	0.953556	−	0.301215i	$-0.0973922\pi$
$360$		0			0
$361$	−67.3633			−0.186602
$362$	66.0313	+	17.6930i	0.182407	+	0.0488758i
$363$		0			0
$364$	154.756	+	89.3485i	0.425154	+	0.245463i
$365$	−83.8212	+	268.565i	−0.229647	+	0.735795i
$366$		0			0
$367$	328.542	+	88.0327i	0.895211	+	0.239871i	0.676958	−	0.736021i	$-0.263298\pi$
$367$	328.542	+	88.0327i	0.895211	+	0.239871i	0.218252	+	0.975892i	$0.429964\pi$
$368$	−78.9240	−	78.9240i	−0.214467	−	0.214467i
$369$		0			0
$370$	715.176	+	452.702i	1.93291	+	1.22352i
$371$	−41.5959	−	72.0462i	−0.112118	−	0.194195i
$372$		0			0
$373$	451.071	−	120.864i	1.20930	−	0.324032i	0.402816	−	0.915281i	$-0.368032\pi$
$373$	451.071	−	120.864i	1.20930	−	0.324032i	0.806489	+	0.591249i	$0.201365\pi$
$374$	34.2124	+	19.7526i	0.0914771	+	0.0528143i
$375$		0			0
$376$	−83.4495	−	144.539i	−0.221940	−	0.384412i
$377$	8.91939	−	8.91939i	0.0236589	−	0.0236589i
$378$		0			0
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$	609.948	+	24.8556i	1.60513	+	0.0654094i
$381$		0			0
$382$	32.6465	+	121.838i	0.0854620	+	0.318948i
$383$	233.086	−	62.4553i	0.608581	−	0.163069i	0.0586495	−	0.998279i	$-0.481321\pi$
$383$	233.086	−	62.4553i	0.608581	−	0.163069i	0.549931	+	0.835210i	$0.314654\pi$
$384$		0			0
$385$	−25.2358	+	23.2596i	−0.0655476	+	0.0604146i
$386$	345.126			0.894109
$387$		0			0
$388$	−86.1010	−	86.1010i	−0.221910	−	0.221910i
$389$	474.008	−	273.669i	1.21853	−	0.703518i	0.253926	−	0.967224i	$-0.418278\pi$
$389$	474.008	−	273.669i	1.21853	−	0.703518i	0.964603	+	0.263705i	$0.0849446\pi$
$390$		0			0
$391$	43.6163	−	75.5457i	0.111551	−	0.193212i
$392$	69.2739	+	258.534i	0.176719	+	0.659525i
$393$		0			0
$394$	−259.344	+	149.732i	−0.658233	+	0.380031i
$395$	103.485	+	65.5051i	0.261987	+	0.165836i
$396$		0			0
$397$	45.2577	−	45.2577i	0.113999	−	0.113999i	−0.647806	−	0.761805i	$-0.724313\pi$
$397$	45.2577	−	45.2577i	0.113999	−	0.113999i	0.761805	+	0.647806i	$0.224313\pi$
$398$	−204.713	+	764.001i	−0.514355	+	1.91960i
$399$		0			0
$400$	119.551	+	9.75971i	0.298878	+	0.0243993i
$401$	−260.151	+	450.595i	−0.648756	+	1.12368i	0.334665	+	0.942337i	$0.391377\pi$
$401$	−260.151	+	450.595i	−0.648756	+	1.12368i	−0.983420	+	0.181340i	$0.941956\pi$
$402$		0			0
$403$	71.5117	−	266.885i	0.177448	−	0.662246i
$404$			1024.19i			2.53511i
$405$		0			0
$406$	−5.50510			−0.0135594
$407$	−174.023	−	46.6294i	−0.427576	−	0.114569i
$408$		0			0
$409$	300.606	+	173.555i	0.734979	+	0.424340i	0.820241	−	0.572018i	$-0.193839\pi$
$409$	300.606	+	173.555i	0.734979	+	0.424340i	−0.0852621	+	0.996359i	$0.527173\pi$
$410$	−430.939	−	134.499i	−1.05107	−	0.328047i
$411$		0			0
$412$	521.786	+	139.812i	1.26647	+	0.339350i
$413$	−162.247	−	162.247i	−0.392851	−	0.392851i
$414$		0			0
$415$	−145.889	+	32.7878i	−0.351539	+	0.0790066i
$416$	288.126	+	499.049i	0.692611	+	1.19964i
$417$		0			0
$418$	−210.616	+	56.4344i	−0.503866	+	0.135011i
$419$	505.238	+	291.699i	1.20582	+	0.696180i	0.961843	−	0.273602i	$-0.0882151\pi$
$419$	505.238	+	291.699i	1.20582	+	0.696180i	0.243975	+	0.969781i	$0.421548\pi$
$420$		0			0
$421$	−106.576	−	184.594i	−0.253148	−	0.438466i	0.711243	−	0.702947i	$-0.248133\pi$
$421$	−106.576	−	184.594i	−0.253148	−	0.438466i	−0.964391	+	0.264481i	$0.914799\pi$
$422$	589.085	−	589.085i	1.39594	−	1.39594i
$423$		0			0
$424$			242.474i			0.571874i
$425$	16.8150	+	92.2254i	0.0395646	+	0.217001i
$426$		0			0
$427$	−49.9199	−	186.304i	−0.116908	−	0.436308i
$428$	38.2146	−	10.2396i	0.0892864	−	0.0239242i
$429$		0			0
$430$	500.039	+	20.3768i	1.16288	+	0.0473878i
$431$	−187.364			−0.434720			−0.217360	−	0.976092i	$-0.569745\pi$
$431$	−187.364			−0.434720			−0.217360	+	0.976092i	$0.569745\pi$
$432$		0			0
$433$	154.848	+	154.848i	0.357617	+	0.357617i	0.862934	−	0.505317i	$-0.168624\pi$
$433$	154.848	+	154.848i	0.357617	+	0.357617i	−0.505317	+	0.862934i	$0.668624\pi$
$434$	−104.430	+	60.2929i	−0.240623	+	0.138924i
$435$		0			0
$436$	115.924	−	200.786i	0.265881	−	0.460519i
$437$	124.615	+	465.069i	0.285160	+	1.06423i
$438$		0			0
$439$	219.043	−	126.464i	0.498958	−	0.288074i	−0.229325	−	0.973350i	$-0.573652\pi$
$439$	219.043	−	126.464i	0.498958	−	0.288074i	0.728283	+	0.685276i	$0.240319\pi$
$440$	97.5959	−	21.9342i	0.221809	−	0.0498504i
$441$		0			0
$442$	−123.283	+	123.283i	−0.278920	+	0.278920i
$443$	154.144	−	575.275i	0.347956	−	1.29859i	−0.541165	−	0.840917i	$-0.682016\pi$
$443$	154.144	−	575.275i	0.347956	−	1.29859i	0.889121	−	0.457673i	$-0.151317\pi$
$444$		0			0
$445$	−417.067	+	218.654i	−0.937229	+	0.491357i
$446$	74.3712	−	128.815i	0.166752	−	0.288822i
$447$		0			0
$448$	54.9092	−	204.924i	0.122565	−	0.457420i
$449$			297.909i			0.663495i	0.943368	+	0.331747i	$0.107638\pi$
$449$			297.909i			0.663495i	−0.943368	+	0.331747i	$0.892362\pi$
$450$		0			0
$451$	96.0908			0.213062
$452$	115.704	+	31.0029i	0.255983	+	0.0685905i
$453$		0			0
$454$	81.5814	+	47.1010i	0.179695	+	0.103747i
$455$	−70.3285	−	134.147i	−0.154568	−	0.294828i
$456$		0			0
$457$	−390.338	−	104.591i	−0.854130	−	0.228864i	−0.194917	−	0.980820i	$-0.562444\pi$
$457$	−390.338	−	104.591i	−0.854130	−	0.228864i	−0.659213	+	0.751956i	$0.729110\pi$
$458$	542.388	+	542.388i	1.18425	+	1.18425i
$459$		0			0
$460$	−150.454	−	669.444i	−0.327074	−	1.45531i
$461$	263.310	+	456.066i	0.571171	+	0.989298i	0.996446	+	0.0842333i	$0.0268441\pi$
$461$	263.310	+	456.066i	0.571171	+	0.989298i	−0.425275	+	0.905064i	$0.639823\pi$
$462$		0			0
$463$	−458.577	+	122.875i	−0.990447	+	0.265389i	−0.717438	−	0.696622i	$-0.754685\pi$
$463$	−458.577	+	122.875i	−0.990447	+	0.265389i	−0.273009	+	0.962012i	$0.588019\pi$
$464$	−3.54672	−	2.04770i	−0.00764380	−	0.00441315i
$465$		0			0
$466$	359.767	+	623.135i	0.772033	+	1.33720i
$467$	−488.742	+	488.742i	−1.04656	+	1.04656i	−0.0476956	+	0.998862i	$0.515188\pi$
$467$	−488.742	+	488.742i	−1.04656	+	1.04656i	−0.998862	+	0.0476956i	$0.984812\pi$
$468$		0			0
$469$		−	159.151i		−	0.339341i
$470$	−17.8926	+	439.079i	−0.0380694	+	0.934212i
$471$		0			0
$472$	173.091	+	645.984i	0.366718	+	1.36861i
$473$	−102.894	+	27.5703i	−0.217534	+	0.0582882i
$474$		0			0
$475$	−425.566	−	294.314i	−0.895928	−	0.619608i
$476$	45.3439			0.0952603
$477$		0			0
$478$	−725.716	−	725.716i	−1.51823	−	1.51823i
$479$	−160.171	+	92.4745i	−0.334385	+	0.193057i	−0.657786	−	0.753205i	$-0.728507\pi$
$479$	−160.171	+	92.4745i	−0.334385	+	0.193057i	0.323401	+	0.946262i	$0.395174\pi$
$480$		0			0
$481$	397.555	−	688.586i	0.826518	−	1.43157i
$482$	−108.772	−	405.944i	−0.225669	−	0.842207i
$483$		0			0
$484$	560.869	−	323.818i	1.15882	−	0.669045i
$485$	22.6311	+	100.697i	0.0466621	+	0.207623i
$486$		0			0
$487$	−120.682	+	120.682i	−0.247807	+	0.247807i	−0.820070	−	0.572263i	$-0.806066\pi$
$487$	−120.682	+	120.682i	−0.247807	+	0.247807i	0.572263	+	0.820070i	$0.306066\pi$
$488$	−145.499	+	543.008i	−0.298153	+	1.11272i
$489$		0			0
$490$	209.963	−	672.727i	0.428496	−	1.37291i
$491$	−52.8411	+	91.5234i	−0.107619	+	0.186402i	−0.914805	−	0.403895i	$-0.867656\pi$
$491$	−52.8411	+	91.5234i	−0.107619	+	0.186402i	0.807186	+	0.590297i	$0.200989\pi$
$492$		0			0
$493$	0.828415	−	3.09169i	0.00168035	−	0.00627117i
$494$		−	962.302i		−	1.94798i
$495$		0			0
$496$	−89.7071			−0.180861
$497$	134.643	+	36.0774i	0.270911	+	0.0725904i
$498$		0			0
$499$	−640.499	−	369.792i	−1.28357	−	0.741067i	−0.306067	−	0.952010i	$-0.599013\pi$
$499$	−640.499	−	369.792i	−1.28357	−	0.741067i	−0.977498	+	0.210943i	$0.932347\pi$
$500$	588.887	+	443.768i	1.17777	+	0.887536i
$501$		0			0
$502$	−1230.04	−	329.587i	−2.45027	−	0.656548i
$503$	406.409	+	406.409i	0.807970	+	0.807970i	0.984326	−	0.176357i	$-0.0564312\pi$
$503$	406.409	+	406.409i	0.807970	+	0.807970i	−0.176357	+	0.984326i	$0.556431\pi$
$504$		0			0
$505$	464.303	−	733.504i	0.919412	−	1.45248i
$506$	122.540	+	212.246i	0.242175	+	0.419459i
$507$		0			0
$508$	−923.633	+	247.487i	−1.81818	+	0.487179i
$509$	−168.451	−	97.2554i	−0.330945	−	0.191071i	0.325315	−	0.945606i	$-0.394530\pi$
$509$	−168.451	−	97.2554i	−0.330945	−	0.191071i	−0.656261	+	0.754534i	$0.727863\pi$
$510$		0			0
$511$	−57.6719	−	99.8907i	−0.112861	−	0.195481i
$512$	213.376	−	213.376i	0.416750	−	0.416750i
$513$		0			0
$514$		−	397.060i		−	0.772491i
$515$	−310.312	−	336.677i	−0.602547	−	0.653741i
$516$		0			0
$517$	−24.2092	−	90.3500i	−0.0468263	−	0.174758i
$518$	−335.186	+	89.8129i	−0.647078	+	0.173384i
$519$		0			0
$520$	−17.9749	+	441.098i	−0.0345671	+	0.848266i
$521$	589.605			1.13168			0.565840	−	0.824515i	$-0.308552\pi$
$521$	589.605			1.13168			0.565840	+	0.824515i	$0.308552\pi$
$522$		0			0
$523$	−141.546	−	141.546i	−0.270642	−	0.270642i	0.558716	−	0.829359i	$-0.311294\pi$
$523$	−141.546	−	141.546i	−0.270642	−	0.270642i	−0.829359	+	0.558716i	$0.811294\pi$
$524$	−133.521	+	77.0885i	−0.254812	+	0.147115i
$525$		0			0
$526$	−760.514	+	1317.25i	−1.44584	+	2.50428i
$527$	−18.1459	−	67.7214i	−0.0344324	−	0.128504i
$528$		0			0
$529$	10.5408	−	6.08571i	0.0199258	−	0.0115042i
$530$	341.464	−	539.444i	0.644272	−	1.01782i
$531$		0			0
$532$	−176.969	+	176.969i	−0.332649	+	0.332649i
$533$	−109.759	+	409.628i	−0.205928	+	0.768532i
$534$		0			0
$535$	−32.0106	−	9.99074i	−0.0598329	−	0.0186743i
$536$	−231.934	+	401.722i	−0.432713	+	0.749481i
$537$		0			0
$538$	−2.85052	+	10.6383i	−0.00529836	+	0.0197737i
$539$			150.005i			0.278302i
$540$		0			0
$541$	431.303			0.797233			0.398617	−	0.917118i	$-0.369490\pi$
$541$	431.303			0.797233			0.398617	+	0.917118i	$0.369490\pi$
$542$	314.772	+	84.3429i	0.580760	+	0.155614i
$543$		0			0
$544$	126.632	+	73.1112i	0.232780	+	0.134396i
$545$	−174.047	+	91.2467i	−0.319352	+	0.167425i
$546$		0			0
$547$	609.551	+	163.329i	1.11435	+	0.298590i	0.768596	−	0.639734i	$-0.220956\pi$
$547$	609.551	+	163.329i	1.11435	+	0.298590i	0.345757	+	0.938324i	$0.387622\pi$
$548$	86.3087	+	86.3087i	0.157498	+	0.157498i
$549$		0			0
$550$	−248.015	−	88.6413i	−0.450936	−	0.161166i
$551$	8.83316	+	15.2995i	0.0160311	+	0.0277668i
$552$		0			0
$553$	−48.5009	+	12.9958i	−0.0877050	+	0.0235005i
$554$	−1100.17	−	635.186i	−1.98588	−	1.14655i
$555$		0			0
$556$	245.313	+	424.895i	0.441211	+	0.764200i
$557$	−214.091	+	214.091i	−0.384364	+	0.384364i	−0.872672	−	0.488308i	$-0.837614\pi$
$557$	−214.091	+	214.091i	−0.384364	+	0.384364i	0.488308	+	0.872672i	$0.337614\pi$
$558$		0			0
$559$		−	470.120i		−	0.841003i
$560$	−36.1600	+	33.3283i	−0.0645714	+	0.0595148i
$561$		0			0
$562$	−303.492	−	1132.65i	−0.540021	−	2.01539i
$563$	917.982	−	245.972i	1.63052	−	0.436896i	0.676451	−	0.736488i	$-0.263517\pi$
$563$	917.982	−	245.972i	1.63052	−	0.436896i	0.954067	+	0.299592i	$0.0968506\pi$
$564$		0			0
$565$	−68.8107	−	74.6570i	−0.121789	−	0.132136i
$566$	−343.464			−0.606827
$567$		0			0
$568$	−287.283	−	287.283i	−0.505779	−	0.505779i
$569$	−841.916	+	486.081i	−1.47964	+	0.854272i	−0.999734	−	0.0230473i	$-0.992663\pi$
$569$	−841.916	+	486.081i	−1.47964	+	0.854272i	−0.479908	+	0.877319i	$0.659330\pi$
$570$		0			0
$571$	462.015	−	800.233i	0.809133	−	1.40146i	−0.104333	−	0.994542i	$-0.533271\pi$
$571$	462.015	−	800.233i	0.809133	−	1.40146i	0.913465	−	0.406917i	$-0.133396\pi$
$572$	−75.5491	−	281.953i	−0.132079	−	0.492925i
$573$		0			0
$574$	160.285	−	92.5403i	0.279241	−	0.161220i
$575$	−195.732	+	547.650i	−0.340404	+	0.952436i
$576$		0			0
$577$	−497.879	+	497.879i	−0.862874	+	0.862874i	−0.991671	−	0.128797i	$-0.958889\pi$
$577$	−497.879	+	497.879i	−0.862874	+	0.862874i	0.128797	+	0.991671i	$0.458889\pi$
$578$	223.886	−	835.555i	0.387346	−	1.44560i
$579$		0			0
$580$	−11.6898	−	22.2975i	−0.0201549	−	0.0384440i
$581$	30.6515	−	53.0900i	0.0527565	−	0.0913770i
$582$		0			0
$583$	−35.1717	+	131.262i	−0.0603288	+	0.225150i
$584$			336.186i			0.575661i
$585$		0			0
$586$	1052.59			1.79624
$587$	399.949	+	107.166i	0.681345	+	0.182566i	0.582860	−	0.812573i	$-0.301934\pi$
$587$	399.949	+	107.166i	0.681345	+	0.182566i	0.0984849	+	0.995139i	$0.468600\pi$
$588$		0			0
$589$	335.125	+	193.485i	0.568973	+	0.328497i
$590$	524.623	−	1680.91i	0.889192	−	2.84899i
$591$		0			0
$592$	−249.355	−	66.8144i	−0.421207	−	0.112862i
$593$	−451.258	−	451.258i	−0.760974	−	0.760974i	0.215524	−	0.976498i	$-0.430854\pi$
$593$	−451.258	−	451.258i	−0.760974	−	0.760974i	−0.976498	+	0.215524i	$0.930854\pi$
$594$		0			0
$595$	−32.4745	−	20.5561i	−0.0545790	−	0.0345481i
$596$	−351.421	−	608.679i	−0.589633	−	1.02127i
$597$		0			0
$598$	−1044.76	+	279.943i	−1.74709	+	0.468131i
$599$	−28.4560	−	16.4291i	−0.0475058	−	0.0274275i	0.476059	−	0.879413i	$-0.342065\pi$
$599$	−28.4560	−	16.4291i	−0.0475058	−	0.0274275i	−0.523565	+	0.851986i	$0.675398\pi$
$600$		0			0
$601$	92.2418	+	159.768i	0.153481	+	0.265836i	0.932505	−	0.361158i	$-0.117618\pi$
$601$	92.2418	+	159.768i	0.153481	+	0.265836i	−0.779024	+	0.626994i	$0.784285\pi$
$602$	−145.081	+	145.081i	−0.240998	+	0.240998i
$603$		0			0
$604$			855.171i			1.41585i
$605$	−548.484	−	22.3509i	−0.906584	−	0.0369436i
$606$		0			0
$607$	49.9219	+	186.311i	0.0822437	+	0.306938i	0.994778	−	0.102062i	$-0.0325442\pi$
$607$	49.9219	+	186.311i	0.0822437	+	0.306938i	−0.912534	+	0.409000i	$0.865878\pi$
$608$	−779.565	+	208.884i	−1.28218	+	0.343559i
$609$		0			0
$610$	1088.39	−	1003.16i	1.78424	−	1.64452i
$611$	412.808			0.675627
$612$		0			0
$613$	−12.7128	−	12.7128i	−0.0207386	−	0.0207386i	0.696661	−	0.717400i	$-0.254668\pi$
$613$	−12.7128	−	12.7128i	−0.0207386	−	0.0207386i	−0.717400	+	0.696661i	$0.754668\pi$
$614$	−651.102	+	375.914i	−1.06043	+	0.612237i
$615$		0			0
$616$	−20.5051	+	35.5159i	−0.0332875	+	0.0576556i
$617$	145.953	+	544.705i	0.236553	+	0.882828i	0.977443	+	0.211201i	$0.0677375\pi$
$617$	145.953	+	544.705i	0.236553	+	0.882828i	−0.740890	+	0.671627i	$0.765596\pi$
$618$		0			0
$619$	−709.388	+	409.565i	−1.14602	+	0.661656i	−0.947915	−	0.318524i	$-0.896813\pi$
$619$	−709.388	+	409.565i	−1.14602	+	0.661656i	−0.198108	+	0.980180i	$0.563480\pi$
$620$	−465.959	−	294.949i	−0.751547	−	0.475724i
$621$		0			0
$622$	−788.232	+	788.232i	−1.26725	+	1.26725i
$623$	49.9681	−	186.483i	0.0802056	−	0.299331i
$624$		0			0
$625$	−220.574	−	584.784i	−0.352918	−	0.935654i
$626$	−338.992	+	587.152i	−0.541521	+	0.937942i
$627$		0			0
$628$	−110.434	+	412.146i	−0.175851	+	0.656283i
$629$		−	201.757i		−	0.320759i
$630$		0			0
$631$	105.485			0.167171			0.0835853	−	0.996501i	$-0.473363\pi$
$631$	105.485			0.167171			0.0835853	+	0.996501i	$0.473363\pi$
$632$	141.363	+	37.8780i	0.223675	+	0.0599336i
$633$		0			0
$634$	1646.23	+	950.448i	2.59657	+	1.49913i
$635$	773.685	+	241.473i	1.21840	+	0.380272i
$636$		0			0
$637$	−639.458	−	171.342i	−1.00386	−	0.268983i
$638$	6.35867	+	6.35867i	0.00996657	+	0.00996657i
$639$		0			0
$640$	827.580	−	185.994i	1.29309	−	0.290616i
$641$	82.3939	+	142.710i	0.128540	+	0.222637i	0.923111	−	0.384534i	$-0.125638\pi$
$641$	82.3939	+	142.710i	0.128540	+	0.222637i	−0.794571	+	0.607171i	$0.792304\pi$
$642$		0			0
$643$	1044.15	−	279.780i	1.62388	−	0.435116i	0.671739	−	0.740788i	$-0.265548\pi$
$643$	1044.15	−	279.780i	1.62388	−	0.435116i	0.952137	+	0.305672i	$0.0988810\pi$
$644$	243.616	+	140.652i	0.378285	+	0.218403i
$645$		0			0
$646$	−122.091	−	211.467i	−0.188995	−	0.327349i
$647$	−321.287	+	321.287i	−0.496580	+	0.496580i	−0.910372	−	0.413792i	$-0.864204\pi$
$647$	−321.287	+	321.287i	−0.496580	+	0.496580i	0.413792	+	0.910372i	$0.364204\pi$
$648$		0			0
$649$			374.808i			0.577516i
$650$	661.165	−	956.018i	1.01718	−	1.47080i
$651$		0			0
$652$	408.935	+	1526.17i	0.627201	+	2.34074i
$653$	−231.982	+	62.1595i	−0.355256	+	0.0951907i	−0.432033	−	0.901858i	$-0.642204\pi$
$653$	−231.982	+	62.1595i	−0.355256	+	0.0951907i	0.0767769	+	0.997048i	$0.475537\pi$
$654$		0			0
$655$	130.573	+	5.32088i	0.199348	+	0.00812348i
$656$	137.687			0.209888
$657$		0			0
$658$	−127.394	−	127.394i	−0.193608	−	0.193608i
$659$	830.313	−	479.381i	1.25996	−	0.727438i	0.286893	−	0.957963i	$-0.407378\pi$
$659$	830.313	−	479.381i	1.25996	−	0.727438i	0.973066	+	0.230525i	$0.0740444\pi$
$660$		0			0
$661$	−198.196	+	343.286i	−0.299843	+	0.519344i	−0.976100	−	0.217322i	$-0.930268\pi$
$661$	−198.196	+	343.286i	−0.299843	+	0.519344i	0.676257	+	0.736666i	$0.263601\pi$
$662$	398.544	+	1487.39i	0.602030	+	2.24681i
$663$		0			0
$664$	−154.738	+	89.3383i	−0.233040	+	0.134546i
$665$	206.969	−	46.5153i	0.311232	−	0.0699478i
$666$		0			0
$667$	14.0408	−	14.0408i	0.0210507	−	0.0210507i
$668$	209.516	−	781.925i	0.313647	−	1.17055i
$669$		0			0
$670$	1081.72	−	567.108i	1.61451	−	0.846429i
$671$	−157.530	+	272.850i	−0.234769	+	0.406632i
$672$		0			0
$673$	60.2870	−	224.994i	0.0895795	−	0.334315i	−0.906562	−	0.422072i	$-0.861303\pi$
$673$	60.2870	−	224.994i	0.0895795	−	0.334315i	0.996142	+	0.0877564i	$0.0279697\pi$
$674$		−	1300.10i		−	1.92894i
$675$		0			0
$676$	291.313			0.430937
$677$	743.648	+	199.260i	1.09845	+	0.294328i	0.762132	−	0.647422i	$-0.224153\pi$
$677$	743.648	+	199.260i	1.09845	+	0.294328i	0.336315	+	0.941750i	$0.390819\pi$
$678$		0			0
$679$	−36.6444	−	21.1566i	−0.0539681	−	0.0311585i
$680$	52.0137	+	99.2126i	0.0764908	+	0.145901i
$681$		0			0
$682$	190.264	+	50.9810i	0.278979	+	0.0747522i
$683$	−786.590	−	786.590i	−1.15167	−	1.15167i	−0.986218	−	0.165452i	$-0.947092\pi$
$683$	−786.590	−	786.590i	−1.15167	−	1.15167i	−0.165452	−	0.986218i	$-0.552908\pi$
$684$		0			0
$685$	−22.6857	−	100.940i	−0.0331178	−	0.147357i
$686$	302.474	+	523.901i	0.440925	+	0.763704i
$687$		0			0
$688$	−147.435	+	39.5050i	−0.214294	+	0.0574200i
$689$	−519.387	−	299.868i	−0.753828	−	0.435223i
$690$		0			0
$691$	−178.439	−	309.066i	−0.258233	−	0.447273i	0.707535	−	0.706678i	$-0.249807\pi$
$691$	−178.439	−	309.066i	−0.258233	−	0.447273i	−0.965769	+	0.259405i	$0.916474\pi$
$692$	204.288	−	204.288i	0.295214	−	0.295214i
$693$		0			0
$694$			1424.06i			2.05196i
$695$	16.9323	−	415.512i	0.0243630	−	0.597859i
$696$		0			0
$697$	27.8512	+	103.942i	0.0399586	+	0.149128i
$698$	1744.45	−	467.423i	2.49921	−	0.669661i
$699$		0			0
$700$	−297.403	+	54.2240i	−0.424862	+	0.0774629i
$701$	−885.680			−1.26345			−0.631726	−	0.775192i	$-0.717653\pi$
$701$	−885.680			−1.26345			−0.631726	+	0.775192i	$0.717653\pi$
$702$		0			0
$703$	787.423	+	787.423i	1.12009	+	1.12009i
$704$	−300.121	+	173.275i	−0.426308	+	0.246129i
$705$		0			0
$706$	592.939	−	1027.00i	0.839857	−	1.45467i
$707$	92.1146	+	343.776i	0.130289	+	0.486247i
$708$		0			0
$709$	633.107	−	365.524i	0.892958	−	0.515549i	0.0180489	−	0.999837i	$-0.494255\pi$
$709$	633.107	−	365.524i	0.892958	−	0.515549i	0.874909	+	0.484288i	$0.160921\pi$
$710$	234.565	+	1043.70i	0.330374	+	1.46999i
$711$		0			0
$712$	−397.893	+	397.893i	−0.558839	+	0.558839i
$713$	112.573	−	420.128i	0.157886	−	0.589240i
$714$		0			0
$715$	−73.7133	+	236.179i	−0.103096	+	0.330321i
$716$	541.856	−	938.522i	0.756782	−	1.31078i
$717$		0			0
$718$	−176.113	+	657.265i	−0.245283	+	0.915410i
$719$			629.271i			0.875204i	0.899169	+	0.437602i	$0.144172\pi$
$719$			629.271i			0.875204i	−0.899169	+	0.437602i	$0.855828\pi$
$720$		0			0
$721$	187.716			0.260356
$722$	204.721	+	54.8548i	0.283547	+	0.0759762i
$723$		0			0
$724$	−110.999	−	64.0852i	−0.153313	−	0.0885155i
$725$	−1.73628	+	21.2685i	−0.00239487	+	0.0293359i
$726$		0			0
$727$	21.6843	+	5.81028i	0.0298270	+	0.00799213i	0.273702	−	0.961815i	$-0.411752\pi$
$727$	21.6843	+	5.81028i	0.0298270	+	0.00799213i	−0.243875	+	0.969807i	$0.578419\pi$
$728$	−127.980	−	127.980i	−0.175796	−	0.175796i
$729$		0			0
$730$	473.434	−	747.929i	0.648539	−	1.02456i
$731$	−59.6459	−	103.310i	−0.0815950	−	0.141327i
$732$		0			0
$733$	537.172	−	143.935i	0.732840	−	0.196364i	0.126947	−	0.991910i	$-0.459482\pi$
$733$	537.172	−	143.935i	0.732840	−	0.196364i	0.605894	+	0.795546i	$0.292816\pi$
$734$	−926.773	−	535.073i	−1.26263	−	0.728982i
$735$		0			0
$736$	453.565	+	785.598i	0.616257	+	1.06739i
$737$	−183.828	+	183.828i	−0.249427	+	0.249427i
$738$		0			0
$739$			192.334i			0.260262i	0.991497	+	0.130131i	$0.0415398\pi$
$739$			192.334i			0.260262i	−0.991497	+	0.130131i	$0.958460\pi$
$740$	−1075.52	−	1166.90i	−1.45341	−	1.57690i
$741$		0			0
$742$	67.7442	+	252.825i	0.0912995	+	0.340734i
$743$	−61.0634	+	16.3619i	−0.0821850	+	0.0220214i	−0.299677	−	0.954041i	$-0.596879\pi$
$743$	−61.0634	+	16.3619i	−0.0821850	+	0.0220214i	0.217492	+	0.976062i	$0.430212\pi$
$744$		0			0
$745$	−24.2561	+	595.238i	−0.0325586	+	0.798977i
$746$	−1469.25			−1.96951
$747$		0			0
$748$	−52.3745	−	52.3745i	−0.0700194	−	0.0700194i
$749$	11.9061	−	6.87398i	0.0158960	−	0.00917755i
$750$		0			0
$751$	−113.893	+	197.269i	−0.151656	+	0.262675i	−0.931836	−	0.362879i	$-0.881794\pi$
$751$	−113.893	+	197.269i	−0.151656	+	0.262675i	0.780181	+	0.625554i	$0.215127\pi$
$752$	−34.6889	−	129.461i	−0.0461289	−	0.172155i
$753$		0			0
$754$	−34.3697	+	19.8434i	−0.0455832	+	0.0263175i
$755$	387.682	−	612.459i	0.513486	−	0.811204i
$756$		0			0
$757$	−235.925	+	235.925i	−0.311658	+	0.311658i	−0.845552	−	0.533894i	$-0.820728\pi$
$757$	−235.925	+	235.925i	−0.311658	+	0.311658i	0.533894	+	0.845552i	$0.320728\pi$
$758$	171.006	−	638.202i	0.225601	−	0.841955i
$759$		0			0
$760$	−590.211	−	184.209i	−0.776593	−	0.242380i
$761$	−440.621	+	763.178i	−0.579003	+	1.00286i	0.416592	+	0.909094i	$0.363225\pi$
$761$	−440.621	+	763.178i	−0.579003	+	1.00286i	−0.995594	+	0.0937680i	$0.970109\pi$
$762$		0			0
$763$	20.8522	−	77.8216i	0.0273293	−	0.101994i
$764$		−	236.495i		−	0.309548i
$765$		0			0
$766$	−759.221			−0.991151
$767$	−1597.78	−	428.123i	−2.08315	−	0.558179i
$768$		0			0
$769$	−1046.51	−	604.201i	−1.36087	−	0.785697i	−0.371128	−	0.928582i	$-0.621029\pi$
$769$	−1046.51	−	604.201i	−1.36087	−	0.785697i	−0.989739	+	0.142885i	$0.954362\pi$
$770$	95.6338	−	50.1375i	0.124200	−	0.0651136i
$771$		0			0
$772$	−625.033	−	167.477i	−0.809629	−	0.216939i
$773$	815.226	+	815.226i	1.05463	+	1.05463i	0.998419	+	0.0562070i	$0.0179007\pi$
$773$	815.226	+	815.226i	1.05463	+	1.05463i	0.0562070	+	0.998419i	$0.482099\pi$
$774$		0			0
$775$	200.000	+	422.474i	0.258065	+	0.545128i
$776$	61.6640	+	106.805i	0.0794640	+	0.137636i
$777$		0			0
$778$	−1663.39	+	445.704i	−2.13803	+	0.572884i
$779$	−514.366	−	296.969i	−0.660290	−	0.381219i
$780$		0			0
$781$	−113.848	−	197.190i	−0.145772	−	0.252485i
$782$	−194.070	+	194.070i	−0.248172	+	0.248172i
$783$		0			0
$784$			214.939i			0.274157i
$785$	265.933	−	245.108i	0.338768	−	0.312239i
$786$		0			0
$787$	297.582	+	1110.59i	0.378122	+	1.41117i	0.848728	+	0.528829i	$0.177369\pi$
$787$	297.582	+	1110.59i	0.378122	+	1.41117i	−0.470606	+	0.882343i	$0.655965\pi$
$788$	542.339	−	145.319i	0.688247	−	0.184415i
$789$		0			0
$790$	−261.154	−	283.343i	−0.330575	−	0.358662i
$791$	41.6255			0.0526239
$792$		0			0
$793$	−983.201	−	983.201i	−1.23985	−	1.23985i
$794$	−174.395	+	100.687i	−0.219640	+	0.126809i
$795$		0			0
$796$	741.484	−	1284.29i	0.931512	−	1.61343i
$797$	−113.913	−	425.130i	−0.142928	−	0.533413i	−0.999839	−	0.0179491i	$-0.994286\pi$
$797$	−113.913	−	425.130i	−0.142928	−	0.533413i	0.856911	−	0.515464i	$-0.172380\pi$
$798$		0			0
$799$	90.7153	−	52.3745i	0.113536	−	0.0655501i
$800$	−917.991	−	328.093i	−1.14749	−	0.410116i
$801$		0			0
$802$	1157.54	−	1157.54i	1.44332	−	1.44332i
$803$	−48.7649	+	181.993i	−0.0607283	+	0.226641i
$804$		0			0
$805$	−110.710	−	211.172i	−0.137528	−	0.262326i
$806$	−434.656	+	752.846i	−0.539276	+	0.934053i
$807$		0			0
$808$	268.481	−	1001.99i	0.332279	−	1.24008i
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		0			0
$811$	−132.847			−0.163806			−0.0819032	−	0.996640i	$-0.526100\pi$
$811$	−132.847			−0.163806			−0.0819032	+	0.996640i	$0.526100\pi$
$812$	9.96990	+	2.67143i	0.0122782	+	0.00328993i
$813$		0			0
$814$	490.896	+	283.419i	0.603066	+	0.348180i
$815$	398.998	−	1278.40i	0.489568	−	1.56859i
$816$		0			0
$817$	635.988	+	170.412i	0.778443	+	0.208583i
$818$	−772.232	−	772.232i	−0.944048	−	0.944048i
$819$		0			0
$820$	715.176	+	452.702i	0.872166	+	0.552075i
$821$	254.947	+	441.581i	0.310532	+	0.537857i	0.978478	−	0.206353i	$-0.0661595\pi$
$821$	254.947	+	441.581i	0.310532	+	0.537857i	−0.667946	+	0.744210i	$0.732826\pi$
$822$		0			0
$823$	−410.312	+	109.943i	−0.498556	+	0.133588i	−0.499330	−	0.866412i	$-0.666420\pi$
$823$	−410.312	+	109.943i	−0.498556	+	0.133588i	0.000773801		1.00000i	$0.499754\pi$
$824$	−473.825	−	273.563i	−0.575030	−	0.331994i
$825$		0			0
$826$	360.959	+	625.200i	0.436997	+	0.756900i
$827$	1030.76	−	1030.76i	1.24638	−	1.24638i	0.289073	−	0.957307i	$-0.406653\pi$
$827$	1030.76	−	1030.76i	1.24638	−	1.24638i	0.957307	−	0.289073i	$-0.0933469\pi$
$828$		0			0
$829$		−	37.4235i		−	0.0451429i	−0.999745	−	0.0225714i	$-0.992815\pi$
$829$		−	37.4235i		−	0.0451429i	0.999745	−	0.0225714i	$-0.00718533\pi$
$830$	470.064	+	19.1553i	0.566342	+	0.0230786i
$831$		0			0
$832$	−395.845	−	1477.31i	−0.475775	−	1.77562i
$833$	−162.261	+	43.4777i	−0.194791	+	0.0521941i
$834$		0			0
$835$	−504.528	+	465.019i	−0.604226	+	0.556909i
$836$	408.817			0.489016
$837$		0			0
$838$	−1297.91	−	1297.91i	−1.54882	−	1.54882i
$839$	−997.984	+	576.186i	−1.18949	+	0.686754i	−0.958191	−	0.286129i	$-0.907631\pi$
$839$	−997.984	+	576.186i	−1.18949	+	0.686754i	−0.231301	+	0.972882i	$0.574298\pi$
$840$		0			0
$841$	−420.136	+	727.696i	−0.499567	+	0.865275i
$842$	173.572	+	647.778i	0.206142	+	0.769333i
$843$		0			0
$844$	−1352.71	+	780.989i	−1.60274	+	0.925342i
$845$	−208.633	−	132.064i	−0.246903	−	0.156288i
$846$		0			0
$847$	159.136	−	159.136i	0.187882	−	0.187882i
$848$	−50.3968	+	188.084i	−0.0594302	+	0.221797i
$849$		0			0
$850$	23.9987	−	293.971i	0.0282337	−	0.345848i
$851$	625.828	−	1083.97i	0.735403	−	1.27375i
$852$		0			0
$853$	254.230	−	948.800i	0.298042	−	1.11231i	−0.640728	−	0.767768i	$-0.721368\pi$
$853$	254.230	−	948.800i	0.298042	−	1.11231i	0.938771	−	0.344542i	$-0.111966\pi$
$854$			606.838i			0.710583i
$855$		0			0
$856$	−40.0704			−0.0468112
$857$	569.873	+	152.697i	0.664963	+	0.178176i	0.575485	−	0.817813i	$-0.304813\pi$
$857$	569.873	+	152.697i	0.664963	+	0.178176i	0.0894780	+	0.995989i	$0.471480\pi$
$858$		0			0
$859$	421.639	+	243.434i	0.490849	+	0.283392i	0.724927	−	0.688826i	$-0.241874\pi$
$859$	421.639	+	243.434i	0.490849	+	0.283392i	−0.234077	+	0.972218i	$0.575207\pi$
$860$	−895.697	−	279.554i	−1.04151	−	0.325063i
$861$		0			0
$862$	569.411	+	152.573i	0.660570	+	0.176999i
$863$	411.319	+	411.319i	0.476615	+	0.476615i	0.904047	−	0.427432i	$-0.140582\pi$
$863$	411.319	+	411.319i	0.476615	+	0.476615i	−0.427432	+	0.904047i	$0.640582\pi$
$864$		0			0
$865$	−238.919	+	53.6959i	−0.276207	+	0.0620762i
$866$	−344.497	−	596.687i	−0.397803	−	0.689015i
$867$		0			0
$868$	218.384	−	58.5159i	0.251595	−	0.0674146i
$869$	71.0318	+	41.0102i	0.0817397	+	0.0471924i
$870$		0			0
$871$	−573.666	−	993.619i	−0.658630	−	1.14078i
$872$	−166.045	+	166.045i	−0.190419	+	0.190419i
$873$		0			0
$874$		−	1514.85i		−	1.73323i
$875$	237.577	+	95.9902i	0.271516	+	0.109703i
$876$		0			0
$877$	121.718	+	454.259i	0.138789	+	0.517969i	0.999954	+	0.00964182i	$0.00306914\pi$
$877$	121.718	+	454.259i	0.138789	+	0.517969i	−0.861164	+	0.508327i	$0.830264\pi$
$878$	−768.665	+	205.963i	−0.875472	+	0.234582i
$879$		0			0
$880$	80.2625	+	3.27072i	0.0912074	+	0.00371673i
$881$	−533.151			−0.605166			−0.302583	−	0.953123i	$-0.597849\pi$
$881$	−533.151			−0.605166			−0.302583	+	0.953123i	$0.597849\pi$
$882$		0			0
$883$	−745.939	−	745.939i	−0.844778	−	0.844778i	0.144698	−	0.989476i	$-0.453779\pi$
$883$	−745.939	−	745.939i	−0.844778	−	0.844778i	−0.989476	+	0.144698i	$0.953779\pi$
$884$	283.093	−	163.444i	0.320241	−	0.184891i
$885$		0			0
$886$	−936.908	+	1622.77i	−1.05746	+	1.83157i
$887$	141.361	+	527.568i	0.159370	+	0.594778i	0.998691	+	0.0511420i	$0.0162861\pi$
$887$	141.361	+	527.568i	0.159370	+	0.594778i	−0.839321	+	0.543636i	$0.817047\pi$
$888$		0			0
$889$	−287.766	+	166.142i	−0.323696	+	0.186886i
$890$	1445.54	−	324.879i	1.62421	−	0.365032i
$891$		0			0
$892$	−197.197	+	197.197i	−0.221073	+	0.221073i
$893$	−149.638	+	558.455i	−0.167567	+	0.625369i
$894$		0			0
$895$	−813.536	+	426.509i	−0.908978	+	0.476546i
$896$	−173.876	+	301.163i	−0.194058	+	0.336119i
$897$		0			0
$898$	242.591	−	905.363i	0.270146	−	1.00820i
$899$		−	15.9592i		−	0.0177521i
$900$		0			0
$901$	−152.182			−0.168903
$902$	−292.026	−	78.2480i	−0.323753	−	0.0867495i
$903$		0			0
$904$	−105.069	−	60.6617i	−0.116227	−	0.0671037i
$905$	50.4431	+	96.2167i	0.0557382	+	0.106317i
$906$		0			0
$907$	1294.09	+	346.751i	1.42678	+	0.382306i	0.887885	−	0.460065i	$-0.152174\pi$
$907$	1294.09	+	346.751i	1.42678	+	0.382306i	0.538899	+	0.842371i	$0.318841\pi$
$908$	−124.890	−	124.890i	−0.137544	−	0.137544i
$909$		0			0
$910$	104.495	+	464.949i	0.114830	+	0.510933i
$911$	−574.681	−	995.377i	−0.630824	−	1.09262i	−0.987383	−	0.158347i	$-0.949383\pi$
$911$	−574.681	−	995.377i	−0.630824	−	1.09262i	0.356559	−	0.934273i	$-0.383950\pi$
$912$		0			0
$913$	−96.7258	+	25.9176i	−0.105943	+	0.0283873i
$914$	1101.09	+	635.714i	1.20469	+	0.695530i
$915$		0			0
$916$	−719.080	−	1245.48i	−0.785021	−	1.35970i
$917$	−37.8842	+	37.8842i	−0.0413132	+	0.0413132i
$918$		0			0
$919$		−	412.577i		−	0.448941i	−0.974481	−	0.224470i	$-0.927935\pi$
$919$		−	412.577i		−	0.448941i	0.974481	−	0.224470i	$-0.0720652\pi$
$920$	−28.2959	+	694.373i	−0.0307564	+	0.754753i
$921$		0			0
$922$	−428.833	−	1600.43i	−0.465112	−	1.73582i
$923$	970.650	−	260.085i	1.05163	−	0.281782i
$924$		0			0
$925$	241.269	+	1323.29i	0.260831	+	1.43059i
$926$	1493.70			1.61307
$927$		0			0
$928$	23.5357	+	23.5357i	0.0253618	+	0.0253618i
$929$	−131.382	+	75.8536i	−0.141423	+	0.0816508i	−0.569042	−	0.822308i	$-0.692686\pi$
$929$	−131.382	+	75.8536i	−0.141423	+	0.0816508i	0.427619	+	0.903959i	$0.359353\pi$
$930$		0			0
$931$	463.590	−	802.962i	0.497949	−	0.862473i
$932$	−349.164	−	1303.10i	−0.374640	−	1.39817i
$933$		0			0
$934$	1883.31	−	1087.33i	2.01639	−	1.16416i
$935$	13.7663	+	61.2531i	0.0147233	+	0.0655113i
$936$		0			0
$937$	662.090	−	662.090i	0.706606	−	0.706606i	−0.259214	−	0.965820i	$-0.583463\pi$
$937$	662.090	−	662.090i	0.706606	−	0.706606i	0.965820	+	0.259214i	$0.0834635\pi$
$938$	−129.599	+	483.669i	−0.138165	+	0.515639i
$939$		0			0
$940$	245.473	−	786.503i	0.261142	−	0.836705i
$941$	−766.885	+	1328.28i	−0.814969	+	1.41157i	0.0943819	+	0.995536i	$0.469913\pi$
$941$	−766.885	+	1328.28i	−0.814969	+	1.41157i	−0.909350	+	0.416031i	$0.863421\pi$
$942$		0			0
$943$	−172.782	+	644.832i	−0.183226	+	0.683809i
$944$			537.056i			0.568915i
$945$		0			0
$946$	335.151			0.354282
$947$	1602.61	+	429.417i	1.69230	+	0.453450i	0.970982	−	0.239155i	$-0.0768703\pi$
$947$	1602.61	+	429.417i	1.69230	+	0.453450i	0.721317	+	0.692605i	$0.243537\pi$
$948$		0			0
$949$	−720.120	−	415.762i	−0.758820	−	0.438105i
$950$	1053.66	+	1240.98i	1.10911	+	1.30630i
$951$		0			0
$952$	−44.3610	−	11.8865i	−0.0465977	−	0.0124858i
$953$	145.501	+	145.501i	0.152676	+	0.152676i	0.779312	−	0.626636i	$-0.215569\pi$
$953$	145.501	+	145.501i	0.152676	+	0.152676i	−0.626636	+	0.779312i	$0.715569\pi$
$954$		0			0
$955$	−107.212	+	169.373i	−0.112264	+	0.177354i
$956$	962.130	+	1666.46i	1.00641	+	1.74316i
$957$		0			0
$958$	562.071	−	150.606i	0.586713	−	0.157209i
$959$	36.7327	+	21.2077i	0.0383032	+	0.0221143i
$960$		0			0
$961$	305.712	+	529.509i	0.318119	+	0.550998i
$962$	−1768.92	+	1768.92i	−1.83879	+	1.83879i
$963$		0			0
$964$			787.959i			0.817385i
$965$	371.714	+	403.296i	0.385196	+	0.417923i
$966$		0			0
$967$	421.548	+	1573.24i	0.435934	+	1.62693i	0.738822	+	0.673901i	$0.235382\pi$
$967$	421.548	+	1573.24i	0.435934	+	1.62693i	−0.302888	+	0.953026i	$0.597951\pi$
$968$	−633.597	+	169.772i	−0.654542	+	0.175384i
$969$		0			0
$970$	13.2216	−	324.453i	0.0136305	−	0.334487i
$971$	−72.4383			−0.0746017			−0.0373009	−	0.999304i	$-0.511876\pi$
$971$	−72.4383			−0.0746017			−0.0373009	+	0.999304i	$0.511876\pi$
$972$		0			0
$973$	120.556	+	120.556i	0.123901	+	0.123901i
$974$	465.033	−	268.487i	0.477447	−	0.275654i
$975$		0			0
$976$	−225.722	+	390.962i	−0.231272	+	0.400576i
$977$	−258.538	−	964.876i	−0.264624	−	0.987591i	−0.962480	−	0.271352i	$-0.912529\pi$
$977$	−258.538	−	964.876i	−0.264624	−	0.987591i	0.697856	−	0.716238i	$-0.254138\pi$
$978$		0			0
$979$	−273.113	+	157.682i	−0.278972	+	0.161065i
$980$	−706.699	+	1116.44i	−0.721122	+	1.13923i
$981$		0			0
$982$	235.116	−	235.116i	0.239425	−	0.239425i
$983$	49.2900	−	183.953i	0.0501424	−	0.187134i	−0.936312	−	0.351169i	$-0.885784\pi$
$983$	49.2900	−	183.953i	0.0501424	−	0.187134i	0.986455	+	0.164035i	$0.0524510\pi$
$984$		0			0
$985$	−454.292	−	141.788i	−0.461210	−	0.143947i
$986$	−5.03520	+	8.72123i	−0.00510670	+	0.00884506i
$987$		0			0
$988$	−466.970	+	1742.76i	−0.472642	+	1.76392i
$989$		−	740.059i		−	0.748290i
$990$		0			0
$991$	−1131.94			−1.14222			−0.571109	−	0.820874i	$-0.693487\pi$
$991$	−1131.94			−1.14222			−0.571109	+	0.820874i	$0.693487\pi$
$992$	704.233	+	188.699i	0.709913	+	0.190221i
$993$		0			0
$994$	−379.809	−	219.283i	−0.382101	−	0.220606i
$995$	−1113.25	+	583.641i	−1.11885	+	0.586574i
$996$		0			0
$997$	1523.48	+	408.216i	1.52807	+	0.409444i	0.922388	−	0.386265i	$-0.126235\pi$
$997$	1523.48	+	408.216i	1.52807	+	0.409444i	0.605679	+	0.795709i	$0.292902\pi$
$998$	1645.39	+	1645.39i	1.64868	+	1.64868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.f.28.1		8
3.2	odd	2		405.3.l.h.28.2		8
5.2	odd	4	inner	405.3.l.f.352.2		8
9.2	odd	6		405.3.l.h.298.1		8
9.4	even	3		45.3.g.b.28.2		4
9.5	odd	6		15.3.f.a.13.1	yes	4
9.7	even	3	inner	405.3.l.f.298.2		8
15.2	even	4		405.3.l.h.352.1		8
36.23	even	6		240.3.bg.a.193.1		4
36.31	odd	6		720.3.bh.k.433.1		4
45.2	even	12		405.3.l.h.217.2		8
45.4	even	6		225.3.g.a.118.1		4
45.7	odd	12	inner	405.3.l.f.217.1		8
45.13	odd	12		225.3.g.a.82.1		4
45.14	odd	6		75.3.f.c.43.2		4
45.22	odd	12		45.3.g.b.37.2		4
45.23	even	12		75.3.f.c.7.2		4
45.32	even	12		15.3.f.a.7.1	✓	4
72.5	odd	6		960.3.bg.i.193.1		4
72.59	even	6		960.3.bg.h.193.2		4
180.23	odd	12		1200.3.bg.k.1057.2		4
180.59	even	6		1200.3.bg.k.193.2		4
180.67	even	12		720.3.bh.k.577.1		4
180.167	odd	12		240.3.bg.a.97.1		4
360.77	even	12		960.3.bg.i.577.1		4
360.347	odd	12		960.3.bg.h.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	45.32	even	12
15.3.f.a.13.1	yes	4	9.5	odd	6
45.3.g.b.28.2		4	9.4	even	3
45.3.g.b.37.2		4	45.22	odd	12
75.3.f.c.7.2		4	45.23	even	12
75.3.f.c.43.2		4	45.14	odd	6
225.3.g.a.82.1		4	45.13	odd	12
225.3.g.a.118.1		4	45.4	even	6
240.3.bg.a.97.1		4	180.167	odd	12
240.3.bg.a.193.1		4	36.23	even	6
405.3.l.f.28.1		8	1.1	even	1	trivial
405.3.l.f.217.1		8	45.7	odd	12	inner
405.3.l.f.298.2		8	9.7	even	3	inner
405.3.l.f.352.2		8	5.2	odd	4	inner
405.3.l.h.28.2		8	3.2	odd	2
405.3.l.h.217.2		8	45.2	even	12
405.3.l.h.298.1		8	9.2	odd	6
405.3.l.h.352.1		8	15.2	even	4
720.3.bh.k.433.1		4	36.31	odd	6
720.3.bh.k.577.1		4	180.67	even	12
960.3.bg.h.193.2		4	72.59	even	6
960.3.bg.h.577.2		4	360.347	odd	12
960.3.bg.i.193.1		4	72.5	odd	6
960.3.bg.i.577.1		4	360.77	even	12
1200.3.bg.k.193.2		4	180.59	even	6
1200.3.bg.k.1057.2		4	180.23	odd	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.03906 - 0.814313i) q^{2} +(5.10867 + 2.94949i) q^{4} +(-2.32162 - 4.42833i) q^{5} +(1.98004 + 0.530550i) q^{7} +(-4.22474 - 4.22474i) q^{8} +(3.44949 + 15.3485i) q^{10} +(-1.67423 - 2.89986i) q^{11} +(14.2743 - 3.82478i) q^{13} +(-5.58542 - 3.22474i) q^{14} +(-2.39898 - 4.15515i) q^{16} +(2.65153 - 2.65153i) q^{17} +20.6969i q^{19} +(1.20093 - 29.4704i) q^{20} +(2.72670 + 10.1762i) q^{22} +(22.4704 - 6.02093i) q^{23} +(-14.2202 + 20.5618i) q^{25} -46.4949 q^{26} +(8.55051 + 8.55051i) q^{28} +(0.739215 - 0.426786i) q^{29} +(9.34847 - 16.1920i) q^{31} +(10.0925 + 37.6657i) q^{32} +(-10.2173 + 5.89898i) q^{34} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +(16.8538 - 62.8992i) q^{38} +(-8.90031 + 28.5168i) q^{40} +(-14.3485 + 24.8523i) q^{41} +(8.23370 - 30.7286i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(26.9825 + 7.22994i) q^{47} +(-38.7962 - 22.3990i) q^{49} +(59.9596 - 50.9088i) q^{50} +(84.2036 + 22.5623i) q^{52} +(-28.6969 - 28.6969i) q^{53} +(-8.95459 + 14.1464i) q^{55} +(-6.12372 - 10.6066i) q^{56} +(-2.59405 + 0.695075i) q^{58} +(-96.9378 - 55.9671i) q^{59} +(-47.0454 - 81.4850i) q^{61} +(-41.5959 + 41.5959i) q^{62} -103.495i q^{64} +(-50.0768 - 54.3315i) q^{65} +(-20.0944 - 74.9934i) q^{67} +(21.3664 - 5.72512i) q^{68} +(-1.31300 + 32.2207i) q^{70} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} +(-146.603 + 84.6413i) q^{74} +(-61.0454 + 105.734i) q^{76} +(-1.77653 - 6.63010i) q^{77} +(-21.2132 + 12.2474i) q^{79} +(-12.8309 + 20.2702i) q^{80} +(63.8434 - 63.8434i) q^{82} +(7.74013 - 28.8866i) q^{83} +(-17.8977 - 5.58600i) q^{85} +(-50.0454 + 86.6812i) q^{86} +(-5.17795 + 19.3244i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(132.553 + 35.5173i) q^{92} +(-76.1139 - 43.9444i) q^{94} +(91.6528 - 48.0504i) q^{95} +(-19.9384 - 5.34248i) q^{97} +(99.6640 + 99.6640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{5} - 4 q^{7} - 24 q^{8} + 8 q^{10} + 16 q^{11} + 32 q^{13} + 20 q^{16} + 80 q^{17} - 36 q^{20} - 20 q^{22} + 56 q^{23} - 16 q^{25} - 176 q^{26} + 88 q^{28} + 16 q^{31} - 76 q^{32} + 80 q^{35}+ \cdots + 376 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 - 24 * q^8 + 8 * q^10 + 16 * q^11 + 32 * q^13 + 20 * q^16 + 80 * q^17 - 36 * q^20 - 20 * q^22 + 56 * q^23 - 16 * q^25 - 176 * q^26 + 88 * q^28 + 16 * q^31 - 76 * q^32 + 80 * q^35 + 128 * q^37 - 96 * q^38 - 48 * q^40 - 56 * q^41 + 8 * q^43 - 272 * q^46 + 128 * q^47 + 164 * q^50 + 80 * q^52 - 112 * q^53 - 248 * q^55 + 12 * q^58 - 200 * q^61 - 176 * q^62 - 112 * q^65 + 200 * q^67 - 104 * q^68 + 60 * q^70 + 544 * q^71 + 152 * q^73 - 312 * q^76 + 88 * q^77 - 328 * q^80 + 256 * q^82 - 16 * q^83 - 232 * q^85 - 224 * q^86 - 12 * q^88 - 32 * q^91 + 104 * q^92 + 144 * q^95 + 20 * q^97 + 376 * q^98

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