LMFDB - Embedded newform 153.3.p.a.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(10,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.10"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.p (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,24,0,-16,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			10.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	153.10
Dual form			153.3.p.a.46.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.324423 + 0.783227i) q^{2} +(2.32023 + 2.32023i) q^{4} +(6.70292 - 1.33329i) q^{5} +(0.886687 + 0.176373i) q^{7} +(-5.70292 + 2.36223i) q^{8} +(-1.13031 + 5.68246i) q^{10} +(-3.73690 - 5.59267i) q^{11} +(10.5602 - 10.5602i) q^{13} +(-0.425802 + 0.637258i) q^{14} +7.89218i q^{16} +(14.7921 + 8.37823i) q^{17} +(-12.9821 + 31.3415i) q^{19} +(18.6459 + 12.4588i) q^{20} +(5.59267 - 1.11245i) q^{22} +(-15.4758 + 10.3406i) q^{23} +(20.0544 - 8.30682i) q^{25} +(4.84504 + 11.6970i) q^{26} +(1.64809 + 2.46655i) q^{28} +(-4.13027 - 20.7643i) q^{29} +(21.1305 - 31.6240i) q^{31} +(-28.9930 - 12.0093i) q^{32} +(-11.3609 + 8.86746i) q^{34} +6.17855 q^{35} +(-33.3284 - 22.2693i) q^{37} +(-20.3359 - 20.3359i) q^{38} +(-35.0766 + 23.4375i) q^{40} +(3.70199 + 0.736372i) q^{41} +(-5.21542 - 12.5911i) q^{43} +(4.30581 - 21.6468i) q^{44} +(-3.07832 - 15.4758i) q^{46} +(9.20504 - 9.20504i) q^{47} +(-44.5150 - 18.4387i) q^{49} +18.4021i q^{50} +49.0040 q^{52} +(-0.763466 + 1.84317i) q^{53} +(-32.5048 - 32.5048i) q^{55} +(-5.47334 + 1.08871i) q^{56} +(17.6031 + 3.50147i) q^{58} +(-31.7838 + 13.1653i) q^{59} +(6.92641 - 34.8214i) q^{61} +(17.9136 + 26.8096i) q^{62} +(-3.51042 + 3.51042i) q^{64} +(56.7040 - 84.8636i) q^{65} +31.9912i q^{67} +(14.8816 + 53.7605i) q^{68} +(-2.00446 + 4.83921i) q^{70} +(-86.1606 - 57.5707i) q^{71} +(61.7546 - 12.2837i) q^{73} +(28.2544 - 18.8790i) q^{74} +(-102.841 + 42.5982i) q^{76} +(-2.32707 - 5.61804i) q^{77} +(-36.2984 - 54.3244i) q^{79} +(10.5226 + 52.9006i) q^{80} +(-1.77776 + 2.66060i) q^{82} +(39.7149 + 16.4505i) q^{83} +(110.321 + 36.4364i) q^{85} +11.5537 q^{86} +(34.5224 + 23.0671i) q^{88} +(-49.5695 - 49.5695i) q^{89} +(11.2261 - 7.50103i) q^{91} +(-59.9000 - 11.9148i) q^{92} +(4.22331 + 10.1960i) q^{94} +(-45.2304 + 227.389i) q^{95} +(24.9233 + 125.298i) q^{97} +(28.8834 - 28.8834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 24 q^{5} - 16 q^{7} - 16 q^{8} - 40 q^{11} - 16 q^{14} + 16 q^{17} - 32 q^{19} + 40 q^{20} + 8 q^{23} + 16 q^{25} + 80 q^{28} - 24 q^{29} + 32 q^{31} + 24 q^{32} + 64 q^{34} - 80 q^{35}+ \cdots - 16 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 + 24 * q^5 - 16 * q^7 - 16 * q^8 - 40 * q^11 - 16 * q^14 + 16 * q^17 - 32 * q^19 + 40 * q^20 + 8 * q^23 + 16 * q^25 + 80 * q^28 - 24 * q^29 + 32 * q^31 + 24 * q^32 + 64 * q^34 - 80 * q^35 - 168 * q^37 - 8 * q^38 - 200 * q^40 + 96 * q^43 + 96 * q^44 + 80 * q^47 + 8 * q^49 + 240 * q^52 - 96 * q^53 - 8 * q^55 - 72 * q^56 - 8 * q^59 + 264 * q^61 + 136 * q^62 - 120 * q^64 + 32 * q^65 + 176 * q^68 - 80 * q^70 - 32 * q^71 + 24 * q^73 - 176 * q^74 - 80 * q^76 + 216 * q^77 - 96 * q^79 - 24 * q^80 - 408 * q^82 + 88 * q^83 + 512 * q^85 - 288 * q^86 + 176 * q^88 - 288 * q^89 - 24 * q^91 - 336 * q^92 - 8 * q^94 + 152 * q^95 - 344 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

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 $

$2$	−0.324423	+	0.783227i	−0.162212	+	0.391614i	−0.983997	−	0.178183i	$-0.942978\pi$
$2$	−0.324423	+	0.783227i	−0.162212	+	0.391614i	0.821786	+	0.569797i	$0.192978\pi$
$3$		0			0
$3$		0			0
$4$	2.32023	+	2.32023i	0.580058	+	0.580058i
$5$	6.70292	−	1.33329i	1.34058	−	0.266659i	0.527871	−	0.849324i	$-0.322990\pi$
$5$	6.70292	−	1.33329i	1.34058	−	0.266659i	0.812712	+	0.582666i	$0.197990\pi$
$6$		0			0
$7$	0.886687	+	0.176373i	0.126670	+	0.0251962i	0.258018	−	0.966140i	$-0.416931\pi$
$7$	0.886687	+	0.176373i	0.126670	+	0.0251962i	−0.131348	+	0.991336i	$0.541931\pi$
$8$	−5.70292	+	2.36223i	−0.712865	+	0.295278i
$9$		0			0
$10$	−1.13031	+	5.68246i	−0.113031	+	0.568246i
$11$	−3.73690	−	5.59267i	−0.339718	−	0.508424i	0.621796	−	0.783179i	$-0.286403\pi$
$11$	−3.73690	−	5.59267i	−0.339718	−	0.508424i	−0.961514	+	0.274755i	$0.911403\pi$
$12$		0			0
$13$	10.5602	−	10.5602i	0.812320	−	0.812320i	−0.172662	−	0.984981i	$-0.555237\pi$
$13$	10.5602	−	10.5602i	0.812320	−	0.812320i	0.984981	+	0.172662i	$0.0552367\pi$
$14$	−0.425802	+	0.637258i	−0.0304144	+	0.0455184i
$15$		0			0
$16$			7.89218i			0.493261i
$17$	14.7921	+	8.37823i	0.870122	+	0.492837i
$17$	14.7921	+	8.37823i	0.870122	+	0.492837i
$18$		0			0
$19$	−12.9821	+	31.3415i	−0.683268	+	1.64955i	0.0746542	+	0.997209i	$0.476215\pi$
$19$	−12.9821	+	31.3415i	−0.683268	+	1.64955i	−0.757922	+	0.652345i	$0.773785\pi$
$20$	18.6459	+	12.4588i	0.932294	+	0.622939i
$21$		0			0
$22$	5.59267	−	1.11245i	0.254212	−	0.0505659i
$23$	−15.4758	+	10.3406i	−0.672860	+	0.449590i	−0.844490	−	0.535571i	$-0.820096\pi$
$23$	−15.4758	+	10.3406i	−0.672860	+	0.449590i	0.171631	+	0.985161i	$0.445096\pi$
$24$		0			0
$25$	20.0544	−	8.30682i	0.802177	−	0.332273i
$26$	4.84504	+	11.6970i	0.186348	+	0.449883i
$27$		0			0
$28$	1.64809	+	2.46655i	0.0588605	+	0.0880910i
$29$	−4.13027	−	20.7643i	−0.142423	−	0.716009i	−0.984323	−	0.176376i	$-0.943563\pi$
$29$	−4.13027	−	20.7643i	−0.142423	−	0.716009i	0.841900	−	0.539634i	$-0.181437\pi$
$30$		0			0
$31$	21.1305	−	31.6240i	0.681629	−	1.02013i	−0.315825	−	0.948818i	$-0.602281\pi$
$31$	21.1305	−	31.6240i	0.681629	−	1.02013i	0.997454	−	0.0713127i	$-0.0227188\pi$
$32$	−28.9930	−	12.0093i	−0.906032	−	0.375291i
$33$		0			0
$34$	−11.3609	+	8.86746i	−0.334146	+	0.260808i
$35$	6.17855			0.176530
$36$		0			0
$37$	−33.3284	−	22.2693i	−0.900767	−	0.601873i	0.0166233	−	0.999862i	$-0.494708\pi$
$37$	−33.3284	−	22.2693i	−0.900767	−	0.601873i	−0.917390	+	0.397988i	$0.869708\pi$
$38$	−20.3359	−	20.3359i	−0.535154	−	0.535154i
$39$		0			0
$40$	−35.0766	+	23.4375i	−0.876916	+	0.585936i
$41$	3.70199	+	0.736372i	0.0902925	+	0.0179603i	0.240030	−	0.970766i	$-0.422843\pi$
$41$	3.70199	+	0.736372i	0.0902925	+	0.0179603i	−0.149737	+	0.988726i	$0.547843\pi$
$42$		0			0
$43$	−5.21542	−	12.5911i	−0.121289	−	0.292817i	0.851561	−	0.524256i	$-0.175657\pi$
$43$	−5.21542	−	12.5911i	−0.121289	−	0.292817i	−0.972849	+	0.231439i	$0.925657\pi$
$44$	4.30581	−	21.6468i	0.0978593	−	0.491972i
$45$		0			0
$46$	−3.07832	−	15.4758i	−0.0669201	−	0.336430i
$47$	9.20504	−	9.20504i	0.195852	−	0.195852i	−0.602367	−	0.798219i	$-0.705776\pi$
$47$	9.20504	−	9.20504i	0.195852	−	0.195852i	0.798219	+	0.602367i	$0.205776\pi$
$48$		0			0
$49$	−44.5150	−	18.4387i	−0.908469	−	0.376300i
$50$			18.4021i			0.368042i
$51$		0			0
$52$	49.0040			0.942385
$53$	−0.763466	+	1.84317i	−0.0144050	+	0.0347768i	−0.930918	−	0.365227i	$-0.880991\pi$
$53$	−0.763466	+	1.84317i	−0.0144050	+	0.0347768i	0.916513	+	0.400004i	$0.130991\pi$
$54$		0			0
$55$	−32.5048	−	32.5048i	−0.590996	−	0.590996i
$56$	−5.47334	+	1.08871i	−0.0977381	+	0.0194413i
$57$		0			0
$58$	17.6031	+	3.50147i	0.303502	+	0.0603703i
$59$	−31.7838	+	13.1653i	−0.538708	+	0.223140i	−0.635412	−	0.772173i	$-0.719170\pi$
$59$	−31.7838	+	13.1653i	−0.538708	+	0.223140i	0.0967043	+	0.995313i	$0.469170\pi$
$60$		0			0
$61$	6.92641	−	34.8214i	0.113548	−	0.570843i	−0.881562	−	0.472068i	$-0.843508\pi$
$61$	6.92641	−	34.8214i	0.113548	−	0.570843i	0.995110	−	0.0987749i	$-0.0314924\pi$
$62$	17.9136	+	26.8096i	0.288929	+	0.432412i
$63$		0			0
$64$	−3.51042	+	3.51042i	−0.0548503	+	0.0548503i
$65$	56.7040	−	84.8636i	0.872370	−	1.30559i
$66$		0			0
$67$			31.9912i			0.477480i	0.971084	+	0.238740i	$0.0767344\pi$
$67$			31.9912i			0.477480i	−0.971084	+	0.238740i	$0.923266\pi$
$68$	14.8816	+	53.7605i	0.218847	+	0.790595i
$69$		0			0
$70$	−2.00446	+	4.83921i	−0.0286352	+	0.0691315i
$71$	−86.1606	−	57.5707i	−1.21353	−	0.810854i	−0.226913	−	0.973915i	$-0.572863\pi$
$71$	−86.1606	−	57.5707i	−1.21353	−	0.810854i	−0.986616	+	0.163061i	$0.947863\pi$
$72$		0			0
$73$	61.7546	−	12.2837i	0.845953	−	0.168270i	0.246961	−	0.969025i	$-0.420568\pi$
$73$	61.7546	−	12.2837i	0.845953	−	0.168270i	0.598992	+	0.800755i	$0.295568\pi$
$74$	28.2544	−	18.8790i	0.381817	−	0.255122i
$75$		0			0
$76$	−102.841	+	42.5982i	−1.35317	+	0.560502i
$77$	−2.32707	−	5.61804i	−0.0302216	−	0.0729615i
$78$		0			0
$79$	−36.2984	−	54.3244i	−0.459474	−	0.687651i	0.527314	−	0.849671i	$-0.323199\pi$
$79$	−36.2984	−	54.3244i	−0.459474	−	0.687651i	−0.986788	+	0.162020i	$0.948199\pi$
$80$	10.5226	+	52.9006i	0.131532	+	0.661258i
$81$		0			0
$82$	−1.77776	+	2.66060i	−0.0216800	+	0.0324464i
$83$	39.7149	+	16.4505i	0.478493	+	0.198198i	0.608876	−	0.793265i	$-0.291621\pi$
$83$	39.7149	+	16.4505i	0.478493	+	0.198198i	−0.130383	+	0.991464i	$0.541621\pi$
$84$		0			0
$85$	110.321	+	36.4364i	1.29789	+	0.428664i
$86$	11.5537			0.134346
$87$		0			0
$88$	34.5224	+	23.0671i	0.392300	+	0.262126i
$89$	−49.5695	−	49.5695i	−0.556961	−	0.556961i	0.371480	−	0.928441i	$-0.378850\pi$
$89$	−49.5695	−	49.5695i	−0.556961	−	0.556961i	−0.928441	+	0.371480i	$0.878850\pi$
$90$		0			0
$91$	11.2261	−	7.50103i	0.123364	−	0.0824289i
$92$	−59.9000	−	11.9148i	−0.651086	−	0.129509i
$93$		0			0
$94$	4.22331	+	10.1960i	0.0449288	+	0.108468i
$95$	−45.2304	+	227.389i	−0.476110	+	2.39356i
$96$		0			0
$97$	24.9233	+	125.298i	0.256941	+	1.29173i	0.866574	+	0.499048i	$0.166317\pi$
$97$	24.9233	+	125.298i	0.256941	+	1.29173i	−0.609633	+	0.792684i	$0.708683\pi$
$98$	28.8834	−	28.8834i	0.294729	−	0.294729i
$99$		0			0
$100$	65.8047	+	27.2572i	0.658047	+	0.272572i
$101$		−	37.1128i		−	0.367453i	−0.982977	−	0.183727i	$-0.941184\pi$
$101$		−	37.1128i		−	0.367453i	0.982977	−	0.183727i	$-0.0588162\pi$
$102$		0			0
$103$	−54.9138			−0.533144			−0.266572	−	0.963815i	$-0.585891\pi$
$103$	−54.9138			−0.533144			−0.266572	+	0.963815i	$0.585891\pi$
$104$	−35.2782	+	85.1691i	−0.339214	+	0.818934i
$105$		0			0
$106$	−1.19594	−	1.19594i	−0.0112824	−	0.0112824i
$107$	145.657	−	28.9729i	1.36128	−	0.270775i	0.540173	−	0.841554i	$-0.318359\pi$
$107$	145.657	−	28.9729i	1.36128	−	0.270775i	0.821104	+	0.570779i	$0.193359\pi$
$108$		0			0
$109$	23.4177	+	4.65808i	0.214842	+	0.0427347i	0.301338	−	0.953518i	$-0.402567\pi$
$109$	23.4177	+	4.65808i	0.214842	+	0.0427347i	−0.0864958	+	0.996252i	$0.527567\pi$
$110$	36.0040	−	14.9133i	0.327309	−	0.135576i
$111$		0			0
$112$	−1.39197	+	6.99789i	−0.0124283	+	0.0624812i
$113$	26.9507	+	40.3346i	0.238502	+	0.356943i	0.931341	−	0.364149i	$-0.118640\pi$
$113$	26.9507	+	40.3346i	0.238502	+	0.356943i	−0.692839	+	0.721093i	$0.743640\pi$
$114$		0			0
$115$	−89.9458	+	89.9458i	−0.782137	+	0.782137i
$116$	38.5948	−	57.7611i	0.332713	−	0.497941i
$117$		0			0
$118$		−	29.1650i		−	0.247161i
$119$	11.6382	+	10.0378i	0.0978004	+	0.0843512i
$120$		0			0
$121$	28.9912	−	69.9909i	0.239597	−	0.578437i
$122$	25.0260	+	16.7218i	0.205131	+	0.137064i
$123$		0			0
$124$	122.403	−	24.3474i	0.987120	−	0.196350i
$125$	−18.7137	+	12.5041i	−0.149710	+	0.100033i
$126$		0			0
$127$	44.5892	−	18.4694i	0.351096	−	0.145429i	−0.200164	−	0.979762i	$-0.564147\pi$
$127$	44.5892	−	18.4694i	0.351096	−	0.145429i	0.551260	+	0.834334i	$0.314147\pi$
$128$	−49.6478	−	119.860i	−0.387874	−	0.936410i
$129$		0			0
$130$	48.0714	+	71.9439i	0.369780	+	0.553415i
$131$	−0.637092	−	3.20288i	−0.00486330	−	0.0244495i	0.978277	−	0.207300i	$-0.0664676\pi$
$131$	−0.637092	−	3.20288i	−0.00486330	−	0.0244495i	−0.983141	+	0.182850i	$0.941468\pi$
$132$		0			0
$133$	−17.0389	+	25.5004i	−0.128112	+	0.191733i
$134$	−25.0563	−	10.3787i	−0.186988	−	0.0774528i
$135$		0			0
$136$	−104.149	−	12.8381i	−0.765803	−	0.0943981i
$137$	89.9517			0.656581			0.328291	−	0.944577i	$-0.393527\pi$
$137$	89.9517			0.656581			0.328291	+	0.944577i	$0.393527\pi$
$138$		0			0
$139$	108.219	+	72.3095i	0.778553	+	0.520212i	0.880197	−	0.474608i	$-0.157410\pi$
$139$	108.219	+	72.3095i	0.778553	+	0.520212i	−0.101644	+	0.994821i	$0.532410\pi$
$140$	14.3357	+	14.3357i	0.102398	+	0.102398i
$141$		0			0
$142$	73.0434	−	48.8061i	0.514390	−	0.343705i
$143$	−98.5217	−	19.5972i	−0.688963	−	0.137043i
$144$		0			0
$145$	−55.3697	−	133.674i	−0.381860	−	0.921892i
$146$	−10.4137	+	52.3530i	−0.0713264	+	0.358582i
$147$		0			0
$148$	−25.6596	−	129.000i	−0.173376	−	0.871619i
$149$	−149.894	+	149.894i	−1.00600	+	1.00600i	−0.00602015	+	0.999982i	$0.501916\pi$
$149$	−149.894	+	149.894i	−1.00600	+	1.00600i	−0.999982	+	0.00602015i	$0.998084\pi$
$150$		0			0
$151$	−55.2876	−	22.9009i	−0.366143	−	0.151661i	0.192023	−	0.981390i	$-0.438495\pi$
$151$	−55.2876	−	22.9009i	−0.366143	−	0.151661i	−0.558167	+	0.829729i	$0.688495\pi$
$152$		−	209.405i		−	1.37766i
$153$		0			0
$154$	5.15515			0.0334750
$155$	99.4719	−	240.146i	0.641754	−	1.54933i
$156$		0			0
$157$	−104.330	−	104.330i	−0.664524	−	0.664524i	0.291919	−	0.956443i	$-0.405706\pi$
$157$	−104.330	−	104.330i	−0.664524	−	0.664524i	−0.956443	+	0.291919i	$0.905706\pi$
$158$	54.3244	−	10.8058i	0.343826	−	0.0683912i
$159$		0			0
$160$	−210.350	−	41.8412i	−1.31469	−	0.261507i
$161$	−15.5460	+	6.43935i	−0.0965588	+	0.0399960i
$162$		0			0
$163$	−63.2704	+	318.082i	−0.388162	+	1.95142i	−0.0944348	+	0.995531i	$0.530104\pi$
$163$	−63.2704	+	318.082i	−0.388162	+	1.95142i	−0.293727	+	0.955889i	$0.594896\pi$
$164$	6.88093	+	10.2980i	0.0419569	+	0.0627929i
$165$		0			0
$166$	−25.7689	+	25.7689i	−0.155234	+	0.155234i
$167$	−87.6108	+	131.119i	−0.524615	+	0.785142i	−0.995267	−	0.0971767i	$-0.969019\pi$
$167$	−87.6108	+	131.119i	−0.524615	+	0.785142i	0.470652	+	0.882319i	$0.344019\pi$
$168$		0			0
$169$		−	54.0337i		−	0.319726i
$170$	−64.3286	+	74.5853i	−0.378403	+	0.438737i
$171$		0			0
$172$	17.1134	−	41.3153i	0.0994963	−	0.240205i
$173$	136.654	+	91.3096i	0.789910	+	0.527801i	0.883846	−	0.467777i	$-0.154945\pi$
$173$	136.654	+	91.3096i	0.789910	+	0.527801i	−0.0939363	+	0.995578i	$0.529945\pi$
$174$		0			0
$175$	19.2471	−	3.82849i	0.109983	−	0.0218771i
$176$	44.1383	−	29.4923i	0.250786	−	0.167570i
$177$		0			0
$178$	54.9057	−	22.7427i	0.308459	−	0.127768i
$179$	74.2691	+	179.301i	0.414911	+	1.00168i	0.983800	+	0.179269i	$0.0573734\pi$
$179$	74.2691	+	179.301i	0.414911	+	1.00168i	−0.568889	+	0.822414i	$0.692627\pi$
$180$		0			0
$181$	27.7497	+	41.5304i	0.153313	+	0.229450i	0.900173	−	0.435532i	$-0.143440\pi$
$181$	27.7497	+	41.5304i	0.153313	+	0.229450i	−0.746860	+	0.664981i	$0.768440\pi$
$182$	2.23301	+	11.2261i	0.0122693	+	0.0616818i
$183$		0			0
$184$	63.8303	−	95.5287i	0.346904	−	0.519178i
$185$	−253.089	−	104.833i	−1.36805	−	0.566664i
$186$		0			0
$187$	−8.41985	−	114.036i	−0.0450259	−	0.609817i
$188$	42.7157			0.227211
$189$		0			0
$190$	−163.423	−	109.196i	−0.860122	−	0.574715i
$191$	−210.946	−	210.946i	−1.10443	−	1.10443i	−0.993869	−	0.110561i	$-0.964735\pi$
$191$	−210.946	−	210.946i	−1.10443	−	1.10443i	−0.110561	−	0.993869i	$-0.535265\pi$
$192$		0			0
$193$	46.8606	−	31.3112i	0.242801	−	0.162234i	−0.428216	−	0.903676i	$-0.640858\pi$
$193$	46.8606	−	31.3112i	0.242801	−	0.162234i	0.671017	+	0.741442i	$0.265858\pi$
$194$	−106.223	−	21.1290i	−0.547539	−	0.108912i
$195$		0			0
$196$	−60.5030	−	146.067i	−0.308689	−	0.745241i
$197$	−0.730502	+	3.67248i	−0.00370813	+	0.0186420i	−0.982595	−	0.185760i	$-0.940525\pi$
$197$	−0.730502	+	3.67248i	−0.00370813	+	0.0186420i	0.978887	+	0.204403i	$0.0655251\pi$
$198$		0			0
$199$	29.0628	+	146.108i	0.146044	+	0.734213i	0.982512	+	0.186198i	$0.0596165\pi$
$199$	29.0628	+	146.108i	0.146044	+	0.734213i	−0.836468	+	0.548016i	$0.815383\pi$
$200$	−94.7461	+	94.7461i	−0.473731	+	0.473731i
$201$		0			0
$202$	29.0678	+	12.0403i	0.143900	+	0.0596052i
$203$		−	19.1399i		−	0.0942851i
$204$		0			0
$205$	25.7959			0.125834
$206$	17.8153	−	43.0100i	0.0864821	−	0.208786i
$207$		0			0
$208$	83.3426	+	83.3426i	0.400686	+	0.400686i
$209$	223.796	−	44.5157i	1.07079	−	0.212994i
$210$		0			0
$211$	−291.187	−	57.9207i	−1.38003	−	0.274506i	−0.551374	−	0.834258i	$-0.685896\pi$
$211$	−291.187	−	57.9207i	−1.38003	−	0.274506i	−0.828660	+	0.559752i	$0.810896\pi$
$212$	−6.04800	+	2.50517i	−0.0285283	+	0.0118168i
$213$		0			0
$214$	−24.5620	+	123.482i	−0.114776	+	0.577017i
$215$	−51.7462	−	77.4436i	−0.240680	−	0.360203i
$216$		0			0
$217$	24.3138	−	24.3138i	0.112045	−	0.112045i
$218$	−11.2456	+	16.8302i	−0.0515853	+	0.0772029i
$219$		0			0
$220$		−	150.837i		−	0.685625i
$221$	244.682	−	67.7311i	1.10716	−	0.306476i
$222$		0			0
$223$	−34.4629	+	83.2008i	−0.154542	+	0.373098i	−0.982121	−	0.188252i	$-0.939718\pi$
$223$	−34.4629	+	83.2008i	−0.154542	+	0.373098i	0.827579	+	0.561350i	$0.189718\pi$
$224$	−23.5896	−	15.7621i	−0.105311	−	0.0703665i
$225$		0			0
$226$	−40.3346	+	8.02305i	−0.178472	+	0.0355002i
$227$	124.031	−	82.8747i	0.546391	−	0.365087i	−0.251529	−	0.967850i	$-0.580934\pi$
$227$	124.031	−	82.8747i	0.546391	−	0.365087i	0.797920	+	0.602763i	$0.205934\pi$
$228$		0			0
$229$	126.494	−	52.3955i	0.552375	−	0.228801i	−0.0889961	−	0.996032i	$-0.528366\pi$
$229$	126.494	−	52.3955i	0.552375	−	0.228801i	0.641371	+	0.767231i	$0.278366\pi$
$230$	−41.2675	−	99.6285i	−0.179424	−	0.433167i
$231$		0			0
$232$	72.6045	+	108.660i	0.312950	+	0.468363i
$233$	69.6099	+	349.953i	0.298755	+	1.50194i	0.780235	+	0.625486i	$0.215099\pi$
$233$	69.6099	+	349.953i	0.298755	+	1.50194i	−0.481480	+	0.876457i	$0.659901\pi$
$234$		0			0
$235$	49.4276	−	73.9736i	0.210330	−	0.314781i
$236$	−104.292	−	43.1993i	−0.441916	−	0.183048i
$237$		0			0
$238$	−11.6376	+	5.85890i	−0.0488974	+	0.0246172i
$239$	398.078			1.66560			0.832800	−	0.553574i	$-0.186736\pi$
$239$	398.078			1.66560			0.832800	+	0.553574i	$0.186736\pi$
$240$		0			0
$241$	−65.9725	−	44.0814i	−0.273745	−	0.182910i	0.411119	−	0.911582i	$-0.365138\pi$
$241$	−65.9725	−	44.0814i	−0.273745	−	0.182910i	−0.684863	+	0.728671i	$0.740138\pi$
$242$	45.4134	+	45.4134i	0.187659	+	0.187659i
$243$		0			0
$244$	96.8647	−	64.7229i	0.396987	−	0.265258i
$245$	−322.964	−	64.2416i	−1.31822	−	0.262211i
$246$		0			0
$247$	193.879	+	468.064i	0.784934	+	1.89500i
$248$	−45.8024	+	230.264i	−0.184687	+	0.928485i
$249$		0			0
$250$	−3.72239	−	18.7137i	−0.0148896	−	0.0748549i
$251$	−320.583	+	320.583i	−1.27722	+	1.27722i	−0.335010	+	0.942215i	$0.608740\pi$
$251$	−320.583	+	320.583i	−1.27722	+	1.27722i	−0.942215	+	0.335010i	$0.891260\pi$
$252$		0			0
$253$	115.663	+	47.9091i	0.457166	+	0.189364i
$254$			40.9154i			0.161084i
$255$		0			0
$256$	90.1270			0.352058
$257$	−37.6834	+	90.9757i	−0.146628	+	0.353991i	−0.980081	−	0.198600i	$-0.936361\pi$
$257$	−37.6834	+	90.9757i	−0.146628	+	0.353991i	0.833453	+	0.552591i	$0.186361\pi$
$258$		0			0
$259$	−25.6241	−	25.6241i	−0.0989349	−	0.0989349i
$260$	328.470	−	65.3367i	1.26335	−	0.251295i
$261$		0			0
$262$	2.71527	+	0.540101i	0.0103636	+	0.00206145i
$263$	83.1206	−	34.4297i	0.316048	−	0.130911i	−0.219020	−	0.975720i	$-0.570286\pi$
$263$	83.1206	−	34.4297i	0.316048	−	0.130911i	0.535068	+	0.844809i	$0.320286\pi$
$264$		0			0
$265$	−2.65996	+	13.3725i	−0.0100376	+	0.0504624i
$266$	−14.4448	−	21.6182i	−0.0543039	−	0.0812716i
$267$		0			0
$268$	−74.2269	+	74.2269i	−0.276966	+	0.276966i
$269$	262.976	−	393.571i	0.977605	−	1.46309i	0.0936016	−	0.995610i	$-0.470162\pi$
$269$	262.976	−	393.571i	0.977605	−	1.46309i	0.884004	−	0.467480i	$-0.154838\pi$
$270$		0			0
$271$			61.4406i			0.226718i	0.993554	+	0.113359i	$0.0361611\pi$
$271$			61.4406i			0.226718i	−0.993554	+	0.113359i	$0.963839\pi$
$272$	−66.1225	+	116.742i	−0.243097	+	0.429197i
$273$		0			0
$274$	−29.1824	+	70.4526i	−0.106505	+	0.257126i
$275$	−121.399	−	81.1160i	−0.441450	−	0.294967i
$276$		0			0
$277$	146.302	−	29.1012i	0.528165	−	0.105058i	0.0761970	−	0.997093i	$-0.475722\pi$
$277$	146.302	−	29.1012i	0.528165	−	0.105058i	0.451968	+	0.892034i	$0.350722\pi$
$278$	−91.7435	+	61.3011i	−0.330013	+	0.220507i
$279$		0			0
$280$	−35.2357	+	14.5951i	−0.125842	+	0.0521254i
$281$	12.9932	+	31.3685i	0.0462393	+	0.111632i	0.945312	−	0.326169i	$-0.105758\pi$
$281$	12.9932	+	31.3685i	0.0462393	+	0.111632i	−0.899072	+	0.437800i	$0.855758\pi$
$282$		0			0
$283$	−105.039	−	157.202i	−0.371162	−	0.555484i	0.598129	−	0.801400i	$-0.295911\pi$
$283$	−105.039	−	157.202i	−0.371162	−	0.555484i	−0.969291	+	0.245916i	$0.920911\pi$
$284$	−66.3353	−	333.490i	−0.233575	−	1.17426i
$285$		0			0
$286$	47.3118	−	70.8071i	0.165426	−	0.247577i
$287$	3.15263	+	1.30586i	0.0109848	+	0.00455005i
$288$		0			0
$289$	148.611	+	247.863i	0.514223	+	0.857656i
$290$	122.661			0.422968
$291$		0			0
$292$	171.786	+	114.784i	0.588309	+	0.393095i
$293$	−125.147	−	125.147i	−0.427121	−	0.427121i	0.460525	−	0.887647i	$-0.347661\pi$
$293$	−125.147	−	125.147i	−0.427121	−	0.427121i	−0.887647	+	0.460525i	$0.847661\pi$
$294$		0			0
$295$	−195.491	+	130.623i	−0.662681	+	0.442789i
$296$	242.674	+	48.2709i	0.819845	+	0.163077i
$297$		0			0
$298$	−68.7721	−	166.031i	−0.230779	−	0.557149i
$299$	−54.2284	+	272.625i	−0.181366	+	0.911788i
$300$		0			0
$301$	−2.40371	−	12.0843i	−0.00798574	−	0.0401470i
$302$	35.8732	−	35.8732i	0.118785	−	0.118785i
$303$		0			0
$304$	−247.353	−	102.457i	−0.813661	−	0.337029i
$305$		−	242.640i		−	0.795541i
$306$		0			0
$307$	368.138			1.19914			0.599572	−	0.800320i	$-0.295337\pi$
$307$	368.138			1.19914			0.599572	+	0.800320i	$0.295337\pi$
$308$	7.63581	−	18.4345i	0.0247916	−	0.0598522i
$309$		0			0
$310$	155.818	+	155.818i	0.502639	+	0.502639i
$311$	−103.068	+	20.5015i	−0.331408	+	0.0659211i	−0.357990	−	0.933726i	$-0.616538\pi$
$311$	−103.068	+	20.5015i	−0.331408	+	0.0659211i	0.0265819	+	0.999647i	$0.491538\pi$
$312$		0			0
$313$	425.555	+	84.6482i	1.35960	+	0.270441i	0.820426	−	0.571752i	$-0.193736\pi$
$313$	425.555	+	84.6482i	1.35960	+	0.270441i	0.539175	+	0.842194i	$0.318736\pi$
$314$	115.562	−	47.8672i	0.368030	−	0.152443i
$315$		0			0
$316$	41.8245	−	210.266i	0.132356	−	0.665399i
$317$	291.124	+	435.698i	0.918372	+	1.37444i	0.927235	+	0.374480i	$0.122179\pi$
$317$	291.124	+	435.698i	0.918372	+	1.37444i	−0.00886288	+	0.999961i	$0.502821\pi$
$318$		0			0
$319$	−100.693	+	100.693i	−0.315653	+	0.315653i
$320$	−18.8496	+	28.2104i	−0.0589050	+	0.0881576i
$321$		0			0
$322$		−	14.2651i		−	0.0443016i
$323$	−454.619	+	354.839i	−1.40749	+	1.09857i
$324$		0			0
$325$	124.057	−	299.499i	0.381713	−	0.921536i
$326$	−228.604	−	152.748i	−0.701238	−	0.468553i
$327$		0			0
$328$	−22.8516	+	4.54547i	−0.0696696	+	0.0138581i
$329$	9.78551	−	6.53847i	0.0297432	−	0.0198738i
$330$		0			0
$331$	−325.078	+	134.652i	−0.982109	+	0.406803i	−0.815206	−	0.579171i	$-0.803377\pi$
$331$	−325.078	+	134.652i	−0.982109	+	0.406803i	−0.166903	+	0.985973i	$0.553377\pi$
$332$	53.9790	+	130.317i	0.162587	+	0.392520i
$333$		0			0
$334$	−74.2728	−	111.157i	−0.222374	−	0.332806i
$335$	42.6536	+	214.434i	0.127324	+	0.640102i
$336$		0			0
$337$	−86.3544	+	129.239i	−0.256245	+	0.383497i	−0.937180	−	0.348846i	$-0.886573\pi$
$337$	−86.3544	+	129.239i	−0.256245	+	0.383497i	0.680935	+	0.732344i	$0.261573\pi$
$338$	42.3207	+	17.5298i	0.125209	+	0.0518633i
$339$		0			0
$340$	171.429	+	340.510i	0.504202	+	1.00150i
$341$	−255.825			−0.750221
$342$		0			0
$343$	−73.0519	−	48.8117i	−0.212979	−	0.142308i
$344$	59.4862	+	59.4862i	0.172925	+	0.172925i
$345$		0			0
$346$	−115.850	+	77.4085i	−0.334827	+	0.223724i
$347$	262.388	+	52.1922i	0.756161	+	0.150410i	0.558093	−	0.829779i	$-0.311533\pi$
$347$	262.388	+	52.1922i	0.756161	+	0.150410i	0.198068	+	0.980188i	$0.436533\pi$
$348$		0			0
$349$	75.5583	+	182.414i	0.216499	+	0.522676i	0.994396	−	0.105716i	$-0.0337135\pi$
$349$	75.5583	+	182.414i	0.216499	+	0.522676i	−0.777897	+	0.628392i	$0.783713\pi$
$350$	−3.24563	+	16.3169i	−0.00927324	+	0.0466197i
$351$		0			0
$352$	41.1800	+	207.026i	0.116989	+	0.588142i
$353$	303.609	−	303.609i	0.860081	−	0.860081i	−0.131266	−	0.991347i	$-0.541904\pi$
$353$	303.609	−	303.609i	0.860081	−	0.860081i	0.991347	+	0.131266i	$0.0419041\pi$
$354$		0			0
$355$	−654.286	−	271.014i	−1.84306	−	0.763420i
$356$		−	230.026i		−	0.646139i
$357$		0			0
$358$	−164.528			−0.459576
$359$	−21.7296	+	52.4599i	−0.0605281	+	0.146128i	−0.951250	−	0.308421i	$-0.900199\pi$
$359$	−21.7296	+	52.4599i	−0.0605281	+	0.146128i	0.890722	+	0.454549i	$0.150199\pi$
$360$		0			0
$361$	−558.492	−	558.492i	−1.54707	−	1.54707i
$362$	−41.5304	+	8.26091i	−0.114725	+	0.0228202i
$363$		0			0
$364$	43.4512	+	8.64299i	0.119372	+	0.0237445i
$365$	397.558	−	164.674i	1.08920	−	0.451161i
$366$		0			0
$367$	44.3636	−	223.031i	0.120882	−	0.607714i	−0.872088	−	0.489348i	$-0.837235\pi$
$367$	44.3636	−	223.031i	0.120882	−	0.607714i	0.992970	−	0.118365i	$-0.0377654\pi$
$368$	−81.6097	−	122.138i	−0.221766	−	0.331896i
$369$		0			0
$370$	164.216	−	164.216i	0.443827	−	0.443827i
$371$	−1.00204	+	1.49966i	−0.00270092	+	0.00404221i
$372$		0			0
$373$		−	460.172i		−	1.23370i	−0.787079	−	0.616852i	$-0.788408\pi$
$373$		−	460.172i		−	1.23370i	0.787079	−	0.616852i	$-0.211592\pi$
$374$	92.0475	+	30.4012i	0.246116	+	0.0812866i
$375$		0			0
$376$	−30.7512	+	74.2400i	−0.0817851	+	0.197447i
$377$	−262.890	−	175.658i	−0.697322	−	0.465935i
$378$		0			0
$379$	60.3712	−	12.0086i	0.159291	−	0.0316849i	−0.114801	−	0.993389i	$-0.536623\pi$
$379$	60.3712	−	12.0086i	0.159291	−	0.0316849i	0.274091	+	0.961704i	$0.411623\pi$
$380$	−632.540	+	422.649i	−1.66458	+	1.11224i
$381$		0			0
$382$	233.655	−	96.7829i	0.611661	−	0.253358i
$383$	−235.671	−	568.960i	−0.615329	−	1.48554i	−0.857073	−	0.515196i	$-0.827719\pi$
$383$	−235.671	−	568.960i	−0.615329	−	1.48554i	0.241744	−	0.970340i	$-0.422281\pi$
$384$		0			0
$385$	−23.0886	−	34.5546i	−0.0599704	−	0.0897521i
$386$	9.32115	+	46.8606i	0.0241481	+	0.121400i
$387$		0			0
$388$	−232.893	+	348.548i	−0.600239	+	0.898321i
$389$	−336.723	−	139.475i	−0.865613	−	0.358549i	−0.0947127	−	0.995505i	$-0.530193\pi$
$389$	−336.723	−	139.475i	−0.865613	−	0.358549i	−0.770900	+	0.636956i	$0.780193\pi$
$390$		0			0
$391$	−315.554	+	23.2990i	−0.807045	+	0.0595883i
$392$	297.422			0.758729
$393$		0			0
$394$	−2.63940	−	1.76359i	−0.00669898	−	0.00447611i
$395$	−315.736	−	315.736i	−0.799331	−	0.799331i
$396$		0			0
$397$	−50.0566	+	33.4467i	−0.126087	+	0.0842487i	−0.617015	−	0.786952i	$-0.711658\pi$
$397$	−50.0566	+	33.4467i	−0.126087	+	0.0842487i	0.490927	+	0.871200i	$0.336658\pi$
$398$	−123.865	−	24.6382i	−0.311218	−	0.0619051i
$399$		0			0
$400$	65.5589	+	158.273i	0.163897	+	0.395683i
$401$	−3.79806	+	19.0941i	−0.00947147	+	0.0476163i	−0.985232	−	0.171225i	$-0.945228\pi$
$401$	−3.79806	+	19.0941i	−0.00947147	+	0.0476163i	0.975761	+	0.218841i	$0.0702276\pi$
$402$		0			0
$403$	−110.813	−	557.096i	−0.274971	−	1.38237i
$404$	86.1103	−	86.1103i	0.213144	−	0.213144i
$405$		0			0
$406$	14.9909	+	6.20943i	0.0369233	+	0.0152942i
$407$			269.613i			0.662439i
$408$		0			0
$409$	434.868			1.06325			0.531623	−	0.846981i	$-0.321582\pi$
$409$	434.868			1.06325			0.531623	+	0.846981i	$0.321582\pi$
$410$	−8.36881	+	20.2041i	−0.0204117	+	0.0492783i
$411$		0			0
$412$	−127.413	−	127.413i	−0.309254	−	0.309254i
$413$	−30.5043	+	6.06768i	−0.0738602	+	0.0146917i
$414$		0			0
$415$	288.139	+	57.3144i	0.694311	+	0.138107i
$416$	−432.991	+	179.351i	−1.04084	+	0.431132i
$417$		0			0
$418$	−37.7386	+	189.725i	−0.0902837	+	0.453887i
$419$	44.9826	+	67.3212i	0.107357	+	0.160671i	0.881258	−	0.472635i	$-0.156697\pi$
$419$	44.9826	+	67.3212i	0.107357	+	0.160671i	−0.773901	+	0.633307i	$0.781697\pi$
$420$		0			0
$421$	211.099	−	211.099i	0.501423	−	0.501423i	−0.410457	−	0.911880i	$-0.634631\pi$
$421$	211.099	−	211.099i	0.501423	−	0.501423i	0.911880	+	0.410457i	$0.134631\pi$
$422$	139.833	−	209.275i	0.331358	−	0.495912i
$423$		0			0
$424$		−	12.3149i		−	0.0290446i
$425$	366.243	+	45.1456i	0.861748	+	0.106225i
$426$		0			0
$427$	12.2831	−	29.6541i	0.0287661	−	0.0694475i
$428$	405.181	+	270.733i	0.946685	+	0.632555i
$429$		0			0
$430$	77.4436	−	15.4045i	0.180101	−	0.0358244i
$431$	499.936	−	334.047i	1.15994	−	0.775050i	0.181873	−	0.983322i	$-0.441784\pi$
$431$	499.936	−	334.047i	1.15994	−	0.775050i	0.978071	+	0.208272i	$0.0667840\pi$
$432$		0			0
$433$	−405.728	+	168.058i	−0.937017	+	0.388125i	−0.798336	−	0.602212i	$-0.794286\pi$
$433$	−405.728	+	168.058i	−0.937017	+	0.388125i	−0.138681	+	0.990337i	$0.544286\pi$
$434$	11.1553	+	26.9312i	0.0257034	+	0.0620534i
$435$		0			0
$436$	43.5268	+	65.1425i	0.0998321	+	0.149409i
$437$	−123.182	−	619.277i	−0.281881	−	1.41711i
$438$		0			0
$439$	354.911	−	531.162i	0.808453	−	1.20994i	−0.166173	−	0.986097i	$-0.553141\pi$
$439$	354.911	−	531.162i	0.808453	−	1.20994i	0.974626	−	0.223839i	$-0.0718589\pi$
$440$	262.156	+	108.588i	0.595809	+	0.246792i
$441$		0			0
$442$	−26.3317	+	213.615i	−0.0595739	+	0.483292i
$443$	79.9030			0.180368			0.0901839	−	0.995925i	$-0.471255\pi$
$443$	79.9030			0.180368			0.0901839	+	0.995925i	$0.471255\pi$
$444$		0			0
$445$	−398.351	−	266.170i	−0.895170	−	0.598134i
$446$	−53.9846	−	53.9846i	−0.121042	−	0.121042i
$447$		0			0
$448$	−3.73178	+	2.49350i	−0.00832987	+	0.00556584i
$449$	−144.414	−	28.7257i	−0.321634	−	0.0639770i	0.0316329	−	0.999500i	$-0.489929\pi$
$449$	−144.414	−	28.7257i	−0.321634	−	0.0639770i	−0.353267	+	0.935523i	$0.614929\pi$
$450$		0			0
$451$	−9.71569	−	23.4558i	−0.0215426	−	0.0520083i
$452$	−31.0537	+	156.118i	−0.0687029	+	0.345393i
$453$		0			0
$454$	24.6712	+	124.031i	0.0543420	+	0.273195i
$455$	65.2464	−	65.2464i	0.143399	−	0.143399i
$456$		0			0
$457$	595.804	+	246.790i	1.30373	+	0.540022i	0.923048	−	0.384684i	$-0.125690\pi$
$457$	595.804	+	246.790i	1.30373	+	0.540022i	0.380681	+	0.924706i	$0.375690\pi$
$458$			116.072i			0.253432i
$459$		0			0
$460$	−417.390			−0.907370
$461$	−98.1211	+	236.885i	−0.212844	+	0.513851i	−0.993858	−	0.110663i	$-0.964703\pi$
$461$	−98.1211	+	236.885i	−0.212844	+	0.513851i	0.781014	+	0.624513i	$0.214703\pi$
$462$		0			0
$463$	422.873	+	422.873i	0.913332	+	0.913332i	0.996533	−	0.0832008i	$-0.0265143\pi$
$463$	422.873	+	422.873i	0.913332	+	0.913332i	−0.0832008	+	0.996533i	$0.526514\pi$
$464$	163.875	−	32.5968i	0.353180	−	0.0702518i
$465$		0			0
$466$	−296.676	−	59.0124i	−0.636643	−	0.126636i
$467$	−469.394	+	194.429i	−1.00513	+	0.416337i	−0.823674	−	0.567063i	$-0.808080\pi$
$467$	−469.394	+	194.429i	−1.00513	+	0.416337i	−0.181452	+	0.983400i	$0.558080\pi$
$468$		0			0
$469$	−5.64238	+	28.3661i	−0.0120307	+	0.0604822i
$470$	41.9027	+	62.7118i	0.0891547	+	0.133429i
$471$		0			0
$472$	150.161	−	150.161i	0.318137	−	0.318137i
$473$	−50.9285	+	76.2199i	−0.107671	+	0.161141i
$474$		0			0
$475$			736.376i			1.55027i
$476$	3.71343	+	50.2934i	0.00780131	+	0.105658i
$477$		0			0
$478$	−129.146	+	311.786i	−0.270180	+	0.652272i
$479$	329.863	+	220.407i	0.688649	+	0.460141i	0.850018	−	0.526753i	$-0.176591\pi$
$479$	329.863	+	220.407i	0.688649	+	0.460141i	−0.161369	+	0.986894i	$0.551591\pi$
$480$		0			0
$481$	−587.120	+	116.785i	−1.22062	+	0.242797i
$482$	55.9288	−	37.3704i	0.116035	−	0.0775320i
$483$		0			0
$484$	229.662	−	95.1289i	0.474507	−	0.196547i
$485$	334.118	+	806.632i	0.688903	+	1.66316i
$486$		0			0
$487$	214.400	+	320.872i	0.440246	+	0.658875i	0.983545	−	0.180665i	$-0.0578249\pi$
$487$	214.400	+	320.872i	0.440246	+	0.658875i	−0.543299	+	0.839539i	$0.682825\pi$
$488$	42.7553	+	214.945i	0.0876133	+	0.440462i
$489$		0			0
$490$	155.093	−	232.113i	0.316516	−	0.473700i
$491$	−430.764	−	178.428i	−0.877319	−	0.363398i	−0.101863	−	0.994798i	$-0.532480\pi$
$491$	−430.764	−	178.428i	−0.877319	−	0.363398i	−0.775457	+	0.631401i	$0.782480\pi$
$492$		0			0
$493$	112.873	−	341.751i	0.228950	−	0.693207i
$494$	−429.499			−0.869432
$495$		0			0
$496$	249.583	+	166.766i	0.503191	+	0.336221i
$497$	−66.2436	−	66.2436i	−0.133287	−	0.133287i
$498$		0			0
$499$	152.031	−	101.584i	0.304671	−	0.203574i	−0.393831	−	0.919183i	$-0.628850\pi$
$499$	152.031	−	101.584i	0.304671	−	0.203574i	0.698502	+	0.715608i	$0.253850\pi$
$500$	−72.4327	−	14.4078i	−0.144865	−	0.0288155i
$501$		0			0
$502$	−147.085	−	355.094i	−0.292998	−	0.707359i
$503$	125.290	−	629.877i	0.249086	−	1.25224i	−0.630383	−	0.776284i	$-0.717102\pi$
$503$	125.290	−	629.877i	0.249086	−	1.25224i	0.879469	−	0.475956i	$-0.157898\pi$
$504$		0			0
$505$	−49.4822	−	248.764i	−0.0979846	−	0.492602i
$506$	−75.0475	+	75.0475i	−0.148315	+	0.148315i
$507$		0			0
$508$	146.311	+	60.6039i	0.288013	+	0.119299i
$509$			177.040i			0.347819i	0.984762	+	0.173909i	$0.0556400\pi$
$509$			177.040i			0.347819i	−0.984762	+	0.173909i	$0.944360\pi$
$510$		0			0
$511$	56.9235			0.111396
$512$	169.352	−	408.852i	0.330766	−	0.798539i
$513$		0			0
$514$	−59.0293	−	59.0293i	−0.114843	−	0.114843i
$515$	−368.083	+	73.2162i	−0.714724	+	0.142167i
$516$		0			0
$517$	−85.8791	−	17.0824i	−0.166110	−	0.0330414i
$518$	28.3826	−	11.7565i	0.0547927	−	0.0226959i
$519$		0			0
$520$	−122.911	+	617.918i	−0.236368	+	1.18830i
$521$	169.681	+	253.946i	0.325684	+	0.487420i	0.957793	−	0.287459i	$-0.0928106\pi$
$521$	169.681	+	253.946i	0.325684	+	0.487420i	−0.632109	+	0.774879i	$0.717811\pi$
$522$		0			0
$523$	−291.958	+	291.958i	−0.558238	+	0.558238i	−0.928806	−	0.370568i	$-0.879163\pi$
$523$	−291.958	+	291.958i	−0.558238	+	0.558238i	0.370568	+	0.928806i	$0.379163\pi$
$524$	5.95322	−	8.90963i	0.0113611	−	0.0170031i
$525$		0			0
$526$			76.2721i			0.145004i
$527$	577.517	−	290.749i	1.09586	−	0.551705i
$528$		0			0
$529$	−69.8676	+	168.675i	−0.132075	+	0.318857i
$530$	−9.61078	−	6.42172i	−0.0181336	−	0.0121165i
$531$		0			0
$532$	−98.7011	+	19.6329i	−0.185528	+	0.0369039i
$533$	46.8698	−	31.3174i	0.0879359	−	0.0587569i
$534$		0			0
$535$	937.695	−	388.406i	1.75270	−	0.725992i
$536$	−75.5703	−	182.443i	−0.140989	−	0.340379i
$537$		0			0
$538$	222.940	+	333.653i	0.414387	+	0.620174i
$539$	63.2265	+	317.861i	0.117303	+	0.589724i
$540$		0			0
$541$	−397.133	+	594.351i	−0.734072	+	1.09862i	0.257145	+	0.966373i	$0.417218\pi$
$541$	−397.133	+	594.351i	−0.734072	+	1.09862i	−0.991217	+	0.132243i	$0.957782\pi$
$542$	−48.1220	−	19.9328i	−0.0887859	−	0.0367763i
$543$		0			0
$544$	−328.250	−	420.553i	−0.603401	−	0.773075i
$545$	163.178			0.299409
$546$		0			0
$547$	251.742	+	168.209i	0.460223	+	0.307511i	0.763982	−	0.645238i	$-0.223242\pi$
$547$	251.742	+	168.209i	0.460223	+	0.307511i	−0.303759	+	0.952749i	$0.598242\pi$
$548$	208.709	+	208.709i	0.380855	+	0.380855i
$549$		0			0
$550$	102.917	−	68.7668i	0.187121	−	0.125031i
$551$	704.404	+	140.115i	1.27841	+	0.254292i
$552$		0			0
$553$	−22.6040	−	54.5708i	−0.0408752	−	0.0986815i
$554$	−24.6708	+	124.029i	−0.0445321	+	0.223878i
$555$		0			0
$556$	83.3180	+	418.868i	0.149853	+	0.753360i
$557$	−708.431	+	708.431i	−1.27187	+	1.27187i	−0.326762	+	0.945107i	$0.605958\pi$
$557$	−708.431	+	708.431i	−1.27187	+	1.27187i	−0.945107	+	0.326762i	$0.894042\pi$
$558$		0			0
$559$	−188.040	−	77.8887i	−0.336386	−	0.139336i
$560$			48.7622i			0.0870753i
$561$		0			0
$562$	−28.7839			−0.0512170
$563$	314.331	−	758.863i	0.558315	−	1.34789i	−0.352784	−	0.935705i	$-0.614765\pi$
$563$	314.331	−	758.863i	0.558315	−	1.34789i	0.911099	−	0.412187i	$-0.135235\pi$
$564$		0			0
$565$	234.426	+	234.426i	0.414914	+	0.414914i
$566$	157.202	−	31.2694i	0.277742	−	0.0552463i
$567$		0			0
$568$	627.361	+	124.790i	1.10451	+	0.219701i
$569$	−395.568	+	163.849i	−0.695198	+	0.287960i	−0.702164	−	0.712015i	$-0.747783\pi$
$569$	−395.568	+	163.849i	−0.695198	+	0.287960i	0.00696604	+	0.999976i	$0.497783\pi$
$570$		0			0
$571$	78.3724	−	394.005i	0.137255	−	0.690026i	−0.849472	−	0.527634i	$-0.823079\pi$
$571$	78.3724	−	394.005i	0.137255	−	0.690026i	0.986726	−	0.162392i	$-0.0519208\pi$
$572$	−183.123	−	274.063i	−0.320145	−	0.479132i
$573$		0			0
$574$	−2.04558	+	2.04558i	−0.00356372	+	0.00356372i
$575$	−224.460	+	335.929i	−0.390366	+	0.584224i
$576$		0			0
$577$		−	324.254i		−	0.561965i	−0.959713	−	0.280982i	$-0.909340\pi$
$577$		−	324.254i		−	0.561965i	0.959713	−	0.280982i	$-0.0906602\pi$
$578$	−242.346	+	35.9834i	−0.419283	+	0.0622550i
$579$		0			0
$580$	181.685	−	438.626i	0.313250	−	0.756252i
$581$	32.3133	+	21.5910i	0.0556167	+	0.0371619i
$582$		0			0
$583$	13.1612	−	2.61793i	0.0225750	−	0.00449045i
$584$	−323.164	+	215.931i	−0.553363	+	0.369745i
$585$		0			0
$586$	138.619	−	57.4177i	0.236551	−	0.0979825i
$587$	103.107	+	248.922i	0.175651	+	0.424058i	0.987046	−	0.160440i	$-0.0512914\pi$
$587$	103.107	+	248.922i	0.175651	+	0.424058i	−0.811395	+	0.584498i	$0.801291\pi$
$588$		0			0
$589$	716.828	+	1072.81i	1.21703	+	1.82141i
$590$	−38.8855	−	195.491i	−0.0659077	−	0.331340i
$591$		0			0
$592$	175.753	−	263.034i	0.296881	−	0.444313i
$593$	662.174	+	274.282i	1.11665	+	0.462532i	0.863223	−	0.504822i	$-0.168442\pi$
$593$	662.174	+	274.282i	1.11665	+	0.462532i	0.253428	+	0.967354i	$0.418442\pi$
$594$		0			0
$595$	91.3935	+	51.7653i	0.153603	+	0.0870005i
$596$	−695.579			−1.16708
$597$		0			0
$598$	−195.934	−	130.919i	−0.327649	−	0.218928i
$599$	330.421	+	330.421i	0.551622	+	0.551622i	0.926909	−	0.375287i	$-0.122456\pi$
$599$	330.421	+	330.421i	0.551622	+	0.551622i	−0.375287	+	0.926909i	$0.622456\pi$
$600$		0			0
$601$	−26.7271	+	17.8585i	−0.0444710	+	0.0297146i	−0.577607	−	0.816315i	$-0.696013\pi$
$601$	−26.7271	+	17.8585i	−0.0444710	+	0.0297146i	0.533136	+	0.846030i	$0.321013\pi$
$602$	10.2445	+	2.03776i	0.0170175	+	0.00338499i
$603$		0			0
$604$	−75.1448	−	181.416i	−0.124412	−	0.300357i
$605$	101.007	−	507.797i	0.166954	−	0.839334i
$606$		0			0
$607$	−51.7408	−	260.119i	−0.0852402	−	0.428531i	−0.999715	−	0.0238877i	$-0.992396\pi$
$607$	−51.7408	−	260.119i	−0.0852402	−	0.428531i	0.914474	−	0.404644i	$-0.132604\pi$
$608$	752.780	−	752.780i	1.23813	−	1.23813i
$609$		0			0
$610$	190.042	+	78.7181i	0.311545	+	0.129046i
$611$		−	194.413i		−	0.318189i
$612$		0			0
$613$	−700.076			−1.14205			−0.571025	−	0.820933i	$-0.693454\pi$
$613$	−700.076			−1.14205			−0.571025	+	0.820933i	$0.693454\pi$
$614$	−119.432	+	288.335i	−0.194515	+	0.469602i
$615$		0			0
$616$	26.5421	+	26.5421i	0.0430879	+	0.0430879i
$617$	−703.990	+	140.032i	−1.14099	+	0.226957i	−0.729185	−	0.684316i	$-0.760101\pi$
$617$	−703.990	+	140.032i	−1.14099	+	0.226957i	−0.411803	+	0.911273i	$0.635101\pi$
$618$		0			0
$619$	−898.874	−	178.797i	−1.45214	−	0.288848i	−0.594913	−	0.803790i	$-0.702814\pi$
$619$	−898.874	−	178.797i	−1.45214	−	0.288848i	−0.857225	+	0.514941i	$0.827814\pi$
$620$	787.994	−	326.398i	1.27096	−	0.526448i
$621$		0			0
$622$	17.3803	−	87.3767i	0.0279426	−	0.140477i
$623$	−35.2099	−	52.6954i	−0.0565167	−	0.0845833i
$624$		0			0
$625$	−492.490	+	492.490i	−0.787984	+	0.787984i
$626$	−204.359	+	305.845i	−0.326452	+	0.488570i
$627$		0			0
$628$		−	484.141i		−	0.770926i
$629$	−306.418	−	608.642i	−0.487152	−	0.967634i
$630$		0			0
$631$	313.464	−	756.768i	0.496773	−	1.19932i	−0.454439	−	0.890778i	$-0.650160\pi$
$631$	313.464	−	756.768i	0.496773	−	1.19932i	0.951212	−	0.308538i	$-0.0998397\pi$
$632$	335.333	+	224.063i	0.530591	+	0.354529i
$633$		0			0
$634$	−435.698	+	86.6657i	−0.687220	+	0.136697i
$635$	274.252	−	183.250i	0.431893	−	0.288582i
$636$		0			0
$637$	−664.801	+	275.370i	−1.04364	+	0.432291i
$638$	−46.1985	−	111.533i	−0.0724114	−	0.174817i
$639$		0			0
$640$	−492.594	−	737.219i	−0.769679	−	1.15191i
$641$	−206.112	−	1036.19i	−0.321547	−	1.61653i	−0.716337	−	0.697754i	$-0.754183\pi$
$641$	−206.112	−	1036.19i	−0.321547	−	1.61653i	0.394790	−	0.918771i	$-0.370817\pi$
$642$		0			0
$643$	198.642	−	297.289i	0.308931	−	0.462347i	−0.644221	−	0.764839i	$-0.722818\pi$
$643$	198.642	−	297.289i	0.308931	−	0.462347i	0.953152	+	0.302492i	$0.0978185\pi$
$644$	−51.0111	−	21.1295i	−0.0792097	−	0.0328097i
$645$		0			0
$646$	−130.431	−	471.188i	−0.201905	−	0.729393i
$647$	−414.046			−0.639947			−0.319973	−	0.947427i	$-0.603674\pi$
$647$	−414.046			−0.639947			−0.319973	+	0.947427i	$0.603674\pi$
$648$		0			0
$649$	192.402	+	128.559i	0.296459	+	0.198088i
$650$	194.329	+	194.329i	0.298968	+	0.298968i
$651$		0			0
$652$	−884.825	+	591.221i	−1.35709	+	0.906781i
$653$	−714.568	−	142.136i	−1.09428	−	0.217667i	−0.385230	−	0.922821i	$-0.625878\pi$
$653$	−714.568	−	142.136i	−1.09428	−	0.217667i	−0.709054	+	0.705154i	$0.750878\pi$
$654$		0			0
$655$	−8.54075	−	20.6192i	−0.0130393	−	0.0314797i
$656$	−5.81158	+	29.2168i	−0.00885911	+	0.0445378i
$657$		0			0
$658$	1.94646	+	9.78551i	0.00295815	+	0.0148716i
$659$	310.871	−	310.871i	0.471731	−	0.471731i	−0.430743	−	0.902474i	$-0.641749\pi$
$659$	310.871	−	310.871i	0.471731	−	0.471731i	0.902474	+	0.430743i	$0.141749\pi$
$660$		0			0
$661$	−163.337	−	67.6563i	−0.247105	−	0.102354i	0.255693	−	0.966758i	$-0.417696\pi$
$661$	−163.337	−	67.6563i	−0.247105	−	0.102354i	−0.502799	+	0.864404i	$0.667696\pi$
$662$		−	298.294i		−	0.450595i
$663$		0			0
$664$	−265.351			−0.399624
$665$	−80.2104	+	193.645i	−0.120617	+	0.291196i
$666$		0			0
$667$	278.634	+	278.634i	0.417742	+	0.417742i
$668$	−507.503	+	100.949i	−0.759736	+	0.151121i
$669$		0			0
$670$	−181.788	−	36.1600i	−0.271326	−	0.0539701i
$671$	−220.628	+	91.3871i	−0.328805	+	0.136195i
$672$		0			0
$673$	121.389	−	610.263i	0.180370	−	0.906780i	−0.779515	−	0.626384i	$-0.784534\pi$
$673$	121.389	−	610.263i	0.180370	−	0.906780i	0.959884	−	0.280396i	$-0.0904658\pi$
$674$	−73.2077	−	109.563i	−0.108617	−	0.162557i
$675$		0			0
$676$	125.371	−	125.371i	0.185460	−	0.185460i
$677$	26.5471	−	39.7306i	0.0392129	−	0.0586862i	−0.811345	−	0.584567i	$-0.801264\pi$
$677$	26.5471	−	39.7306i	0.0392129	−	0.0586862i	0.850558	+	0.525881i	$0.176264\pi$
$678$		0			0
$679$			115.496i			0.170097i
$680$	−715.220	+	52.8084i	−1.05179	+	0.0776594i
$681$		0			0
$682$	82.9957	−	200.369i	0.121695	−	0.293797i
$683$	−618.830	−	413.489i	−0.906048	−	0.605402i	0.0128416	−	0.999918i	$-0.495912\pi$
$683$	−618.830	−	413.489i	−0.906048	−	0.605402i	−0.918889	+	0.394516i	$0.870912\pi$
$684$		0			0
$685$	602.938	−	119.932i	0.880202	−	0.175083i
$686$	61.9304	−	41.3806i	0.0902776	−	0.0603216i
$687$		0			0
$688$	99.3714	−	41.1610i	0.144435	−	0.0598270i
$689$	11.4018	+	27.5265i	0.0165484	+	0.0399514i
$690$		0			0
$691$	−713.306	−	1067.54i	−1.03228	−	1.54492i	−0.823792	−	0.566893i	$-0.808145\pi$
$691$	−713.306	−	1067.54i	−1.03228	−	1.54492i	−0.208489	−	0.978025i	$-0.566855\pi$
$692$	105.211	+	528.930i	0.152038	+	0.764349i
$693$		0			0
$694$	−126.003	+	188.577i	−0.181561	+	0.271725i
$695$	821.792	+	340.397i	1.18243	+	0.489780i
$696$		0			0
$697$	48.5906	+	41.9086i	0.0697140	+	0.0601271i
$698$	−167.384			−0.239806
$699$		0			0
$700$	53.5407	+	35.7748i	0.0764868	+	0.0511068i
$701$	895.228	+	895.228i	1.27707	+	1.27707i	0.942298	+	0.334774i	$0.108660\pi$
$701$	895.228	+	895.228i	1.27707	+	1.27707i	0.334774	+	0.942298i	$0.391340\pi$
$702$		0			0
$703$	1130.63	−	755.461i	1.60829	−	1.07462i
$704$	32.7507	+	6.51451i	0.0465208	+	0.00925357i
$705$		0			0
$706$	139.297	+	336.292i	0.197304	+	0.476335i
$707$	6.54570	−	32.9074i	0.00925841	−	0.0465452i
$708$		0			0
$709$	145.154	+	729.738i	0.204730	+	1.02925i	0.937291	+	0.348547i	$0.113325\pi$
$709$	145.154	+	729.738i	0.204730	+	1.02925i	−0.732561	+	0.680702i	$0.761675\pi$
$710$	424.531	−	424.531i	0.597931	−	0.597931i
$711$		0			0
$712$	399.785	+	165.596i	0.561496	+	0.232579i
$713$			707.908i			0.992859i
$714$		0			0
$715$	−686.511			−0.960156
$716$	−243.699	+	588.342i	−0.340362	+	0.821707i
$717$		0			0
$718$	−34.0384	−	34.0384i	−0.0474073	−	0.0474073i
$719$	−141.631	+	28.1722i	−0.196984	+	0.0391825i	−0.292596	−	0.956236i	$-0.594519\pi$
$719$	−141.631	+	28.1722i	−0.196984	+	0.0391825i	0.0956124	+	0.995419i	$0.469519\pi$
$720$		0			0
$721$	−48.6914	−	9.68532i	−0.0675331	−	0.0134332i
$722$	618.614	−	256.238i	0.856806	−	0.354901i
$723$		0			0
$724$	−31.9744	+	160.746i	−0.0441635	+	0.222025i
$725$	−255.315	−	382.106i	−0.352159	−	0.527043i
$726$		0			0
$727$	33.3667	−	33.3667i	0.0458965	−	0.0458965i	−0.683786	−	0.729683i	$-0.739668\pi$
$727$	33.3667	−	33.3667i	0.0458965	−	0.0458965i	0.729683	+	0.683786i	$0.239668\pi$
$728$	−46.3023	+	69.2963i	−0.0636020	+	0.0951872i
$729$		0			0
$730$			364.802i			0.499729i
$731$	28.3446	−	229.945i	0.0387750	−	0.314562i
$732$		0			0
$733$	−250.284	+	604.239i	−0.341452	+	0.824337i	0.656118	+	0.754658i	$0.272197\pi$
$733$	−250.284	+	604.239i	−0.341452	+	0.824337i	−0.997569	+	0.0696787i	$0.977803\pi$
$734$	160.291	+	107.103i	0.218381	+	0.145917i
$735$		0			0
$736$	572.873	−	113.951i	0.778360	−	0.154825i
$737$	178.916	−	119.548i	0.242762	−	0.162209i
$738$		0			0
$739$	−1135.07	+	470.162i	−1.53596	+	0.636214i	−0.980709	−	0.195472i	$-0.937376\pi$
$739$	−1135.07	+	470.162i	−1.53596	+	0.636214i	−0.555247	+	0.831685i	$0.687376\pi$
$740$	−343.988	−	830.462i	−0.464849	−	1.12225i
$741$		0			0
$742$	−0.849490	−	1.27135i	−0.00114486	−	0.00171341i
$743$	219.382	+	1102.91i	0.295266	+	1.48440i	0.788787	+	0.614667i	$0.210710\pi$
$743$	219.382	+	1102.91i	0.295266	+	1.48440i	−0.493521	+	0.869734i	$0.664290\pi$
$744$		0			0
$745$	−804.876	+	1204.58i	−1.08037	+	1.61689i
$746$	360.419	+	149.290i	0.483135	+	0.200121i
$747$		0			0
$748$	245.053	−	284.125i	0.327612	−	0.379847i
$749$	134.262			0.179255
$750$		0			0
$751$	1063.32	+	710.490i	1.41588	+	0.946059i	0.999317	+	0.0369501i	$0.0117643\pi$
$751$	1063.32	+	710.490i	1.41588	+	0.946059i	0.416560	+	0.909108i	$0.363236\pi$
$752$	72.6478	+	72.6478i	0.0966061	+	0.0966061i
$753$		0			0
$754$	222.868	−	148.915i	0.295580	−	0.197500i
$755$	−401.122	−	79.7881i	−0.531287	−	0.105680i
$756$		0			0
$757$	−75.7752	−	182.937i	−0.100099	−	0.241661i	0.865894	−	0.500227i	$-0.166750\pi$
$757$	−75.7752	−	182.937i	−0.100099	−	0.241661i	−0.965994	+	0.258566i	$0.916750\pi$
$758$	−10.1804	+	51.1802i	−0.0134306	+	0.0675201i
$759$		0			0
$760$	−279.198	−	1403.62i	−0.367366	−	1.84687i
$761$	−380.948	+	380.948i	−0.500588	+	0.500588i	−0.911621	−	0.411032i	$-0.865168\pi$
$761$	−380.948	+	380.948i	−0.500588	+	0.500588i	0.411032	+	0.911621i	$0.365168\pi$
$762$		0			0
$763$	19.9427	+	8.26052i	0.0261372	+	0.0108264i
$764$		−	978.888i		−	1.28127i
$765$		0			0
$766$	522.082			0.681570
$767$	−196.614	+	474.669i	−0.256342	+	0.618864i
$768$		0			0
$769$	−90.3571	−	90.3571i	−0.117500	−	0.117500i	0.645912	−	0.763412i	$-0.276477\pi$
$769$	−90.3571	−	90.3571i	−0.117500	−	0.117500i	−0.763412	+	0.645912i	$0.776477\pi$
$770$	34.5546	−	6.87333i	0.0448761	−	0.00892640i
$771$		0			0
$772$	181.377	+	36.0781i	0.234944	+	0.0467333i
$773$	−134.981	+	55.9110i	−0.174620	+	0.0723298i	−0.468281	−	0.883580i	$-0.655126\pi$
$773$	−134.981	+	55.9110i	−0.174620	+	0.0723298i	0.293661	+	0.955910i	$0.405126\pi$
$774$		0			0
$775$	161.065	−	809.729i	0.207826	−	1.04481i
$776$	−438.118	−	655.689i	−0.564585	−	0.844961i
$777$		0			0
$778$	218.482	−	218.482i	0.280825	−	0.280825i
$779$	−71.1386	+	106.466i	−0.0913204	+	0.136671i
$780$		0			0
$781$			697.003i			0.892450i
$782$	84.1248	−	254.710i	0.107576	−	0.325716i
$783$		0			0
$784$	145.522	−	351.320i	0.185614	−	0.448113i
$785$	−838.420	−	560.215i	−1.06805	−	0.713649i
$786$		0			0
$787$	−678.506	+	134.963i	−0.862142	+	0.171491i	−0.606308	−	0.795230i	$-0.707350\pi$
$787$	−678.506	+	134.963i	−0.862142	+	0.171491i	−0.255834	+	0.966721i	$0.582350\pi$
$788$	−10.2159	+	6.82608i	−0.0129644	+	0.00866254i
$789$		0			0
$790$	349.725	−	144.861i	0.442690	−	0.183368i
$791$	16.7829	+	40.5176i	0.0212174	+	0.0512232i
$792$		0			0
$793$	−294.576	−	440.864i	−0.371470	−	0.555944i
$794$	−9.95687	−	50.0566i	−0.0125401	−	0.0630436i
$795$		0			0
$796$	−271.573	+	406.438i	−0.341172	+	0.510601i
$797$	997.012	+	412.976i	1.25096	+	0.518163i	0.907122	−	0.420867i	$-0.138274\pi$
$797$	997.012	+	412.976i	1.25096	+	0.518163i	0.343834	+	0.939030i	$0.388274\pi$
$798$		0			0
$799$	213.284	−	59.0397i	0.266938	−	0.0738919i
$800$	−681.198			−0.851497
$801$		0			0
$802$	−13.7229	−	9.16932i	−0.0171108	−	0.0114331i
$803$	−299.470	−	299.470i	−0.372938	−	0.372938i
$804$		0			0
$805$	−95.6178	+	63.8898i	−0.118780	+	0.0793662i
$806$	472.283	+	93.9430i	0.585959	+	0.116555i
$807$		0			0
$808$	87.6688	+	211.651i	0.108501	+	0.261945i
$809$	111.178	−	558.928i	0.137426	−	0.690887i	−0.849224	−	0.528033i	$-0.822930\pi$
$809$	111.178	−	558.928i	0.137426	−	0.690887i	0.986650	−	0.162855i	$-0.0520701\pi$
$810$		0			0
$811$	221.750	+	1114.81i	0.273428	+	1.37461i	0.836392	+	0.548132i	$0.184661\pi$
$811$	221.750	+	1114.81i	0.273428	+	1.37461i	−0.562964	+	0.826481i	$0.690339\pi$
$812$	44.4090	−	44.4090i	0.0546909	−	0.0546909i
$813$		0			0
$814$	−211.168	−	87.4687i	−0.259420	−	0.107455i
$815$			2216.43i			2.71955i
$816$		0			0
$817$	462.332			0.565890
$818$	−141.081	+	340.600i	−0.172471	+	0.416382i
$819$		0			0
$820$	59.8526	+	59.8526i	0.0729910	+	0.0729910i
$821$	20.5375	−	4.08517i	0.0250153	−	0.00497585i	−0.182567	−	0.983193i	$-0.558441\pi$
$821$	20.5375	−	4.08517i	0.0250153	−	0.00497585i	0.207582	+	0.978218i	$0.433441\pi$
$822$		0			0
$823$	1543.55	+	307.031i	1.87551	+	0.373063i	0.994908	−	0.100787i	$-0.0321361\pi$
$823$	1543.55	+	307.031i	1.87551	+	0.373063i	0.880606	+	0.473850i	$0.157136\pi$
$824$	313.169	−	129.719i	0.380059	−	0.157426i
$825$		0			0
$826$	5.14393	−	25.8603i	0.00622752	−	0.0313078i
$827$	−299.622	−	448.417i	−0.362300	−	0.542221i	0.604878	−	0.796318i	$-0.293222\pi$
$827$	−299.622	−	448.417i	−0.362300	−	0.542221i	−0.967179	+	0.254097i	$0.918222\pi$
$828$		0			0
$829$	−145.931	+	145.931i	−0.176032	+	0.176032i	−0.789624	−	0.613591i	$-0.789724\pi$
$829$	−145.931	+	145.931i	−0.176032	+	0.176032i	0.613591	+	0.789624i	$0.289724\pi$
$830$	−138.369	+	207.084i	−0.166710	+	0.249499i
$831$		0			0
$832$			74.1411i			0.0891119i
$833$	−503.985	−	645.703i	−0.605024	−	0.775154i
$834$		0			0
$835$	−412.428	+	995.689i	−0.493926	+	1.19244i
$836$	622.545	+	415.971i	0.744671	+	0.497573i
$837$		0			0
$838$	−67.3212	+	13.3910i	−0.0803355	+	0.0159797i
$839$	587.153	−	392.323i	0.699824	−	0.467608i	−0.154066	−	0.988061i	$-0.549237\pi$
$839$	587.153	−	392.323i	0.699824	−	0.467608i	0.853890	+	0.520453i	$0.174237\pi$
$840$		0			0
$841$	362.887	−	150.313i	0.431494	−	0.178731i
$842$	96.8532	+	233.824i	0.115028	+	0.277701i
$843$		0			0
$844$	−541.233	−	810.012i	−0.641271	−	0.959730i
$845$	−72.0428	−	362.183i	−0.0852577	−	0.428620i
$846$		0			0
$847$	38.0506	−	56.9468i	0.0449240	−	0.0672335i
$848$	−14.5466	−	6.02541i	−0.0171540	−	0.00710544i
$849$		0			0
$850$	−154.177	+	272.205i	−0.181385	+	0.320241i
$851$	746.060			0.876686
$852$		0			0
$853$	−940.733	−	628.578i	−1.10285	−	0.736903i	−0.135612	−	0.990762i	$-0.543300\pi$
$853$	−940.733	−	628.578i	−1.10285	−	0.736903i	−0.967241	+	0.253860i	$0.918300\pi$
$854$	19.2410	+	19.2410i	0.0225304	+	0.0225304i
$855$		0			0
$856$	−762.227	+	509.304i	−0.890452	+	0.594981i
$857$	1477.19	+	293.831i	1.72368	+	0.342860i	0.954961	−	0.296732i	$-0.0958967\pi$
$857$	1477.19	+	293.831i	1.72368	+	0.342860i	0.768715	+	0.639592i	$0.220897\pi$
$858$		0			0
$859$	−39.2673	−	94.7998i	−0.0457129	−	0.110361i	0.899374	−	0.437181i	$-0.144023\pi$
$859$	−39.2673	−	94.7998i	−0.0457129	−	0.110361i	−0.945087	+	0.326820i	$0.894023\pi$
$860$	59.6240	−	299.750i	0.0693303	−	0.348547i
$861$		0			0
$862$	99.4434	+	499.936i	0.115364	+	0.579972i
$863$	533.064	−	533.064i	0.617687	−	0.617687i	−0.327250	−	0.944938i	$-0.606122\pi$
$863$	533.064	−	533.064i	0.617687	−	0.617687i	0.944938	+	0.327250i	$0.106122\pi$
$864$		0			0
$865$	1037.73	+	429.840i	1.19968	+	0.496925i
$866$		−	372.300i		−	0.429907i
$867$		0			0
$868$	112.827			0.129985
$869$	−168.175	+	406.010i	−0.193527	+	0.467215i
$870$		0			0
$871$	337.832	+	337.832i	0.387866	+	0.387866i
$872$	−144.553	+	28.7534i	−0.165772	+	0.0329740i
$873$		0			0
$874$	524.998	+	104.429i	0.600684	+	0.119483i
$875$	−18.7986	+	7.78664i	−0.0214841	+	0.00889902i
$876$		0			0
$877$	173.231	−	870.893i	0.197527	−	0.993036i	−0.747055	−	0.664762i	$-0.768533\pi$
$877$	173.231	−	870.893i	0.197527	−	0.993036i	0.944582	−	0.328274i	$-0.106467\pi$
$878$	300.879	+	450.297i	0.342687	+	0.512867i
$879$		0			0
$880$	256.534	−	256.534i	0.291516	−	0.291516i
$881$	−850.061	+	1272.21i	−0.964882	+	1.44405i	−0.0701022	+	0.997540i	$0.522333\pi$
$881$	−850.061	+	1272.21i	−0.964882	+	1.44405i	−0.894780	+	0.446508i	$0.852667\pi$
$882$		0			0
$883$			625.063i			0.707885i	0.935267	+	0.353943i	$0.115159\pi$
$883$			625.063i			0.707885i	−0.935267	+	0.353943i	$0.884841\pi$
$884$	724.871	+	410.567i	0.819990	+	0.464442i
$885$		0			0
$886$	−25.9224	+	62.5822i	−0.0292578	+	0.0706345i
$887$	24.3095	+	16.2431i	0.0274064	+	0.0183124i	0.569198	−	0.822200i	$-0.307254\pi$
$887$	24.3095	+	16.2431i	0.0274064	+	0.0183124i	−0.541792	+	0.840513i	$0.682254\pi$
$888$		0			0
$889$	42.7942	−	8.51229i	0.0481374	−	0.00957513i
$890$	337.706	−	225.648i	0.379444	−	0.253537i
$891$		0			0
$892$	−273.007	+	113.083i	−0.306062	+	0.126775i
$893$	168.999	+	408.001i	0.189249	+	0.456888i
$894$		0			0
$895$	736.880	+	1102.82i	0.823330	+	1.23220i
$896$	−22.8819	−	115.035i	−0.0255379	−	0.128388i
$897$		0			0
$898$	69.3499	−	103.789i	0.0772271	−	0.115578i
$899$	−743.925	−	308.144i	−0.827503	−	0.342763i
$900$		0			0
$901$	−26.7357	+	20.8678i	−0.0296734	+	0.0231607i
$902$	21.5232			0.0238616
$903$		0			0
$904$	−248.977	−	166.361i	−0.275417	−	0.184028i
$905$	241.376	+	241.376i	0.266714	+	0.266714i
$906$		0			0
$907$	848.139	−	566.708i	0.935104	−	0.624816i	0.00813978	−	0.999967i	$-0.497409\pi$
$907$	848.139	−	566.708i	0.935104	−	0.624816i	0.926964	+	0.375151i	$0.122409\pi$
$908$	480.069	+	95.4916i	0.528710	+	0.105167i
$909$		0			0
$910$	29.9353	+	72.2702i	0.0328959	+	0.0794178i
$911$	281.322	−	1414.30i	0.308805	−	1.55247i	−0.445097	−	0.895483i	$-0.646831\pi$
$911$	281.322	−	1414.30i	0.308805	−	1.55247i	0.753902	−	0.656987i	$-0.228169\pi$
$912$		0			0
$913$	−56.4088	−	283.586i	−0.0617840	−	0.310609i
$914$	−386.586	+	386.586i	−0.422960	+	0.422960i
$915$		0			0
$916$	415.065	+	171.926i	0.453128	+	0.187692i
$917$		−	2.95232i		−	0.00321954i
$918$		0			0
$919$	811.637			0.883175			0.441587	−	0.897218i	$-0.354416\pi$
$919$	811.637			0.883175			0.441587	+	0.897218i	$0.354416\pi$
$920$	300.481	−	725.426i	0.326610	−	0.788506i
$921$		0			0
$922$	−153.702	−	153.702i	−0.166705	−	0.166705i
$923$	−1517.82	+	301.914i	−1.64445	+	0.327101i
$924$		0			0
$925$	−853.369	−	169.746i	−0.922561	−	0.183509i
$926$	−468.395	+	194.016i	−0.505826	+	0.209520i
$927$		0			0
$928$	−129.615	+	651.621i	−0.139672	+	0.702178i
$929$	32.1049	+	48.0484i	0.0345586	+	0.0517206i	0.848347	−	0.529441i	$-0.177598\pi$
$929$	32.1049	+	48.0484i	0.0345586	+	0.0517206i	−0.813788	+	0.581162i	$0.802598\pi$
$930$		0			0
$931$	1155.80	−	1155.80i	1.24146	−	1.24146i
$932$	−650.461	+	973.483i	−0.697919	+	1.04451i
$933$		0			0
$934$		−	430.720i		−	0.461156i
$935$	−208.481	−	753.146i	−0.222974	−	0.805504i
$936$		0			0
$937$	−571.943	+	1380.79i	−0.610398	+	1.47363i	0.252167	+	0.967684i	$0.418857\pi$
$937$	−571.943	+	1380.79i	−0.610398	+	1.47363i	−0.862565	+	0.505946i	$0.831143\pi$
$938$	−20.3866	−	13.6219i	−0.0217341	−	0.0145223i
$939$		0			0
$940$	286.320	−	56.9525i	0.304595	−	0.0605878i
$941$	−834.402	+	557.530i	−0.886719	+	0.592487i	−0.913357	−	0.407159i	$-0.866520\pi$
$941$	−834.402	+	557.530i	−0.886719	+	0.592487i	0.0266387	+	0.999645i	$0.491520\pi$
$942$		0			0
$943$	−64.9057	+	26.8848i	−0.0688290	+	0.0285099i
$944$	−103.903	−	250.843i	−0.110066	−	0.265724i
$945$		0			0
$946$	−43.1751	−	64.6161i	−0.0456396	−	0.0683045i
$947$	−271.675	−	1365.80i	−0.286879	−	1.44224i	−0.808215	−	0.588888i	$-0.799566\pi$
$947$	−271.675	−	1365.80i	−0.286879	−	1.44224i	0.521336	−	0.853352i	$-0.325434\pi$
$948$		0			0
$949$	522.419	−	781.856i	0.550495	−	0.823873i
$950$	−576.750	−	238.898i	−0.607105	−	0.251471i
$951$		0			0
$952$	−90.0835	−	29.7525i	−0.0946255	−	0.0312527i
$953$	1378.59			1.44658			0.723292	−	0.690543i	$-0.242628\pi$
$953$	1378.59			1.44658			0.723292	+	0.690543i	$0.242628\pi$
$954$		0			0
$955$	−1695.21	−	1132.70i	−1.77509	−	1.18607i
$956$	923.635	+	923.635i	0.966145	+	0.966145i
$957$		0			0
$958$	−279.644	+	186.852i	−0.291904	+	0.195044i
$959$	79.7590	+	15.8650i	0.0831689	+	0.0165433i
$960$		0			0
$961$	−185.823	−	448.616i	−0.193364	−	0.466822i
$962$	99.0060	−	497.737i	0.102917	−	0.517398i
$963$		0			0
$964$	−50.7924	−	255.351i	−0.0526892	−	0.264887i
$965$	272.356	−	272.356i	0.282234	−	0.282234i
$966$		0			0
$967$	−964.483	−	399.502i	−0.997398	−	0.413136i	−0.176555	−	0.984291i	$-0.556495\pi$
$967$	−964.483	−	399.502i	−0.997398	−	0.413136i	−0.820842	+	0.571155i	$0.806495\pi$
$968$			467.636i			0.483095i
$969$		0			0
$970$	−740.172			−0.763064
$971$	68.3025	−	164.897i	0.0703424	−	0.169822i	−0.884798	−	0.465975i	$-0.845704\pi$
$971$	68.3025	−	164.897i	0.0703424	−	0.169822i	0.955141	+	0.296153i	$0.0957038\pi$
$972$		0			0
$973$	83.2028	+	83.2028i	0.0855116	+	0.0855116i
$974$	−320.872	+	63.8254i	−0.329437	+	0.0655292i
$975$		0			0
$976$	274.817	+	54.6645i	0.281575	+	0.0560087i
$977$	−1094.70	+	453.439i	−1.12047	+	0.464113i	−0.864531	−	0.502580i	$-0.832384\pi$
$977$	−1094.70	+	453.439i	−1.12047	+	0.464113i	−0.255938	+	0.966693i	$0.582384\pi$
$978$		0			0
$979$	−91.9894	+	462.462i	−0.0939626	+	0.472382i
$980$	−600.297	−	898.408i	−0.612548	−	0.916743i
$981$		0			0
$982$	279.500	−	279.500i	0.284623	−	0.284623i
$983$	876.560	−	1311.86i	0.891719	−	1.33455i	−0.0502093	−	0.998739i	$-0.515989\pi$
$983$	876.560	−	1311.86i	0.891719	−	1.33455i	0.941929	−	0.335813i	$-0.109011\pi$
$984$		0			0
$985$			25.5903i			0.0259800i
$986$	231.050	+	199.277i	0.234331	+	0.202106i
$987$		0			0
$988$	−636.175	+	1535.86i	−0.643902	+	1.55452i
$989$	210.912	+	140.927i	0.213258	+	0.142494i
$990$		0			0
$991$	−891.097	+	177.250i	−0.899190	+	0.178860i	−0.622980	−	0.782238i	$-0.714078\pi$
$991$	−891.097	+	177.250i	−0.899190	+	0.178860i	−0.276209	+	0.961098i	$0.589078\pi$
$992$	−992.420	+	663.114i	−1.00042	+	0.668462i
$993$		0			0
$994$	73.3747	−	30.3928i	0.0738176	−	0.0305763i
$995$	389.611	+	940.604i	0.391569	+	0.945330i
$996$		0			0
$997$	−965.850	−	1445.50i	−0.968757	−	1.44985i	−0.891598	−	0.452828i	$-0.850415\pi$
$997$	−965.850	−	1445.50i	−0.968757	−	1.44985i	−0.0771586	−	0.997019i	$-0.524585\pi$
$998$	30.2408	+	152.031i	0.0303014	+	0.152335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.p.a.10.1		8
3.2	odd	2		17.3.e.b.10.1	✓	8
12.11	even	2		272.3.bh.b.129.1		8
15.2	even	4		425.3.t.d.299.1		8
15.8	even	4		425.3.t.b.299.1		8
15.14	odd	2		425.3.u.a.401.1		8
17.12	odd	16	inner	153.3.p.a.46.1		8
51.2	odd	8		289.3.e.j.40.1		8
51.5	even	16		289.3.e.g.131.1		8
51.8	odd	8		289.3.e.e.249.1		8
51.11	even	16		289.3.e.n.224.1		8
51.14	even	16		289.3.e.f.158.1		8
51.20	even	16		289.3.e.h.158.1		8
51.23	even	16		289.3.e.j.224.1		8
51.26	odd	8		289.3.e.a.249.1		8
51.29	even	16		17.3.e.b.12.1	yes	8
51.32	odd	8		289.3.e.n.40.1		8
51.38	odd	4		289.3.e.h.75.1		8
51.41	even	16		289.3.e.a.65.1		8
51.44	even	16		289.3.e.e.65.1		8
51.47	odd	4		289.3.e.f.75.1		8
51.50	odd	2		289.3.e.g.214.1		8
204.131	odd	16		272.3.bh.b.97.1		8
255.29	even	16		425.3.u.a.301.1		8
255.182	odd	16		425.3.t.b.199.1		8
255.233	odd	16		425.3.t.d.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.10.1	✓	8	3.2	odd	2
17.3.e.b.12.1	yes	8	51.29	even	16
153.3.p.a.10.1		8	1.1	even	1	trivial
153.3.p.a.46.1		8	17.12	odd	16	inner
272.3.bh.b.97.1		8	204.131	odd	16
272.3.bh.b.129.1		8	12.11	even	2
289.3.e.a.65.1		8	51.41	even	16
289.3.e.a.249.1		8	51.26	odd	8
289.3.e.e.65.1		8	51.44	even	16
289.3.e.e.249.1		8	51.8	odd	8
289.3.e.f.75.1		8	51.47	odd	4
289.3.e.f.158.1		8	51.14	even	16
289.3.e.g.131.1		8	51.5	even	16
289.3.e.g.214.1		8	51.50	odd	2
289.3.e.h.75.1		8	51.38	odd	4
289.3.e.h.158.1		8	51.20	even	16
289.3.e.j.40.1		8	51.2	odd	8
289.3.e.j.224.1		8	51.23	even	16
289.3.e.n.40.1		8	51.32	odd	8
289.3.e.n.224.1		8	51.11	even	16
425.3.t.b.199.1		8	255.182	odd	16
425.3.t.b.299.1		8	15.8	even	4
425.3.t.d.199.1		8	255.233	odd	16
425.3.t.d.299.1		8	15.2	even	4
425.3.u.a.301.1		8	255.29	even	16
425.3.u.a.401.1		8	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.324423 + 0.783227i) q^{2} +(2.32023 + 2.32023i) q^{4} +(6.70292 - 1.33329i) q^{5} +(0.886687 + 0.176373i) q^{7} +(-5.70292 + 2.36223i) q^{8} +(-1.13031 + 5.68246i) q^{10} +(-3.73690 - 5.59267i) q^{11} +(10.5602 - 10.5602i) q^{13} +(-0.425802 + 0.637258i) q^{14} +7.89218i q^{16} +(14.7921 + 8.37823i) q^{17} +(-12.9821 + 31.3415i) q^{19} +(18.6459 + 12.4588i) q^{20} +(5.59267 - 1.11245i) q^{22} +(-15.4758 + 10.3406i) q^{23} +(20.0544 - 8.30682i) q^{25} +(4.84504 + 11.6970i) q^{26} +(1.64809 + 2.46655i) q^{28} +(-4.13027 - 20.7643i) q^{29} +(21.1305 - 31.6240i) q^{31} +(-28.9930 - 12.0093i) q^{32} +(-11.3609 + 8.86746i) q^{34} +6.17855 q^{35} +(-33.3284 - 22.2693i) q^{37} +(-20.3359 - 20.3359i) q^{38} +(-35.0766 + 23.4375i) q^{40} +(3.70199 + 0.736372i) q^{41} +(-5.21542 - 12.5911i) q^{43} +(4.30581 - 21.6468i) q^{44} +(-3.07832 - 15.4758i) q^{46} +(9.20504 - 9.20504i) q^{47} +(-44.5150 - 18.4387i) q^{49} +18.4021i q^{50} +49.0040 q^{52} +(-0.763466 + 1.84317i) q^{53} +(-32.5048 - 32.5048i) q^{55} +(-5.47334 + 1.08871i) q^{56} +(17.6031 + 3.50147i) q^{58} +(-31.7838 + 13.1653i) q^{59} +(6.92641 - 34.8214i) q^{61} +(17.9136 + 26.8096i) q^{62} +(-3.51042 + 3.51042i) q^{64} +(56.7040 - 84.8636i) q^{65} +31.9912i q^{67} +(14.8816 + 53.7605i) q^{68} +(-2.00446 + 4.83921i) q^{70} +(-86.1606 - 57.5707i) q^{71} +(61.7546 - 12.2837i) q^{73} +(28.2544 - 18.8790i) q^{74} +(-102.841 + 42.5982i) q^{76} +(-2.32707 - 5.61804i) q^{77} +(-36.2984 - 54.3244i) q^{79} +(10.5226 + 52.9006i) q^{80} +(-1.77776 + 2.66060i) q^{82} +(39.7149 + 16.4505i) q^{83} +(110.321 + 36.4364i) q^{85} +11.5537 q^{86} +(34.5224 + 23.0671i) q^{88} +(-49.5695 - 49.5695i) q^{89} +(11.2261 - 7.50103i) q^{91} +(-59.9000 - 11.9148i) q^{92} +(4.22331 + 10.1960i) q^{94} +(-45.2304 + 227.389i) q^{95} +(24.9233 + 125.298i) q^{97} +(28.8834 - 28.8834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 24 q^{5} - 16 q^{7} - 16 q^{8} - 40 q^{11} - 16 q^{14} + 16 q^{17} - 32 q^{19} + 40 q^{20} + 8 q^{23} + 16 q^{25} + 80 q^{28} - 24 q^{29} + 32 q^{31} + 24 q^{32} + 64 q^{34} - 80 q^{35}+ \cdots - 16 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 + 24 * q^5 - 16 * q^7 - 16 * q^8 - 40 * q^11 - 16 * q^14 + 16 * q^17 - 32 * q^19 + 40 * q^20 + 8 * q^23 + 16 * q^25 + 80 * q^28 - 24 * q^29 + 32 * q^31 + 24 * q^32 + 64 * q^34 - 80 * q^35 - 168 * q^37 - 8 * q^38 - 200 * q^40 + 96 * q^43 + 96 * q^44 + 80 * q^47 + 8 * q^49 + 240 * q^52 - 96 * q^53 - 8 * q^55 - 72 * q^56 - 8 * q^59 + 264 * q^61 + 136 * q^62 - 120 * q^64 + 32 * q^65 + 176 * q^68 - 80 * q^70 - 32 * q^71 + 24 * q^73 - 176 * q^74 - 80 * q^76 + 216 * q^77 - 96 * q^79 - 24 * q^80 - 408 * q^82 + 88 * q^83 + 512 * q^85 - 288 * q^86 + 176 * q^88 - 288 * q^89 - 24 * q^91 - 336 * q^92 - 8 * q^94 + 152 * q^95 - 344 * q^97 - 16 * q^98

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