LMFDB - Embedded newform 324.3.j.a.307.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,3,Mod(19,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			307.16
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.277531 - 1.98065i) q^{2} +(-3.84595 + 1.09938i) q^{4} +(0.542224 - 3.07510i) q^{5} +(-2.98812 - 3.56110i) q^{7} +(3.24486 + 7.31238i) q^{8} +(-6.24119 - 0.220520i) q^{10} +(-2.54564 + 0.448865i) q^{11} +(-16.7420 + 6.09358i) q^{13} +(-6.22401 + 6.90674i) q^{14} +(13.5827 - 8.45635i) q^{16} +(10.3549 - 17.9352i) q^{17} +(-24.5104 + 14.1511i) q^{19} +(1.29535 + 12.4228i) q^{20} +(1.59554 + 4.91745i) q^{22} +(-14.6669 + 17.4793i) q^{23} +(14.3301 + 5.21572i) q^{25} +(16.7157 + 31.4689i) q^{26} +(15.4072 + 10.4108i) q^{28} +(-5.90052 - 2.14762i) q^{29} +(-22.3759 + 26.6666i) q^{31} +(-20.5187 - 24.5557i) q^{32} +(-38.3971 - 15.5318i) q^{34} +(-12.5710 + 7.25787i) q^{35} +(-22.9733 + 39.7909i) q^{37} +(34.8307 + 44.6192i) q^{38} +(24.2458 - 6.01334i) q^{40} +(4.27327 - 1.55534i) q^{41} +(-12.6921 + 2.23796i) q^{43} +(9.29693 - 4.52494i) q^{44} +(38.6910 + 24.1990i) q^{46} +(-1.37925 - 1.64373i) q^{47} +(4.75617 - 26.9736i) q^{49} +(6.35348 - 29.8304i) q^{50} +(57.6897 - 41.8415i) q^{52} +31.8446 q^{53} +8.07149i q^{55} +(16.3441 - 33.4056i) q^{56} +(-2.61610 + 12.2829i) q^{58} +(-111.470 - 19.6551i) q^{59} +(63.3215 - 53.1331i) q^{61} +(59.0272 + 36.9181i) q^{62} +(-42.9417 + 47.4553i) q^{64} +(9.66050 + 54.7874i) q^{65} +(10.8572 + 29.8298i) q^{67} +(-20.1068 + 80.3619i) q^{68} +(17.8641 + 22.8845i) q^{70} +(0.0648998 + 0.0374699i) q^{71} +(-60.1132 - 104.119i) q^{73} +(85.1877 + 34.4589i) q^{74} +(78.7084 - 81.3707i) q^{76} +(9.20513 + 7.72402i) q^{77} +(-0.117809 + 0.323678i) q^{79} +(-18.6393 - 46.3535i) q^{80} +(-4.26656 - 8.03220i) q^{82} +(32.5283 - 89.3708i) q^{83} +(-49.5379 - 41.5672i) q^{85} +(7.95507 + 24.5175i) q^{86} +(-11.5425 - 17.1582i) q^{88} +(-59.4029 - 102.889i) q^{89} +(71.7269 + 41.4116i) q^{91} +(37.1918 - 83.3493i) q^{92} +(-2.87287 + 3.18801i) q^{94} +(30.2259 + 83.0451i) q^{95} +(11.2136 + 63.5953i) q^{97} +(-54.7452 - 1.93431i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37}+ \cdots - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−0.277531	−	1.98065i	−0.138765	−	0.990325i
$2$	−0.277531	−	1.98065i	−0.138765	−	0.990325i
$3$		0			0
$3$		0			0
$4$	−3.84595	+	1.09938i	−0.961488	+	0.274846i
$5$	0.542224	−	3.07510i	0.108445	−	0.615021i	−0.881344	−	0.472476i	$-0.843360\pi$
$5$	0.542224	−	3.07510i	0.108445	−	0.615021i	0.989788	−	0.142545i	$-0.0455285\pi$
$6$		0			0
$7$	−2.98812	−	3.56110i	−0.426874	−	0.508729i	0.509143	−	0.860682i	$-0.329962\pi$
$7$	−2.98812	−	3.56110i	−0.426874	−	0.508729i	−0.936018	+	0.351953i	$0.885518\pi$
$8$	3.24486	+	7.31238i	0.405608	+	0.914047i
$9$		0			0
$10$	−6.24119	−	0.220520i	−0.624119	−	0.0220520i
$11$	−2.54564	+	0.448865i	−0.231422	+	0.0408059i	−0.288156	−	0.957583i	$-0.593042\pi$
$11$	−2.54564	+	0.448865i	−0.231422	+	0.0408059i	0.0567345	+	0.998389i	$0.481931\pi$
$12$		0			0
$13$	−16.7420	+	6.09358i	−1.28784	+	0.468737i	−0.893019	−	0.450019i	$-0.851417\pi$
$13$	−16.7420	+	6.09358i	−1.28784	+	0.468737i	−0.394825	+	0.918756i	$0.629195\pi$
$14$	−6.22401	+	6.90674i	−0.444572	+	0.493339i
$15$		0			0
$16$	13.5827	−	8.45635i	0.848920	−	0.528522i
$17$	10.3549	−	17.9352i	0.609111	−	1.05501i	−0.382276	−	0.924048i	$-0.624860\pi$
$17$	10.3549	−	17.9352i	0.609111	−	1.05501i	0.991387	−	0.130963i	$-0.0418069\pi$
$18$		0			0
$19$	−24.5104	+	14.1511i	−1.29002	+	0.744794i	−0.978658	−	0.205497i	$-0.934119\pi$
$19$	−24.5104	+	14.1511i	−1.29002	+	0.744794i	−0.311363	+	0.950291i	$0.600786\pi$
$20$	1.29535	+	12.4228i	0.0647674	+	0.621141i
$21$		0			0
$22$	1.59554	+	4.91745i	0.0725244	+	0.223520i
$23$	−14.6669	+	17.4793i	−0.637692	+	0.759972i	−0.984004	−	0.178148i	$-0.942989\pi$
$23$	−14.6669	+	17.4793i	−0.637692	+	0.759972i	0.346312	+	0.938119i	$0.387434\pi$
$24$		0			0
$25$	14.3301	+	5.21572i	0.573202	+	0.208629i
$26$	16.7157	+	31.4689i	0.642910	+	1.21034i
$27$		0			0
$28$	15.4072	+	10.4108i	0.550257	+	0.371813i
$29$	−5.90052	−	2.14762i	−0.203466	−	0.0740557i	0.238277	−	0.971197i	$-0.423417\pi$
$29$	−5.90052	−	2.14762i	−0.203466	−	0.0740557i	−0.441743	+	0.897142i	$0.645640\pi$
$30$		0			0
$31$	−22.3759	+	26.6666i	−0.721804	+	0.860213i	−0.994805	−	0.101801i	$-0.967539\pi$
$31$	−22.3759	+	26.6666i	−0.721804	+	0.860213i	0.273001	+	0.962014i	$0.411984\pi$
$32$	−20.5187	−	24.5557i	−0.641209	−	0.767366i
$33$		0			0
$34$	−38.3971	−	15.5318i	−1.12933	−	0.456819i
$35$	−12.5710	+	7.25787i	−0.359171	+	0.207368i
$36$		0			0
$37$	−22.9733	+	39.7909i	−0.620900	+	1.07543i	0.368419	+	0.929660i	$0.379899\pi$
$37$	−22.9733	+	39.7909i	−0.620900	+	1.07543i	−0.989318	+	0.145770i	$0.953434\pi$
$38$	34.8307	+	44.6192i	0.916599	+	1.17419i
$39$		0			0
$40$	24.2458	−	6.01334i	0.606144	−	0.150334i
$41$	4.27327	−	1.55534i	0.104226	−	0.0379352i	−0.289381	−	0.957214i	$-0.593449\pi$
$41$	4.27327	−	1.55534i	0.104226	−	0.0379352i	0.393607	+	0.919279i	$0.371227\pi$
$42$		0			0
$43$	−12.6921	+	2.23796i	−0.295165	+	0.0520456i	−0.319270	−	0.947664i	$-0.603438\pi$
$43$	−12.6921	+	2.23796i	−0.295165	+	0.0520456i	0.0241045	+	0.999709i	$0.492327\pi$
$44$	9.29693	−	4.52494i	0.211294	−	0.102840i
$45$		0			0
$46$	38.6910	+	24.1990i	0.841109	+	0.526065i
$47$	−1.37925	−	1.64373i	−0.0293458	−	0.0349730i	0.751172	−	0.660107i	$-0.229489\pi$
$47$	−1.37925	−	1.64373i	−0.0293458	−	0.0349730i	−0.780518	+	0.625134i	$0.785044\pi$
$48$		0			0
$49$	4.75617	−	26.9736i	0.0970646	−	0.550481i
$50$	6.35348	−	29.8304i	0.127070	−	0.596607i
$51$		0			0
$52$	57.6897	−	41.8415i	1.10942	−	0.804644i
$53$	31.8446			0.600841			0.300420	−	0.953807i	$-0.402873\pi$
$53$	31.8446			0.600841			0.300420	+	0.953807i	$0.402873\pi$
$54$		0			0
$55$			8.07149i			0.146754i
$56$	16.3441	−	33.4056i	0.291859	−	0.596528i
$57$		0			0
$58$	−2.61610	+	12.2829i	−0.0451052	+	0.211774i
$59$	−111.470	−	19.6551i	−1.88932	−	0.333138i	−0.895583	−	0.444894i	$-0.853241\pi$
$59$	−111.470	−	19.6551i	−1.88932	−	0.333138i	−0.993736	+	0.111757i	$0.964352\pi$
$60$		0			0
$61$	63.3215	−	53.1331i	1.03806	−	0.871034i	0.0462698	−	0.998929i	$-0.485267\pi$
$61$	63.3215	−	53.1331i	1.03806	−	0.871034i	0.991788	+	0.127895i	$0.0408222\pi$
$62$	59.0272	+	36.9181i	0.952052	+	0.595453i
$63$		0			0
$64$	−42.9417	+	47.4553i	−0.670965	+	0.741489i
$65$	9.66050	+	54.7874i	0.148623	+	0.842883i
$66$		0			0
$67$	10.8572	+	29.8298i	0.162047	+	0.445221i	0.993968	−	0.109674i	$-0.0349807\pi$
$67$	10.8572	+	29.8298i	0.162047	+	0.445221i	−0.831921	+	0.554895i	$0.812759\pi$
$68$	−20.1068	+	80.3619i	−0.295688	+	1.18179i
$69$		0			0
$70$	17.8641	+	22.8845i	0.255202	+	0.326921i
$71$	0.0648998	+	0.0374699i	0.000914081	+	0.000527745i	0.500457	−	0.865761i	$-0.333165\pi$
$71$	0.0648998	+	0.0374699i	0.000914081	+	0.000527745i	−0.499543	+	0.866289i	$0.666499\pi$
$72$		0			0
$73$	−60.1132	−	104.119i	−0.823469	−	1.42629i	−0.903084	−	0.429465i	$-0.858702\pi$
$73$	−60.1132	−	104.119i	−0.823469	−	1.42629i	0.0796145	−	0.996826i	$-0.474631\pi$
$74$	85.1877	+	34.4589i	1.15119	+	0.465660i
$75$		0			0
$76$	78.7084	−	81.3707i	1.03564	−	1.07067i
$77$	9.20513	+	7.72402i	0.119547	+	0.100312i
$78$		0			0
$79$	−0.117809	+	0.323678i	−0.00149126	+	0.00409720i	−0.940436	−	0.339971i	$-0.889583\pi$
$79$	−0.117809	+	0.323678i	−0.00149126	+	0.00409720i	0.938945	+	0.344068i	$0.111805\pi$
$80$	−18.6393	−	46.3535i	−0.232991	−	0.579419i
$81$		0			0
$82$	−4.26656	−	8.03220i	−0.0520312	−	0.0979537i
$83$	32.5283	−	89.3708i	0.391907	−	1.07676i	−0.574222	−	0.818700i	$-0.694695\pi$
$83$	32.5283	−	89.3708i	0.391907	−	1.07676i	0.966130	−	0.258057i	$-0.0830824\pi$
$84$		0			0
$85$	−49.5379	−	41.5672i	−0.582799	−	0.489026i
$86$	7.95507	+	24.5175i	0.0925008	+	0.285088i
$87$		0			0
$88$	−11.5425	−	17.1582i	−0.131165	−	0.194979i
$89$	−59.4029	−	102.889i	−0.667449	−	1.15605i	−0.978615	−	0.205700i	$-0.934053\pi$
$89$	−59.4029	−	102.889i	−0.667449	−	1.15605i	0.311167	−	0.950355i	$-0.399280\pi$
$90$		0			0
$91$	71.7269	+	41.4116i	0.788208	+	0.455072i
$92$	37.1918	−	83.3493i	0.404258	−	0.905971i
$93$		0			0
$94$	−2.87287	+	3.18801i	−0.0305625	+	0.0339150i
$95$	30.2259	+	83.0451i	0.318168	+	0.874159i
$96$		0			0
$97$	11.2136	+	63.5953i	0.115604	+	0.655622i	0.986449	+	0.164065i	$0.0524608\pi$
$97$	11.2136	+	63.5953i	0.115604	+	0.655622i	−0.870846	+	0.491556i	$0.836428\pi$
$98$	−54.7452	−	1.93431i	−0.558624	−	0.0197379i
$99$		0			0
$100$	−60.8468	−	4.30518i	−0.608468	−	0.0430518i
$101$	−96.7701	+	81.1997i	−0.958120	+	0.803958i	−0.980646	−	0.195788i	$-0.937273\pi$
$101$	−96.7701	+	81.1997i	−0.958120	+	0.803958i	0.0225265	+	0.999746i	$0.492829\pi$
$102$		0			0
$103$	−154.727	−	27.2826i	−1.50221	−	0.264879i	−0.638794	−	0.769378i	$-0.720566\pi$
$103$	−154.727	−	27.2826i	−1.50221	−	0.264879i	−0.863412	+	0.504499i	$0.831677\pi$
$104$	−98.8840	−	102.651i	−0.950807	−	0.987027i
$105$		0			0
$106$	−8.83784	−	63.0730i	−0.0833759	−	0.595028i
$107$		−	135.536i		−	1.26670i	−0.773867	−	0.633348i	$-0.781680\pi$
$107$		−	135.536i		−	1.26670i	0.773867	−	0.633348i	$-0.218320\pi$
$108$		0			0
$109$	−19.3978			−0.177962			−0.0889809	−	0.996033i	$-0.528361\pi$
$109$	−19.3978			−0.177962			−0.0889809	+	0.996033i	$0.528361\pi$
$110$	15.9868	−	2.24008i	0.145335	−	0.0203644i
$111$		0			0
$112$	−70.7007	−	23.1009i	−0.631257	−	0.206258i
$113$	15.9448	−	90.4277i	0.141105	−	0.800245i	−0.829308	−	0.558792i	$-0.811265\pi$
$113$	15.9448	−	90.4277i	0.141105	−	0.800245i	0.970413	−	0.241453i	$-0.0776239\pi$
$114$		0			0
$115$	45.7980	+	54.5800i	0.398244	+	0.474609i
$116$	25.0542	+	1.77270i	0.215984	+	0.0152819i
$117$		0			0
$118$	−7.99367	+	226.238i	−0.0677430	+	1.91727i
$119$	−94.8107	+	16.7177i	−0.796729	+	0.140485i
$120$		0			0
$121$	−107.424	+	39.0991i	−0.887802	+	0.323133i
$122$	−122.812	−	110.672i	−1.00665	−	0.907145i
$123$		0			0
$124$	56.7400	−	127.158i	0.457581	−	1.02547i
$125$	62.8407	−	108.843i	0.502726	−	0.870747i
$126$		0			0
$127$	184.813	−	106.702i	1.45522	−	0.840170i	0.456448	−	0.889750i	$-0.349122\pi$
$127$	184.813	−	106.702i	1.45522	−	0.840170i	0.998770	+	0.0495799i	$0.0157883\pi$
$128$	105.910	+	71.8823i	0.827422	+	0.561580i
$129$		0			0
$130$	105.834	−	34.3392i	0.814105	−	0.264148i
$131$	−1.67775	+	1.99947i	−0.0128073	+	0.0152631i	−0.772410	−	0.635124i	$-0.780949\pi$
$131$	−1.67775	+	1.99947i	−0.0128073	+	0.0152631i	0.759603	+	0.650387i	$0.225393\pi$
$132$		0			0
$133$	123.634	+	44.9989i	0.929576	+	0.338338i
$134$	56.0692	−	29.7829i	0.418427	−	0.222260i
$135$		0			0
$136$	164.749	+	17.5216i	1.21139	+	0.128835i
$137$	−179.564	−	65.3560i	−1.31069	−	0.477051i	−0.410225	−	0.911985i	$-0.634550\pi$
$137$	−179.564	−	65.3560i	−1.31069	−	0.477051i	−0.900463	+	0.434933i	$0.856772\pi$
$138$		0			0
$139$	53.4641	−	63.7160i	0.384634	−	0.458389i	−0.538637	−	0.842538i	$-0.681061\pi$
$139$	53.4641	−	63.7160i	0.384634	−	0.458389i	0.923271	+	0.384149i	$0.125505\pi$
$140$	40.3683	−	41.7337i	0.288345	−	0.298098i
$141$		0			0
$142$	0.0562031	−	0.138943i	0.000395797	−	0.000978470i
$143$	39.8838	−	23.0269i	0.278908	−	0.161028i
$144$		0			0
$145$	−9.80354	+	16.9802i	−0.0676106	+	0.117105i
$146$	−189.540	+	147.960i	−1.29822	+	1.01342i
$147$		0			0
$148$	44.6088	−	178.290i	0.301411	−	1.20467i
$149$	50.4885	−	18.3763i	0.338849	−	0.123331i	−0.166991	−	0.985958i	$-0.553405\pi$
$149$	50.4885	−	18.3763i	0.338849	−	0.123331i	0.505840	+	0.862628i	$0.331183\pi$
$150$		0			0
$151$	−49.1219	+	8.66152i	−0.325311	+	0.0573610i	−0.333919	−	0.942602i	$-0.608371\pi$
$151$	−49.1219	+	8.66152i	−0.325311	+	0.0573610i	0.00860797	+	0.999963i	$0.497260\pi$
$152$	−183.011	−	133.311i	−1.20402	−	0.877046i
$153$		0			0
$154$	12.7439	−	20.3758i	0.0827525	−	0.132310i
$155$	69.8698	+	83.2676i	0.450773	+	0.537210i
$156$		0			0
$157$	−31.3995	+	178.075i	−0.199997	+	1.13424i	0.705124	+	0.709084i	$0.250891\pi$
$157$	−31.3995	+	178.075i	−0.199997	+	1.13424i	−0.905121	+	0.425154i	$0.860220\pi$
$158$	0.673790	+	0.143508i	0.00426449	+	0.000908281i
$159$		0			0
$160$	−86.6371	+	49.7824i	−0.541482	+	0.311140i
$161$	106.072			0.658834
$162$		0			0
$163$		−	8.91711i		−	0.0547062i	−0.999626	−	0.0273531i	$-0.991292\pi$
$163$		−	8.91711i		−	0.0547062i	0.999626	−	0.0273531i	$-0.00870785\pi$
$164$	−14.7249	+	10.6797i	−0.0897859	+	0.0651204i
$165$		0			0
$166$	−186.040	−	39.6241i	−1.12072	−	0.238699i
$167$	285.053	+	50.2625i	1.70690	+	0.300973i	0.940097	−	0.340908i	$-0.110734\pi$
$167$	285.053	+	50.2625i	1.70690	+	0.300973i	0.766805	+	0.641880i	$0.221845\pi$
$168$		0			0
$169$	113.701	−	95.4061i	0.672784	−	0.564533i
$170$	−68.5819	+	109.653i	−0.403423	+	0.645020i
$171$		0			0
$172$	46.3529	−	22.5606i	0.269494	−	0.131166i
$173$	55.6641	+	315.687i	0.321758	+	1.82478i	0.531541	+	0.847032i	$0.321613\pi$
$173$	55.6641	+	315.687i	0.321758	+	1.82478i	−0.209783	+	0.977748i	$0.567276\pi$
$174$		0			0
$175$	−24.2463	−	66.6160i	−0.138550	−	0.380663i
$176$	−30.7809	+	27.6236i	−0.174892	+	0.156952i
$177$		0			0
$178$	−187.301	+	146.211i	−1.05225	+	0.821412i
$179$	162.728	+	93.9512i	0.909096	+	0.524867i	0.880140	−	0.474714i	$-0.157448\pi$
$179$	162.728	+	93.9512i	0.909096	+	0.524867i	0.0289558	+	0.999581i	$0.490782\pi$
$180$		0			0
$181$	−87.5994	−	151.727i	−0.483975	−	0.838269i	0.515856	−	0.856675i	$-0.327474\pi$
$181$	−87.5994	−	151.727i	−0.483975	−	0.838269i	−0.999831	+	0.0184065i	$0.994141\pi$
$182$	62.1154	−	153.559i	0.341294	−	0.843731i
$183$		0			0
$184$	−175.408	−	50.5319i	−0.953303	−	0.274630i
$185$	109.905	+	92.2208i	0.594078	+	0.498491i
$186$		0			0
$187$	−18.3093	+	50.3044i	−0.0979108	+	0.269008i
$188$	7.11164	+	4.80539i	0.0378279	+	0.0255606i
$189$		0			0
$190$	156.095	−	82.9146i	0.821551	−	0.436393i
$191$	27.9840	−	76.8854i	0.146513	−	0.402541i	−0.844628	−	0.535353i	$-0.820178\pi$
$191$	27.9840	−	76.8854i	0.146513	−	0.402541i	0.991141	+	0.132812i	$0.0424006\pi$
$192$		0			0
$193$	235.485	+	197.596i	1.22013	+	1.02381i	0.998818	+	0.0486086i	$0.0154787\pi$
$193$	235.485	+	197.596i	1.22013	+	1.02381i	0.221313	+	0.975203i	$0.428966\pi$
$194$	122.848	−	39.8598i	0.633237	−	0.205463i
$195$		0			0
$196$	11.3623	+	108.968i	0.0579707	+	0.555959i
$197$	−7.31189	−	12.6646i	−0.0371162	−	0.0642871i	0.846871	−	0.531799i	$-0.178484\pi$
$197$	−7.31189	−	12.6646i	−0.0371162	−	0.0642871i	−0.883987	+	0.467512i	$0.845150\pi$
$198$		0			0
$199$	−9.61962	−	5.55389i	−0.0483398	−	0.0279090i	0.475635	−	0.879643i	$-0.342218\pi$
$199$	−9.61962	−	5.55389i	−0.0483398	−	0.0279090i	−0.523975	+	0.851734i	$0.675552\pi$
$200$	8.35979	+	121.711i	0.0417989	+	0.608555i
$201$		0			0
$202$	187.685	+	169.132i	0.929134	+	0.837289i
$203$	9.98360	+	27.4297i	0.0491803	+	0.135122i
$204$		0			0
$205$	−2.46577	−	13.9841i	−0.0120282	−	0.0682151i
$206$	−11.0957	+	314.032i	−0.0538627	+	1.52443i
$207$		0			0
$208$	−175.872	+	224.343i	−0.845539	+	1.07857i
$209$	56.0427	−	47.0254i	0.268147	−	0.225002i
$210$		0			0
$211$	−227.524	−	40.1186i	−1.07831	−	0.190135i	−0.393843	−	0.919178i	$-0.628855\pi$
$211$	−227.524	−	40.1186i	−1.07831	−	0.190135i	−0.684468	+	0.729042i	$0.739966\pi$
$212$	−122.473	+	35.0094i	−0.577702	+	0.165138i
$213$		0			0
$214$	−268.450	+	37.6155i	−1.25444	+	0.175773i
$215$			40.2430i			0.187177i
$216$		0			0
$217$	161.825			0.745735
$218$	5.38349	+	38.4203i	0.0246949	+	0.176240i
$219$		0			0
$220$	−8.87365	−	31.0426i	−0.0403348	−	0.141103i
$221$	−64.0717	+	363.369i	−0.289917	+	1.64420i
$222$		0			0
$223$	−15.4066	−	18.3609i	−0.0690879	−	0.0823358i	0.730393	−	0.683027i	$-0.239337\pi$
$223$	−15.4066	−	18.3609i	−0.0690879	−	0.0823358i	−0.799481	+	0.600691i	$0.794892\pi$
$224$	−26.1332	+	146.445i	−0.116666	+	0.653771i
$225$		0			0
$226$	−183.531	−	6.48470i	−0.812083	−	0.0286934i
$227$	−288.723	+	50.9096i	−1.27191	+	0.224271i	−0.768540	−	0.639802i	$-0.779016\pi$
$227$	−288.723	+	50.9096i	−1.27191	+	0.224271i	−0.503366	+	0.864073i	$0.667905\pi$
$228$		0			0
$229$	−235.290	+	85.6387i	−1.02747	+	0.373968i	−0.800117	−	0.599844i	$-0.795229\pi$
$229$	−235.290	+	85.6387i	−1.02747	+	0.373968i	−0.227352	+	0.973813i	$0.573007\pi$
$230$	95.3935	−	105.858i	0.414754	−	0.460250i
$231$		0			0
$232$	−3.44221	−	50.1156i	−0.0148371	−	0.216015i
$233$	−44.3299	+	76.7816i	−0.190257	+	0.329535i	−0.945335	−	0.326100i	$-0.894265\pi$
$233$	−44.3299	+	76.7816i	−0.190257	+	0.329535i	0.755078	+	0.655635i	$0.227599\pi$
$234$		0			0
$235$	−5.80251	+	3.35008i	−0.0246915	+	0.0142557i
$236$	450.316	−	46.9552i	1.90812	−	0.198963i
$237$		0			0
$238$	59.4248	+	183.147i	0.249684	+	0.769526i
$239$	−193.538	+	230.649i	−0.809781	+	0.965059i	−0.999860	−	0.0167096i	$-0.994681\pi$
$239$	−193.538	+	230.649i	−0.809781	+	0.965059i	0.190080	+	0.981769i	$0.439125\pi$
$240$		0			0
$241$	293.914	+	106.976i	1.21956	+	0.443883i	0.870009	−	0.493035i	$-0.164113\pi$
$241$	293.914	+	106.976i	1.21956	+	0.443883i	0.349549	+	0.936918i	$0.386335\pi$
$242$	107.255	+	201.918i	0.443203	+	0.834373i
$243$		0			0
$244$	−185.118	+	273.962i	−0.758680	+	1.12279i
$245$	−80.3676	−	29.2514i	−0.328031	−	0.119393i
$246$		0			0
$247$	324.122	−	386.273i	1.31223	−	1.56386i
$248$	−267.603	−	77.0918i	−1.07904	−	0.310854i
$249$		0			0
$250$	−233.021	−	94.2582i	−0.932084	−	0.377033i
$251$	179.464	−	103.614i	0.714997	−	0.412804i	−0.0979113	−	0.995195i	$-0.531216\pi$
$251$	179.464	−	103.614i	0.714997	−	0.412804i	0.812909	+	0.582391i	$0.197883\pi$
$252$		0			0
$253$	29.4908	−	51.0796i	0.116564	−	0.201895i
$254$	−262.630	−	336.436i	−1.03398	−	1.32455i
$255$		0			0
$256$	112.980	−	229.720i	0.441330	−	0.897345i
$257$	348.175	−	126.725i	1.35477	−	0.493095i	0.440335	−	0.897834i	$-0.354860\pi$
$257$	348.175	−	126.725i	1.35477	−	0.493095i	0.914432	+	0.404739i	$0.132637\pi$
$258$		0			0
$259$	210.347	−	37.0898i	0.812149	−	0.143204i
$260$	−97.3861	−	200.089i	−0.374562	−	0.769574i
$261$		0			0
$262$	4.42587	+	2.76813i	0.0168926	+	0.0105654i
$263$	118.833	+	141.619i	0.451836	+	0.538477i	0.943089	−	0.332540i	$-0.107906\pi$
$263$	118.833	+	141.619i	0.451836	+	0.538477i	−0.491253	+	0.871017i	$0.663461\pi$
$264$		0			0
$265$	17.2669	−	97.9253i	0.0651580	−	0.369530i
$266$	54.8151	−	257.363i	0.206072	−	0.967532i
$267$		0			0
$268$	−74.5504	−	102.788i	−0.278173	−	0.383536i
$269$	−496.062			−1.84410			−0.922049	−	0.387074i	$-0.873486\pi$
$269$	−496.062			−1.84410			−0.922049	+	0.387074i	$0.873486\pi$
$270$		0			0
$271$		−	316.792i		−	1.16897i	−0.811403	−	0.584487i	$-0.801296\pi$
$271$		−	316.792i		−	1.16897i	0.811403	−	0.584487i	$-0.198704\pi$
$272$	−11.0187	−	331.173i	−0.0405099	−	1.21755i
$273$		0			0
$274$	−79.6129	+	373.792i	−0.290558	+	1.36420i
$275$	−38.8203	−	6.84507i	−0.141165	−	0.0248912i
$276$		0			0
$277$	−228.590	+	191.810i	−0.825235	+	0.692455i	−0.954192	−	0.299196i	$-0.903282\pi$
$277$	−228.590	+	191.810i	−0.825235	+	0.692455i	0.128957	+	0.991650i	$0.458837\pi$
$278$	−141.037	−	88.2105i	−0.507328	−	0.317304i
$279$		0			0
$280$	−93.8634	−	68.3731i	−0.335226	−	0.244190i
$281$	−28.7377	−	162.980i	−0.102270	−	0.579999i	−0.992276	−	0.124051i	$-0.960411\pi$
$281$	−28.7377	−	162.980i	−0.102270	−	0.579999i	0.890006	−	0.455948i	$-0.150700\pi$
$282$		0			0
$283$	128.140	+	352.062i	0.452792	+	1.24404i	0.930751	+	0.365654i	$0.119155\pi$
$283$	128.140	+	352.062i	0.452792	+	1.24404i	−0.477959	+	0.878382i	$0.658623\pi$
$284$	−0.290795	−	0.0727578i	−0.00102393	−	0.000256190i
$285$		0			0
$286$	−56.6773	−	72.6053i	−0.198172	−	0.253865i
$287$	−18.3078	−	10.5700i	−0.0637902	−	0.0368293i
$288$		0			0
$289$	−69.9473	−	121.152i	−0.242032	−	0.419212i
$290$	36.3527	+	14.7049i	0.125354	+	0.0507064i
$291$		0			0
$292$	345.660	+	334.350i	1.18377	+	1.14503i
$293$	275.790	+	231.416i	0.941264	+	0.789815i	0.977805	−	0.209518i	$-0.0671894\pi$
$293$	275.790	+	231.416i	0.941264	+	0.789815i	−0.0365406	+	0.999332i	$0.511634\pi$
$294$		0			0
$295$	−120.883	+	332.124i	−0.409773	+	1.12584i
$296$	−365.511	−	38.8734i	−1.23484	−	0.131329i
$297$		0			0
$298$	−50.4092	−	94.9001i	−0.169158	−	0.318457i
$299$	139.041	−	382.013i	0.465021	−	1.27763i
$300$		0			0
$301$	45.8952	+	38.5106i	0.152476	+	0.127942i
$302$	30.7883	+	94.8895i	0.101948	+	0.314204i
$303$		0			0
$304$	−213.251	+	399.479i	−0.701485	+	1.31407i
$305$	−129.055	−	223.530i	−0.423132	−	0.732886i
$306$		0			0
$307$	−25.9467	−	14.9803i	−0.0845168	−	0.0487958i	0.457146	−	0.889392i	$-0.348872\pi$
$307$	−25.9467	−	14.9803i	−0.0845168	−	0.0487958i	−0.541663	+	0.840596i	$0.682205\pi$
$308$	−43.8942	−	19.5863i	−0.142514	−	0.0635918i
$309$		0			0
$310$	145.533	−	161.497i	0.469461	−	0.520958i
$311$	−90.6051	−	248.936i	−0.291335	−	0.800436i	−0.995872	−	0.0907688i	$-0.971068\pi$
$311$	−90.6051	−	248.936i	−0.291335	−	0.800436i	0.704537	−	0.709667i	$-0.251155\pi$
$312$		0			0
$313$	−24.1122	−	136.747i	−0.0770356	−	0.436891i	−0.998793	−	0.0491230i	$-0.984357\pi$
$313$	−24.1122	−	136.747i	−0.0770356	−	0.436891i	0.921757	−	0.387768i	$-0.126754\pi$
$314$	361.419	+	12.7700i	1.15102	+	0.0406689i
$315$		0			0
$316$	0.0972428	−	1.37437i	0.000307730	−	0.00434927i
$317$	149.944	−	125.818i	0.473009	−	0.396902i	−0.374882	−	0.927073i	$-0.622317\pi$
$317$	149.944	−	125.818i	0.473009	−	0.396902i	0.847891	+	0.530171i	$0.177872\pi$
$318$		0			0
$319$	15.9846	+	2.81852i	0.0501084	+	0.00883547i
$320$	122.646	+	157.782i	0.383269	+	0.493068i
$321$		0			0
$322$	−29.4383	−	210.092i	−0.0914233	−	0.652460i
$323$			586.132i			1.81465i
$324$		0			0
$325$	−271.696			−0.835987
$326$	−17.6617	+	2.47477i	−0.0541769	+	0.00759132i
$327$		0			0
$328$	25.2394	+	26.2009i	0.0769495	+	0.0798808i
$329$	−1.73212	+	9.82334i	−0.00526480	+	0.0298582i
$330$		0			0
$331$	−7.54276	−	8.98911i	−0.0227878	−	0.0271574i	0.754530	−	0.656265i	$-0.227865\pi$
$331$	−7.54276	−	8.98911i	−0.0227878	−	0.0271574i	−0.777318	+	0.629108i	$0.783420\pi$
$332$	−26.8497	+	379.477i	−0.0808726	+	1.14300i
$333$		0			0
$334$	20.4416	−	578.539i	0.0612023	−	1.73215i
$335$	97.6167	−	17.2125i	0.291393	−	0.0513804i
$336$		0			0
$337$	86.0445	−	31.3176i	0.255325	−	0.0929307i	−0.211187	−	0.977446i	$-0.567733\pi$
$337$	86.0445	−	31.3176i	0.255325	−	0.0929307i	0.466512	+	0.884515i	$0.345511\pi$
$338$	−220.522	−	198.723i	−0.652430	−	0.587938i
$339$		0			0
$340$	236.219	+	105.405i	0.694761	+	0.310013i
$341$	44.9913	−	77.9273i	0.131939	−	0.228526i
$342$		0			0
$343$	−307.536	+	177.556i	−0.896606	+	0.517656i
$344$	−57.5490	−	85.5477i	−0.167294	−	0.248685i
$345$		0			0
$346$	609.817	−	197.864i	1.76248	−	0.571861i
$347$	230.389	−	274.567i	0.663944	−	0.791258i	−0.324002	−	0.946056i	$-0.605028\pi$
$347$	230.389	−	274.567i	0.663944	−	0.791258i	0.987946	+	0.154798i	$0.0494728\pi$
$348$		0			0
$349$	−424.517	−	154.511i	−1.21638	−	0.442726i	−0.347468	−	0.937692i	$-0.612958\pi$
$349$	−424.517	−	154.511i	−1.21638	−	0.442726i	−0.868913	+	0.494966i	$0.835181\pi$
$350$	−125.214	+	66.5113i	−0.357754	+	0.190032i
$351$		0			0
$352$	63.2554	+	53.2999i	0.179703	+	0.151420i
$353$	−174.348	−	63.4575i	−0.493903	−	0.179766i	0.0830465	−	0.996546i	$-0.473535\pi$
$353$	−174.348	−	63.4575i	−0.493903	−	0.179766i	−0.576950	+	0.816780i	$0.695757\pi$
$354$		0			0
$355$	0.150414	−	0.179256i	0.000423701	−	0.000504948i
$356$	341.575	+	330.399i	0.959481	+	0.928088i
$357$		0			0
$358$	140.922	−	348.382i	0.393638	−	0.973134i
$359$	−19.1474	+	11.0548i	−0.0533354	+	0.0307932i	−0.526431	−	0.850218i	$-0.676470\pi$
$359$	−19.1474	+	11.0548i	−0.0533354	+	0.0307932i	0.473095	+	0.881011i	$0.343137\pi$
$360$		0			0
$361$	220.007	−	381.063i	0.609437	−	1.05558i
$362$	−276.206	+	215.613i	−0.763000	+	0.595615i
$363$		0			0
$364$	−321.386	−	80.4116i	−0.882927	−	0.220911i
$365$	−352.772	+	128.399i	−0.966499	+	0.351777i
$366$		0			0
$367$	−64.1920	+	11.3188i	−0.174910	+	0.0308414i	−0.260417	−	0.965496i	$-0.583860\pi$
$367$	−64.1920	+	11.3188i	−0.174910	+	0.0308414i	0.0855071	+	0.996338i	$0.472749\pi$
$368$	−51.4051	+	361.446i	−0.139688	+	0.982189i
$369$		0			0
$370$	152.155	−	243.277i	0.411231	−	0.657504i
$371$	−95.1554	−	113.402i	−0.256484	−	0.305665i
$372$		0			0
$373$	−13.9077	+	78.8746i	−0.0372861	+	0.211460i	−0.997759	−	0.0669145i	$-0.978685\pi$
$373$	−13.9077	+	78.8746i	−0.0372861	+	0.211460i	0.960473	+	0.278375i	$0.0897956\pi$
$374$	104.717	+	22.3033i	0.279992	+	0.0596346i
$375$		0			0
$376$	7.54410	−	15.4193i	0.0200641	−	0.0410088i
$377$	111.873			0.296746
$378$		0			0
$379$			108.170i			0.285410i	0.989765	+	0.142705i	$0.0455799\pi$
$379$			108.170i			0.285410i	−0.989765	+	0.142705i	$0.954420\pi$
$380$	−207.546	−	286.158i	−0.546173	−	0.753047i
$381$		0			0
$382$	−160.050	−	34.0885i	−0.418978	−	0.0892369i
$383$	−314.011	−	55.3687i	−0.819873	−	0.144566i	−0.252048	−	0.967715i	$-0.581104\pi$
$383$	−314.011	−	55.3687i	−0.819873	−	0.144566i	−0.567825	+	0.823149i	$0.692215\pi$
$384$		0			0
$385$	28.7434	−	24.1186i	0.0746582	−	0.0626457i
$386$	326.013	−	521.253i	0.844595	−	1.35040i
$387$		0			0
$388$	−113.042	−	232.257i	−0.291346	−	0.598599i
$389$	−22.7566	−	129.059i	−0.0585003	−	0.331772i	0.941486	−	0.337053i	$-0.109430\pi$
$389$	−22.7566	−	129.059i	−0.0585003	−	0.331772i	−0.999986	+	0.00528095i	$0.998319\pi$
$390$		0			0
$391$	161.621	+	444.050i	0.413353	+	1.13568i
$392$	212.674	−	52.7466i	0.542536	−	0.134558i
$393$		0			0
$394$	−23.0548	+	17.9971i	−0.0585147	+	0.0456779i
$395$	0.931466	+	0.537782i	0.00235814	+	0.00136147i
$396$		0			0
$397$	179.796	+	311.416i	0.452887	+	0.784423i	0.998564	−	0.0535725i	$-0.0170608\pi$
$397$	179.796	+	311.416i	0.452887	+	0.784423i	−0.545677	+	0.837996i	$0.683727\pi$
$398$	−8.33058	+	20.5945i	−0.0209311	+	0.0517449i
$399$		0			0
$400$	238.747	−	50.3364i	0.596868	−	0.125841i
$401$	−259.700	−	217.914i	−0.647631	−	0.543427i	0.258720	−	0.965952i	$-0.416699\pi$
$401$	−259.700	−	217.914i	−0.647631	−	0.543427i	−0.906351	+	0.422525i	$0.861144\pi$
$402$		0			0
$403$	212.122	−	582.801i	0.526358	−	1.44616i
$404$	282.904	−	418.678i	0.700257	−	1.03633i
$405$		0			0
$406$	51.5579	−	27.3866i	0.126990	−	0.0674547i
$407$	40.6210	−	111.605i	0.0998058	−	0.274214i
$408$		0			0
$409$	283.138	+	237.581i	0.692270	+	0.580883i	0.919563	−	0.392943i	$-0.128543\pi$
$409$	283.138	+	237.581i	0.692270	+	0.580883i	−0.227293	+	0.973826i	$0.572988\pi$
$410$	−27.0133	+	8.76485i	−0.0658861	+	0.0213777i
$411$		0			0
$412$	625.068	−	65.1768i	1.51715	−	0.158196i
$413$	263.091	+	455.687i	0.637025	+	1.10336i
$414$		0			0
$415$	−257.187	−	148.487i	−0.619727	−	0.357800i
$416$	493.156	+	286.079i	1.18547	+	0.687690i
$417$		0			0
$418$	−108.694	−	97.9500i	−0.260035	−	0.234330i
$419$	−21.0810	−	57.9195i	−0.0503125	−	0.138233i	0.911991	−	0.410210i	$-0.134545\pi$
$419$	−21.0810	−	57.9195i	−0.0503125	−	0.138233i	−0.962304	+	0.271977i	$0.912322\pi$
$420$		0			0
$421$	−4.86271	−	27.5778i	−0.0115504	−	0.0655055i	0.978488	−	0.206305i	$-0.0661439\pi$
$421$	−4.86271	−	27.5778i	−0.0115504	−	0.0655055i	−0.990038	+	0.140799i	$0.955033\pi$
$422$	−16.3161	+	461.779i	−0.0386637	+	1.09426i
$423$		0			0
$424$	103.331	+	232.860i	0.243706	+	0.549197i
$425$	241.931	−	203.004i	0.569249	−	0.477657i
$426$		0			0
$427$	−378.425	−	66.7265i	−0.886240	−	0.156268i
$428$	149.006	+	521.267i	0.348146	+	1.21791i
$429$		0			0
$430$	79.7074	−	11.1687i	0.185366	−	0.0259737i
$431$		−	405.263i		−	0.940286i	−0.882590	−	0.470143i	$-0.844202\pi$
$431$		−	405.263i		−	0.940286i	0.882590	−	0.470143i	$-0.155798\pi$
$432$		0			0
$433$	208.330			0.481131			0.240565	−	0.970633i	$-0.422667\pi$
$433$	208.330			0.481131			0.240565	+	0.970633i	$0.422667\pi$
$434$	−44.9113	−	320.518i	−0.103482	−	0.738520i
$435$		0			0
$436$	74.6032	−	21.3256i	0.171108	−	0.0489120i
$437$	112.140	−	635.979i	0.256614	−	1.45533i
$438$		0			0
$439$	272.688	+	324.977i	0.621157	+	0.740266i	0.981269	−	0.192643i	$-0.0617060\pi$
$439$	272.688	+	324.977i	0.621157	+	0.740266i	−0.360112	+	0.932909i	$0.617262\pi$
$440$	−59.0218	+	26.1909i	−0.134140	+	0.0595247i
$441$		0			0
$442$	737.488	+	26.0577i	1.66853	+	0.0589541i
$443$	−613.592	+	108.193i	−1.38508	+	0.244228i	−0.816000	−	0.578052i	$-0.803813\pi$
$443$	−613.592	+	108.193i	−1.38508	+	0.244228i	−0.569084	+	0.822280i	$0.692702\pi$
$444$		0			0
$445$	−348.604	+	126.881i	−0.783379	+	0.285127i
$446$	−32.0907	+	35.6108i	−0.0719522	+	0.0798449i
$447$		0			0
$448$	297.308	+	11.1178i	0.663635	+	0.0248164i
$449$	14.5045	−	25.1226i	0.0323041	−	0.0559523i	−0.849421	−	0.527715i	$-0.823049\pi$
$449$	14.5045	−	25.1226i	0.0323041	−	0.0559523i	0.881725	+	0.471763i	$0.156382\pi$
$450$		0			0
$451$	−10.1801	+	5.87747i	−0.0225722	+	0.0130321i
$452$	38.0915	+	365.310i	0.0842732	+	0.808208i
$453$		0			0
$454$	180.963	+	557.730i	0.398598	+	1.22848i
$455$	166.237	−	198.113i	0.365356	−	0.435414i
$456$		0			0
$457$	−396.716	−	144.393i	−0.868088	−	0.315958i	−0.130695	−	0.991423i	$-0.541721\pi$
$457$	−396.716	−	144.393i	−0.868088	−	0.315958i	−0.737393	+	0.675464i	$0.763943\pi$
$458$	234.921	+	442.261i	0.512927	+	0.965635i
$459$		0			0
$460$	−236.141	−	159.563i	−0.513351	−	0.346875i
$461$	−26.9765	−	9.81863i	−0.0585173	−	0.0212985i	0.312596	−	0.949886i	$-0.398802\pi$
$461$	−26.9765	−	9.81863i	−0.0585173	−	0.0212985i	−0.371113	+	0.928588i	$0.621024\pi$
$462$		0			0
$463$	253.832	−	302.505i	0.548233	−	0.653359i	−0.418779	−	0.908088i	$-0.637542\pi$
$463$	253.832	−	302.505i	0.548233	−	0.653359i	0.967012	+	0.254729i	$0.0819863\pi$
$464$	−98.3061	+	20.7264i	−0.211867	+	0.0446690i
$465$		0			0
$466$	164.380	+	66.4927i	0.352748	+	0.142688i
$467$	−264.780	+	152.871i	−0.566982	+	0.327347i	−0.755943	−	0.654638i	$-0.772821\pi$
$467$	−264.780	+	152.871i	−0.566982	+	0.327347i	0.188961	+	0.981985i	$0.439488\pi$
$468$		0			0
$469$	73.7845	−	127.798i	0.157323	−	0.272491i
$470$	8.24571	+	10.5630i	0.0175441	+	0.0224745i
$471$		0			0
$472$	−217.978	−	878.887i	−0.461819	−	1.86205i
$473$	31.3050	−	11.3941i	0.0661839	−	0.0240890i
$474$		0			0
$475$	−425.044	+	74.9467i	−0.894829	+	0.157782i
$476$	346.258	−	168.529i	0.727434	−	0.354052i
$477$		0			0
$478$	510.548	+	319.318i	1.06809	+	0.668030i
$479$	−58.4435	−	69.6502i	−0.122011	−	0.145408i	0.701581	−	0.712590i	$-0.252478\pi$
$479$	−58.4435	−	69.6502i	−0.122011	−	0.145408i	−0.823592	+	0.567182i	$0.808033\pi$
$480$		0			0
$481$	142.149	−	806.168i	0.295529	−	1.67603i
$482$	130.312	−	611.829i	0.270356	−	1.26936i
$483$		0			0
$484$	370.163	−	268.474i	0.764799	−	0.554697i
$485$	201.642			0.415758
$486$		0			0
$487$			696.162i			1.42949i	0.699385	+	0.714745i	$0.253457\pi$
$487$			696.162i			1.42949i	−0.699385	+	0.714745i	$0.746543\pi$
$488$	593.999	+	290.621i	1.21721	+	0.595536i
$489$		0			0
$490$	−35.6324	+	167.298i	−0.0727191	+	0.341425i
$491$	−120.362	−	21.2231i	−0.245137	−	0.0432243i	0.0497294	−	0.998763i	$-0.484164\pi$
$491$	−120.362	−	21.2231i	−0.245137	−	0.0432243i	−0.294867	+	0.955538i	$0.595275\pi$
$492$		0			0
$493$	−99.6171	+	83.5887i	−0.202063	+	0.169551i
$494$	−855.026	−	534.769i	−1.73082	−	1.08253i
$495$		0			0
$496$	−78.4239	+	551.423i	−0.158113	+	1.11174i
$497$	−0.0604942	−	0.343079i	−0.000121719	−	0.000690301i
$498$		0			0
$499$	84.7569	+	232.868i	0.169853	+	0.466669i	0.995189	−	0.0979740i	$-0.0312362\pi$
$499$	84.7569	+	232.868i	0.169853	+	0.466669i	−0.825335	+	0.564643i	$0.809014\pi$
$500$	−122.022	+	487.692i	−0.244044	+	0.975385i
$501$		0			0
$502$	−255.030	−	326.700i	−0.508027	−	0.650797i
$503$	−672.109	−	388.042i	−1.33620	−	0.771456i	−0.349958	−	0.936765i	$-0.613804\pi$
$503$	−672.109	−	388.042i	−1.33620	−	0.771456i	−0.986242	+	0.165310i	$0.947138\pi$
$504$		0			0
$505$	197.227	+	341.606i	0.390548	+	0.676448i
$506$	−109.355	−	44.2348i	−0.216117	−	0.0874206i
$507$		0			0
$508$	−593.475	+	613.549i	−1.16826	+	1.20777i
$509$	−146.977	−	123.328i	−0.288756	−	0.242295i	0.486890	−	0.873463i	$-0.338131\pi$
$509$	−146.977	−	123.328i	−0.288756	−	0.242295i	−0.775646	+	0.631168i	$0.782576\pi$
$510$		0			0
$511$	−191.154	+	525.190i	−0.374078	+	1.02777i
$512$	−486.351	−	160.020i	−0.949905	−	0.312540i
$513$		0			0
$514$	−347.628	−	654.443i	−0.676319	−	1.27324i
$515$	−167.794	+	461.009i	−0.325813	+	0.895163i
$516$		0			0
$517$	4.24890	+	3.56525i	0.00821837	+	0.00689603i
$518$	−131.840	−	406.330i	−0.254516	−	0.784420i
$519$		0			0
$520$	−369.279	+	248.419i	−0.710152	+	0.477728i
$521$	−91.6758	−	158.787i	−0.175961	−	0.304774i	0.764532	−	0.644585i	$-0.222970\pi$
$521$	−91.6758	−	158.787i	−0.175961	−	0.304774i	−0.940494	+	0.339812i	$0.889637\pi$
$522$		0			0
$523$	133.492	+	77.0714i	0.255242	+	0.147364i	0.622162	−	0.782888i	$-0.286254\pi$
$523$	133.492	+	77.0714i	0.255242	+	0.147364i	−0.366920	+	0.930252i	$0.619588\pi$
$524$	4.25437	−	9.53434i	0.00811904	−	0.0181953i
$525$		0			0
$526$	247.519	−	274.670i	0.470568	−	0.522186i
$527$	246.570	+	677.446i	0.467875	+	1.28548i
$528$		0			0
$529$	1.45068	+	8.22723i	0.00274231	+	0.0155524i
$530$	−198.748	−	7.02238i	−0.374996	−	0.0132498i
$531$		0			0
$532$	−524.960	−	37.1433i	−0.986767	−	0.0698182i
$533$	−62.0654	+	52.0791i	−0.116445	+	0.0977093i
$534$		0			0
$535$	−416.789	−	73.4911i	−0.779044	−	0.137366i
$536$	−182.897	+	176.185i	−0.341225	+	0.328704i
$537$		0			0
$538$	137.672	+	982.526i	0.255897	+	1.82626i
$539$			70.7998i			0.131354i
$540$		0			0
$541$	−914.557			−1.69049			−0.845246	−	0.534377i	$-0.820546\pi$
$541$	−914.557			−1.69049			−0.845246	+	0.534377i	$0.820546\pi$
$542$	−627.454	+	87.9194i	−1.15766	+	0.162213i
$543$		0			0
$544$	−652.880	+	113.735i	−1.20015	+	0.209071i
$545$	−10.5180	+	59.6504i	−0.0192990	+	0.109450i
$546$		0			0
$547$	−518.289	−	617.673i	−0.947512	−	1.12920i	−0.991492	−	0.130169i	$-0.958448\pi$
$547$	−518.289	−	617.673i	−0.947512	−	1.12920i	0.0439796	−	0.999032i	$-0.485996\pi$
$548$	762.447	+	53.9465i	1.39133	+	0.0984425i
$549$		0			0
$550$	−2.78386	+	78.7892i	−0.00506157	+	0.143253i
$551$	175.015	−	30.8599i	0.317632	−	0.0560071i
$552$		0			0
$553$	1.50468	−	0.547659i	0.00272094	−	0.000990342i
$554$	443.349	+	399.524i	0.800269	+	0.721163i
$555$		0			0
$556$	−135.572	+	303.826i	−0.243835	+	0.546450i
$557$	−309.208	+	535.563i	−0.555130	+	0.961514i	0.442763	+	0.896639i	$0.353998\pi$
$557$	−309.208	+	535.563i	−0.555130	+	0.961514i	−0.997893	+	0.0648754i	$0.979335\pi$
$558$		0			0
$559$	198.854	−	114.808i	0.355731	−	0.205382i
$560$	−109.373	+	204.886i	−0.195309	+	0.365868i
$561$		0			0
$562$	−314.830	+	102.151i	−0.560197	+	0.181764i
$563$	22.9512	−	27.3522i	0.0407660	−	0.0485830i	−0.745276	−	0.666756i	$-0.767682\pi$
$563$	22.9512	−	27.3522i	0.0407660	−	0.0485830i	0.786042	+	0.618173i	$0.212127\pi$
$564$		0			0
$565$	−269.429	−	98.0640i	−0.476865	−	0.173565i
$566$	661.749	−	351.509i	1.16917	−	0.621040i
$567$		0			0
$568$	−0.0634033	+	0.596156i	−0.000111625	+	0.00104957i
$569$	519.027	+	188.910i	0.912174	+	0.332004i	0.755120	−	0.655586i	$-0.227578\pi$
$569$	519.027	+	188.910i	0.912174	+	0.332004i	0.157053	+	0.987590i	$0.449801\pi$
$570$		0			0
$571$	114.533	−	136.496i	0.200584	−	0.239046i	−0.656371	−	0.754439i	$-0.727909\pi$
$571$	114.533	−	136.496i	0.200584	−	0.239046i	0.856954	+	0.515392i	$0.172354\pi$
$572$	−128.076	+	132.408i	−0.223909	+	0.231483i
$573$		0			0
$574$	−15.8545	+	39.1948i	−0.0276211	+	0.0682837i
$575$	−301.345	+	173.982i	−0.524078	+	0.302577i
$576$		0			0
$577$	−112.675	+	195.160i	−0.195278	+	0.338231i	−0.946992	−	0.321258i	$-0.895894\pi$
$577$	−112.675	+	195.160i	−0.195278	+	0.338231i	0.751714	+	0.659490i	$0.229228\pi$
$578$	−220.548	+	172.165i	−0.381570	+	0.297862i
$579$		0			0
$580$	19.0362	−	76.0830i	0.0328210	−	0.131178i
$581$	−415.457	+	151.214i	−0.715073	+	0.260265i
$582$		0			0
$583$	−81.0648	+	14.2939i	−0.139048	+	0.0245178i
$584$	566.300	−	777.423i	0.969691	−	1.33120i
$585$		0			0
$586$	381.813	−	610.469i	0.651558	−	1.04176i
$587$	574.331	+	684.461i	0.978418	+	1.16603i	0.986115	+	0.166062i	$0.0531053\pi$
$587$	574.331	+	684.461i	0.978418	+	1.16603i	−0.00769749	+	0.999970i	$0.502450\pi$
$588$		0			0
$589$	171.082	−	970.253i	0.290461	−	1.64729i
$590$	691.370	+	147.253i	1.17181	+	0.249581i
$591$		0			0
$592$	24.4460	+	734.739i	0.0412939	+	1.24111i
$593$	272.894			0.460192			0.230096	−	0.973168i	$-0.426096\pi$
$593$	272.894			0.460192			0.230096	+	0.973168i	$0.426096\pi$
$594$		0			0
$595$			300.617i			0.505239i
$596$	−173.974	+	126.181i	−0.291902	+	0.211712i
$597$		0			0
$598$	−795.222	−	169.372i	−1.32980	−	0.283231i
$599$	104.010	+	18.3398i	0.173639	+	0.0306173i	0.259792	−	0.965665i	$-0.416346\pi$
$599$	104.010	+	18.3398i	0.173639	+	0.0306173i	−0.0861523	+	0.996282i	$0.527457\pi$
$600$		0			0
$601$	60.5640	−	50.8193i	0.100772	−	0.0845578i	−0.591010	−	0.806665i	$-0.701270\pi$
$601$	60.5640	−	50.8193i	0.100772	−	0.0845578i	0.691782	+	0.722107i	$0.256826\pi$
$602$	63.5388	−	101.590i	0.105546	−	0.168755i
$603$		0			0
$604$	179.398	−	87.3156i	0.297017	−	0.144562i
$605$	61.9861	+	351.540i	0.102456	+	0.581059i
$606$		0			0
$607$	290.469	+	798.058i	0.478533	+	1.31476i	0.910739	+	0.412983i	$0.135513\pi$
$607$	290.469	+	798.058i	0.478533	+	1.31476i	−0.432206	+	0.901775i	$0.642265\pi$
$608$	850.412	+	311.509i	1.39870	+	0.512350i
$609$		0			0
$610$	−406.918	+	317.650i	−0.667079	+	0.520737i
$611$	33.1077	+	19.1147i	0.0541860	+	0.0312843i
$612$		0			0
$613$	481.100	+	833.290i	0.784829	+	1.35936i	0.929101	+	0.369825i	$0.120583\pi$
$613$	481.100	+	833.290i	0.784829	+	1.35936i	−0.144272	+	0.989538i	$0.546084\pi$
$614$	−22.4698	+	55.5488i	−0.0365957	+	0.0904703i
$615$		0			0
$616$	−26.6116	+	92.3748i	−0.0432006	+	0.149959i
$617$	−635.302	−	533.081i	−1.02966	−	0.863989i	−0.0388514	−	0.999245i	$-0.512370\pi$
$617$	−635.302	−	533.081i	−1.02966	−	0.863989i	−0.990811	+	0.135256i	$0.956814\pi$
$618$		0			0
$619$	126.739	−	348.213i	0.204748	−	0.562541i	−0.794236	−	0.607610i	$-0.792129\pi$
$619$	126.739	−	348.213i	0.204748	−	0.562541i	0.998984	+	0.0450690i	$0.0143508\pi$
$620$	−360.259	−	243.430i	−0.581063	−	0.392628i
$621$		0			0
$622$	−467.909	+	248.544i	−0.752265	+	0.399589i
$623$	−188.895	+	518.985i	−0.303202	+	0.833041i
$624$		0			0
$625$	−8.58152	−	7.20075i	−0.0137304	−	0.0115212i
$626$	−264.156	+	85.7092i	−0.421974	+	0.136916i
$627$		0			0
$628$	−75.0119	−	719.389i	−0.119446	−	1.14552i
$629$	475.772	+	824.061i	0.756394	+	1.31011i
$630$		0			0
$631$	−153.085	−	88.3837i	−0.242607	−	0.140069i	0.373767	−	0.927523i	$-0.378066\pi$
$631$	−153.085	−	88.3837i	−0.242607	−	0.140069i	−0.616374	+	0.787453i	$0.711399\pi$
$632$	−2.74913	+	0.188826i	−0.00434990	+	0.000298775i
$633$		0			0
$634$	−290.815	−	262.068i	−0.458699	−	0.413357i
$635$	−227.909	−	626.174i	−0.358911	−	0.986101i
$636$		0			0
$637$	84.7379	+	480.573i	0.133027	+	0.754431i
$638$	1.14628	−	32.4421i	0.00179668	−	0.0508497i
$639$		0			0
$640$	278.472	−	286.708i	0.435113	−	0.447981i
$641$	603.967	−	506.789i	0.942227	−	0.790622i	−0.0357447	−	0.999361i	$-0.511380\pi$
$641$	603.967	−	506.789i	0.942227	−	0.790622i	0.977971	+	0.208739i	$0.0669359\pi$
$642$		0			0
$643$	−887.935	−	156.567i	−1.38093	−	0.243494i	−0.566643	−	0.823963i	$-0.691758\pi$
$643$	−887.935	−	156.567i	−1.38093	−	0.243494i	−0.814282	+	0.580469i	$0.802869\pi$
$644$	−407.949	+	116.614i	−0.633461	+	0.181078i
$645$		0			0
$646$	1160.92	−	162.669i	1.79709	−	0.251810i
$647$		−	609.723i		−	0.942385i	−0.882030	−	0.471193i	$-0.843824\pi$
$647$		−	609.723i		−	0.942385i	0.882030	−	0.471193i	$-0.156176\pi$
$648$		0			0
$649$	292.584			0.450823
$650$	75.4039	+	538.135i	0.116006	+	0.827900i
$651$		0			0
$652$	9.80331	+	34.2948i	0.0150358	+	0.0525994i
$653$	−100.348	+	569.103i	−0.153673	+	0.871521i	0.806317	+	0.591484i	$0.201458\pi$
$653$	−100.348	+	569.103i	−0.153673	+	0.871521i	−0.959989	+	0.280037i	$0.909653\pi$
$654$		0			0
$655$	5.23885	+	6.24342i	0.00799824	+	0.00953193i
$656$	44.8901	−	57.2621i	0.0684301	−	0.0872897i
$657$		0			0
$658$	19.9373	+	0.704447i	0.0302999	+	0.00107059i
$659$	649.326	−	114.494i	0.985320	−	0.173739i	0.342302	−	0.939590i	$-0.388793\pi$
$659$	649.326	−	114.494i	0.985320	−	0.173739i	0.643018	+	0.765851i	$0.277682\pi$
$660$		0			0
$661$	270.159	−	98.3300i	0.408713	−	0.148759i	−0.129478	−	0.991582i	$-0.541330\pi$
$661$	270.159	−	98.3300i	0.408713	−	0.148759i	0.538191	+	0.842823i	$0.319108\pi$
$662$	−15.7109	+	17.4343i	−0.0237325	+	0.0263358i
$663$		0			0
$664$	759.063	−	52.1366i	1.14317	−	0.0785190i
$665$	205.413	−	355.786i	0.308892	−	0.535017i
$666$		0			0
$667$	124.081	−	71.6384i	0.186029	−	0.107404i
$668$	−1151.56	+	120.075i	−1.72389	+	0.179753i
$669$		0			0
$670$	−61.1835	−	188.568i	−0.0913186	−	0.281444i
$671$	−137.344	+	163.680i	−0.204686	+	0.243935i
$672$		0			0
$673$	615.335	+	223.963i	0.914316	+	0.332784i	0.755975	−	0.654601i	$-0.227163\pi$
$673$	615.335	+	223.963i	0.914316	+	0.332784i	0.158341	+	0.987384i	$0.449385\pi$
$674$	−85.9093	−	161.733i	−0.127462	−	0.239959i
$675$		0			0
$676$	−332.399	+	491.928i	−0.491715	+	0.727704i
$677$	350.399	+	127.535i	0.517576	+	0.188382i	0.587583	−	0.809164i	$-0.300080\pi$
$677$	350.399	+	127.535i	0.517576	+	0.188382i	−0.0700062	+	0.997547i	$0.522302\pi$
$678$		0			0
$679$	192.962	−	229.963i	0.284186	−	0.338679i
$680$	143.212	−	497.120i	0.210605	−	0.731058i
$681$		0			0
$682$	−166.833	−	67.4849i	−0.244623	−	0.0989515i
$683$	403.114	−	232.738i	0.590211	−	0.340758i	−0.174970	−	0.984574i	$-0.555983\pi$
$683$	403.114	−	232.738i	0.590211	−	0.340758i	0.765181	+	0.643815i	$0.222650\pi$
$684$		0			0
$685$	−298.340	+	516.741i	−0.435533	+	0.754366i
$686$	437.027	+	559.844i	0.637066	+	0.816099i
$687$		0			0
$688$	−153.468	+	137.727i	−0.223065	+	0.200184i
$689$	−533.141	+	194.047i	−0.773790	+	0.281636i
$690$		0			0
$691$	822.564	−	145.040i	1.19040	−	0.209899i	0.456853	−	0.889542i	$-0.348976\pi$
$691$	822.564	−	145.040i	1.19040	−	0.209899i	0.733543	+	0.679643i	$0.237865\pi$
$692$	−561.142	−	1152.92i	−0.810899	−	1.66607i
$693$		0			0
$694$	−607.760	−	380.119i	−0.875735	−	0.547722i
$695$	−166.944	−	198.956i	−0.240207	−	0.286268i
$696$		0			0
$697$	16.3539	−	92.7473i	0.0234632	−	0.133066i
$698$	−188.217	+	883.701i	−0.269652	+	1.26605i
$699$		0			0
$700$	166.486	+	229.546i	0.237838	+	0.327923i
$701$	318.239			0.453978			0.226989	−	0.973897i	$-0.427112\pi$
$701$	318.239			0.453978			0.226989	+	0.973897i	$0.427112\pi$
$702$		0			0
$703$		−	1300.39i		−	1.84977i
$704$	88.0131	−	140.079i	0.125019	−	0.198976i
$705$		0			0
$706$	−77.3002	+	362.934i	−0.109490	+	0.514070i
$707$	578.321	+	101.974i	0.817994	+	0.144234i
$708$		0			0
$709$	−153.512	+	128.812i	−0.216519	+	0.181681i	−0.744596	−	0.667515i	$-0.767358\pi$
$709$	−153.512	+	128.812i	−0.216519	+	0.181681i	0.528077	+	0.849197i	$0.322913\pi$
$710$	−0.396789	−	0.248168i	−0.000558858	−	0.000349533i
$711$		0			0
$712$	559.608	−	768.237i	0.785966	−	1.07898i
$713$	−137.929	−	782.233i	−0.193449	−	1.09710i
$714$		0			0
$715$	−49.1843	−	135.133i	−0.0687892	−	0.188997i
$716$	−729.133	−	182.431i	−1.01834	−	0.254792i
$717$		0			0
$718$	27.2096	+	34.8563i	0.0378964	+	0.0485464i
$719$	−95.7306	−	55.2701i	−0.133144	−	0.0768708i	0.431948	−	0.901898i	$-0.357826\pi$
$719$	−95.7306	−	55.2701i	−0.133144	−	0.0768708i	−0.565093	+	0.825027i	$0.691160\pi$
$720$		0			0
$721$	365.188	+	632.523i	0.506501	+	0.877286i
$722$	−815.810	−	330.000i	−1.12993	−	0.457063i
$723$		0			0
$724$	503.709	+	487.228i	0.695731	+	0.672968i
$725$	−73.3535	−	61.5509i	−0.101177	−	0.0848978i
$726$		0			0
$727$	258.380	−	709.893i	0.355406	−	0.976469i	−0.625198	−	0.780466i	$-0.714982\pi$
$727$	258.380	−	709.893i	0.355406	−	0.976469i	0.980603	−	0.196002i	$-0.0627961\pi$
$728$	−70.0730	+	658.869i	−0.0962541	+	0.905040i
$729$		0			0
$730$	352.218	+	663.084i	0.482490	+	0.908334i
$731$	−91.2871	+	250.809i	−0.124880	+	0.343104i
$732$		0			0
$733$	−217.881	−	182.824i	−0.297245	−	0.249419i	0.481951	−	0.876198i	$-0.339928\pi$
$733$	−217.881	−	182.824i	−0.297245	−	0.249419i	−0.779197	+	0.626780i	$0.784373\pi$
$734$	40.2338	+	124.001i	0.0548144	+	0.168938i
$735$		0			0
$736$	730.164	+	1.50337i	0.992070	+	0.00204262i
$737$	−41.0279	−	71.0624i	−0.0556688	−	0.0964212i
$738$		0			0
$739$	336.529	+	194.295i	0.455385	+	0.262916i	0.710102	−	0.704099i	$-0.248649\pi$
$739$	336.529	+	194.295i	0.455385	+	0.262916i	−0.254717	+	0.967016i	$0.581982\pi$
$740$	−524.074	−	233.850i	−0.708208	−	0.316013i
$741$		0			0
$742$	−198.201	+	219.942i	−0.267117	+	0.296418i
$743$	53.3057	+	146.456i	0.0717439	+	0.197115i	0.970382	−	0.241576i	$-0.0776644\pi$
$743$	53.3057	+	146.456i	0.0717439	+	0.197115i	−0.898638	+	0.438691i	$0.855442\pi$
$744$		0			0
$745$	−29.1330	−	165.221i	−0.0391047	−	0.221774i
$746$	160.083	+	5.65622i	0.214588	+	0.00758206i
$747$		0			0
$748$	15.1130	−	213.598i	0.0202045	−	0.285558i
$749$	−482.659	+	404.999i	−0.644405	+	0.540720i
$750$		0			0
$751$	565.429	+	99.7004i	0.752901	+	0.132757i	0.536911	−	0.843639i	$-0.319591\pi$
$751$	565.429	+	99.7004i	0.752901	+	0.132757i	0.215990	+	0.976396i	$0.430702\pi$
$752$	−32.6340	−	10.6629i	−0.0433963	−	0.0141794i
$753$		0			0
$754$	−31.0482	−	221.582i	−0.0411780	−	0.293875i
$755$			155.751i			0.206293i
$756$		0			0
$757$	759.370			1.00313			0.501566	−	0.865120i	$-0.332758\pi$
$757$	759.370			1.00313			0.501566	+	0.865120i	$0.332758\pi$
$758$	214.247	−	30.0205i	0.282648	−	0.0396049i
$759$		0			0
$760$	−509.178	+	490.493i	−0.669971	+	0.645386i
$761$	155.466	−	881.691i	0.204292	−	1.15860i	−0.694259	−	0.719725i	$-0.744268\pi$
$761$	155.466	−	881.691i	0.204292	−	1.15860i	0.898550	−	0.438870i	$-0.144621\pi$
$762$		0			0
$763$	57.9631	+	69.0777i	0.0759674	+	0.0905344i
$764$	−23.0987	+	326.463i	−0.0302339	+	0.427307i
$765$		0			0
$766$	−22.5182	+	637.313i	−0.0293972	+	0.832002i
$767$	1985.99	−	350.184i	2.58930	−	0.456564i
$768$		0			0
$769$	525.038	−	191.098i	0.682755	−	0.248502i	0.0227249	−	0.999742i	$-0.492766\pi$
$769$	525.038	−	191.098i	0.682755	−	0.248502i	0.660030	+	0.751239i	$0.270544\pi$
$770$	−55.7477	−	50.2370i	−0.0723996	−	0.0652429i
$771$		0			0
$772$	−1122.90	−	501.055i	−1.45453	−	0.649035i
$773$	−452.627	+	783.973i	−0.585546	+	1.01420i	0.409261	+	0.912417i	$0.365787\pi$
$773$	−452.627	+	783.973i	−0.585546	+	1.01420i	−0.994807	+	0.101779i	$0.967547\pi$
$774$		0			0
$775$	−459.734	+	265.427i	−0.593205	+	0.342487i
$776$	−428.646	+	288.356i	−0.552379	+	0.371593i
$777$		0			0
$778$	−249.306	+	80.8908i	−0.320444	+	0.103973i
$779$	−82.7298	+	98.5936i	−0.106200	+	0.126564i
$780$		0			0
$781$	−0.182030	−	0.0662536i	−0.000233073	−	8.48318e-5i
$782$	834.654	−	443.353i	1.06733	−	0.566947i
$783$		0			0
$784$	−163.496	−	406.594i	−0.208541	−	0.518615i
$785$	530.574	+	193.113i	0.675891	+	0.246004i
$786$		0			0
$787$	858.505	−	1023.13i	1.09086	−	1.30003i	0.140088	−	0.990139i	$-0.455262\pi$
$787$	858.505	−	1023.13i	1.09086	−	1.30003i	0.950771	−	0.309895i	$-0.100294\pi$
$788$	42.0444	+	40.6688i	0.0533558	+	0.0516101i
$789$		0			0
$790$	0.806648	−	1.99416i	0.00102107	−	0.00252425i
$791$	−369.667	+	213.428i	−0.467342	+	0.269820i
$792$		0			0
$793$	−736.357	+	1275.41i	−0.928571	+	1.60833i
$794$	566.907	−	442.541i	0.713989	−	0.557356i
$795$		0			0
$796$	43.1025	+	10.7844i	0.0541488	+	0.0135482i
$797$	188.861	−	68.7400i	0.236965	−	0.0862484i	−0.220808	−	0.975317i	$-0.570869\pi$
$797$	188.861	−	68.7400i	0.236965	−	0.0862484i	0.457773	+	0.889069i	$0.348647\pi$
$798$		0			0
$799$	−43.7627	+	7.71654i	−0.0547718	+	0.00965774i
$800$	−165.958	−	458.905i	−0.207448	−	0.573631i
$801$		0			0
$802$	−359.537	+	574.853i	−0.448301	+	0.716775i
$803$	199.762	+	238.067i	0.248770	+	0.296472i
$804$		0			0
$805$	57.5149	−	326.183i	0.0714471	−	0.405197i
$806$	−1213.20	−	258.395i	−1.50521	−	0.320589i
$807$		0			0
$808$	−907.769	−	444.137i	−1.12348	−	0.549675i
$809$	−177.768			−0.219738			−0.109869	−	0.993946i	$-0.535043\pi$
$809$	−177.768			−0.219738			−0.109869	+	0.993946i	$0.535043\pi$
$810$		0			0
$811$			928.342i			1.14469i	0.820014	+	0.572344i	$0.193966\pi$
$811$			928.342i			1.14469i	−0.820014	+	0.572344i	$0.806034\pi$
$812$	−68.5522	−	94.5176i	−0.0844239	−	0.116401i
$813$		0			0
$814$	−232.324	−	49.4821i	−0.285411	−	0.0607888i
$815$	−27.4210	−	4.83507i	−0.0336454	−	0.00593260i
$816$		0			0
$817$	279.419	−	234.461i	0.342006	−	0.286977i
$818$	391.986	−	626.734i	0.479200	−	0.766179i
$819$		0			0
$820$	24.8571	+	51.0714i	0.0303136	+	0.0622822i
$821$	45.7241	+	259.314i	0.0556931	+	0.315851i	0.999909	−	0.0134752i	$-0.00428941\pi$
$821$	45.7241	+	259.314i	0.0556931	+	0.315851i	−0.944216	+	0.329327i	$0.893178\pi$
$822$		0			0
$823$	310.142	+	852.108i	0.376843	+	1.03537i	0.972657	+	0.232246i	$0.0746073\pi$
$823$	310.142	+	852.108i	0.376843	+	1.03537i	−0.595814	+	0.803122i	$0.703170\pi$
$824$	−302.568	−	1219.95i	−0.367194	−	1.48052i
$825$		0			0
$826$	829.542	−	647.559i	1.00429	−	0.783970i
$827$	1041.84	+	601.507i	1.25978	+	0.727337i	0.973032	−	0.230668i	$-0.0740913\pi$
$827$	1041.84	+	601.507i	1.25978	+	0.727337i	0.286751	+	0.958005i	$0.407425\pi$
$828$		0			0
$829$	−354.368	−	613.784i	−0.427465	−	0.740390i	0.569183	−	0.822211i	$-0.307260\pi$
$829$	−354.368	−	613.784i	−0.427465	−	0.740390i	−0.996647	+	0.0818209i	$0.973926\pi$
$830$	−222.723	+	550.607i	−0.268342	+	0.663382i
$831$		0			0
$832$	429.757	−	1056.16i	0.516535	−	1.26943i
$833$	−434.526	−	364.611i	−0.521640	−	0.437708i
$834$		0			0
$835$	309.125	−	849.313i	0.370209	−	1.01714i
$836$	−163.839	+	242.470i	−0.195979	+	0.290036i
$837$		0			0
$838$	−108.868	+	57.8284i	−0.129914	+	0.0690077i
$839$	384.167	−	1055.49i	0.457887	−	1.25803i	−0.469168	−	0.883109i	$-0.655446\pi$
$839$	384.167	−	1055.49i	0.457887	−	1.25803i	0.927055	−	0.374925i	$-0.122331\pi$
$840$		0			0
$841$	−614.039	−	515.240i	−0.730130	−	0.612652i
$842$	−53.2725	+	17.2850i	−0.0632690	+	0.0205285i
$843$		0			0
$844$	919.151	−	95.8414i	1.08904	−	0.113556i
$845$	−231.732	−	401.372i	−0.274240	−	0.474997i
$846$		0			0
$847$	460.232	+	265.715i	0.543367	+	0.313713i
$848$	432.536	−	269.289i	0.510066	−	0.317557i
$849$		0			0
$850$	−469.224	−	422.841i	−0.552028	−	0.497460i
$851$	−358.572	−	985.168i	−0.421354	−	1.15766i
$852$		0			0
$853$	−94.3663	−	535.178i	−0.110629	−	0.627407i	−0.988822	−	0.149101i	$-0.952362\pi$
$853$	−94.3663	−	535.178i	−0.110629	−	0.627407i	0.878193	−	0.478306i	$-0.158749\pi$
$854$	−27.1374	+	768.046i	−0.0317768	+	0.899351i
$855$		0			0
$856$	991.094	−	439.797i	1.15782	−	0.513782i
$857$	−1203.43	+	1009.80i	−1.40424	+	1.17830i	−0.445057	+	0.895502i	$0.646817\pi$
$857$	−1203.43	+	1009.80i	−1.40424	+	1.17830i	−0.959181	+	0.282794i	$0.908739\pi$
$858$		0			0
$859$	−486.259	−	85.7406i	−0.566076	−	0.0998145i	−0.116716	−	0.993165i	$-0.537237\pi$
$859$	−486.259	−	85.7406i	−0.566076	−	0.0998145i	−0.449360	+	0.893351i	$0.648348\pi$
$860$	−44.2425	−	154.773i	−0.0514448	−	0.179968i
$861$		0			0
$862$	−802.685	+	112.473i	−0.931189	+	0.130479i
$863$			237.241i			0.274902i	0.990509	+	0.137451i	$0.0438910\pi$
$863$			237.241i			0.274902i	−0.990509	+	0.137451i	$0.956109\pi$
$864$		0			0
$865$	1000.95			1.15717
$866$	−57.8178	−	412.628i	−0.0667642	−	0.476476i
$867$		0			0
$868$	−622.370	+	177.907i	−0.717016	+	0.204962i
$869$	0.154612	−	0.876849i	0.000177920	−	0.00100903i
$870$		0			0
$871$	−363.540	−	433.250i	−0.417383	−	0.497417i
$872$	−62.9433	−	141.844i	−0.0721827	−	0.162666i
$873$		0			0
$874$	−1290.77	−	45.6070i	−1.47686	−	0.0521819i
$875$	−575.378	+	101.455i	−0.657575	+	0.115948i
$876$		0			0
$877$	−657.052	+	239.147i	−0.749204	+	0.272688i	−0.688271	−	0.725454i	$-0.741630\pi$
$877$	−657.052	+	239.147i	−0.749204	+	0.272688i	−0.0609331	+	0.998142i	$0.519408\pi$
$878$	567.986	−	630.290i	0.646909	−	0.717871i
$879$		0			0
$880$	68.2553	+	109.633i	0.0775628	+	0.124583i
$881$	201.312	−	348.683i	0.228504	−	0.395781i	−0.728861	−	0.684662i	$-0.759950\pi$
$881$	201.312	−	348.683i	0.228504	−	0.395781i	0.957365	+	0.288881i	$0.0932833\pi$
$882$		0			0
$883$	−70.5932	+	40.7570i	−0.0799470	+	0.0461574i	−0.539441	−	0.842024i	$-0.681364\pi$
$883$	−70.5932	+	40.7570i	−0.0799470	+	0.0461574i	0.459494	+	0.888181i	$0.348031\pi$
$884$	−153.064	−	1467.94i	−0.173150	−	1.66056i
$885$		0			0
$886$	384.583	+	1185.28i	0.434066	+	1.33779i
$887$	289.982	−	345.587i	0.326924	−	0.389613i	−0.577399	−	0.816462i	$-0.695932\pi$
$887$	289.982	−	345.587i	0.326924	−	0.389613i	0.904323	+	0.426849i	$0.140377\pi$
$888$		0			0
$889$	−932.218	−	339.300i	−1.04861	−	0.381664i
$890$	348.056	+	655.249i	0.391074	+	0.736234i
$891$		0			0
$892$	79.4387	+	53.6773i	0.0890569	+	0.0601764i
$893$	57.0667	+	20.7706i	0.0639045	+	0.0232593i
$894$		0			0
$895$	377.145	−	449.463i	0.421391	−	0.502194i
$896$	−60.4918	−	591.950i	−0.0675131	−	0.660658i
$897$		0			0
$898$	−53.7845	−	21.7561i	−0.0598936	−	0.0242273i
$899$	189.299	−	109.292i	0.210567	−	0.121571i
$900$		0			0
$901$	329.747	−	571.138i	0.365979	−	0.633894i
$902$	14.4665	+	18.5320i	0.0160382	+	0.0205454i
$903$		0			0
$904$	712.980	−	176.831i	0.788695	−	0.195609i
$905$	−514.074	+	187.108i	−0.568037	+	0.206749i
$906$		0			0
$907$	359.604	−	63.4079i	0.396477	−	0.0699095i	0.0281447	−	0.999604i	$-0.491040\pi$
$907$	359.604	−	63.4079i	0.396477	−	0.0699095i	0.368332	+	0.929694i	$0.379929\pi$
$908$	1054.44	−	513.212i	1.16128	−	0.565212i
$909$		0			0
$910$	−438.529	−	274.275i	−0.481900	−	0.301401i
$911$	−786.779	−	937.647i	−0.863644	−	1.02925i	−0.999259	−	0.0384887i	$-0.987746\pi$
$911$	−786.779	−	937.647i	−0.863644	−	1.02925i	0.135616	−	0.990762i	$-0.456699\pi$
$912$		0			0
$913$	−42.6899	+	242.107i	−0.0467579	+	0.265177i
$914$	−175.891	+	825.830i	−0.192441	+	0.903534i
$915$		0			0
$916$	810.766	−	588.037i	0.885116	−	0.641961i
$917$	12.1336			0.0132319
$918$		0			0
$919$		−	733.236i		−	0.797863i	−0.916981	−	0.398931i	$-0.869381\pi$
$919$		−	733.236i		−	0.797863i	0.916981	−	0.398931i	$-0.130619\pi$
$920$	−250.501	+	511.997i	−0.272284	+	0.556519i
$921$		0			0
$922$	−11.9605	+	56.1559i	−0.0129723	+	0.0609066i
$923$	−1.31488	−	0.231848i	−0.00142457	−	0.000251190i
$924$		0			0
$925$	−536.747	+	450.384i	−0.580267	+	0.486902i
$926$	−669.603	−	418.798i	−0.723114	−	0.452266i
$927$		0			0
$928$	68.3348	+	188.958i	0.0736366	+	0.203618i
$929$	−34.2914	−	194.476i	−0.0369122	−	0.209339i	0.960773	−	0.277334i	$-0.0894509\pi$
$929$	−34.2914	−	194.476i	−0.0369122	−	0.209339i	−0.997686	+	0.0679949i	$0.978340\pi$
$930$		0			0
$931$	265.130	+	728.438i	0.284779	+	0.782425i
$932$	86.0783	−	344.034i	0.0923587	−	0.369135i
$933$		0			0
$934$	376.269	+	482.011i	0.402857	+	0.516072i
$935$	144.764	+	83.5793i	0.154827	+	0.0893896i
$936$		0			0
$937$	−822.848	−	1425.21i	−0.878173	−	1.52104i	−0.853344	−	0.521349i	$-0.825429\pi$
$937$	−822.848	−	1425.21i	−0.878173	−	1.52104i	−0.0248295	−	0.999692i	$-0.507904\pi$
$938$	−273.601	−	110.673i	−0.291686	−	0.117989i
$939$		0			0
$940$	18.6332	−	19.2634i	0.0198225	−	0.0204930i
$941$	49.9757	+	41.9346i	0.0531092	+	0.0445639i	0.668956	−	0.743302i	$-0.266741\pi$
$941$	49.9757	+	41.9346i	0.0531092	+	0.0445639i	−0.615847	+	0.787866i	$0.711186\pi$
$942$		0			0
$943$	−35.4893	+	97.5061i	−0.0376345	+	0.103400i
$944$	−1680.27	+	675.657i	−1.77995	+	0.715739i
$945$		0			0
$946$	−31.2558	−	58.8421i	−0.0330400	−	0.0622009i
$947$	−578.159	+	1588.48i	−0.610517	+	1.67738i	0.118558	+	0.992947i	$0.462173\pi$
$947$	−578.159	+	1588.48i	−0.610517	+	1.67738i	−0.729075	+	0.684434i	$0.760049\pi$
$948$		0			0
$949$	1640.87	+	1376.86i	1.72906	+	1.45085i
$950$	266.406	+	821.063i	0.280427	+	0.864277i
$951$		0			0
$952$	−429.894	−	639.045i	−0.451569	−	0.671266i
$953$	804.382	+	1393.23i	0.844052	+	1.46194i	0.886442	+	0.462841i	$0.153170\pi$
$953$	804.382	+	1393.23i	0.844052	+	1.46194i	−0.0423891	+	0.999101i	$0.513497\pi$
$954$		0			0
$955$	−221.257	−	127.743i	−0.231683	−	0.133762i
$956$	490.765	−	1099.84i	0.513352	−	1.15046i
$957$		0			0
$958$	−121.733	+	135.086i	−0.127070	+	0.141009i
$959$	303.820	+	834.738i	0.316809	+	0.870426i
$960$		0			0
$961$	−43.5491	−	246.979i	−0.0453165	−	0.257002i
$962$	−1636.19	−	57.8116i	−1.70082	−	0.0600952i
$963$		0			0
$964$	−1247.99	−	88.3005i	−1.29459	−	0.0915981i
$965$	735.313	−	617.001i	0.761982	−	0.639379i
$966$		0			0
$967$	1161.14	+	204.740i	1.20076	+	0.211727i	0.738028	−	0.674770i	$-0.235757\pi$
$967$	1161.14	+	204.740i	1.20076	+	0.211727i	0.462735	+	0.886497i	$0.346868\pi$
$968$	−634.484	−	658.654i	−0.655458	−	0.680427i
$969$		0			0
$970$	−55.9619	−	399.383i	−0.0576927	−	0.411735i
$971$		−	796.242i		−	0.820023i	−0.912080	−	0.410011i	$-0.865525\pi$
$971$		−	796.242i		−	0.820023i	0.912080	−	0.410011i	$-0.134475\pi$
$972$		0			0
$973$	−386.657			−0.397386
$974$	1378.85	−	193.206i	1.41566	−	0.198364i
$975$		0			0
$976$	410.767	−	1257.16i	0.420867	−	1.28807i
$977$	−232.161	+	1316.65i	−0.237626	+	1.34765i	0.599385	+	0.800461i	$0.295412\pi$
$977$	−232.161	+	1316.65i	−0.237626	+	1.34765i	−0.837012	+	0.547185i	$0.815699\pi$
$978$		0			0
$979$	197.402	+	235.254i	0.201636	+	0.240300i
$980$	341.248	+	24.1449i	0.348213	+	0.0246376i
$981$		0			0
$982$	−8.63137	+	244.286i	−0.00878958	+	0.248764i
$983$	613.490	−	108.175i	0.624100	−	0.110046i	0.147350	−	0.989084i	$-0.452926\pi$
$983$	613.490	−	108.175i	0.624100	−	0.110046i	0.476750	+	0.879039i	$0.341815\pi$
$984$		0			0
$985$	−42.9095	+	15.6178i	−0.0435630	+	0.0158556i
$986$	193.207	+	174.108i	0.195950	+	0.176580i
$987$		0			0
$988$	−821.895	+	1841.92i	−0.831878	+	1.86429i
$989$	147.036	−	254.674i	0.148671	−	0.257506i
$990$		0			0
$991$	−513.695	+	296.582i	−0.518360	+	0.299275i	−0.736264	−	0.676695i	$-0.763412\pi$
$991$	−513.695	+	296.582i	−0.518360	+	0.299275i	0.217903	+	0.975970i	$0.430078\pi$
$992$	1113.94	+	2.29354i	1.12293	+	0.00231204i
$993$		0			0
$994$	−0.662731	+	0.215033i	−0.000666732	+	0.000216331i
$995$	−22.2948	+	26.5699i	−0.0224068	+	0.0267034i
$996$		0			0
$997$	377.002	+	137.218i	0.378136	+	0.137630i	0.524094	−	0.851660i	$-0.324404\pi$
$997$	377.002	+	137.218i	0.378136	+	0.137630i	−0.145958	+	0.989291i	$0.546626\pi$
$998$	437.707	−	232.502i	0.438584	−	0.232968i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.16		204
3.2	odd	2		108.3.j.a.31.19	yes	204
4.3	odd	2	inner	324.3.j.a.307.7		204
12.11	even	2		108.3.j.a.31.28	yes	204
27.7	even	9	inner	324.3.j.a.19.7		204
27.20	odd	18		108.3.j.a.7.28	yes	204
108.7	odd	18	inner	324.3.j.a.19.16		204
108.47	even	18		108.3.j.a.7.19	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.19	✓	204	108.47	even	18
108.3.j.a.7.28	yes	204	27.20	odd	18
108.3.j.a.31.19	yes	204	3.2	odd	2
108.3.j.a.31.28	yes	204	12.11	even	2
324.3.j.a.19.7		204	27.7	even	9	inner
324.3.j.a.19.16		204	108.7	odd	18	inner
324.3.j.a.307.7		204	4.3	odd	2	inner
324.3.j.a.307.16		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.277531 - 1.98065i) q^{2} +(-3.84595 + 1.09938i) q^{4} +(0.542224 - 3.07510i) q^{5} +(-2.98812 - 3.56110i) q^{7} +(3.24486 + 7.31238i) q^{8} +(-6.24119 - 0.220520i) q^{10} +(-2.54564 + 0.448865i) q^{11} +(-16.7420 + 6.09358i) q^{13} +(-6.22401 + 6.90674i) q^{14} +(13.5827 - 8.45635i) q^{16} +(10.3549 - 17.9352i) q^{17} +(-24.5104 + 14.1511i) q^{19} +(1.29535 + 12.4228i) q^{20} +(1.59554 + 4.91745i) q^{22} +(-14.6669 + 17.4793i) q^{23} +(14.3301 + 5.21572i) q^{25} +(16.7157 + 31.4689i) q^{26} +(15.4072 + 10.4108i) q^{28} +(-5.90052 - 2.14762i) q^{29} +(-22.3759 + 26.6666i) q^{31} +(-20.5187 - 24.5557i) q^{32} +(-38.3971 - 15.5318i) q^{34} +(-12.5710 + 7.25787i) q^{35} +(-22.9733 + 39.7909i) q^{37} +(34.8307 + 44.6192i) q^{38} +(24.2458 - 6.01334i) q^{40} +(4.27327 - 1.55534i) q^{41} +(-12.6921 + 2.23796i) q^{43} +(9.29693 - 4.52494i) q^{44} +(38.6910 + 24.1990i) q^{46} +(-1.37925 - 1.64373i) q^{47} +(4.75617 - 26.9736i) q^{49} +(6.35348 - 29.8304i) q^{50} +(57.6897 - 41.8415i) q^{52} +31.8446 q^{53} +8.07149i q^{55} +(16.3441 - 33.4056i) q^{56} +(-2.61610 + 12.2829i) q^{58} +(-111.470 - 19.6551i) q^{59} +(63.3215 - 53.1331i) q^{61} +(59.0272 + 36.9181i) q^{62} +(-42.9417 + 47.4553i) q^{64} +(9.66050 + 54.7874i) q^{65} +(10.8572 + 29.8298i) q^{67} +(-20.1068 + 80.3619i) q^{68} +(17.8641 + 22.8845i) q^{70} +(0.0648998 + 0.0374699i) q^{71} +(-60.1132 - 104.119i) q^{73} +(85.1877 + 34.4589i) q^{74} +(78.7084 - 81.3707i) q^{76} +(9.20513 + 7.72402i) q^{77} +(-0.117809 + 0.323678i) q^{79} +(-18.6393 - 46.3535i) q^{80} +(-4.26656 - 8.03220i) q^{82} +(32.5283 - 89.3708i) q^{83} +(-49.5379 - 41.5672i) q^{85} +(7.95507 + 24.5175i) q^{86} +(-11.5425 - 17.1582i) q^{88} +(-59.4029 - 102.889i) q^{89} +(71.7269 + 41.4116i) q^{91} +(37.1918 - 83.3493i) q^{92} +(-2.87287 + 3.18801i) q^{94} +(30.2259 + 83.0451i) q^{95} +(11.2136 + 63.5953i) q^{97} +(-54.7452 - 1.93431i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37}+ \cdots - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

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