LMFDB - Embedded newform 363.3.h.j.323.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.245"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-10,8,0,33,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 $ x^16 - 12x^14 + 180x^12 - 2562x^10 + 25179x^8 - 96398x^6 + 239275x^4 - 536393*x^2 + 1771561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			323.4
Root			$2.10855 - 2.90217i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.j.245.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.10855 - 2.90217i) q^{2} +(0.307087 + 2.98424i) q^{3} +(-2.74053 - 8.43448i) q^{4} +(-1.22635 - 1.68793i) q^{5} +(9.30827 + 5.40120i) q^{6} +(-2.73883 - 8.42924i) q^{7} +(-16.6100 - 5.39692i) q^{8} +(-8.81140 + 1.83284i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +(-1.33068 - 0.966792i) q^{13} +(-30.2380 - 9.82492i) q^{14} +(4.66059 - 4.17807i) q^{15} +(-21.9865 + 15.9742i) q^{16} +(-7.30235 - 10.0508i) q^{17} +(-13.2600 + 29.4368i) q^{18} +(-3.26497 + 10.0485i) q^{19} +(-10.8759 + 14.9695i) q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(11.0050 - 51.2256i) q^{24} +(6.38026 - 19.6364i) q^{25} +(-5.61158 + 1.82331i) q^{26} +(-8.17551 - 25.7325i) q^{27} +(-63.5904 + 46.2012i) q^{28} +(-11.0405 + 3.58727i) q^{29} +(-2.29838 - 22.3355i) q^{30} +(18.9215 + 13.7473i) q^{31} +27.6317i q^{32} -44.5665 q^{34} +(-10.8692 + 14.9601i) q^{35} +(39.6070 + 69.2966i) q^{36} +(2.23911 + 6.89128i) q^{37} +(22.2782 + 30.6633i) q^{38} +(2.47651 - 4.26795i) q^{39} +(11.2601 + 34.6550i) q^{40} +(36.9741 + 12.0136i) q^{41} +(20.0342 - 93.2546i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +(-59.0236 - 42.8832i) q^{46} +(-43.0910 - 14.0011i) q^{47} +(-54.4225 - 60.7077i) q^{48} +(-23.9091 + 17.3709i) q^{49} +(-43.5351 - 59.9209i) q^{50} +(27.7516 - 24.8784i) q^{51} +(-4.50764 + 13.8731i) q^{52} +(-23.6972 + 32.6164i) q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(-30.9899 - 6.65768i) q^{57} +(-12.8685 + 39.6053i) q^{58} +(107.642 - 34.9750i) q^{59} +(-48.0123 - 27.8595i) q^{60} +(62.7118 - 45.5628i) q^{61} +(79.7937 - 25.9266i) q^{62} +(39.5823 + 69.2535i) q^{63} +(-7.75446 - 5.63395i) q^{64} +3.43171i q^{65} +62.9082 q^{67} +(-64.7612 + 89.1361i) q^{68} +(60.6928 - 6.24546i) q^{69} +(20.4987 + 63.0884i) q^{70} +(-6.00278 - 8.26212i) q^{71} +(156.249 + 17.1109i) q^{72} +(23.0595 + 70.9699i) q^{73} +(24.7209 + 8.03232i) q^{74} +(60.5591 + 13.0102i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} +(69.8281 + 50.7331i) q^{79} +(53.9264 + 17.5218i) q^{80} +(74.2814 - 32.2998i) q^{81} +(112.827 - 81.9736i) q^{82} +(-6.94074 - 9.55311i) q^{83} +(-157.403 - 175.581i) q^{84} +(-8.00981 + 24.6517i) q^{85} +(33.4086 - 45.9830i) q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(65.9486 - 13.7178i) q^{90} +(-4.50483 + 13.8645i) q^{91} +(-171.539 + 55.7363i) q^{92} +(-35.2146 + 60.6879i) q^{93} +(-131.493 + 95.5353i) q^{94} +(20.9652 - 6.81201i) q^{95} +(-82.4596 + 8.48532i) q^{96} +(62.4301 + 45.3581i) q^{97} +106.016i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	2.10855	−	2.90217i	1.05427	−	1.45108i	0.169229	−	0.985577i	$-0.445872\pi$
$2$	2.10855	−	2.90217i	1.05427	−	1.45108i	0.885045	−	0.465506i	$-0.154128\pi$
$3$	0.307087	+	2.98424i	0.102362	+	0.994747i
$3$	0.307087	+	2.98424i	0.102362	+	0.994747i
$4$	−2.74053	−	8.43448i	−0.685132	−	2.10862i
$5$	−1.22635	−	1.68793i	−0.245270	−	0.337586i	0.668578	−	0.743642i	$-0.266903\pi$
$5$	−1.22635	−	1.68793i	−0.245270	−	0.337586i	−0.913848	+	0.406057i	$0.866903\pi$
$6$	9.30827	+	5.40120i	1.55138	+	0.900200i
$7$	−2.73883	−	8.42924i	−0.391261	−	1.20418i	−0.931836	−	0.362881i	$-0.881793\pi$
$7$	−2.73883	−	8.42924i	−0.391261	−	1.20418i	0.540575	−	0.841296i	$-0.318207\pi$
$8$	−16.6100	−	5.39692i	−2.07625	−	0.674615i
$9$	−8.81140	+	1.83284i	−0.979044	+	0.203649i
$10$	−7.48447			−0.748447
$11$		0			0
$11$		0			0
$12$	24.3290	−	10.7685i	2.02741	−	0.897377i
$13$	−1.33068	−	0.966792i	−0.102360	−	0.0743686i	0.535428	−	0.844581i	$-0.320150\pi$
$13$	−1.33068	−	0.966792i	−0.102360	−	0.0743686i	−0.637788	+	0.770212i	$0.720150\pi$
$14$	−30.2380	−	9.82492i	−2.15986	−	0.701780i
$15$	4.66059	−	4.17807i	0.310706	−	0.278538i
$16$	−21.9865	+	15.9742i	−1.37416	+	0.998385i
$17$	−7.30235	−	10.0508i	−0.429550	−	0.591225i	0.538300	−	0.842753i	$-0.319067\pi$
$17$	−7.30235	−	10.0508i	−0.429550	−	0.591225i	−0.967850	+	0.251529i	$0.919067\pi$
$18$	−13.2600	+	29.4368i	−0.736668	+	1.63538i
$19$	−3.26497	+	10.0485i	−0.171841	+	0.528871i	−0.999475	−	0.0323966i	$-0.989686\pi$
$19$	−3.26497	+	10.0485i	−0.171841	+	0.528871i	0.827635	+	0.561267i	$0.189686\pi$
$20$	−10.8759	+	14.9695i	−0.543797	+	0.748473i
$21$	24.3138	−	10.7618i	1.15780	−	0.512468i
$22$		0			0
$23$		−	20.3378i		−	0.884251i	−0.896953	−	0.442126i	$-0.854225\pi$
$23$		−	20.3378i		−	0.884251i	0.896953	−	0.442126i	$-0.145775\pi$
$24$	11.0050	−	51.2256i	0.458541	−	2.13440i
$25$	6.38026	−	19.6364i	0.255210	−	0.785457i
$26$	−5.61158	+	1.82331i	−0.215830	+	0.0701275i
$27$	−8.17551	−	25.7325i	−0.302797	−	0.953055i
$28$	−63.5904	+	46.2012i	−2.27109	+	1.65004i
$29$	−11.0405	+	3.58727i	−0.380707	+	0.123699i	−0.493118	−	0.869963i	$-0.664143\pi$
$29$	−11.0405	+	3.58727i	−0.380707	+	0.123699i	0.112411	+	0.993662i	$0.464143\pi$
$30$	−2.29838	−	22.3355i	−0.0766127	−	0.744515i
$31$	18.9215	+	13.7473i	0.610371	+	0.443460i	0.849545	−	0.527516i	$-0.176877\pi$
$31$	18.9215	+	13.7473i	0.610371	+	0.443460i	−0.239174	+	0.970977i	$0.576877\pi$
$32$			27.6317i			0.863489i
$33$		0			0
$34$	−44.5665			−1.31078
$35$	−10.8692	+	14.9601i	−0.310548	+	0.427433i
$36$	39.6070	+	69.2966i	1.10019	+	1.92491i
$37$	2.23911	+	6.89128i	0.0605166	+	0.186251i	0.976745	−	0.214407i	$-0.0687817\pi$
$37$	2.23911	+	6.89128i	0.0605166	+	0.186251i	−0.916228	+	0.400657i	$0.868782\pi$
$38$	22.2782	+	30.6633i	0.586269	+	0.806929i
$39$	2.47651	−	4.26795i	0.0635002	−	0.109434i
$40$	11.2601	+	34.6550i	0.281502	+	0.866375i
$41$	36.9741	+	12.0136i	0.901806	+	0.293015i	0.722982	−	0.690866i	$-0.242771\pi$
$41$	36.9741	+	12.0136i	0.901806	+	0.293015i	0.178824	+	0.983881i	$0.442771\pi$
$42$	20.0342	−	93.2546i	0.477006	−	2.22035i
$43$	15.8444			0.368474			0.184237	−	0.982882i	$-0.441019\pi$
$43$	15.8444			0.368474			0.184237	+	0.982882i	$0.441019\pi$
$44$		0			0
$45$	13.8996	+	12.6253i	0.308879	+	0.280562i
$46$	−59.0236	−	42.8832i	−1.28312	−	0.932243i
$47$	−43.0910	−	14.0011i	−0.916831	−	0.297896i	−0.187665	−	0.982233i	$-0.560092\pi$
$47$	−43.0910	−	14.0011i	−0.916831	−	0.297896i	−0.729166	+	0.684337i	$0.760092\pi$
$48$	−54.4225	−	60.7077i	−1.13380	−	1.26474i
$49$	−23.9091	+	17.3709i	−0.487940	+	0.354509i
$50$	−43.5351	−	59.9209i	−0.870702	−	1.19842i
$51$	27.7516	−	24.8784i	0.544149	−	0.487813i
$52$	−4.50764	+	13.8731i	−0.0866853	+	0.266790i
$53$	−23.6972	+	32.6164i	−0.447116	+	0.615403i	−0.971775	−	0.235910i	$-0.924193\pi$
$53$	−23.6972	+	32.6164i	−0.447116	+	0.615403i	0.524658	+	0.851313i	$0.324193\pi$
$54$	−91.9184	−	30.5315i	−1.70219	−	0.565398i
$55$		0			0
$56$			154.791i			2.76412i
$57$	−30.9899	−	6.65768i	−0.543683	−	0.116801i
$58$	−12.8685	+	39.6053i	−0.221871	+	0.682850i
$59$	107.642	−	34.9750i	1.82444	−	0.592797i	0.824816	−	0.565402i	$-0.191279\pi$
$59$	107.642	−	34.9750i	1.82444	−	0.592797i	0.999625	−	0.0273946i	$-0.00872108\pi$
$60$	−48.0123	−	27.8595i	−0.800206	−	0.464326i
$61$	62.7118	−	45.5628i	1.02806	−	0.746931i	0.0601426	−	0.998190i	$-0.480844\pi$
$61$	62.7118	−	45.5628i	1.02806	−	0.746931i	0.967920	+	0.251259i	$0.0808445\pi$
$62$	79.7937	−	25.9266i	1.28700	−	0.418170i
$63$	39.5823	+	69.2535i	0.628291	+	1.09926i
$64$	−7.75446	−	5.63395i	−0.121163	−	0.0880304i
$65$			3.43171i			0.0527956i
$66$		0			0
$67$	62.9082			0.938929			0.469464	−	0.882951i	$-0.344447\pi$
$67$	62.9082			0.938929			0.469464	+	0.882951i	$0.344447\pi$
$68$	−64.7612	+	89.1361i	−0.952370	+	1.31082i
$69$	60.6928	−	6.24546i	0.879606	−	0.0905139i
$70$	20.4987	+	63.0884i	0.292838	+	0.901262i
$71$	−6.00278	−	8.26212i	−0.0845462	−	0.116368i	0.764649	−	0.644447i	$-0.222912\pi$
$71$	−6.00278	−	8.26212i	−0.0845462	−	0.116368i	−0.849195	+	0.528079i	$0.822912\pi$
$72$	156.249	+	17.1109i	2.17013	+	0.237651i
$73$	23.0595	+	70.9699i	0.315884	+	0.972191i	0.975389	+	0.220491i	$0.0707659\pi$
$73$	23.0595	+	70.9699i	0.315884	+	0.972191i	−0.659505	+	0.751700i	$0.729234\pi$
$74$	24.7209	+	8.03232i	0.334067	+	0.108545i
$75$	60.5591	+	13.0102i	0.807455	+	0.173469i
$76$	93.7020			1.23292
$77$		0			0
$78$	−7.16445	−	16.1864i	−0.0918519	−	0.207518i
$79$	69.8281	+	50.7331i	0.883900	+	0.642191i	0.934280	−	0.356539i	$-0.116043\pi$
$79$	69.8281	+	50.7331i	0.883900	+	0.642191i	−0.0503802	+	0.998730i	$0.516043\pi$
$80$	53.9264	+	17.5218i	0.674081	+	0.219022i
$81$	74.2814	−	32.2998i	0.917054	−	0.398763i
$82$	112.827	−	81.9736i	1.37594	−	0.999678i
$83$	−6.94074	−	9.55311i	−0.0836234	−	0.115098i	0.765156	−	0.643845i	$-0.222662\pi$
$83$	−6.94074	−	9.55311i	−0.0836234	−	0.115098i	−0.848779	+	0.528747i	$0.822662\pi$
$84$	−157.403	−	175.581i	−1.87385	−	2.09026i
$85$	−8.00981	+	24.6517i	−0.0942331	+	0.290020i
$86$	33.4086	−	45.9830i	0.388472	−	0.534686i
$87$	−14.0957	−	31.8459i	−0.162019	−	0.366045i
$88$		0			0
$89$		−	74.5782i		−	0.837957i	−0.907996	−	0.418979i	$-0.862388\pi$
$89$		−	74.5782i		−	0.837957i	0.907996	−	0.418979i	$-0.137612\pi$
$90$	65.9486	−	13.7178i	0.732762	−	0.152421i
$91$	−4.50483	+	13.8645i	−0.0495037	+	0.152357i
$92$	−171.539	+	55.7363i	−1.86455	+	0.605829i
$93$	−35.2146	+	60.6879i	−0.378652	+	0.652558i
$94$	−131.493	+	95.5353i	−1.39886	+	1.01633i
$95$	20.9652	−	6.81201i	0.220687	−	0.0717054i
$96$	−82.4596	+	8.48532i	−0.858954	+	0.0883887i
$97$	62.4301	+	45.3581i	0.643609	+	0.467609i	0.861088	−	0.508456i	$-0.169783\pi$
$97$	62.4301	+	45.3581i	0.643609	+	0.467609i	−0.217479	+	0.976065i	$0.569783\pi$
$98$			106.016i			1.08179i
$99$		0			0
$100$	−183.108			−1.83108
$101$	7.52095	−	10.3517i	0.0744649	−	0.102492i	−0.770160	−	0.637851i	$-0.779824\pi$
$101$	7.52095	−	10.3517i	0.0744649	−	0.102492i	0.844625	+	0.535359i	$0.179824\pi$
$102$	−13.6858	−	132.997i	−0.134174	−	1.30389i
$103$	21.8055	+	67.1104i	0.211704	+	0.651558i	0.999371	+	0.0354567i	$0.0112886\pi$
$103$	21.8055	+	67.1104i	0.211704	+	0.651558i	−0.787667	+	0.616101i	$0.788711\pi$
$104$	16.8848	+	23.2400i	0.162354	+	0.223461i
$105$	−47.9825	−	27.8422i	−0.456976	−	0.265164i
$106$	44.6915	+	137.546i	0.421618	+	1.29761i
$107$	−175.204	−	56.9272i	−1.63742	−	0.532029i	−0.661459	−	0.749981i	$-0.730062\pi$
$107$	−175.204	−	56.9272i	−1.63742	−	0.532029i	−0.975959	+	0.217952i	$0.930062\pi$
$108$	−194.635	+	139.477i	−1.80218	+	1.29145i
$109$	58.5394			0.537058			0.268529	−	0.963272i	$-0.413462\pi$
$109$	58.5394			0.537058			0.268529	+	0.963272i	$0.413462\pi$
$110$		0			0
$111$	−19.8777	+	8.79828i	−0.179078	+	0.0792638i
$112$	194.867	+	141.579i	1.73989	+	1.26410i
$113$	−144.558	−	46.9698i	−1.27927	−	0.415662i	−0.410950	−	0.911658i	$-0.634803\pi$
$113$	−144.558	−	46.9698i	−1.27927	−	0.415662i	−0.868325	+	0.495996i	$0.834803\pi$
$114$	−84.6654	+	75.8998i	−0.742679	+	0.665788i
$115$	−34.3287	+	24.9413i	−0.298510	+	0.216881i
$116$	60.5136	+	83.2899i	0.521669	+	0.718016i
$117$	13.4971	+	6.07987i	0.115360	+	0.0519647i
$118$	125.465	−	386.141i	1.06326	−	3.27238i
$119$	−64.7209	+	89.0807i	−0.543873	+	0.748577i
$120$	−99.9611	+	44.2449i	−0.833009	+	0.368708i
$121$		0			0
$122$		−	278.071i		−	2.27927i
$123$	−24.4972	+	114.029i	−0.199165	+	0.927063i
$124$	64.0962	−	197.268i	0.516905	−	1.59087i
$125$	−90.5763	+	29.4300i	−0.724610	+	0.235440i
$126$	284.446	+	31.1498i	2.25751	+	0.247221i
$127$	−11.5481	+	8.39020i	−0.0909301	+	0.0660646i	−0.632321	−	0.774706i	$-0.717898\pi$
$127$	−11.5481	+	8.39020i	−0.0909301	+	0.0660646i	0.541391	+	0.840771i	$0.317898\pi$
$128$	−137.818	+	44.7799i	−1.07671	+	0.349843i
$129$	4.86560	+	47.2834i	0.0377178	+	0.366538i
$130$	9.95940	+	7.23592i	0.0766107	+	0.0556610i
$131$		−	153.686i		−	1.17318i	−0.809885	−	0.586589i	$-0.800471\pi$
$131$		−	153.686i		−	1.17318i	0.809885	−	0.586589i	$-0.199529\pi$
$132$		0			0
$133$	93.6438			0.704088
$134$	132.645	−	182.570i	0.989888	−	1.36246i
$135$	−33.4085	+	45.3567i	−0.247471	+	0.335976i
$136$	67.0486	+	206.354i	0.493004	+	1.51731i
$137$	−47.3996	−	65.2400i	−0.345983	−	0.476205i	0.600194	−	0.799854i	$-0.295090\pi$
$137$	−47.3996	−	65.2400i	−0.345983	−	0.476205i	−0.946177	+	0.323650i	$0.895090\pi$
$138$	109.848	−	189.310i	0.796003	−	1.37181i
$139$	−65.4935	−	201.568i	−0.471176	−	1.45013i	−0.851046	−	0.525091i	$-0.824031\pi$
$139$	−65.4935	−	201.568i	−0.471176	−	1.45013i	0.379870	−	0.925040i	$-0.375969\pi$
$140$	155.968	+	50.6772i	1.11406	+	0.361980i
$141$	28.5501	−	132.894i	0.202483	−	0.942508i
$142$	−36.6352			−0.257994
$143$		0			0
$144$	164.454	−	181.052i	1.14204	−	1.25731i
$145$	19.5946	+	14.2363i	0.135135	+	0.0981814i
$146$	254.589	+	82.7209i	1.74376	+	0.566581i
$147$	−59.1813	−	66.0160i	−0.402594	−	0.449089i
$148$	51.9881	−	37.7715i	0.351271	−	0.255213i
$149$	133.033	+	183.104i	0.892840	+	1.22889i	0.972696	+	0.232083i	$0.0745540\pi$
$149$	133.033	+	183.104i	0.892840	+	1.22889i	−0.0798559	+	0.996806i	$0.525446\pi$
$150$	165.449	−	148.320i	1.10300	−	0.988801i
$151$	−84.2779	+	259.381i	−0.558132	+	1.71775i	0.129395	+	0.991593i	$0.458696\pi$
$151$	−84.2779	+	259.381i	−0.558132	+	1.71775i	−0.687527	+	0.726159i	$0.741304\pi$
$152$	108.462	−	149.286i	0.713568	−	0.982142i
$153$	82.7654	+	75.1777i	0.540951	+	0.491357i
$154$		0			0
$155$		−	48.7971i		−	0.314820i
$156$	−42.7849	−	9.19164i	−0.274262	−	0.0589208i
$157$	1.87243	−	5.76274i	0.0119263	−	0.0367054i	−0.944916	−	0.327312i	$-0.893857\pi$
$157$	1.87243	−	5.76274i	0.0119263	−	0.0367054i	0.956843	+	0.290607i	$0.0938571\pi$
$158$	294.472	−	95.6797i	1.86375	−	0.605568i
$159$	−104.612	−	60.7020i	−0.657938	−	0.381774i
$160$	46.6403	−	33.8861i	0.291502	−	0.211788i
$161$	−171.432	+	55.7016i	−1.06479	+	0.345973i
$162$	62.8864	−	283.683i	0.388188	−	1.75113i
$163$	−131.002	−	95.1782i	−0.803691	−	0.583915i	0.108304	−	0.994118i	$-0.465458\pi$
$163$	−131.002	−	95.1782i	−0.803691	−	0.583915i	−0.911994	+	0.410202i	$0.865458\pi$
$164$		−	344.781i		−	2.10232i
$165$		0			0
$166$	−42.3596			−0.255178
$167$	93.5806	−	128.803i	0.560363	−	0.771274i	−0.431010	−	0.902347i	$-0.641842\pi$
$167$	93.5806	−	128.803i	0.560363	−	0.771274i	0.991373	+	0.131074i	$0.0418425\pi$
$168$	−461.933	+	47.5342i	−2.74960	+	0.282942i
$169$	−51.3879	−	158.156i	−0.304070	−	0.935832i
$170$	54.6542	+	75.2250i	0.321495	+	0.442500i
$171$	10.3515	−	94.5259i	0.0605354	−	0.552783i
$172$	−43.4220	−	133.639i	−0.252453	−	0.776972i
$173$	−36.5394	−	11.8724i	−0.211210	−	0.0686264i	0.201501	−	0.979488i	$-0.435418\pi$
$173$	−36.5394	−	11.8724i	−0.211210	−	0.0686264i	−0.412711	+	0.910862i	$0.635418\pi$
$174$	−122.144	−	26.2406i	−0.701974	−	0.150808i
$175$	−182.995			−1.04568
$176$		0			0
$177$	137.429	+	310.489i	0.776437	+	1.75418i
$178$	−216.438	−	157.252i	−1.21595	−	0.883436i
$179$	129.490	+	42.0738i	0.723407	+	0.235049i	0.647500	−	0.762066i	$-0.275815\pi$
$179$	129.490	+	42.0738i	0.723407	+	0.235049i	0.0759072	+	0.997115i	$0.475815\pi$
$180$	68.3956	−	151.836i	0.379976	−	0.843532i
$181$	105.447	−	76.6119i	0.582581	−	0.423270i	−0.257072	−	0.966392i	$-0.582758\pi$
$181$	105.447	−	76.6119i	0.582581	−	0.423270i	0.839654	+	0.543122i	$0.182758\pi$
$182$	30.7383	+	42.3076i	0.168892	+	0.232460i
$183$	155.228	+	173.155i	0.848242	+	0.946205i
$184$	−109.761	+	337.811i	−0.596529	+	1.83593i
$185$	8.88605	−	12.2306i	0.0480327	−	0.0661114i
$186$	101.875	+	230.162i	0.547713	+	1.23743i
$187$		0			0
$188$			401.821i			2.13735i
$189$	−194.514	+	139.390i	−1.02917	+	0.737514i
$190$	24.4366	−	75.2080i	0.128613	−	0.395832i
$191$	−300.134	+	97.5195i	−1.57138	+	0.510574i	−0.959819	−	0.280621i	$-0.909460\pi$
$191$	−300.134	+	97.5195i	−1.57138	+	0.510574i	−0.611565	+	0.791194i	$0.709460\pi$
$192$	14.4318	−	24.8713i	0.0751654	−	0.129538i
$193$	118.448	−	86.0576i	0.613721	−	0.445894i	−0.237002	−	0.971509i	$-0.576165\pi$
$193$	118.448	−	86.0576i	0.613721	−	0.445894i	0.850723	+	0.525615i	$0.176165\pi$
$194$	263.273	−	85.5427i	1.35708	−	0.440942i
$195$	−10.2411	+	1.05383i	−0.0525182	+	0.00540427i
$196$	212.038	+	154.055i	1.08183	+	0.785995i
$197$			229.459i			1.16476i	0.812915	+	0.582382i	$0.197879\pi$
$197$			229.459i			1.16476i	−0.812915	+	0.582382i	$0.802121\pi$
$198$		0			0
$199$	−389.358			−1.95657			−0.978287	−	0.207253i	$-0.933548\pi$
$199$	−389.358			−1.95657			−0.978287	+	0.207253i	$0.933548\pi$
$200$	−211.952	+	291.727i	−1.05976	+	1.45864i
$201$	19.3183	+	187.733i	0.0961109	+	0.933997i
$202$	−14.1841	−	43.6541i	−0.0702182	−	0.216109i
$203$	60.4760	+	83.2381i	0.297911	+	0.410040i
$204$	−285.891	−	165.890i	−1.40143	−	0.813188i
$205$	−25.0651	−	77.1425i	−0.122269	−	0.376305i
$206$	240.744	+	78.2223i	1.16866	+	0.379720i
$207$	37.2759	+	179.204i	0.180077	+	0.865721i
$208$	44.7006			0.214907
$209$		0			0
$210$	−181.976	+	80.5465i	−0.866553	+	0.383555i
$211$	165.031	+	119.902i	0.782137	+	0.568256i	0.905620	−	0.424091i	$-0.139406\pi$
$211$	165.031	+	119.902i	0.782137	+	0.568256i	−0.123483	+	0.992347i	$0.539406\pi$
$212$	340.045	+	110.487i	1.60399	+	0.521167i
$213$	22.8128	−	20.4509i	0.107102	−	0.0960138i
$214$	−534.637	+	388.437i	−2.49831	+	1.81513i
$215$	−19.4308	−	26.7442i	−0.0903757	−	0.124391i
$216$	−3.08093	+	471.539i	−0.0142636	+	2.18305i
$217$	64.0564	−	197.145i	0.295191	−	0.908503i
$218$	123.433	−	169.891i	0.566207	−	0.779316i
$219$	−204.710	+	90.6091i	−0.934750	+	0.413740i
$220$		0			0
$221$			20.4342i			0.0924626i
$222$	−16.3789	+	76.2398i	−0.0737788	+	0.343423i
$223$	−5.10490	+	15.7113i	−0.0228919	+	0.0704542i	−0.961850	−	0.273578i	$-0.911793\pi$
$223$	−5.10490	+	15.7113i	−0.0228919	+	0.0704542i	0.938958	+	0.344032i	$0.111793\pi$
$224$	232.914	−	75.6783i	1.03979	−	0.337850i
$225$	−20.2285	+	184.718i	−0.0899046	+	0.820970i
$226$	−441.122	+	320.494i	−1.95187	+	1.41811i
$227$	−107.335	+	34.8751i	−0.472840	+	0.153635i	−0.535737	−	0.844385i	$-0.679966\pi$
$227$	−107.335	+	34.8751i	−0.472840	+	0.153635i	0.0628969	+	0.998020i	$0.479966\pi$
$228$	28.7747	+	279.629i	0.126205	+	1.22645i
$229$	298.218	+	216.668i	1.30226	+	0.946150i	0.999975	−	0.00706607i	$-0.00224922\pi$
$229$	298.218	+	216.668i	1.30226	+	0.946150i	0.302289	+	0.953216i	$0.402249\pi$
$230$			152.217i			0.661815i
$231$		0			0
$232$	202.743			0.873892
$233$	102.592	−	141.206i	0.440310	−	0.606034i	−0.529971	−	0.848016i	$-0.677797\pi$
$233$	102.592	−	141.206i	0.440310	−	0.606034i	0.970281	+	0.241981i	$0.0777972\pi$
$234$	46.1040	−	26.3511i	0.197026	−	0.112611i
$235$	29.2119	+	89.9049i	0.124306	+	0.382574i
$236$	−589.992	−	812.054i	−2.49997	−	3.44091i
$237$	−129.957	+	223.963i	−0.548340	+	0.944993i
$238$	122.060	+	375.662i	0.512856	+	1.57841i
$239$	−328.450	−	106.720i	−1.37427	−	0.446527i	−0.473488	−	0.880800i	$-0.657005\pi$
$239$	−328.450	−	106.720i	−1.37427	−	0.446527i	−0.900781	+	0.434273i	$0.857005\pi$
$240$	−35.7291	+	166.310i	−0.148871	+	0.692959i
$241$	261.447			1.08484			0.542421	−	0.840107i	$-0.317508\pi$
$241$	261.447			1.08484			0.542421	+	0.840107i	$0.317508\pi$
$242$		0			0
$243$	119.201	+	211.755i	0.490540	+	0.871419i
$244$	−556.162	−	404.076i	−2.27935	−	1.65605i
$245$	58.6418	+	19.0539i	0.239354	+	0.0777710i
$246$	279.277	+	311.530i	1.13527	+	1.26638i
$247$	14.0595	−	10.2148i	0.0569209	−	0.0413555i
$248$	−240.093	−	330.460i	−0.968118	−	1.33250i
$249$	26.3774	−	23.6465i	0.105933	−	0.0949658i
$250$	−105.574	+	324.922i	−0.422294	+	1.29969i
$251$	116.584	−	160.465i	0.464480	−	0.639302i	−0.510950	−	0.859610i	$-0.670706\pi$
$251$	116.584	−	160.465i	0.464480	−	0.639302i	0.975430	+	0.220309i	$0.0707064\pi$
$252$	475.641	−	523.648i	1.88746	−	2.07797i
$253$		0			0
$254$			51.2057i			0.201597i
$255$	−76.0263	−	16.3330i	−0.298142	−	0.0640510i
$256$	−148.790	+	457.929i	−0.581211	+	1.78878i
$257$	−1.77390	+	0.576376i	−0.00690234	+	0.00224271i	−0.312466	−	0.949929i	$-0.601155\pi$
$257$	−1.77390	+	0.576376i	−0.00690234	+	0.00224271i	0.305564	+	0.952172i	$0.401155\pi$
$258$	147.484	+	85.5786i	0.571642	+	0.331700i
$259$	51.9557	−	37.7481i	0.200601	−	0.145745i
$260$	28.9447	−	9.40471i	0.111326	−	0.0361719i
$261$	90.7073	−	51.8444i	0.347537	−	0.198637i
$262$	−446.023	−	324.055i	−1.70238	−	1.23685i
$263$		−	27.0901i		−	0.103004i	−0.998673	−	0.0515020i	$-0.983599\pi$
$263$		−	27.0901i		−	0.103004i	0.998673	−	0.0515020i	$-0.0164009\pi$
$264$		0			0
$265$	84.1151			0.317416
$266$	197.452	−	271.770i	0.742302	−	1.02169i
$267$	222.559	−	22.9020i	0.833556	−	0.0857752i
$268$	−172.402	−	530.599i	−0.643291	−	1.97985i
$269$	83.9639	+	115.566i	0.312133	+	0.429615i	0.936045	−	0.351880i	$-0.114458\pi$
$269$	83.9639	+	115.566i	0.312133	+	0.429615i	−0.623912	+	0.781495i	$0.714458\pi$
$270$	61.1893	+	192.594i	0.226627	+	0.713311i
$271$	32.5479	+	100.172i	0.120103	+	0.369639i	0.992977	−	0.118306i	$-0.0377465\pi$
$271$	32.5479	+	100.172i	0.120103	+	0.369639i	−0.872874	+	0.487945i	$0.837746\pi$
$272$	321.107	+	104.334i	1.18054	+	0.383580i
$273$	−42.7583	−	9.18592i	−0.156624	−	0.0336481i
$274$	−289.282			−1.05577
$275$		0			0
$276$	−219.008	−	494.797i	−0.793507	−	1.79274i
$277$	198.144	+	143.960i	0.715322	+	0.519712i	0.884886	−	0.465807i	$-0.154236\pi$
$277$	198.144	+	143.960i	0.715322	+	0.519712i	−0.169564	+	0.985519i	$0.554236\pi$
$278$	−723.081	−	234.943i	−2.60101	−	0.845119i
$279$	−191.921	−	86.4525i	−0.687890	−	0.309866i
$280$	261.276	−	189.828i	0.933128	−	0.677957i
$281$	38.2716	+	52.6763i	0.136198	+	0.187460i	0.871668	−	0.490097i	$-0.163039\pi$
$281$	38.2716	+	52.6763i	0.136198	+	0.187460i	−0.735470	+	0.677557i	$0.763039\pi$
$282$	−325.480	−	363.070i	−1.15419	−	1.28748i
$283$	48.6936	−	149.864i	0.172062	−	0.529553i	−0.827425	−	0.561576i	$-0.810195\pi$
$283$	48.6936	−	149.864i	0.172062	−	0.529553i	0.999487	+	0.0320232i	$0.0101950\pi$
$284$	−53.2359	+	73.2729i	−0.187450	+	0.258003i
$285$	26.7668	+	60.4734i	0.0939187	+	0.212187i
$286$		0			0
$287$		−	344.566i		−	1.20058i
$288$	−50.6445	−	243.473i	−0.175849	−	0.845394i
$289$	41.6112	−	128.066i	0.143984	−	0.443136i
$290$	82.6322	−	26.8488i	0.284939	−	0.0925822i
$291$	−116.188	+	200.235i	−0.399272	+	0.688094i
$292$	535.399	−	388.991i	1.83356	−	1.33216i
$293$	175.003	−	56.8620i	0.597280	−	0.194068i	0.00525314	−	0.999986i	$-0.498328\pi$
$293$	175.003	−	56.8620i	0.597280	−	0.194068i	0.592027	+	0.805918i	$0.298328\pi$
$294$	−316.376	+	32.5560i	−1.07611	+	0.110735i
$295$	−191.042	−	138.800i	−0.647601	−	0.470509i
$296$		−	126.549i		−	0.427529i
$297$		0			0
$298$	811.906			2.72452
$299$	−19.6624	+	27.0630i	−0.0657605	+	0.0905116i
$300$	−56.2302	−	546.440i	−0.187434	−	1.82147i
$301$	−43.3950	−	133.556i	−0.144169	−	0.443708i
$302$	575.062	+	791.505i	1.90418	+	2.62088i
$303$	33.2016	+	19.2655i	0.109576	+	0.0635824i
$304$	−88.7316	−	273.088i	−0.291880	−	0.898315i
$305$	−153.813	−	49.9770i	−0.504306	−	0.163859i
$306$	392.693	−	81.6833i	1.28331	−	0.266939i
$307$	−386.672			−1.25952			−0.629759	−	0.776790i	$-0.716846\pi$
$307$	−386.672			−1.25952			−0.629759	+	0.776790i	$0.716846\pi$
$308$		0			0
$309$	−193.578	+	85.6816i	−0.626465	+	0.277287i
$310$	−141.617	−	102.891i	−0.456830	−	0.331907i
$311$	−87.7273	−	28.5043i	−0.282081	−	0.0916538i	0.164559	−	0.986367i	$-0.447380\pi$
$311$	−87.7273	−	28.5043i	−0.282081	−	0.0916538i	−0.446641	+	0.894713i	$0.647380\pi$
$312$	−64.1686	+	57.5251i	−0.205668	+	0.184375i
$313$	60.1890	−	43.7299i	0.192297	−	0.139712i	−0.487471	−	0.873139i	$-0.662080\pi$
$313$	60.1890	−	43.7299i	0.192297	−	0.139712i	0.679768	+	0.733427i	$0.262080\pi$
$314$	−12.7763	−	17.5851i	−0.0406889	−	0.0560035i
$315$	68.3531	−	151.741i	0.216994	−	0.481718i
$316$	236.541	−	728.000i	0.748549	−	2.30380i
$317$	−307.870	+	423.746i	−0.971198	+	1.33674i	−0.0297582	+	0.999557i	$0.509474\pi$
$317$	−307.870	+	423.746i	−0.971198	+	1.33674i	−0.941440	+	0.337182i	$0.890526\pi$
$318$	−396.747	+	175.609i	−1.24763	+	0.552229i
$319$		0			0
$320$			19.9982i			0.0624943i
$321$	116.082	−	540.332i	0.361625	−	1.68328i
$322$	−199.817	+	614.974i	−0.620550	+	1.90986i
$323$	124.838	−	40.5623i	0.386495	−	0.125580i
$324$	−476.002	−	538.007i	−1.46914	−	1.66051i
$325$	−27.4744	+	19.9613i	−0.0845366	+	0.0614194i
$326$	−552.446	+	179.501i	−1.69462	+	0.550615i
$327$	17.9767	+	174.696i	0.0549745	+	0.534237i
$328$	−549.303	−	399.092i	−1.67470	−	1.21674i
$329$			401.571i			1.22058i
$330$		0			0
$331$	251.706			0.760441			0.380221	−	0.924896i	$-0.375848\pi$
$331$	251.706			0.760441			0.380221	+	0.924896i	$0.375848\pi$
$332$	−61.5542	+	84.7221i	−0.185404	+	0.255187i
$333$	−32.3604	−	56.6179i	−0.0971782	−	0.170024i
$334$	−176.488	−	543.173i	−0.528406	−	1.62627i
$335$	−77.1476	−	106.185i	−0.230291	−	0.316969i
$336$	−362.666	+	625.008i	−1.07936	+	1.86014i
$337$	15.3428	+	47.2202i	0.0455275	+	0.140119i	0.971236	−	0.238118i	$-0.0765304\pi$
$337$	15.3428	+	47.2202i	0.0455275	+	0.140119i	−0.925709	+	0.378237i	$0.876530\pi$
$338$	−567.348	−	184.342i	−1.67854	−	0.545392i
$339$	95.7772	−	445.820i	0.282529	−	1.31510i
$340$	229.875			0.676104
$341$		0			0
$342$	−252.503	−	229.354i	−0.738313	−	0.670626i
$343$	−139.440	−	101.309i	−0.406531	−	0.295362i
$344$	−263.175	−	85.5108i	−0.765044	−	0.248578i
$345$	−84.9727	−	94.7860i	−0.246298	−	0.274742i
$346$	−111.501	+	81.0099i	−0.322256	+	0.234133i
$347$	270.251	+	371.969i	0.778822	+	1.07196i	0.995411	+	0.0956933i	$0.0305068\pi$
$347$	270.251	+	371.969i	0.778822	+	1.07196i	−0.216589	+	0.976263i	$0.569493\pi$
$348$	−229.974	+	206.164i	−0.660845	+	0.592427i
$349$	121.675	−	374.478i	0.348640	−	1.07300i	−0.610967	−	0.791656i	$-0.709219\pi$
$349$	121.675	−	374.478i	0.348640	−	1.07300i	0.959606	−	0.281346i	$-0.0907808\pi$
$350$	−385.853	+	531.081i	−1.10244	+	1.51737i
$351$	−13.9990	+	42.1456i	−0.0398833	+	0.120073i
$352$		0			0
$353$			16.9433i			0.0479980i	0.999712	+	0.0239990i	$0.00763985\pi$
$353$			16.9433i			0.0479980i	−0.999712	+	0.0239990i	$0.992360\pi$
$354$	1190.87	+	255.839i	3.36403	+	0.722708i
$355$	−6.58434	+	20.2645i	−0.0185474	+	0.0570832i
$356$	−629.029	+	204.384i	−1.76693	+	0.574112i
$357$	−285.713	−	165.787i	−0.800317	−	0.464390i
$358$	395.141	−	287.086i	1.10374	−	0.801917i
$359$	72.1739	−	23.4507i	0.201041	−	0.0653223i	−0.206765	−	0.978391i	$-0.566294\pi$
$359$	72.1739	−	23.4507i	0.201041	−	0.0653223i	0.407807	+	0.913068i	$0.366294\pi$
$360$	−162.734	−	284.721i	−0.452040	−	0.790892i
$361$	201.742	+	146.574i	0.558842	+	0.406022i
$362$		−	467.565i		−	1.29162i
$363$		0			0
$364$	129.285			0.355179
$365$	91.5131	−	125.957i	0.250721	−	0.345087i
$366$	829.832	−	85.3921i	2.26730	−	0.233312i
$367$	191.376	+	588.996i	0.521462	+	1.60489i	0.771209	+	0.636583i	$0.219653\pi$
$367$	191.376	+	588.996i	0.521462	+	1.60489i	−0.249747	+	0.968311i	$0.580347\pi$
$368$	324.879	+	447.157i	0.882823	+	1.21510i
$369$	−347.812	−	38.0890i	−0.942580	−	0.103222i
$370$	−16.7586	−	51.5776i	−0.0452935	−	0.139399i
$371$	339.833	+	110.419i	0.915993	+	0.297624i
$372$	608.378	+	130.700i	1.63542	+	0.351345i
$373$	365.674			0.980359			0.490179	−	0.871622i	$-0.336931\pi$
$373$	365.674			0.980359			0.490179	+	0.871622i	$0.336931\pi$
$374$		0			0
$375$	−115.641	−	261.264i	−0.308376	−	0.696704i
$376$	640.180	+	465.118i	1.70261	+	1.23702i
$377$	18.1595	+	5.90037i	0.0481683	+	0.0156508i
$378$	−5.60874	+	858.423i	−0.0148379	+	2.27096i
$379$	331.603	−	240.924i	0.874943	−	0.635683i	−0.0569658	−	0.998376i	$-0.518143\pi$
$379$	331.603	−	240.924i	0.874943	−	0.635683i	0.931909	+	0.362693i	$0.118143\pi$
$380$	−114.912	−	158.162i	−0.302399	−	0.416217i
$381$	−28.5847	−	31.8859i	−0.0750254	−	0.0836900i
$382$	−349.829	+	1076.66i	−0.915784	+	2.81849i
$383$	−31.1300	+	42.8468i	−0.0812795	+	0.111872i	−0.847721	−	0.530443i	$-0.822026\pi$
$383$	−31.1300	+	42.8468i	−0.0812795	+	0.111872i	0.766441	+	0.642314i	$0.222026\pi$
$384$	−175.956	−	397.532i	−0.458219	−	1.03524i
$385$		0			0
$386$		−	525.213i		−	1.36065i
$387$	−139.611	+	29.0402i	−0.360752	+	0.0750394i
$388$	211.481	−	650.871i	0.545053	−	1.67750i
$389$	86.2286	−	28.0174i	0.221667	−	0.0720241i	−0.196078	−	0.980588i	$-0.562821\pi$
$389$	86.2286	−	28.0174i	0.221667	−	0.0720241i	0.417745	+	0.908564i	$0.362821\pi$
$390$	−18.5353	+	31.9433i	−0.0475265	+	0.0819059i
$391$	−204.411	+	148.514i	−0.522791	+	0.379830i
$392$	490.879	−	159.496i	1.25224	−	0.406878i
$393$	458.637	−	47.1950i	1.16701	−	0.120089i
$394$	665.927	+	483.824i	1.69017	+	1.22798i
$395$		−	180.081i		−	0.455902i
$396$		0			0
$397$	−335.768			−0.845763			−0.422882	−	0.906185i	$-0.638981\pi$
$397$	−335.768			−0.845763			−0.422882	+	0.906185i	$0.638981\pi$
$398$	−820.981	+	1129.98i	−2.06277	+	2.83915i
$399$	28.7568	+	279.456i	0.0720721	+	0.700390i
$400$	173.395	+	533.656i	0.433489	+	1.33414i
$401$	−11.1216	−	15.3075i	−0.0277346	−	0.0381734i	0.794925	−	0.606708i	$-0.207510\pi$
$401$	−11.1216	−	15.3075i	−0.0277346	−	0.0381734i	−0.822659	+	0.568535i	$0.807510\pi$
$402$	585.567	+	339.780i	1.45663	+	0.845223i
$403$	−11.8876	−	36.5863i	−0.0294978	−	0.0907849i
$404$	−107.923	−	35.0662i	−0.267135	−	0.0867975i
$405$	−145.615	−	85.7707i	−0.359543	−	0.211780i
$406$	369.087			0.909082
$407$		0			0
$408$	−595.221	+	263.458i	−1.45888	+	0.645730i
$409$	−96.4856	−	70.1009i	−0.235906	−	0.171396i	0.463551	−	0.886070i	$-0.346575\pi$
$409$	−96.4856	−	70.1009i	−0.235906	−	0.171396i	−0.699457	+	0.714674i	$0.746575\pi$
$410$	−276.731	−	89.9154i	−0.674954	−	0.219306i
$411$	180.136	−	161.486i	0.438288	−	0.392911i
$412$	506.283	−	367.836i	1.22884	−	0.892806i
$413$	−589.625	−	811.549i	−1.42766	−	1.96501i
$414$	598.678	+	269.680i	1.44608	+	0.651400i
$415$	−7.61317	+	23.4309i	−0.0183450	+	0.0564601i
$416$	26.7141	−	36.7688i	0.0642165	−	0.0883865i
$417$	581.416	−	257.347i	1.39428	−	0.617140i
$418$		0			0
$419$			412.874i			0.985381i	0.870205	+	0.492690i	$0.163986\pi$
$419$			412.874i			0.985381i	−0.870205	+	0.492690i	$0.836014\pi$
$420$	−103.337	+	481.010i	−0.246041	+	1.14526i
$421$	186.937	−	575.334i	0.444032	−	1.36659i	−0.439511	−	0.898237i	$-0.644848\pi$
$421$	186.937	−	575.334i	0.444032	−	1.36659i	0.883542	−	0.468351i	$-0.155152\pi$
$422$	695.951	−	226.128i	1.64917	−	0.535849i
$423$	405.354	+	44.3904i	0.958284	+	0.104942i
$424$	569.638	−	413.866i	1.34349	−	0.976100i
$425$	−243.953	+	79.2651i	−0.574007	+	0.186506i
$426$	−11.2502	−	109.328i	−0.0264089	−	0.256639i
$427$	−555.816	−	403.824i	−1.30168	−	0.945724i
$428$			1633.76i			3.81721i
$429$		0			0
$430$	−118.587			−0.275783
$431$	−260.636	+	358.735i	−0.604724	+	0.832331i	−0.996130	−	0.0878868i	$-0.971989\pi$
$431$	−260.636	+	358.735i	−0.604724	+	0.832331i	0.391407	+	0.920218i	$0.371989\pi$
$432$	590.806	+	435.172i	1.36761	+	1.00734i
$433$	67.6685	+	208.262i	0.156278	+	0.480975i	0.998288	−	0.0584870i	$-0.0186276\pi$
$433$	67.6685	+	208.262i	0.156278	+	0.480975i	−0.842010	+	0.539462i	$0.818628\pi$
$434$	−437.082	−	601.592i	−1.00710	−	1.38616i
$435$	−36.4673	+	62.8468i	−0.0838329	+	0.144475i
$436$	−160.429	−	493.749i	−0.367956	−	1.13245i
$437$	204.365	+	66.4022i	0.467655	+	0.151950i
$438$	−168.678	+	785.157i	−0.385110	+	1.79260i
$439$	−171.641			−0.390982			−0.195491	−	0.980705i	$-0.562630\pi$
$439$	−171.641			−0.390982			−0.195491	+	0.980705i	$0.562630\pi$
$440$		0			0
$441$	178.834	−	196.884i	0.405519	−	0.446449i
$442$	59.3035	+	43.0865i	0.134171	+	0.0974808i
$443$	−563.538	−	183.105i	−1.27209	−	0.413328i	−0.406305	−	0.913737i	$-0.633183\pi$
$443$	−563.538	−	183.105i	−1.27209	−	0.413328i	−0.865789	+	0.500409i	$0.833183\pi$
$444$	128.684	+	143.546i	0.289829	+	0.323301i
$445$	−125.883	+	91.4591i	−0.282882	+	0.205526i
$446$	34.8328	+	47.9432i	0.0781005	+	0.107496i
$447$	−505.575	+	453.232i	−1.13104	+	1.01394i
$448$	−26.2518	+	80.7946i	−0.0585977	+	0.180345i
$449$	256.349	−	352.835i	0.570934	−	0.785823i	−0.421731	−	0.906721i	$-0.638577\pi$
$449$	256.349	−	352.835i	0.570934	−	0.785823i	0.992665	+	0.120898i	$0.0385773\pi$
$450$	493.430	+	448.194i	1.09651	+	0.995986i
$451$		0			0
$452$			1347.99i			2.98229i
$453$	−799.935	−	171.853i	−1.76586	−	0.379367i
$454$	−125.107	+	385.039i	−0.275566	+	0.848103i
$455$	28.9267	−	9.39886i	0.0635752	−	0.0206568i
$456$	478.812	+	277.834i	1.05003	+	0.609286i
$457$	192.984	−	140.211i	0.422285	−	0.306808i	−0.356272	−	0.934382i	$-0.615952\pi$
$457$	192.984	−	140.211i	0.422285	−	0.306808i	0.778556	+	0.627575i	$0.215952\pi$
$458$	1257.62	−	408.624i	2.74589	−	0.892192i
$459$	−198.932	+	270.078i	−0.433403	+	0.588405i
$460$	304.446	+	221.193i	0.661838	+	0.480854i
$461$		−	711.175i		−	1.54268i	−0.636424	−	0.771339i	$-0.719587\pi$
$461$		−	711.175i		−	1.54268i	0.636424	−	0.771339i	$-0.280413\pi$
$462$		0			0
$463$	−461.487			−0.996732			−0.498366	−	0.866967i	$-0.666066\pi$
$463$	−461.487			−0.996732			−0.498366	+	0.866967i	$0.666066\pi$
$464$	185.439	−	255.234i	0.399652	−	0.550074i
$465$	145.622	−	14.9849i	0.313166	−	0.0322257i
$466$	−193.483	−	595.479i	−0.415199	−	1.27785i
$467$	−28.4397	−	39.1438i	−0.0608986	−	0.0838198i	0.777481	−	0.628906i	$-0.216497\pi$
$467$	−28.4397	−	39.1438i	−0.0608986	−	0.0838198i	−0.838380	+	0.545086i	$0.816497\pi$
$468$	14.2914	−	130.503i	0.0305372	−	0.278853i
$469$	−172.295	−	530.269i	−0.367366	−	1.13064i
$470$	322.514	+	104.791i	0.686199	+	0.222960i
$471$	17.7724	+	3.81812i	0.0377333	+	0.00810640i
$472$	−1976.69			−4.18790
$473$		0			0
$474$	375.960	+	849.393i	0.793164	+	1.79197i
$475$	176.486	+	128.225i	0.371550	+	0.269947i
$476$	928.719	+	301.759i	1.95109	+	0.633948i
$477$	149.025	−	330.829i	0.312420	−	0.693561i
$478$	−1002.27	+	728.193i	−2.09680	+	1.52342i
$479$	−100.761	−	138.685i	−0.210357	−	0.289531i	0.690781	−	0.723064i	$-0.257267\pi$
$479$	−100.761	−	138.685i	−0.210357	−	0.289531i	−0.901138	+	0.433533i	$0.857267\pi$
$480$	115.447	+	128.780i	0.240515	+	0.268291i
$481$	3.68291	−	11.3348i	0.00765677	−	0.0235651i
$482$	551.274	−	758.763i	1.14372	−	1.57420i
$483$	−218.872	−	494.489i	−0.453150	−	1.02379i
$484$		0			0
$485$		−	161.002i		−	0.331964i
$486$	865.889	+	100.553i	1.78166	+	0.206899i
$487$	−153.117	+	471.247i	−0.314409	+	0.967653i	0.661587	+	0.749868i	$0.269883\pi$
$487$	−153.117	+	471.247i	−0.314409	+	0.967653i	−0.975997	+	0.217785i	$0.930117\pi$
$488$	−1287.54	+	418.348i	−2.63841	+	0.857270i
$489$	243.806	−	420.168i	0.498581	−	0.859240i
$490$	178.947	−	130.012i	0.365197	−	0.265331i
$491$	314.085	−	102.052i	0.639684	−	0.207846i	0.0288242	−	0.999584i	$-0.490824\pi$
$491$	314.085	−	102.052i	0.639684	−	0.207846i	0.610860	+	0.791738i	$0.290824\pi$
$492$	1028.91	−	105.878i	2.09128	−	0.215198i
$493$	116.677	+	84.7705i	0.236666	+	0.171948i
$494$		−	62.3413i		−	0.126197i
$495$		0			0
$496$	−635.619			−1.28149
$497$	−53.2028	+	73.2274i	−0.107048	+	0.147339i
$498$	−13.0081	−	126.411i	−0.0261206	−	0.253838i
$499$	33.9303	+	104.427i	0.0679966	+	0.209272i	0.979281	−	0.202505i	$-0.0649083\pi$
$499$	33.9303	+	104.427i	0.0679966	+	0.209272i	−0.911285	+	0.411777i	$0.864908\pi$
$500$	496.454	+	683.310i	0.992908	+	1.36662i
$501$	413.116	+	239.714i	0.824582	+	0.478470i
$502$	−219.872	−	676.695i	−0.437991	−	1.34800i
$503$	543.721	+	176.666i	1.08096	+	0.351224i	0.794745	−	0.606943i	$-0.207604\pi$
$503$	543.721	+	176.666i	1.08096	+	0.351224i	0.286210	+	0.958167i	$0.407604\pi$
$504$	−283.707	−	1363.92i	−0.562911	−	2.70620i
$505$	−26.6963			−0.0528639
$506$		0			0
$507$	456.194	−	201.921i	0.899791	−	0.398267i
$508$	102.415	+	74.4089i	0.201604	+	0.146474i
$509$	514.449	+	167.155i	1.01071	+	0.328398i	0.767136	−	0.641485i	$-0.221681\pi$
$509$	514.449	+	167.155i	1.01071	+	0.328398i	0.243570	+	0.969883i	$0.421681\pi$
$510$	−207.706	+	186.202i	−0.407267	+	0.365102i
$511$	535.067	−	388.749i	1.04710	−	0.760760i
$512$	674.549	+	928.437i	1.31748	+	1.81335i
$513$	285.267	+	1.86387i	0.556076	+	0.00363327i
$514$	−2.06762	+	6.36348i	−0.00402260	+	0.0123803i
$515$	86.5364	−	119.107i	0.168032	−	0.231276i
$516$	385.477	−	170.620i	0.747049	−	0.330660i
$517$		0			0
$518$		−	230.378i		−	0.444745i
$519$	24.2092	−	112.688i	0.0466459	−	0.217126i
$520$	18.5207	−	57.0007i	0.0356167	−	0.109617i
$521$	321.351	−	104.413i	0.616796	−	0.200409i	0.0160786	−	0.999871i	$-0.494882\pi$
$521$	321.351	−	104.413i	0.616796	−	0.200409i	0.600717	+	0.799462i	$0.294882\pi$
$522$	40.7995	−	372.564i	0.0781600	−	0.713724i
$523$	248.719	−	180.705i	0.475562	−	0.345516i	−0.324043	−	0.946042i	$-0.605042\pi$
$523$	248.719	−	180.705i	0.475562	−	0.345516i	0.799605	+	0.600526i	$0.205042\pi$
$524$	−1296.26	+	421.182i	−2.47379	+	0.803782i
$525$	−56.1952	−	546.100i	−0.107038	−	1.04019i
$526$	−78.6199	−	57.1207i	−0.149467	−	0.108594i
$527$		−	290.564i		−	0.551355i
$528$		0			0
$529$	115.375			0.218100
$530$	177.361	−	244.116i	0.334643	−	0.460596i
$531$	−884.372	+	505.469i	−1.66548	+	0.951920i
$532$	−256.634	−	789.837i	−0.482394	−	1.48466i
$533$	−37.5858	−	51.7324i	−0.0705175	−	0.0970590i
$534$	402.812	−	694.194i	0.754329	−	1.29999i
$535$	118.772	+	365.544i	0.222005	+	0.683260i
$536$	−1044.91	−	339.511i	−1.94945	−	0.633415i
$537$	−85.7937	+	399.349i	−0.159765	+	0.743667i
$538$	512.434			0.952480
$539$		0			0
$540$	474.118	+	157.482i	0.877996	+	0.291634i
$541$	−66.9072	−	48.6109i	−0.123673	−	0.0898538i	0.524229	−	0.851577i	$-0.324354\pi$
$541$	−66.9072	−	48.6109i	−0.123673	−	0.0898538i	−0.647902	+	0.761723i	$0.724354\pi$
$542$	359.345	+	116.758i	0.662998	+	0.215421i
$543$	261.010	+	291.153i	0.480681	+	0.536194i
$544$	277.721	−	201.776i	0.510516	−	0.370912i
$545$	−71.7898	−	98.8103i	−0.131724	−	0.181303i
$546$	−116.817	+	104.723i	−0.213950	+	0.191800i
$547$	122.586	−	377.280i	0.224105	−	0.689725i	−0.774276	−	0.632848i	$-0.781886\pi$
$547$	122.586	−	377.280i	0.224105	−	0.689725i	0.998381	−	0.0568769i	$-0.0181142\pi$
$548$	−420.366	+	578.584i	−0.767091	+	1.05581i
$549$	−469.069	+	516.413i	−0.854407	+	0.940642i
$550$		0			0
$551$		−	122.653i		−	0.222601i
$552$	−1041.81	−	223.817i	−1.88735	−	0.405466i
$553$	236.394	−	727.547i	0.427476	−	1.31564i
$554$	835.593	−	271.500i	1.50829	−	0.490073i
$555$	39.2279	+	22.7623i	0.0706808	+	0.0410131i
$556$	−1520.64	+	1104.81i	−2.73496	+	1.98706i
$557$	364.339	−	118.381i	0.654109	−	0.212533i	0.0368842	−	0.999320i	$-0.488257\pi$
$557$	364.339	−	118.381i	0.654109	−	0.212533i	0.617225	+	0.786787i	$0.288257\pi$
$558$	−655.575	+	374.698i	−1.17487	+	0.671503i
$559$	−21.0837	−	15.3182i	−0.0377168	−	0.0274029i
$560$		−	502.548i		−	0.897407i
$561$		0			0
$562$	233.573			0.415610
$563$	85.1328	−	117.175i	0.151213	−	0.208127i	−0.726690	−	0.686966i	$-0.758942\pi$
$563$	85.1328	−	117.175i	0.151213	−	0.208127i	0.877903	+	0.478839i	$0.158942\pi$
$564$	−1199.13	+	123.394i	−2.12612	+	0.218784i
$565$	97.9974	+	301.605i	0.173447	+	0.533814i
$566$	−332.256	−	457.311i	−0.587025	−	0.807971i
$567$	−475.706	−	537.672i	−0.838988	−	0.948275i
$568$	55.1163	+	169.630i	0.0970357	+	0.298645i
$569$	877.968	+	285.269i	1.54300	+	0.501352i	0.952203	−	0.305466i	$-0.0988124\pi$
$569$	877.968	+	285.269i	1.54300	+	0.501352i	0.590800	+	0.806818i	$0.298812\pi$
$570$	231.943	+	49.8292i	0.406918	+	0.0874197i
$571$	−421.725			−0.738573			−0.369287	−	0.929316i	$-0.620398\pi$
$571$	−421.725			−0.738573			−0.369287	+	0.929316i	$0.620398\pi$
$572$		0			0
$573$	−383.189	−	865.726i	−0.668742	−	1.51087i
$574$	−999.989	−	726.534i	−1.74214	−	1.26574i
$575$	−399.361	−	129.760i	−0.694541	−	0.225670i
$576$	78.6538	+	35.4302i	0.136552	+	0.0615108i
$577$	−372.478	+	270.621i	−0.645542	+	0.469014i	−0.861750	−	0.507334i	$-0.830631\pi$
$577$	−372.478	+	270.621i	−0.645542	+	0.469014i	0.216208	+	0.976347i	$0.430631\pi$
$578$	−283.930	−	390.796i	−0.491229	−	0.676118i
$579$	293.190	+	327.051i	0.506374	+	0.564854i
$580$	66.3763	−	204.285i	0.114442	−	0.352216i
$581$	−61.5160	+	84.6694i	−0.105879	+	0.145731i
$582$	336.128	+	759.403i	0.577539	+	1.30482i
$583$		0			0
$584$		−	1303.26i		−	2.23161i
$585$	−6.28978	−	30.2382i	−0.0107518	−	0.0516892i
$586$	203.979	−	627.784i	0.348088	−	1.07130i
$587$	40.3860	−	13.1222i	0.0688007	−	0.0223547i	−0.274414	−	0.961612i	$-0.588484\pi$
$587$	40.3860	−	13.1222i	0.0688007	−	0.0223547i	0.343215	+	0.939257i	$0.388484\pi$
$588$	−394.623	+	680.082i	−0.671128	+	1.15660i
$589$	−199.918	+	145.249i	−0.339420	+	0.246603i
$590$	−805.643	+	261.769i	−1.36550	+	0.443677i
$591$	−684.760	+	70.4637i	−1.15865	+	0.119228i
$592$	−159.313	−	115.748i	−0.269109	−	0.195519i
$593$			106.267i			0.179203i	0.995978	+	0.0896015i	$0.0285593\pi$
$593$			106.267i			0.179203i	−0.995978	+	0.0896015i	$0.971441\pi$
$594$		0			0
$595$	229.732			0.386105
$596$	1179.81	−	1623.87i	1.97955	−	2.72461i
$597$	−119.567	−	1161.94i	−0.200279	−	1.94630i
$598$	37.0822	+	114.127i	0.0620103	+	0.190848i
$599$	427.915	+	588.974i	0.714382	+	0.983263i	0.999692	+	0.0248274i	$0.00790362\pi$
$599$	427.915	+	588.974i	0.714382	+	0.983263i	−0.285309	+	0.958435i	$0.592096\pi$
$600$	−935.673	−	542.931i	−1.55945	−	0.904886i
$601$	36.6474	+	112.789i	0.0609774	+	0.187669i	0.976905	−	0.213675i	$-0.0685432\pi$
$601$	36.6474	+	112.789i	0.0609774	+	0.187669i	−0.915927	+	0.401344i	$0.868543\pi$
$602$	−479.102	−	155.670i	−0.795851	−	0.258588i
$603$	−554.309	+	115.301i	−0.919253	+	0.191212i
$604$	2418.71			4.00448
$605$		0			0
$606$	125.919	−	55.7343i	0.207787	−	0.0919708i
$607$	576.993	+	419.210i	0.950565	+	0.690626i	0.950941	−	0.309374i	$-0.100119\pi$
$607$	576.993	+	419.210i	0.950565	+	0.690626i	−0.000375194		1.00000i	$0.500119\pi$
$608$	−277.658	−	90.2165i	−0.456674	−	0.148382i
$609$	−229.831	+	206.036i	−0.377391	+	0.338319i
$610$	−469.365	+	341.013i	−0.769450	+	0.559038i
$611$	43.8040	+	60.2910i	0.0716923	+	0.0986760i
$612$	407.264	−	904.110i	0.665464	−	1.47730i
$613$	−212.439	+	653.818i	−0.346555	+	1.06659i	0.614190	+	0.789158i	$0.289483\pi$
$613$	−212.439	+	653.818i	−0.346555	+	1.06659i	−0.960746	+	0.277430i	$0.910517\pi$
$614$	−815.316	+	1122.19i	−1.32788	+	1.82767i
$615$	222.515	−	98.4898i	0.361812	−	0.160146i
$616$		0			0
$617$		−	762.156i		−	1.23526i	−0.786468	−	0.617631i	$-0.788093\pi$
$617$		−	762.156i		−	1.23526i	0.786468	−	0.617631i	$-0.211907\pi$
$618$	−159.505	+	742.458i	−0.258099	+	1.20139i
$619$	−163.995	+	504.724i	−0.264935	+	0.815386i	0.726773	+	0.686877i	$0.241019\pi$
$619$	−163.995	+	504.724i	−0.264935	+	0.815386i	−0.991708	+	0.128509i	$0.958981\pi$
$620$	−411.578	+	133.730i	−0.663836	+	0.215693i
$621$	−523.342	+	166.272i	−0.842740	+	0.267748i
$622$	−267.702	+	194.497i	−0.430388	+	0.312695i
$623$	−628.637	+	204.257i	−1.00905	+	0.327860i
$624$	13.7270	+	133.397i	0.0219983	+	0.213778i
$625$	−256.839	−	186.605i	−0.410943	−	0.298568i
$626$		−	266.885i		−	0.426334i
$627$		0			0
$628$	−53.7372			−0.0855688
$629$	52.9123	−	72.8275i	0.0841212	−	0.115783i
$630$	−296.253	−	518.326i	−0.470242	−	0.822739i
$631$	209.034	+	643.341i	0.331274	+	1.01956i	0.968528	+	0.248904i	$0.0800703\pi$
$631$	209.034	+	643.341i	0.331274	+	1.01956i	−0.637254	+	0.770654i	$0.719930\pi$
$632$	−886.043	−	1219.53i	−1.40197	−	1.92964i
$633$	−307.138	+	529.312i	−0.485210	+	0.836196i
$634$	580.624	+	1786.98i	0.915811	+	2.81858i
$635$	28.3241	+	9.20306i	0.0446049	+	0.0144930i
$636$	−225.298	+	1048.71i	−0.354241	+	1.64891i
$637$	48.6093			0.0763097
$638$		0			0
$639$	68.0360	+	61.7987i	0.106473	+	0.0967115i
$640$	244.599	+	177.712i	0.382186	+	0.277674i
$641$	747.420	+	242.852i	1.16602	+	0.378864i	0.827157	−	0.561971i	$-0.189957\pi$
$641$	747.420	+	242.852i	1.16602	+	0.378864i	0.338865	+	0.940835i	$0.389957\pi$
$642$	−1323.37	−	1476.20i	−2.06132	−	2.29938i
$643$	687.427	−	499.445i	1.06909	−	0.776741i	0.0933438	−	0.995634i	$-0.470244\pi$
$643$	687.427	−	499.445i	1.06909	−	0.776741i	0.975749	+	0.218893i	$0.0702444\pi$
$644$	939.629	+	1293.29i	1.45905	+	2.00821i
$645$	73.8441	−	66.1989i	0.114487	−	0.102634i
$646$	145.508	−	447.828i	0.225245	−	0.693233i
$647$	687.343	−	946.046i	1.06235	−	1.46220i	0.184769	−	0.982782i	$-0.440846\pi$
$647$	687.343	−	946.046i	1.06235	−	1.46220i	0.877584	−	0.479422i	$-0.159154\pi$
$648$	−1408.13	+	135.609i	−2.17305	+	0.209274i
$649$		0			0
$650$			121.825i			0.187423i
$651$	608.000	+	130.619i	0.933947	+	0.200644i
$652$	−443.765	+	1365.77i	−0.680622	+	2.09474i
$653$	509.322	−	165.489i	0.779972	−	0.253428i	0.108144	−	0.994135i	$-0.465509\pi$
$653$	509.322	−	165.489i	0.779972	−	0.253428i	0.671828	+	0.740707i	$0.265509\pi$
$654$	544.900	+	316.183i	0.833181	+	0.483460i
$655$	−259.411	+	188.473i	−0.396048	+	0.287746i
$656$	−1004.84	+	326.492i	−1.53177	+	0.497701i
$657$	−333.263	−	583.080i	−0.507250	−	0.887488i
$658$	1165.43	+	846.732i	1.77117	+	1.28683i
$659$		−	138.756i		−	0.210555i	−0.994443	−	0.105278i	$-0.966427\pi$
$659$		−	138.756i		−	0.210555i	0.994443	−	0.105278i	$-0.0335731\pi$
$660$		0			0
$661$	27.1690			0.0411029			0.0205515	−	0.999789i	$-0.493458\pi$
$661$	27.1690			0.0411029			0.0205515	+	0.999789i	$0.493458\pi$
$662$	530.734	−	730.493i	0.801713	−	1.10346i
$663$	−60.9807	+	6.27508i	−0.0919769	+	0.00946468i
$664$	63.7284	+	196.136i	0.0959765	+	0.295385i
$665$	−114.840	−	158.064i	−0.172692	−	0.237690i
$666$	−232.548	−	25.4664i	−0.349171	−	0.0382378i
$667$	72.9572	+	224.539i	0.109381	+	0.336640i
$668$	−1342.84	−	436.317i	−2.01025	−	0.653169i
$669$	−48.4539	−	10.4095i	−0.0724273	−	0.0155598i
$670$	−470.835			−0.702738
$671$		0			0
$672$	297.367	+	671.831i	0.442511	+	0.999749i
$673$	−531.916	−	386.460i	−0.790366	−	0.574234i	0.117706	−	0.993048i	$-0.462446\pi$
$673$	−531.916	−	386.460i	−0.790366	−	0.574234i	−0.908072	+	0.418814i	$0.862446\pi$
$674$	169.392	+	55.0388i	0.251323	+	0.0816599i
$675$	−557.456	−	3.64229i	−0.825861	−	0.00539599i
$676$	−1193.13	+	866.860i	−1.76499	+	1.28234i
$677$	359.292	+	494.523i	0.530712	+	0.730463i	0.987239	−	0.159247i	$-0.0509066\pi$
$677$	359.292	+	494.523i	0.530712	+	0.730463i	−0.456526	+	0.889710i	$0.650907\pi$
$678$	−1091.89	−	1217.99i	−1.61046	−	1.79645i
$679$	211.349	−	650.466i	0.311265	−	0.957976i
$680$	266.086	−	366.236i	0.391303	−	0.538583i
$681$	−137.037	−	309.603i	−0.201229	−	0.454630i
$682$		0			0
$683$			990.520i			1.45025i	0.688618	+	0.725124i	$0.258218\pi$
$683$			990.520i			1.45025i	−0.688618	+	0.725124i	$0.741782\pi$
$684$	−825.646	+	171.741i	−1.20708	+	0.251083i
$685$	−51.9918	+	160.014i	−0.0759005	+	0.233598i
$686$	−588.032	+	191.063i	−0.857189	+	0.278518i
$687$	−555.012	+	956.492i	−0.807878	+	1.39227i
$688$	−348.363	+	253.100i	−0.506341	+	0.367879i
$689$	63.0665	−	20.4915i	0.0915333	−	0.0297410i
$690$	−454.254	+	46.7440i	−0.658339	+	0.0677449i
$691$	−463.629	−	336.846i	−0.670954	−	0.487477i	0.199390	−	0.979920i	$-0.436104\pi$
$691$	−463.629	−	336.846i	−0.670954	−	0.487477i	−0.870344	+	0.492443i	$0.836104\pi$
$692$			340.727i			0.492380i
$693$		0			0
$694$	1649.35			2.37659
$695$	−259.915	+	357.742i	−0.373978	+	0.514737i
$696$	62.2597	+	605.034i	0.0894536	+	0.869302i
$697$	−149.251	−	459.347i	−0.214133	−	0.659035i
$698$	−830.239	−	1142.73i	−1.18945	−	1.63714i
$699$	452.898	+	262.797i	0.647922	+	0.375962i
$700$	501.502	+	1543.46i	0.716431	+	2.20495i
$701$	−778.940	−	253.093i	−1.11118	−	0.361046i	−0.304787	−	0.952420i	$-0.598585\pi$
$701$	−778.940	−	253.093i	−1.11118	−	0.361046i	−0.806397	+	0.591375i	$0.798585\pi$
$702$	92.7959	+	129.493i	0.132188	+	0.184464i
$703$	−76.5580			−0.108902
$704$		0			0
$705$	−259.327	+	114.784i	−0.367840	+	0.162814i
$706$	49.1722	+	35.7257i	0.0696490	+	0.0506030i
$707$	−107.856	−	35.0444i	−0.152554	−	0.0495677i
$708$	2242.19	−	2010.05i	3.16693	−	2.83905i
$709$	−145.495	+	105.708i	−0.205212	+	0.149095i	−0.685645	−	0.727936i	$-0.740480\pi$
$709$	−145.495	+	105.708i	−0.205212	+	0.149095i	0.480433	+	0.877032i	$0.340480\pi$
$710$	44.9276	+	61.8376i	0.0632783	+	0.0870952i
$711$	−708.269	−	319.045i	−0.996159	−	0.448728i
$712$	−402.492	+	1238.74i	−0.565298	+	1.73981i
$713$	279.589	−	384.821i	0.392130	−	0.539721i
$714$	−1083.58	+	479.617i	−1.51762	+	0.671732i
$715$		0			0
$716$		−	1207.48i		−	1.68643i
$717$	217.615	−	1012.95i	0.303508	−	1.41276i
$718$	84.1241	−	258.907i	0.117165	−	0.360595i
$719$	−633.724	+	205.910i	−0.881397	+	0.286383i	−0.714537	−	0.699597i	$-0.753363\pi$
$719$	−633.724	+	205.910i	−0.881397	+	0.286383i	−0.166860	+	0.985981i	$0.553363\pi$
$720$	−507.282	−	55.5525i	−0.704558	−	0.0771563i
$721$	505.968	−	367.607i	0.701759	−	0.509858i
$722$	850.765	−	276.430i	1.17834	−	0.382867i
$723$	80.2869	+	780.221i	0.111047	+	1.07914i
$724$	−935.163	−	679.436i	−1.29166	−	0.938447i
$725$			239.684i			0.330598i
$726$		0			0
$727$	162.429			0.223424			0.111712	−	0.993741i	$-0.464367\pi$
$727$	162.429			0.223424			0.111712	+	0.993741i	$0.464367\pi$
$728$	149.651	−	205.976i	0.205564	−	0.282935i
$729$	−595.322	+	420.752i	−0.816629	+	0.577164i
$730$	−172.588	−	531.172i	−0.236422	−	0.727633i
$731$	−115.701	−	159.249i	−0.158278	−	0.217851i
$732$	1035.07	−	1783.81i	1.41403	−	2.43690i
$733$	−361.513	−	1112.62i	−0.493196	−	1.51790i	−0.819749	−	0.572723i	$-0.805887\pi$
$733$	−361.513	−	1112.62i	−0.493196	−	1.51790i	0.326552	−	0.945179i	$-0.394113\pi$
$734$	2112.89	+	686.520i	2.87860	+	0.935313i
$735$	−38.8533	+	180.853i	−0.0528616	+	0.246058i
$736$	561.967			0.763542
$737$		0			0
$738$	−843.919	+	929.096i	−1.14352	+	1.25894i
$739$	−196.087	−	142.465i	−0.265341	−	0.192781i	0.447157	−	0.894455i	$-0.352436\pi$
$739$	−196.087	−	142.465i	−0.265341	−	0.192781i	−0.712498	+	0.701674i	$0.752436\pi$
$740$	−127.511	−	41.4309i	−0.172313	−	0.0559877i
$741$	34.8009	+	38.8200i	0.0469648	+	0.0523887i
$742$	1037.01	−	753.430i	1.39759	−	1.01540i
$743$	−484.132	−	666.351i	−0.651591	−	0.896838i	0.347576	−	0.937652i	$-0.387005\pi$
$743$	−484.132	−	666.351i	−0.651591	−	0.896838i	−0.999167	+	0.0408136i	$0.987005\pi$
$744$	912.443	−	817.976i	1.22640	−	1.09943i
$745$	145.922	−	449.101i	0.195868	−	0.602820i
$746$	771.041	−	1061.25i	1.03357	−	1.42258i
$747$	78.6669	+	71.4549i	0.105310	+	0.0956559i
$748$		0			0
$749$			1632.75i			2.17990i
$750$	−1002.07	−	215.278i	−1.33609	−	0.287037i
$751$	−1.89680	+	5.83775i	−0.00252570	+	0.00777330i	−0.952311	−	0.305128i	$-0.901301\pi$
$751$	−1.89680	+	5.83775i	−0.00252570	+	0.00777330i	0.949786	+	0.312901i	$0.101301\pi$
$752$	1171.08	−	380.507i	1.55729	−	0.505993i
$753$	514.667	+	298.640i	0.683489	+	0.396600i
$754$	55.4139	−	40.2606i	0.0734933	−	0.0533960i
$755$	541.170	−	175.837i	0.716782	−	0.232896i
$756$	1708.75	+	1258.62i	2.26026	+	1.66484i
$757$	891.755	+	647.898i	1.17801	+	0.855876i	0.991946	−	0.126661i	$-0.0404261\pi$
$757$	891.755	+	647.898i	1.17801	+	0.855876i	0.186066	+	0.982537i	$0.440426\pi$
$758$		−	1470.37i		−	1.93980i
$759$		0			0
$760$	−384.996			−0.506574
$761$	−705.506	+	971.046i	−0.927078	+	1.27601i	0.0339108	+	0.999425i	$0.489204\pi$
$761$	−705.506	+	971.046i	−0.927078	+	1.27601i	−0.960989	+	0.276588i	$0.910796\pi$
$762$	−152.810	+	15.7246i	−0.200538	+	0.0206360i
$763$	−160.329	−	493.442i	−0.210130	−	0.646713i
$764$	1645.05	+	2264.22i	2.15321	+	2.96364i
$765$	25.3950	−	231.896i	0.0331961	−	0.303132i
$766$	58.7094	+	180.689i	0.0766442	+	0.235887i
$767$	−177.050	−	57.5270i	−0.230834	−	0.0750027i
$768$	−1412.26	−	303.402i	−1.83888	−	0.395054i
$769$	1038.16			1.35001			0.675007	−	0.737811i	$-0.264141\pi$
$769$	1038.16			1.35001			0.675007	+	0.737811i	$0.264141\pi$
$770$		0			0
$771$	−2.26479	−	5.11676i	−0.00293747	−	0.00663652i
$772$	−1050.46	−	763.205i	−1.36070	−	0.988608i
$773$	557.520	+	181.149i	0.721242	+	0.234346i	0.646562	−	0.762862i	$-0.276206\pi$
$773$	557.520	+	181.149i	0.721242	+	0.234346i	0.0746805	+	0.997208i	$0.476206\pi$
$774$	−210.097	+	466.407i	−0.271443	+	0.602593i
$775$	390.671	−	283.839i	0.504092	−	0.366244i
$776$	−792.170	−	1090.33i	−1.02084	−	1.40506i
$777$	128.604	+	143.457i	0.165514	+	0.184629i
$778$	100.506	−	309.326i	0.129185	−	0.397591i
$779$	−241.438	+	332.311i	−0.309934	+	0.426587i
$780$	36.9545	+	83.4899i	0.0473775	+	0.107038i
$781$		0			0
$782$			906.383i			1.15906i
$783$	182.571	+	254.772i	0.233169	+	0.325379i
$784$	248.191	−	763.854i	0.316570	−	0.974303i
$785$	−12.0233	+	3.90662i	−0.0153164	+	0.00497659i
$786$	830.090	−	1430.55i	1.05609	−	1.82004i
$787$	302.139	−	219.517i	0.383912	−	0.278928i	−0.379044	−	0.925379i	$-0.623747\pi$
$787$	302.139	−	219.517i	0.383912	−	0.278928i	0.762956	+	0.646450i	$0.223747\pi$
$788$	1935.36	−	628.838i	2.45605	−	0.798018i
$789$	80.8433	−	8.31900i	0.102463	−	0.0105437i
$790$	−522.626	−	379.710i	−0.661552	−	0.480646i
$791$			1347.16i			1.70311i
$792$		0			0
$793$	−127.499			−0.160780
$794$	−707.983	+	974.454i	−0.891666	+	1.22727i
$795$	25.8306	+	251.020i	0.0324914	+	0.315748i
$796$	1067.05	+	3284.04i	1.34051	+	4.12567i
$797$	−491.864	−	676.992i	−0.617144	−	0.849426i	0.379997	−	0.924988i	$-0.375925\pi$
$797$	−491.864	−	676.992i	−0.617144	−	0.849426i	−0.997141	+	0.0755619i	$0.975925\pi$
$798$	871.662	+	505.788i	1.09231	+	0.633820i
$799$	173.943	+	535.341i	0.217701	+	0.670014i
$800$	542.587	+	176.297i	0.678234	+	0.220372i
$801$	136.690	+	657.138i	0.170649	+	0.820397i
$802$	−67.8754			−0.0846326
$803$		0			0
$804$	1530.49	−	677.429i	1.90360	−	0.842573i
$805$	304.256	+	221.055i	0.377958	+	0.274603i
$806$	−131.245	−	42.6441i	−0.162835	−	0.0529083i
$807$	−319.094	+	286.057i	−0.395407	+	0.354470i
$808$	−180.790	+	131.352i	−0.223750	+	0.162564i
$809$	304.962	+	419.745i	0.376962	+	0.518844i	0.954777	−	0.297324i	$-0.0960942\pi$
$809$	304.962	+	419.745i	0.376962	+	0.518844i	−0.577814	+	0.816168i	$0.696094\pi$
$810$	−555.957	+	241.747i	−0.686366	+	0.298453i
$811$	−241.858	+	744.364i	−0.298222	+	0.917834i	0.683897	+	0.729578i	$0.260284\pi$
$811$	−241.858	+	744.364i	−0.298222	+	0.917834i	−0.982120	+	0.188256i	$0.939716\pi$
$812$	536.334	−	738.200i	0.660510	−	0.909113i
$813$	−288.943	+	127.892i	−0.355403	+	0.157309i
$814$		0			0
$815$			337.843i			0.414531i
$816$	−212.750	+	990.299i	−0.260723	+	1.21360i
$817$	−51.7314	+	159.213i	−0.0633187	+	0.194875i
$818$	−406.889	+	132.206i	−0.497419	+	0.161621i
$819$	14.2825	−	130.422i	0.0174390	−	0.159245i
$820$	−581.965	+	422.822i	−0.709714	+	0.515637i
$821$	524.622	−	170.460i	0.639004	−	0.207625i	0.0284445	−	0.999595i	$-0.490945\pi$
$821$	524.622	−	170.460i	0.639004	−	0.207625i	0.610560	+	0.791970i	$0.290945\pi$
$822$	−88.8346	−	863.287i	−0.108071	−	1.05023i
$823$	37.3544	+	27.1396i	0.0453881	+	0.0329764i	0.610248	−	0.792210i	$-0.291070\pi$
$823$	37.3544	+	27.1396i	0.0453881	+	0.0329764i	−0.564860	+	0.825187i	$0.691070\pi$
$824$		−	1232.39i		−	1.49562i
$825$		0			0
$826$	−3598.50			−4.35654
$827$	350.444	−	482.345i	0.423753	−	0.583247i	−0.542752	−	0.839893i	$-0.682618\pi$
$827$	350.444	−	482.345i	0.423753	−	0.583247i	0.966505	+	0.256646i	$0.0826176\pi$
$828$	1409.34	−	805.518i	1.70210	−	0.972848i
$829$	−428.629	−	1319.18i	−0.517043	−	1.59129i	−0.779534	−	0.626360i	$-0.784544\pi$
$829$	−428.629	−	1319.18i	−0.517043	−	1.59129i	0.262491	−	0.964935i	$-0.415456\pi$
$830$	51.9477	+	71.4999i	0.0625876	+	0.0861445i
$831$	−368.764	+	635.518i	−0.443760	+	0.764763i
$832$	4.87182	+	14.9939i	0.00585555	+	0.0180215i
$833$	349.184	+	113.457i	0.419189	+	0.136203i
$834$	479.079	−	2230.00i	0.574435	−	2.67386i
$835$	−332.172			−0.397811
$836$		0			0
$837$	199.059	−	599.288i	0.237824	−	0.715995i
$838$	1198.23	+	870.565i	1.42987	+	1.03886i
$839$	1583.51	+	514.515i	1.88738	+	0.613247i	0.982076	+	0.188486i	$0.0603581\pi$
$839$	1583.51	+	514.515i	1.88738	+	0.613247i	0.905305	+	0.424761i	$0.139642\pi$
$840$	646.727	+	721.417i	0.769913	+	0.858830i
$841$	−571.359	+	415.117i	−0.679381	+	0.493599i
$842$	−1275.55	−	1755.64i	−1.51490	−	2.08509i
$843$	−145.446	+	130.388i	−0.172534	+	0.154671i
$844$	559.039	−	1720.55i	0.662369	−	2.03856i
$845$	−203.936	+	280.693i	−0.241344	+	0.332181i
$846$	983.537	−	1082.81i	1.16257	−	1.27991i
$847$		0			0
$848$		−	1095.66i		−	1.29206i
$849$	462.182	+	99.2924i	0.544384	+	0.116952i
$850$	−284.346	+	875.127i	−0.334525	+	1.02956i
$851$	140.153	−	45.5386i	0.164693	−	0.0535119i
$852$	−235.012	−	136.368i	−0.275836	−	0.160056i
$853$	−657.366	+	477.604i	−0.770652	+	0.559911i	−0.902159	−	0.431404i	$-0.858018\pi$
$853$	−657.366	+	477.604i	−0.770652	+	0.559911i	0.131507	+	0.991315i	$0.458018\pi$
$854$	−2343.93	+	761.589i	−2.74465	+	0.891791i
$855$	−172.248	+	98.4493i	−0.201459	+	0.115145i
$856$	2602.90	+	1891.12i	3.04078	+	2.20925i
$857$			551.421i			0.643431i	0.946836	+	0.321716i	$0.104260\pi$
$857$			551.421i			0.643431i	−0.946836	+	0.321716i	$0.895740\pi$
$858$		0			0
$859$	−1196.04			−1.39236			−0.696180	−	0.717868i	$-0.745118\pi$
$859$	−1196.04			−1.39236			−0.696180	+	0.717868i	$0.745118\pi$
$860$	−172.323	+	237.182i	−0.200375	+	0.275793i
$861$	1028.27	−	105.812i	1.19427	−	0.122894i
$862$	491.544	+	1512.82i	0.570237	+	1.75501i
$863$	−421.079	−	579.565i	−0.487924	−	0.671570i	0.492079	−	0.870550i	$-0.336237\pi$
$863$	−421.079	−	579.565i	−0.487924	−	0.671570i	−0.980003	+	0.198980i	$0.936237\pi$
$864$	711.031	−	225.903i	0.822953	−	0.261462i
$865$	24.7704	+	76.2355i	0.0286363	+	0.0881335i
$866$	747.094	+	242.745i	0.862695	+	0.280307i
$867$	394.959	+	84.8505i	0.455546	+	0.0978668i
$868$	−1838.37			−2.11793
$869$		0			0
$870$	105.499	+	238.350i	0.121263	+	0.273965i
$871$	−83.7104	−	60.8192i	−0.0961084	−	0.0698269i
$872$	−972.339	−	315.932i	−1.11507	−	0.362308i
$873$	−633.230	−	285.244i	−0.725350	−	0.326740i
$874$	623.624	−	453.089i	0.713528	−	0.518409i
$875$	496.145	+	682.885i	0.567023	+	0.780440i
$876$	1325.26	+	1478.31i	1.51285	+	1.68757i
$877$	−306.432	+	943.101i	−0.349410	+	1.07537i	0.609771	+	0.792578i	$0.291261\pi$
$877$	−306.432	+	943.101i	−0.349410	+	1.07537i	−0.959181	+	0.282794i	$0.908739\pi$
$878$	−361.913	+	498.131i	−0.412202	+	0.567348i
$879$	223.431	+	504.790i	0.254188	+	0.574278i
$880$		0			0
$881$			1256.55i			1.42628i	0.701021	+	0.713140i	$0.252728\pi$
$881$			1256.55i			1.42628i	−0.701021	+	0.713140i	$0.747272\pi$
$882$	−194.310	−	934.145i	−0.220306	−	1.05912i
$883$	86.0075	−	264.704i	0.0974037	−	0.299778i	−0.890469	−	0.455044i	$-0.849624\pi$
$883$	86.0075	−	264.704i	0.0974037	−	0.299778i	0.987873	+	0.155266i	$0.0496235\pi$
$884$	172.352	−	56.0006i	0.194968	−	0.0633491i
$885$	355.547	−	612.740i	0.401748	−	0.692361i
$886$	−1719.65	+	1249.40i	−1.94091	+	1.41015i
$887$	−1116.54	+	362.787i	−1.25879	+	0.409005i	−0.861062	−	0.508500i	$-0.830200\pi$
$887$	−1116.54	+	362.787i	−1.25879	+	0.409005i	−0.397725	+	0.917505i	$0.630200\pi$
$888$	377.652	−	38.8614i	0.425283	−	0.0437628i
$889$	102.351	+	74.3626i	0.115131	+	0.0836475i
$890$			558.178i			0.627166i
$891$		0			0
$892$	146.507			0.164245
$893$	281.382	−	387.289i	0.315097	−	0.433694i
$894$	249.326	+	2422.92i	0.278888	+	2.71021i
$895$	−87.7825	−	270.167i	−0.0980810	−	0.301862i
$896$	754.921	+	1039.06i	0.842546	+	1.15966i
$897$	−86.8005	−	50.3667i	−0.0967676	−	0.0561501i
$898$	−483.460	−	1487.94i	−0.538374	−	1.65695i
$899$	−258.218	−	83.9001i	−0.287228	−	0.0933260i
$900$	1613.44	−	335.609i	1.79271	−	0.372899i
$901$	500.866			0.555900
$902$		0			0
$903$	385.237	−	170.514i	0.426619	−	0.188831i
$904$	2147.62	+	1560.34i	2.37568	+	1.72604i
$905$	−258.631	−	84.0342i	−0.285780	−	0.0928555i
$906$	−2185.45	+	1959.18i	−2.41219	+	2.16245i
$907$	−117.806	+	85.5912i	−0.129885	+	0.0943673i	−0.650831	−	0.759223i	$-0.725579\pi$
$907$	−117.806	+	85.5912i	−0.129885	+	0.0943673i	0.520946	+	0.853590i	$0.325579\pi$
$908$	588.308	+	809.736i	0.647916	+	0.891780i
$909$	−47.2970	+	104.998i	−0.0520319	+	0.115509i
$910$	33.7163	−	103.768i	0.0370509	−	0.114031i
$911$	−632.867	+	871.067i	−0.694695	+	0.956166i	0.305297	+	0.952257i	$0.401244\pi$
$911$	−632.867	+	871.067i	−0.694695	+	0.956166i	−0.999992	+	0.00390866i	$0.998756\pi$
$912$	787.712	−	348.658i	0.863719	−	0.382301i
$913$		0			0
$914$		−	855.714i		−	0.936230i
$915$	101.909	−	474.364i	0.111376	−	0.518430i
$916$	1010.21	−	3109.11i	1.10285	−	3.39422i
$917$	−1295.46	+	420.920i	−1.41271	+	0.459018i
$918$	364.354	+	1146.81i	0.396899	+	1.24924i
$919$	255.740	−	185.806i	0.278280	−	0.202183i	−0.439887	−	0.898053i	$-0.644981\pi$
$919$	255.740	−	185.806i	0.278280	−	0.202183i	0.718167	+	0.695871i	$0.244981\pi$
$920$	704.806	−	229.005i	0.766093	−	0.248919i
$921$	−118.742	−	1153.92i	−0.128927	−	1.25290i
$922$	−2063.95	−	1499.55i	−2.23855	−	1.62640i
$923$			16.7976i			0.0181990i
$924$		0			0
$925$	149.606			0.161737
$926$	−973.067	+	1339.31i	−1.05083	+	1.44634i
$927$	−315.140	−	551.370i	−0.339957	−	0.594790i
$928$	−99.1224	−	305.067i	−0.106813	−	0.328736i
$929$	657.526	+	905.007i	0.707778	+	0.974173i	0.999842	+	0.0177741i	$0.00565796\pi$
$929$	657.526	+	905.007i	0.707778	+	0.974173i	−0.292064	+	0.956399i	$0.594342\pi$
$930$	263.563	−	454.217i	0.283401	−	0.488405i
$931$	−96.4904	−	296.967i	−0.103642	−	0.318976i
$932$	−1472.16	−	478.333i	−1.57957	−	0.513233i
$933$	58.1239	−	270.553i	0.0622979	−	0.289982i
$934$	−173.568			−0.185833
$935$		0			0
$936$	−191.374	−	173.829i	−0.204459	−	0.185715i
$937$	850.451	+	617.889i	0.907632	+	0.659433i	0.940415	−	0.340029i	$-0.110437\pi$
$937$	850.451	+	617.889i	0.907632	+	0.659433i	−0.0327830	+	0.999462i	$0.510437\pi$
$938$	−1902.22	−	618.068i	−2.02795	−	0.658922i
$939$	148.984	+	166.190i	0.158662	+	0.176986i
$940$	678.245	−	492.774i	0.721538	−	0.524228i
$941$	−188.418	−	259.335i	−0.200231	−	0.275595i	0.697080	−	0.716994i	$-0.254482\pi$
$941$	−188.418	−	259.335i	−0.200231	−	0.275595i	−0.897311	+	0.441399i	$0.854482\pi$
$942$	48.5548	−	43.5278i	0.0515443	−	0.0462079i
$943$	244.330	−	751.970i	0.259099	−	0.797423i
$944$	−1807.98	+	2488.47i	−1.91523	+	2.63609i
$945$	473.823	+	157.384i	0.501400	+	0.166544i
$946$		0			0
$947$		−	689.980i		−	0.728596i	−0.931283	−	0.364298i	$-0.881309\pi$
$947$		−	689.980i		−	0.728596i	0.931283	−	0.364298i	$-0.118691\pi$
$948$	2245.17	+	482.338i	2.36832	+	0.508795i
$949$	37.9284	−	116.732i	0.0399667	−	0.123005i
$950$	744.259	−	241.824i	0.783430	−	0.254552i
$951$	−1359.10	−	788.631i	−1.42913	−	0.829265i
$952$	1555.78	−	1130.34i	1.63422	−	1.18733i
$953$	1276.39	−	414.726i	1.33934	−	0.435179i	0.450249	−	0.892903i	$-0.351335\pi$
$953$	1276.39	−	414.726i	1.33934	−	0.435179i	0.889094	+	0.457724i	$0.151335\pi$
$954$	−645.895	−	1130.06i	−0.677039	−	1.18455i
$955$	532.676	+	387.012i	0.557776	+	0.405248i
$956$			3062.78i			3.20374i
$957$		0			0
$958$	−614.947			−0.641907
$959$	−420.104	+	578.224i	−0.438065	+	0.602945i
$960$	−59.6794	+	6.14117i	−0.0621660	+	0.00639706i
$961$	−127.930	−	393.727i	−0.133122	−	0.409706i
$962$	−25.1299	−	34.5884i	−0.0261226	−	0.0359547i
$963$	1648.13	+	180.487i	1.71145	+	0.187421i
$964$	−716.504	−	2205.17i	−0.743261	−	2.28752i
$965$	−290.518	−	94.3950i	−0.301055	−	0.0978187i
$966$	−1896.59	−	407.452i	−1.96334	−	0.421793i
$967$	−1283.30			−1.32709			−0.663546	−	0.748135i	$-0.730949\pi$
$967$	−1283.30			−1.32709			−0.663546	+	0.748135i	$0.730949\pi$
$968$		0			0
$969$	159.384	+	360.091i	0.164483	+	0.371611i
$970$	−467.256	−	339.481i	−0.481707	−	0.349981i
$971$	−809.179	−	262.918i	−0.833346	−	0.270770i	−0.138892	−	0.990308i	$-0.544354\pi$
$971$	−809.179	−	262.918i	−0.833346	−	0.270770i	−0.694454	+	0.719537i	$0.744354\pi$
$972$	1459.37	−	1585.72i	1.50141	−	1.63140i
$973$	−1519.69	+	1104.12i	−1.56186	+	1.13476i
$974$	1044.78	+	1438.02i	1.07267	+	1.47640i
$975$	−68.0064	−	75.8604i	−0.0697502	−	0.0778055i
$976$	−650.988	+	2003.54i	−0.666996	+	2.05280i
$977$	−712.767	+	981.039i	−0.729546	+	1.00413i	0.269606	+	0.962971i	$0.413107\pi$
$977$	−712.767	+	981.039i	−0.729546	+	1.00413i	−0.999152	+	0.0411637i	$0.986893\pi$
$978$	−705.322	−	1593.51i	−0.721188	−	1.62936i
$979$		0			0
$980$		−	546.831i		−	0.557991i
$981$	−515.814	+	107.293i	−0.525804	+	0.109371i
$982$	366.090	−	1126.71i	0.372801	−	1.14736i
$983$	432.404	−	140.496i	0.439882	−	0.142926i	−0.0806993	−	0.996738i	$-0.525715\pi$
$983$	432.404	−	140.496i	0.439882	−	0.142926i	0.520581	+	0.853812i	$0.325715\pi$
$984$	1022.30	−	1761.81i	1.03893	−	1.79046i
$985$	387.310	−	281.397i	0.393208	−	0.285682i
$986$	492.036	−	159.872i	0.499022	−	0.162142i
$987$	−1198.39	+	123.317i	−1.21417	+	0.124941i
$988$	−124.687	−	90.5904i	−0.126201	−	0.0916907i
$989$		−	322.239i		−	0.325823i
$990$		0			0
$991$	697.554			0.703889			0.351945	−	0.936021i	$-0.385521\pi$
$991$	697.554			0.703889			0.351945	+	0.936021i	$0.385521\pi$
$992$	−379.860	+	522.832i	−0.382923	+	0.527049i
$993$	77.2956	+	751.151i	0.0778405	+	0.756447i
$994$	100.337	+	308.807i	0.100943	+	0.310671i
$995$	477.490	+	657.209i	0.479890	+	0.660512i
$996$	−271.734	−	157.676i	−0.272825	−	0.158309i
$997$	−202.089	−	621.967i	−0.202697	−	0.623839i	−0.999800	−	0.0199948i	$-0.993635\pi$
$997$	−202.089	−	621.967i	−0.202697	−	0.623839i	0.797103	−	0.603844i	$-0.206365\pi$
$998$	374.607	+	121.717i	0.375358	+	0.121961i
$999$	159.024	−	113.958i	0.159183	−	0.114072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.j.323.4		16
3.2	odd	2	inner	363.3.h.j.323.1		16
11.2	odd	10		363.3.h.o.269.4		16
11.3	even	5	inner	363.3.h.j.245.1		16
11.4	even	5		363.3.h.n.251.4		16
11.5	even	5		363.3.b.l.122.8		8
11.6	odd	10		363.3.b.m.122.1		8
11.7	odd	10		363.3.h.o.251.1		16
11.8	odd	10		33.3.h.b.14.4	yes	16
11.9	even	5		363.3.h.n.269.1		16
11.10	odd	2		33.3.h.b.26.1	yes	16
33.2	even	10		363.3.h.o.269.1		16
33.5	odd	10		363.3.b.l.122.1		8
33.8	even	10		33.3.h.b.14.1	✓	16
33.14	odd	10	inner	363.3.h.j.245.4		16
33.17	even	10		363.3.b.m.122.8		8
33.20	odd	10		363.3.h.n.269.4		16
33.26	odd	10		363.3.h.n.251.1		16
33.29	even	10		363.3.h.o.251.4		16
33.32	even	2		33.3.h.b.26.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.1	✓	16	33.8	even	10
33.3.h.b.14.4	yes	16	11.8	odd	10
33.3.h.b.26.1	yes	16	11.10	odd	2
33.3.h.b.26.4	yes	16	33.32	even	2
363.3.b.l.122.1		8	33.5	odd	10
363.3.b.l.122.8		8	11.5	even	5
363.3.b.m.122.1		8	11.6	odd	10
363.3.b.m.122.8		8	33.17	even	10
363.3.h.j.245.1		16	11.3	even	5	inner
363.3.h.j.245.4		16	33.14	odd	10	inner
363.3.h.j.323.1		16	3.2	odd	2	inner
363.3.h.j.323.4		16	1.1	even	1	trivial
363.3.h.n.251.1		16	33.26	odd	10
363.3.h.n.251.4		16	11.4	even	5
363.3.h.n.269.1		16	11.9	even	5
363.3.h.n.269.4		16	33.20	odd	10
363.3.h.o.251.1		16	11.7	odd	10
363.3.h.o.251.4		16	33.29	even	10
363.3.h.o.269.1		16	33.2	even	10
363.3.h.o.269.4		16	11.2	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10855 - 2.90217i) q^{2} +(0.307087 + 2.98424i) q^{3} +(-2.74053 - 8.43448i) q^{4} +(-1.22635 - 1.68793i) q^{5} +(9.30827 + 5.40120i) q^{6} +(-2.73883 - 8.42924i) q^{7} +(-16.6100 - 5.39692i) q^{8} +(-8.81140 + 1.83284i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +(-1.33068 - 0.966792i) q^{13} +(-30.2380 - 9.82492i) q^{14} +(4.66059 - 4.17807i) q^{15} +(-21.9865 + 15.9742i) q^{16} +(-7.30235 - 10.0508i) q^{17} +(-13.2600 + 29.4368i) q^{18} +(-3.26497 + 10.0485i) q^{19} +(-10.8759 + 14.9695i) q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(11.0050 - 51.2256i) q^{24} +(6.38026 - 19.6364i) q^{25} +(-5.61158 + 1.82331i) q^{26} +(-8.17551 - 25.7325i) q^{27} +(-63.5904 + 46.2012i) q^{28} +(-11.0405 + 3.58727i) q^{29} +(-2.29838 - 22.3355i) q^{30} +(18.9215 + 13.7473i) q^{31} +27.6317i q^{32} -44.5665 q^{34} +(-10.8692 + 14.9601i) q^{35} +(39.6070 + 69.2966i) q^{36} +(2.23911 + 6.89128i) q^{37} +(22.2782 + 30.6633i) q^{38} +(2.47651 - 4.26795i) q^{39} +(11.2601 + 34.6550i) q^{40} +(36.9741 + 12.0136i) q^{41} +(20.0342 - 93.2546i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +(-59.0236 - 42.8832i) q^{46} +(-43.0910 - 14.0011i) q^{47} +(-54.4225 - 60.7077i) q^{48} +(-23.9091 + 17.3709i) q^{49} +(-43.5351 - 59.9209i) q^{50} +(27.7516 - 24.8784i) q^{51} +(-4.50764 + 13.8731i) q^{52} +(-23.6972 + 32.6164i) q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(-30.9899 - 6.65768i) q^{57} +(-12.8685 + 39.6053i) q^{58} +(107.642 - 34.9750i) q^{59} +(-48.0123 - 27.8595i) q^{60} +(62.7118 - 45.5628i) q^{61} +(79.7937 - 25.9266i) q^{62} +(39.5823 + 69.2535i) q^{63} +(-7.75446 - 5.63395i) q^{64} +3.43171i q^{65} +62.9082 q^{67} +(-64.7612 + 89.1361i) q^{68} +(60.6928 - 6.24546i) q^{69} +(20.4987 + 63.0884i) q^{70} +(-6.00278 - 8.26212i) q^{71} +(156.249 + 17.1109i) q^{72} +(23.0595 + 70.9699i) q^{73} +(24.7209 + 8.03232i) q^{74} +(60.5591 + 13.0102i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} +(69.8281 + 50.7331i) q^{79} +(53.9264 + 17.5218i) q^{80} +(74.2814 - 32.2998i) q^{81} +(112.827 - 81.9736i) q^{82} +(-6.94074 - 9.55311i) q^{83} +(-157.403 - 175.581i) q^{84} +(-8.00981 + 24.6517i) q^{85} +(33.4086 - 45.9830i) q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(65.9486 - 13.7178i) q^{90} +(-4.50483 + 13.8645i) q^{91} +(-171.539 + 55.7363i) q^{92} +(-35.2146 + 60.6879i) q^{93} +(-131.493 + 95.5353i) q^{94} +(20.9652 - 6.81201i) q^{95} +(-82.4596 + 8.48532i) q^{96} +(62.4301 + 45.3581i) q^{97} +106.016i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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