LMFDB - Embedded newform 363.3.h.j.323.1

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)

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);

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")

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			323.1
Root			$-2.10855 + 2.90217i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.j.245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10855 + 2.90217i) q^{2} +(-2.00253 + 2.23380i) q^{3} +(-2.74053 - 8.43448i) q^{4} +(1.22635 + 1.68793i) q^{5} +(-2.26043 - 10.5218i) q^{6} +(-2.73883 - 8.42924i) q^{7} +(16.6100 + 5.39692i) q^{8} +(-0.979734 - 8.94651i) q^{9} -7.48447 q^{10} +(24.3290 + 10.7685i) q^{12} +(-1.33068 - 0.966792i) q^{13} +(30.2380 + 9.82492i) q^{14} +(-6.22630 - 0.640704i) q^{15} +(-21.9865 + 15.9742i) q^{16} +(7.30235 + 10.0508i) q^{17} +(28.0301 + 16.0208i) q^{18} +(-3.26497 + 10.0485i) q^{19} +(10.8759 - 14.9695i) q^{20} +(24.3138 + 10.7618i) q^{21} +20.3378i q^{23} +(-45.3177 + 26.2959i) q^{24} +(6.38026 - 19.6364i) q^{25} +(5.61158 - 1.82331i) q^{26} +(21.9467 + 15.7271i) q^{27} +(-63.5904 + 46.2012i) q^{28} +(11.0405 - 3.58727i) q^{29} +(14.9879 - 16.7188i) q^{30} +(18.9215 + 13.7473i) q^{31} -27.6317i q^{32} -44.5665 q^{34} +(10.8692 - 14.9601i) q^{35} +(-72.7742 + 32.7817i) q^{36} +(2.23911 + 6.89128i) q^{37} +(-22.2782 - 30.6633i) q^{38} +(4.82434 - 1.03643i) q^{39} +(11.2601 + 34.6550i) q^{40} +(-36.9741 - 12.0136i) q^{41} +(-82.4995 + 47.8710i) q^{42} +15.8444 q^{43} +(13.8996 - 12.6253i) q^{45} +(-59.0236 - 42.8832i) q^{46} +(43.0910 + 14.0011i) q^{47} +(8.34565 - 81.1023i) q^{48} +(-23.9091 + 17.3709i) q^{49} +(43.5351 + 59.9209i) q^{50} +(-37.0747 - 3.81509i) q^{51} +(-4.50764 + 13.8731i) q^{52} +(23.6972 - 32.6164i) q^{53} +(-91.9184 + 30.5315i) q^{54} -154.791i q^{56} +(-15.9082 - 27.4158i) q^{57} +(-12.8685 + 39.6053i) q^{58} +(-107.642 + 34.9750i) q^{59} +(11.6594 + 54.2715i) q^{60} +(62.7118 - 45.5628i) q^{61} +(-79.7937 + 25.9266i) q^{62} +(-72.7290 + 32.7614i) q^{63} +(-7.75446 - 5.63395i) q^{64} -3.43171i q^{65} +62.9082 q^{67} +(64.7612 - 89.1361i) q^{68} +(-45.4306 - 40.7270i) q^{69} +(20.4987 + 63.0884i) q^{70} +(6.00278 + 8.26212i) q^{71} +(32.0102 - 153.889i) q^{72} +(23.0595 + 70.9699i) q^{73} +(-24.7209 - 8.03232i) q^{74} +(31.0872 + 53.5748i) q^{75} +93.7020 q^{76} +(-7.16445 + 16.1864i) q^{78} +(69.8281 + 50.7331i) q^{79} +(-53.9264 - 17.5218i) q^{80} +(-79.0802 + 17.5304i) q^{81} +(112.827 - 81.9736i) q^{82} +(6.94074 + 9.55311i) q^{83} +(24.1377 - 234.568i) q^{84} +(-8.00981 + 24.6517i) q^{85} +(-33.4086 + 45.9830i) q^{86} +(-14.0957 + 31.8459i) q^{87} +74.5782i q^{89} +(7.33279 + 66.9599i) q^{90} +(-4.50483 + 13.8645i) q^{91} +(171.539 - 55.7363i) q^{92} +(-68.5996 + 14.7375i) q^{93} +(-131.493 + 95.5353i) q^{94} +(-20.9652 + 6.81201i) q^{95} +(61.7236 + 55.3333i) 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	$0.554128\pi$
$2$	−2.10855	+	2.90217i	−1.05427	+	1.45108i	−0.885045	+	0.465506i	$0.845872\pi$
$3$	−2.00253	+	2.23380i	−0.667511	+	0.744600i
$3$	−2.00253	+	2.23380i	−0.667511	+	0.744600i
$4$	−2.74053	−	8.43448i	−0.685132	−	2.10862i
$5$	1.22635	+	1.68793i	0.245270	+	0.337586i	0.913848	−	0.406057i	$-0.133097\pi$
$5$	1.22635	+	1.68793i	0.245270	+	0.337586i	−0.668578	+	0.743642i	$0.733097\pi$
$6$	−2.26043	−	10.5218i	−0.376738	−	1.75363i
$7$	−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
$9$	−0.979734	−	8.94651i	−0.108859	−	0.994057i
$10$	−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
$15$	−6.22630	−	0.640704i	−0.415087	−	0.0427136i
$16$	−21.9865	+	15.9742i	−1.37416	+	0.998385i
$17$	7.30235	+	10.0508i	0.429550	+	0.591225i	0.967850	−	0.251529i	$-0.0809333\pi$
$17$	7.30235	+	10.0508i	0.429550	+	0.591225i	−0.538300	+	0.842753i	$0.680933\pi$
$18$	28.0301	+	16.0208i	1.55723	+	0.890044i
$19$	−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	$0.145775\pi$
$23$			20.3378i			0.884251i	−0.896953	+	0.442126i	$0.854225\pi$
$24$	−45.3177	+	26.2959i	−1.88824	+	1.09566i
$25$	6.38026	−	19.6364i	0.255210	−	0.785457i
$26$	5.61158	−	1.82331i	0.215830	−	0.0701275i
$27$	21.9467	+	15.7271i	0.812840	+	0.582487i
$28$	−63.5904	+	46.2012i	−2.27109	+	1.65004i
$29$	11.0405	−	3.58727i	0.380707	−	0.123699i	−0.112411	−	0.993662i	$-0.535857\pi$
$29$	11.0405	−	3.58727i	0.380707	−	0.123699i	0.493118	+	0.869963i	$0.335857\pi$
$30$	14.9879	−	16.7188i	0.499596	−	0.557294i
$31$	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
$36$	−72.7742	+	32.7817i	−2.02151	+	0.910604i
$37$	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
$39$	4.82434	−	1.03643i	0.123701	−	0.0265752i
$40$	11.2601	+	34.6550i	0.281502	+	0.866375i
$41$	−36.9741	−	12.0136i	−0.901806	−	0.293015i	−0.178824	−	0.983881i	$-0.557229\pi$
$41$	−36.9741	−	12.0136i	−0.901806	−	0.293015i	−0.722982	+	0.690866i	$0.757229\pi$
$42$	−82.4995	+	47.8710i	−1.96427	+	1.13978i
$43$	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	0.729166	−	0.684337i	$-0.239908\pi$
$47$	43.0910	+	14.0011i	0.916831	+	0.297896i	0.187665	+	0.982233i	$0.439908\pi$
$48$	8.34565	−	81.1023i	0.173868	−	1.68963i
$49$	−23.9091	+	17.3709i	−0.487940	+	0.354509i
$50$	43.5351	+	59.9209i	0.870702	+	1.19842i
$51$	−37.0747	−	3.81509i	−0.726955	−	0.0748057i
$52$	−4.50764	+	13.8731i	−0.0866853	+	0.266790i
$53$	23.6972	−	32.6164i	0.447116	−	0.615403i	−0.524658	−	0.851313i	$-0.675807\pi$
$53$	23.6972	−	32.6164i	0.447116	−	0.615403i	0.971775	+	0.235910i	$0.0758070\pi$
$54$	−91.9184	+	30.5315i	−1.70219	+	0.565398i
$55$		0			0
$56$		−	154.791i		−	2.76412i
$57$	−15.9082	−	27.4158i	−0.279092	−	0.480979i
$58$	−12.8685	+	39.6053i	−0.221871	+	0.682850i
$59$	−107.642	+	34.9750i	−1.82444	+	0.592797i	−0.824816	+	0.565402i	$0.808721\pi$
$59$	−107.642	+	34.9750i	−1.82444	+	0.592797i	−0.999625	+	0.0273946i	$0.991279\pi$
$60$	11.6594	+	54.2715i	0.194323	+	0.904525i
$61$	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
$63$	−72.7290	+	32.7614i	−1.15443	+	0.520022i
$64$	−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
$69$	−45.4306	−	40.7270i	−0.658414	−	0.590247i
$70$	20.4987	+	63.0884i	0.292838	+	0.901262i
$71$	6.00278	+	8.26212i	0.0845462	+	0.116368i	0.849195	−	0.528079i	$-0.177088\pi$
$71$	6.00278	+	8.26212i	0.0845462	+	0.116368i	−0.764649	+	0.644447i	$0.777088\pi$
$72$	32.0102	−	153.889i	0.444586	−	2.13735i
$73$	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
$75$	31.0872	+	53.5748i	0.414496	+	0.714331i
$76$	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
$81$	−79.0802	+	17.5304i	−0.976299	+	0.216425i
$82$	112.827	−	81.9736i	1.37594	−	0.999678i
$83$	6.94074	+	9.55311i	0.0836234	+	0.115098i	0.848779	−	0.528747i	$-0.177338\pi$
$83$	6.94074	+	9.55311i	0.0836234	+	0.115098i	−0.765156	+	0.643845i	$0.777338\pi$
$84$	24.1377	−	234.568i	0.287353	−	2.79247i
$85$	−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	$0.137612\pi$
$89$			74.5782i			0.837957i	−0.907996	+	0.418979i	$0.862388\pi$
$90$	7.33279	+	66.9599i	0.0814755	+	0.743999i
$91$	−4.50483	+	13.8645i	−0.0495037	+	0.152357i
$92$	171.539	−	55.7363i	1.86455	−	0.605829i
$93$	−68.5996	+	14.7375i	−0.737630	+	0.158468i
$94$	−131.493	+	95.5353i	−1.39886	+	1.01633i
$95$	−20.9652	+	6.81201i	−0.220687	+	0.0717054i
$96$	61.7236	+	55.3333i	0.642955	+	0.576388i
$97$	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	−0.844625	−	0.535359i	$-0.820176\pi$
$101$	−7.52095	+	10.3517i	−0.0744649	+	0.102492i	0.770160	+	0.637851i	$0.220176\pi$
$102$	89.2458	−	99.5527i	0.874959	−	0.976007i
$103$	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
$105$	11.6521	+	54.2378i	0.110972	+	0.516550i
$106$	44.6915	+	137.546i	0.421618	+	1.29761i
$107$	175.204	+	56.9272i	1.63742	+	0.532029i	0.975959	−	0.217952i	$-0.0699376\pi$
$107$	175.204	+	56.9272i	1.63742	+	0.532029i	0.661459	+	0.749981i	$0.269938\pi$
$108$	72.5048	−	228.210i	0.671341	−	2.11305i
$109$	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	0.868325	−	0.495996i	$-0.165197\pi$
$113$	144.558	+	46.9698i	1.27927	+	0.415662i	0.410950	+	0.911658i	$0.365197\pi$
$114$	113.109	+	11.6392i	0.992180	+	0.102098i
$115$	−34.3287	+	24.9413i	−0.298510	+	0.216881i
$116$	−60.5136	−	83.2899i	−0.521669	−	0.718016i
$117$	−7.34571	+	12.8521i	−0.0627839	+	0.109847i
$118$	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
$123$	100.878	−	58.5351i	0.820144	−	0.475895i
$124$	64.0962	−	197.268i	0.516905	−	1.59087i
$125$	90.5763	−	29.4300i	0.724610	−	0.235440i
$126$	58.2736	−	280.150i	0.462489	−	2.22342i
$127$	−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
$129$	−31.7289	+	35.3932i	−0.245960	+	0.274366i
$130$	9.95940	+	7.23592i	0.0766107	+	0.0556610i
$131$			153.686i			1.17318i	0.809885	+	0.586589i	$0.199529\pi$
$131$			153.686i			1.17318i	−0.809885	+	0.586589i	$0.800471\pi$
$132$		0			0
$133$	93.6438			0.704088
$134$	−132.645	+	182.570i	−0.989888	+	1.36246i
$135$	0.368057	+	56.3314i	0.00272635	+	0.417270i
$136$	67.0486	+	206.354i	0.493004	+	1.51731i
$137$	47.3996	+	65.2400i	0.345983	+	0.476205i	0.946177	−	0.323650i	$-0.104910\pi$
$137$	47.3996	+	65.2400i	0.345983	+	0.476205i	−0.600194	+	0.799854i	$0.704910\pi$
$138$	213.989	−	45.9721i	1.55065	−	0.333131i
$139$	−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
$141$	−117.567	+	68.2191i	−0.833808	+	0.483824i
$142$	−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
$147$	9.07540	−	88.1940i	0.0617374	−	0.599959i
$148$	51.9881	−	37.7715i	0.351271	−	0.255213i
$149$	−133.033	−	183.104i	−0.892840	−	1.22889i	−0.972696	−	0.232083i	$-0.925446\pi$
$149$	−133.033	−	183.104i	−0.892840	−	1.22889i	0.0798559	−	0.996806i	$-0.474554\pi$
$150$	−221.032	−	22.7448i	−1.47355	−	0.151632i
$151$	−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
$156$	−21.9630	−	37.8504i	−0.140789	−	0.242631i
$157$	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
$159$	25.4041	+	118.250i	0.159774	+	0.743711i
$160$	46.6403	−	33.8861i	0.291502	−	0.211788i
$161$	171.432	−	55.7016i	1.06479	−	0.345973i
$162$	115.868	−	266.468i	0.715236	−	1.64486i
$163$	−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	−0.991373	−	0.131074i	$-0.958158\pi$
$167$	−93.5806	+	128.803i	−0.560363	+	0.771274i	0.431010	+	0.902347i	$0.358158\pi$
$168$	345.772	+	309.974i	2.05817	+	1.84508i
$169$	−51.3879	−	158.156i	−0.304070	−	0.935832i
$170$	−54.6542	−	75.2250i	−0.321495	−	0.442500i
$171$	93.0983	+	19.3652i	0.544434	+	0.113247i
$172$	−43.4220	−	133.639i	−0.252453	−	0.776972i
$173$	36.5394	+	11.8724i	0.211210	+	0.0686264i	0.412711	−	0.910862i	$-0.364582\pi$
$173$	36.5394	+	11.8724i	0.211210	+	0.0686264i	−0.201501	+	0.979488i	$0.564582\pi$
$174$	−62.7007	−	108.057i	−0.360349	−	0.621015i
$175$	−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	−0.0759072	−	0.997115i	$-0.524185\pi$
$179$	−129.490	−	42.0738i	−0.723407	−	0.235049i	−0.647500	+	0.762066i	$0.724185\pi$
$180$	−144.580	−	82.6357i	−0.803222	−	0.459087i
$181$	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
$183$	−23.8042	+	231.327i	−0.130077	+	1.26408i
$184$	−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
$189$	72.4597	−	228.068i	0.383385	−	1.20671i
$190$	24.4366	−	75.2080i	0.128613	−	0.395832i
$191$	300.134	−	97.5195i	1.57138	−	0.510574i	0.611565	−	0.791194i	$-0.290540\pi$
$191$	300.134	−	97.5195i	1.57138	−	0.510574i	0.959819	+	0.280621i	$0.0905403\pi$
$192$	28.1137	−	6.03977i	0.146425	−	0.0314571i
$193$	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
$195$	7.66576	+	6.87211i	0.0393116	+	0.0352416i
$196$	212.038	+	154.055i	1.08183	+	0.785995i
$197$		−	229.459i		−	1.16476i	−0.812915	−	0.582382i	$-0.802121\pi$
$197$		−	229.459i		−	1.16476i	0.812915	−	0.582382i	$-0.197879\pi$
$198$		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
$201$	−125.976	+	140.524i	−0.626745	+	0.699127i
$202$	−14.1841	−	43.6541i	−0.0702182	−	0.216109i
$203$	−60.4760	−	83.2381i	−0.297911	−	0.410040i
$204$	69.4260	+	323.161i	0.340324	+	1.58412i
$205$	−25.0651	−	77.1425i	−0.122269	−	0.376305i
$206$	−240.744	−	78.2223i	−1.16866	−	0.379720i
$207$	181.952	−	19.9256i	0.878996	−	0.0962590i
$208$	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
$213$	−30.4767	−	3.13614i	−0.143083	−	0.0147236i
$214$	−534.637	+	388.437i	−2.49831	+	1.81513i
$215$	19.4308	+	26.7442i	0.0903757	+	0.124391i
$216$	279.656	+	379.672i	1.29471	+	1.75774i
$217$	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
$222$	67.4470	−	39.1367i	0.303816	−	0.176291i
$223$	−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
$225$	−181.929	−	37.8426i	−0.808571	−	0.168189i
$226$	−441.122	+	320.494i	−1.95187	+	1.41811i
$227$	107.335	−	34.8751i	0.472840	−	0.153635i	−0.0628969	−	0.998020i	$-0.520034\pi$
$227$	107.335	−	34.8751i	0.472840	−	0.153635i	0.535737	+	0.844385i	$0.320034\pi$
$228$	−187.641	+	209.312i	−0.822988	+	0.918034i
$229$	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	−0.970281	−	0.241981i	$-0.922203\pi$
$233$	−102.592	+	141.206i	−0.440310	+	0.606034i	0.529971	+	0.848016i	$0.322203\pi$
$234$	−21.8102	−	48.4177i	−0.0932058	−	0.206913i
$235$	29.2119	+	89.9049i	0.124306	+	0.382574i
$236$	589.992	+	812.054i	2.49997	+	3.44091i
$237$	−253.161	+	54.3875i	−1.06819	+	0.229483i
$238$	122.060	+	375.662i	0.512856	+	1.57841i
$239$	328.450	+	106.720i	1.37427	+	0.446527i	0.900781	−	0.434273i	$-0.142995\pi$
$239$	328.450	+	106.720i	1.37427	+	0.446527i	0.473488	+	0.880800i	$0.342995\pi$
$240$	147.130	−	85.3731i	0.613040	−	0.355721i
$241$	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
$246$	−42.8269	+	416.188i	−0.174093	+	1.69182i
$247$	14.0595	−	10.2148i	0.0569209	−	0.0413555i
$248$	240.093	+	330.460i	0.968118	+	1.33250i
$249$	−35.2388	−	3.62617i	−0.141521	−	0.0145629i
$250$	−105.574	+	324.922i	−0.422294	+	1.29969i
$251$	−116.584	+	160.465i	−0.464480	+	0.639302i	−0.975430	−	0.220309i	$-0.929294\pi$
$251$	−116.584	+	160.465i	−0.464480	+	0.639302i	0.510950	+	0.859610i	$0.329294\pi$
$252$	475.641	+	523.648i	1.88746	+	2.07797i
$253$		0			0
$254$		−	51.2057i		−	0.201597i
$255$	−39.0270	−	67.2581i	−0.153047	−	0.263757i
$256$	−148.790	+	457.929i	−0.581211	+	1.78878i
$257$	1.77390	−	0.576376i	0.00690234	−	0.00224271i	−0.305564	−	0.952172i	$-0.598845\pi$
$257$	1.77390	−	0.576376i	0.00690234	−	0.00224271i	0.312466	+	0.949929i	$0.398845\pi$
$258$	−35.8151	−	166.711i	−0.138818	−	0.646165i
$259$	51.9557	−	37.7481i	0.200601	−	0.145745i
$260$	−28.9447	+	9.40471i	−0.111326	+	0.0361719i
$261$	−42.9104	−	95.2594i	−0.164408	−	0.364978i
$262$	−446.023	−	324.055i	−1.70238	−	1.23685i
$263$			27.0901i			0.103004i	0.998673	+	0.0515020i	$0.0164009\pi$
$263$			27.0901i			0.103004i	−0.998673	+	0.0515020i	$0.983599\pi$
$264$		0			0
$265$	84.1151			0.317416
$266$	−197.452	+	271.770i	−0.742302	+	1.02169i
$267$	−166.593	−	149.345i	−0.623943	−	0.559345i
$268$	−172.402	−	530.599i	−0.643291	−	1.97985i
$269$	−83.9639	−	115.566i	−0.312133	−	0.429615i	0.623912	−	0.781495i	$-0.285542\pi$
$269$	−83.9639	−	115.566i	−0.312133	−	0.429615i	−0.936045	+	0.351880i	$0.885542\pi$
$270$	−164.259	−	117.709i	−0.608368	−	0.435960i
$271$	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
$273$	−21.9494	−	37.8269i	−0.0804006	−	0.138560i
$274$	−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
$279$	104.452	−	182.750i	0.374380	−	0.655018i
$280$	261.276	−	189.828i	0.933128	−	0.677957i
$281$	−38.2716	−	52.6763i	−0.136198	−	0.187460i	0.735470	−	0.677557i	$-0.236961\pi$
$281$	−38.2716	−	52.6763i	−0.136198	−	0.187460i	−0.871668	+	0.490097i	$0.836961\pi$
$282$	49.9122	−	485.042i	0.176994	−	1.72001i
$283$	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
$288$	−247.207	+	27.0717i	−0.858358	+	0.0939989i
$289$	41.6112	−	128.066i	0.143984	−	0.443136i
$290$	−82.6322	+	26.8488i	−0.284939	+	0.0925822i
$291$	−226.339	+	48.6253i	−0.777798	+	0.167097i
$292$	535.399	−	388.991i	1.83356	−	1.33216i
$293$	−175.003	+	56.8620i	−0.597280	+	0.194068i	−0.592027	−	0.805918i	$-0.701672\pi$
$293$	−175.003	+	56.8620i	−0.597280	+	0.194068i	−0.00525314	+	0.999986i	$0.501672\pi$
$294$	236.818	+	212.299i	0.805502	+	0.722107i
$295$	−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
$300$	366.680	−	409.028i	1.22227	−	1.36343i
$301$	−43.3950	−	133.556i	−0.144169	−	0.443708i
$302$	−575.062	−	791.505i	−1.90418	−	2.62088i
$303$	−8.06270	−	37.5299i	−0.0266096	−	0.123861i
$304$	−88.7316	−	273.088i	−0.291880	−	0.898315i
$305$	153.813	+	49.9770i	0.504306	+	0.163859i
$306$	43.6633	+	398.715i	0.142691	+	1.30299i
$307$	−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	0.446641	−	0.894713i	$-0.352620\pi$
$311$	87.7273	+	28.5043i	0.282081	+	0.0916538i	−0.164559	+	0.986367i	$0.552620\pi$
$312$	85.7259	+	8.82143i	0.274762	+	0.0282738i
$313$	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
$315$	−144.490	−	82.5843i	−0.458699	−	0.262173i
$316$	236.541	−	728.000i	0.748549	−	2.30380i
$317$	307.870	−	423.746i	0.971198	−	1.33674i	0.0297582	−	0.999557i	$-0.490526\pi$
$317$	307.870	−	423.746i	0.971198	−	1.33674i	0.941440	−	0.337182i	$-0.109474\pi$
$318$	−396.747	−	175.609i	−1.24763	−	0.552229i
$319$		0			0
$320$		−	19.9982i		−	0.0624943i
$321$	−478.015	+	277.372i	−1.48914	+	0.864087i
$322$	−199.817	+	614.974i	−0.620550	+	1.90986i
$323$	−124.838	+	40.5623i	−0.386495	+	0.125580i
$324$	364.582	+	618.958i	1.12525	+	1.91037i
$325$	−27.4744	+	19.9613i	−0.0845366	+	0.0614194i
$326$	552.446	−	179.501i	1.69462	−	0.550615i
$327$	−117.227	+	130.765i	−0.358492	+	0.399894i
$328$	−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
$333$	59.4592	−	26.7839i	0.178556	−	0.0804321i
$334$	−176.488	−	543.173i	−0.528406	−	1.62627i
$335$	77.1476	+	106.185i	0.230291	+	0.316969i
$336$	−706.488	+	151.778i	−2.10264	+	0.451719i
$337$	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
$339$	−394.403	+	228.855i	−1.16343	+	0.675090i
$340$	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
$345$	13.0305	−	126.629i	0.0377695	−	0.367041i
$346$	−111.501	+	81.0099i	−0.322256	+	0.234133i
$347$	−270.251	−	371.969i	−0.778822	−	1.07196i	−0.995411	−	0.0956933i	$-0.969493\pi$
$347$	−270.251	−	371.969i	−0.778822	−	1.07196i	0.216589	−	0.976263i	$-0.430507\pi$
$348$	307.233	+	31.6152i	0.882855	+	0.0908482i
$349$	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	$-0.992360\pi$
$353$		−	16.9433i		−	0.0479980i	0.999712	−	0.0239990i	$-0.00763985\pi$
$354$	611.315	+	1053.52i	1.72688	+	2.97606i
$355$	−6.58434	+	20.2645i	−0.0185474	+	0.0570832i
$356$	629.029	−	204.384i	1.76693	−	0.574112i
$357$	69.3828	+	322.960i	0.194350	+	0.904651i
$358$	395.141	−	287.086i	1.10374	−	0.801917i
$359$	−72.1739	+	23.4507i	−0.201041	+	0.0653223i	−0.407807	−	0.913068i	$-0.633706\pi$
$359$	−72.1739	+	23.4507i	−0.201041	+	0.0653223i	0.206765	+	0.978391i	$0.433706\pi$
$360$	299.010	−	134.691i	0.830582	−	0.374143i
$361$	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
$366$	−621.156	−	556.847i	−1.69715	−	1.52144i
$367$	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
$369$	−71.2551	+	342.559i	−0.193103	+	0.928345i
$370$	−16.7586	−	51.5776i	−0.0452935	−	0.139399i
$371$	−339.833	−	110.419i	−0.915993	−	0.297624i
$372$	312.302	+	538.213i	0.839523	+	1.44681i
$373$	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
$378$	509.106	+	691.182i	1.34684	+	1.82852i
$379$	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
$381$	4.38344	−	42.5979i	0.0115051	−	0.111805i
$382$	−349.829	+	1076.66i	−0.915784	+	2.81849i
$383$	31.1300	−	42.8468i	0.0812795	−	0.111872i	−0.766441	−	0.642314i	$-0.777974\pi$
$383$	31.1300	−	42.8468i	0.0812795	−	0.111872i	0.847721	+	0.530443i	$0.177974\pi$
$384$	−175.956	+	397.532i	−0.458219	+	1.03524i
$385$		0			0
$386$			525.213i			1.36065i
$387$	−15.5233	−	141.752i	−0.0401118	−	0.366284i
$388$	211.481	−	650.871i	0.545053	−	1.67750i
$389$	−86.2286	+	28.0174i	−0.221667	+	0.0720241i	−0.417745	−	0.908564i	$-0.637179\pi$
$389$	−86.2286	+	28.0174i	−0.221667	+	0.0720241i	0.196078	+	0.980588i	$0.437179\pi$
$390$	−36.1076	+	7.75714i	−0.0925836	+	0.0198901i
$391$	−204.411	+	148.514i	−0.522791	+	0.379830i
$392$	−490.879	+	159.496i	−1.25224	+	0.406878i
$393$	−343.304	−	307.762i	−0.873548	−	0.783108i
$394$	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
$399$	−187.525	+	209.182i	−0.469986	+	0.524264i
$400$	173.395	+	533.656i	0.433489	+	1.33414i
$401$	11.1216	+	15.3075i	0.0277346	+	0.0381734i	0.822659	−	0.568535i	$-0.192490\pi$
$401$	11.1216	+	15.3075i	0.0277346	+	0.0381734i	−0.794925	+	0.606708i	$0.792490\pi$
$402$	−142.200	−	661.905i	−0.353730	−	1.64653i
$403$	−11.8876	−	36.5863i	−0.0294978	−	0.0907849i
$404$	107.923	+	35.0662i	0.267135	+	0.0867975i
$405$	−126.570	−	111.983i	−0.312519	−	0.276502i
$406$	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
$411$	−240.653	−	24.7638i	−0.585529	−	0.0602526i
$412$	506.283	−	367.836i	1.22884	−	0.892806i
$413$	589.625	+	811.549i	1.42766	+	1.96501i
$414$	−325.827	+	570.070i	−0.787023	+	1.37698i
$415$	−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	$-0.836014\pi$
$419$		−	412.874i		−	0.985381i	0.870205	−	0.492690i	$-0.163986\pi$
$420$	425.535	−	246.920i	1.01318	−	0.587904i
$421$	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
$423$	83.0435	−	399.232i	0.196320	−	0.943811i
$424$	569.638	−	413.866i	1.34349	−	0.976100i
$425$	243.953	−	79.2651i	0.574007	−	0.186506i
$426$	73.3631	−	81.8357i	0.172214	−	0.192103i
$427$	−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	−0.391407	−	0.920218i	$-0.628011\pi$
$431$	260.636	−	358.735i	0.604724	−	0.832331i	0.996130	+	0.0878868i	$0.0280114\pi$
$432$	−733.759	+	4.79422i	−1.69852	+	0.0110977i
$433$	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
$435$	−71.0399	+	15.2618i	−0.163310	+	0.0350845i
$436$	−160.429	−	493.749i	−0.367956	−	1.13245i
$437$	−204.365	−	66.4022i	−0.467655	−	0.151950i
$438$	694.604	−	403.049i	1.58585	−	0.920204i
$439$	−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	0.865789	−	0.500409i	$-0.166817\pi$
$443$	563.538	+	183.105i	1.27209	+	0.413328i	0.406305	+	0.913737i	$0.366817\pi$
$444$	−19.7336	+	191.770i	−0.0444451	+	0.431914i
$445$	−125.883	+	91.4591i	−0.282882	+	0.205526i
$446$	−34.8328	−	47.9432i	−0.0781005	−	0.107496i
$447$	675.422	+	69.5028i	1.51101	+	0.155487i
$448$	−26.2518	+	80.7946i	−0.0585977	+	0.180345i
$449$	−256.349	+	352.835i	−0.570934	+	0.785823i	−0.992665	−	0.120898i	$-0.961423\pi$
$449$	−256.349	+	352.835i	−0.570934	+	0.785823i	0.421731	+	0.906721i	$0.361423\pi$
$450$	493.430	−	448.194i	1.09651	−	0.995986i
$451$		0			0
$452$		−	1347.99i		−	2.98229i
$453$	−410.636	−	707.678i	−0.906480	−	1.56220i
$454$	−125.107	+	385.039i	−0.275566	+	0.848103i
$455$	−28.9267	+	9.39886i	−0.0635752	+	0.0206568i
$456$	−116.275	−	541.232i	−0.254989	−	1.18691i
$457$	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
$459$	2.19161	+	335.427i	0.00477474	+	0.730778i
$460$	304.446	+	221.193i	0.661838	+	0.480854i
$461$			711.175i			1.54268i	0.636424	+	0.771339i	$0.280413\pi$
$461$			711.175i			1.54268i	−0.636424	+	0.771339i	$0.719587\pi$
$462$		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
$465$	−109.003	−	97.7178i	−0.234415	−	0.210146i
$466$	−193.483	−	595.479i	−0.415199	−	1.27785i
$467$	28.4397	+	39.1438i	0.0608986	+	0.0838198i	0.838380	−	0.545086i	$-0.183503\pi$
$467$	28.4397	+	39.1438i	0.0608986	+	0.0838198i	−0.777481	+	0.628906i	$0.783503\pi$
$468$	128.532	+	26.7357i	0.274641	+	0.0571276i
$469$	−172.295	−	530.269i	−0.367366	−	1.13064i
$470$	−322.514	−	104.791i	−0.686199	−	0.222960i
$471$	9.12322	+	15.7227i	0.0193699	+	0.0333815i
$472$	−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
$477$	−315.020	−	180.052i	−0.660419	−	0.377467i
$478$	−1002.27	+	728.193i	−2.09680	+	1.52342i
$479$	100.761	+	138.685i	0.210357	+	0.289531i	0.901138	−	0.433533i	$-0.142733\pi$
$479$	100.761	+	138.685i	0.210357	+	0.289531i	−0.690781	+	0.723064i	$0.742733\pi$
$480$	−17.7037	+	172.043i	−0.0368827	+	0.358423i
$481$	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
$486$	363.206	+	792.437i	0.747338	+	1.63053i
$487$	−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
$489$	474.944	−	102.034i	0.971256	−	0.208659i
$490$	178.947	−	130.012i	0.365197	−	0.265331i
$491$	−314.085	+	102.052i	−0.639684	+	0.207846i	−0.610860	−	0.791738i	$-0.709176\pi$
$491$	−314.085	+	102.052i	−0.639684	+	0.207846i	−0.0288242	+	0.999584i	$0.509176\pi$
$492$	−770.172	−	690.434i	−1.56539	−	1.40332i
$493$	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
$498$	84.8264	−	94.6229i	0.170334	−	0.190006i
$499$	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
$501$	−100.321	−	466.972i	−0.200242	−	0.932080i
$502$	−219.872	−	676.695i	−0.437991	−	1.34800i
$503$	−543.721	−	176.666i	−1.08096	−	0.351224i	−0.286210	−	0.958167i	$-0.592396\pi$
$503$	−543.721	−	176.666i	−1.08096	−	0.351224i	−0.794745	+	0.606943i	$0.792396\pi$
$504$	−1384.84	+	151.654i	−2.74770	+	0.300901i
$505$	−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	−0.243570	−	0.969883i	$-0.578319\pi$
$509$	−514.449	−	167.155i	−1.01071	−	0.328398i	−0.767136	+	0.641485i	$0.778319\pi$
$510$	277.484	+	28.5539i	0.544087	+	0.0559881i
$511$	535.067	−	388.749i	1.04710	−	0.760760i
$512$	−674.549	−	928.437i	−1.31748	−	1.81335i
$513$	−229.690	+	169.184i	−0.447739	+	0.329793i
$514$	−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
$519$	−99.6917	+	57.8469i	−0.192084	+	0.111458i
$520$	18.5207	−	57.0007i	0.0356167	−	0.109617i
$521$	−321.351	+	104.413i	−0.616796	+	0.200409i	−0.600717	−	0.799462i	$-0.705118\pi$
$521$	−321.351	+	104.413i	−0.616796	+	0.200409i	−0.0160786	+	0.999871i	$0.505118\pi$
$522$	366.937	+	76.3259i	0.702945	+	0.146218i
$523$	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
$525$	366.452	−	408.773i	0.698004	−	0.778616i
$526$	−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
$531$	418.365	+	928.754i	0.787881	+	1.74907i
$532$	−256.634	−	789.837i	−0.482394	−	1.48466i
$533$	37.5858	+	51.7324i	0.0705175	+	0.0970590i
$534$	784.693	−	168.579i	1.46946	−	0.315691i
$535$	118.772	+	365.544i	0.222005	+	0.683260i
$536$	1044.91	+	339.511i	1.94945	+	0.633415i
$537$	353.292	−	205.000i	0.657899	−	0.381751i
$538$	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
$543$	−40.0257	+	388.966i	−0.0737121	+	0.716327i
$544$	277.721	−	201.776i	0.510516	−	0.370912i
$545$	71.7898	+	98.8103i	0.131724	+	0.181303i
$546$	156.061	+	16.0591i	0.285826	+	0.0294123i
$547$	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
$552$	−534.801	−	921.661i	−0.968843	−	1.66968i
$553$	236.394	−	727.547i	0.427476	−	1.31564i
$554$	−835.593	+	271.500i	−1.50829	+	0.490073i
$555$	−9.52613	−	44.3418i	−0.0171642	−	0.0798952i
$556$	−1520.64	+	1104.81i	−2.73496	+	1.98706i
$557$	−364.339	+	118.381i	−0.654109	+	0.212533i	−0.617225	−	0.786787i	$-0.711743\pi$
$557$	−364.339	+	118.381i	−0.654109	+	0.212533i	−0.0368842	+	0.999320i	$0.511743\pi$
$558$	310.129	+	688.475i	0.555787	+	1.23383i
$559$	−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	−0.877903	−	0.478839i	$-0.841058\pi$
$563$	−85.1328	+	117.175i	−0.151213	+	0.208127i	0.726690	+	0.686966i	$0.241058\pi$
$564$	897.589	+	804.660i	1.59147	+	1.42670i
$565$	97.9974	+	301.605i	0.173447	+	0.533814i
$566$	332.256	+	457.311i	0.587025	+	0.807971i
$567$	364.355	+	618.573i	0.642601	+	1.09096i
$568$	55.1163	+	169.630i	0.0970357	+	0.298645i
$569$	−877.968	−	285.269i	−1.54300	−	0.501352i	−0.590800	−	0.806818i	$-0.701188\pi$
$569$	−877.968	−	285.269i	−1.54300	−	0.501352i	−0.952203	+	0.305466i	$0.901188\pi$
$570$	119.065	+	205.193i	0.208886	+	0.359987i
$571$	−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
$576$	−42.8069	+	74.8952i	−0.0743175	+	0.130026i
$577$	−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
$579$	−44.9605	+	436.923i	−0.0776521	+	0.754616i
$580$	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
$585$	−30.7019	+	3.36217i	−0.0524818	+	0.00574729i
$586$	203.979	−	627.784i	0.348088	−	1.07130i
$587$	−40.3860	+	13.1222i	−0.0688007	+	0.0223547i	−0.343215	−	0.939257i	$-0.611516\pi$
$587$	−40.3860	+	13.1222i	−0.0688007	+	0.0223547i	0.274414	+	0.961612i	$0.411516\pi$
$588$	−768.742	+	165.152i	−1.30738	+	0.280870i
$589$	−199.918	+	145.249i	−0.339420	+	0.246603i
$590$	805.643	−	261.769i	1.36550	−	0.443677i
$591$	512.565	+	459.498i	0.867284	+	0.777492i
$592$	−159.313	−	115.748i	−0.269109	−	0.195519i
$593$		−	106.267i		−	0.179203i	−0.995978	−	0.0896015i	$-0.971441\pi$
$593$		−	106.267i		−	0.179203i	0.995978	−	0.0896015i	$-0.0285593\pi$
$594$		0			0
$595$	229.732			0.386105
$596$	−1179.81	+	1623.87i	−1.97955	+	2.72461i
$597$	779.702	−	869.749i	1.30603	−	1.45687i
$598$	37.0822	+	114.127i	0.0620103	+	0.190848i
$599$	−427.915	−	588.974i	−0.714382	−	0.983263i	−0.999692	−	0.0248274i	$-0.992096\pi$
$599$	−427.915	−	588.974i	−0.714382	−	0.983263i	0.285309	−	0.958435i	$-0.407904\pi$
$600$	227.220	+	1057.65i	0.378699	+	1.76275i
$601$	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
$603$	−61.6334	−	562.809i	−0.102211	−	0.933349i
$604$	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
$609$	307.042	+	31.5955i	0.504175	+	0.0518810i
$610$	−469.365	+	341.013i	−0.769450	+	0.559038i
$611$	−43.8040	−	60.2910i	−0.0716923	−	0.0986760i
$612$	−860.906	−	492.057i	−1.40671	−	0.804015i
$613$	−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	$0.211907\pi$
$617$			762.156i			1.23526i	−0.786468	+	0.617631i	$0.788093\pi$
$618$	656.830	−	381.131i	1.06283	−	0.616716i
$619$	−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
$621$	−319.855	+	446.347i	−0.515065	+	0.718755i
$622$	−267.702	+	194.497i	−0.430388	+	0.312695i
$623$	628.637	−	204.257i	1.00905	−	0.327860i
$624$	−89.5144	+	99.8523i	−0.143453	+	0.160020i
$625$	−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
$630$	544.338	−	245.201i	0.864028	−	0.389208i
$631$	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
$633$	−598.317	+	128.539i	−0.945208	+	0.203063i
$634$	580.624	+	1786.98i	0.915811	+	2.81858i
$635$	−28.3241	−	9.20306i	−0.0446049	−	0.0144930i
$636$	927.757	−	538.338i	1.45874	−	0.846444i
$637$	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	−0.338865	−	0.940835i	$-0.610043\pi$
$641$	−747.420	−	242.852i	−1.16602	−	0.378864i	−0.827157	+	0.561971i	$0.810043\pi$
$642$	202.938	−	1972.13i	0.316102	−	3.07185i
$643$	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
$645$	−98.6519	−	10.1516i	−0.152949	−	0.0157388i
$646$	145.508	−	447.828i	0.225245	−	0.693233i
$647$	−687.343	+	946.046i	−1.06235	+	1.46220i	−0.184769	+	0.982782i	$0.559154\pi$
$647$	−687.343	+	946.046i	−1.06235	+	1.46220i	−0.877584	+	0.479422i	$0.840846\pi$
$648$	−1408.13	−	135.609i	−2.17305	−	0.209274i
$649$		0			0
$650$		−	121.825i		−	0.187423i
$651$	312.108	+	537.879i	0.479429	+	0.826234i
$652$	−443.765	+	1365.77i	−0.680622	+	2.09474i
$653$	−509.322	+	165.489i	−0.779972	+	0.253428i	−0.671828	−	0.740707i	$-0.734491\pi$
$653$	−509.322	+	165.489i	−0.779972	+	0.253428i	−0.108144	+	0.994135i	$0.534491\pi$
$654$	−132.324	−	615.937i	−0.202330	−	0.941800i
$655$	−259.411	+	188.473i	−0.396048	+	0.287746i
$656$	1004.84	−	326.492i	1.53177	−	0.497701i
$657$	612.341	−	275.834i	0.932027	−	0.419839i
$658$	1165.43	+	846.732i	1.77117	+	1.28683i
$659$			138.756i			0.210555i	0.994443	+	0.105278i	$0.0335731\pi$
$659$			138.756i			0.210555i	−0.994443	+	0.105278i	$0.966427\pi$
$660$		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
$663$	45.6460	+	40.9202i	0.0688477	+	0.0617197i
$664$	63.7284	+	196.136i	0.0959765	+	0.295385i
$665$	114.840	+	158.064i	0.172692	+	0.237690i
$666$	−47.6413	+	229.036i	−0.0715335	+	0.343897i
$667$	72.9572	+	224.539i	0.109381	+	0.336640i
$668$	1342.84	+	436.317i	2.01025	+	0.653169i
$669$	−24.8731	−	42.8657i	−0.0371796	−	0.0640742i
$670$	−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
$675$	448.851	−	330.611i	0.664964	−	0.489794i
$676$	−1193.13	+	866.860i	−1.76499	+	1.28234i
$677$	−359.292	−	494.523i	−0.530712	−	0.730463i	0.456526	−	0.889710i	$-0.349093\pi$
$677$	−359.292	−	494.523i	−0.530712	−	0.730463i	−0.987239	+	0.159247i	$0.949093\pi$
$678$	167.441	−	1627.18i	0.246963	−	2.39996i
$679$	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	$-0.741782\pi$
$683$		−	990.520i		−	1.45025i	0.688618	−	0.725124i	$-0.258218\pi$
$684$	−91.8031	−	838.307i	−0.134215	−	1.22559i
$685$	−51.9918	+	160.014i	−0.0759005	+	0.233598i
$686$	588.032	−	191.063i	0.857189	−	0.278518i
$687$	−1081.19	+	232.275i	−1.57378	+	0.338101i
$688$	−348.363	+	253.100i	−0.506341	+	0.367879i
$689$	−63.0665	+	20.4915i	−0.0915333	+	0.0297410i
$690$	340.024	+	304.820i	0.492788	+	0.441768i
$691$	−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
$696$	−405.999	+	452.887i	−0.583332	+	0.650700i
$697$	−149.251	−	459.347i	−0.214133	−	0.659035i
$698$	830.239	+	1142.73i	1.18945	+	1.63714i
$699$	−109.982	−	511.940i	−0.157342	−	0.732389i
$700$	501.502	+	1543.46i	0.716431	+	2.20495i
$701$	778.940	+	253.093i	1.11118	+	0.361046i	0.806397	−	0.591375i	$-0.201415\pi$
$701$	778.940	+	253.093i	1.11118	+	0.361046i	0.304787	+	0.952420i	$0.401415\pi$
$702$	151.831	+	48.2385i	0.216284	+	0.0687158i
$703$	−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
$708$	−2995.45	−	308.240i	−4.23086	−	0.435367i
$709$	−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
$711$	385.471	−	674.423i	0.542154	−	0.948556i
$712$	−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
$717$	−896.123	+	519.983i	−1.24982	+	0.725220i
$718$	84.1241	−	258.907i	0.117165	−	0.360595i
$719$	633.724	−	205.910i	0.881397	−	0.286383i	0.166860	−	0.985981i	$-0.446637\pi$
$719$	633.724	−	205.910i	0.881397	−	0.286383i	0.714537	+	0.699597i	$0.246637\pi$
$720$	−103.925	+	499.620i	−0.144340	+	0.693917i
$721$	505.968	−	367.607i	0.701759	−	0.509858i
$722$	−850.765	+	276.430i	−1.17834	+	0.382867i
$723$	−523.556	+	584.021i	−0.724144	+	0.807774i
$724$	−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
$729$	234.314	+	690.317i	0.321418	+	0.946937i
$730$	−172.588	−	531.172i	−0.236422	−	0.727633i
$731$	115.701	+	159.249i	0.158278	+	0.217851i
$732$	2016.36	−	433.182i	2.75459	−	0.591778i
$733$	−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
$735$	159.995	−	92.8382i	0.217680	−	0.126310i
$736$	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
$741$	−5.33669	+	51.8615i	−0.00720202	+	0.0699886i
$742$	1037.01	−	753.430i	1.39759	−	1.01540i
$743$	484.132	+	666.351i	0.651591	+	0.896838i	0.999167	−	0.0408136i	$-0.0129950\pi$
$743$	484.132	+	666.351i	0.651591	+	0.896838i	−0.347576	+	0.937652i	$0.612995\pi$
$744$	−1218.98	−	125.436i	−1.63841	−	0.168597i
$745$	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
$750$	−514.397	−	886.497i	−0.685862	−	1.18200i
$751$	−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
$753$	−124.982	−	581.762i	−0.165979	−	0.772592i
$754$	55.4139	−	40.2606i	0.0734933	−	0.0533960i
$755$	−541.170	+	175.837i	−0.716782	+	0.232896i
$756$	−2122.21	+	13.8660i	−2.80716	+	0.0183413i
$757$	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	$-0.510796\pi$
$761$	705.506	−	971.046i	0.927078	−	1.27601i	0.960989	−	0.276588i	$-0.0892038\pi$
$762$	114.383	+	102.541i	0.150109	+	0.134568i
$763$	−160.329	−	493.442i	−0.210130	−	0.646713i
$764$	−1645.05	−	2264.22i	−2.15321	−	2.96364i
$765$	228.394	+	47.5078i	0.298554	+	0.0621017i
$766$	58.7094	+	180.689i	0.0766442	+	0.235887i
$767$	177.050	+	57.5270i	0.230834	+	0.0750027i
$768$	−724.965	−	1249.38i	−0.943965	−	1.62680i
$769$	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	−0.0746805	−	0.997208i	$-0.523794\pi$
$773$	−557.520	−	181.149i	−0.721242	−	0.234346i	−0.646562	+	0.762862i	$0.723794\pi$
$774$	444.119	+	253.839i	0.573797	+	0.327958i
$775$	390.671	−	283.839i	0.504092	−	0.366244i
$776$	792.170	+	1090.33i	1.02084	+	1.40506i
$777$	−19.7214	+	191.650i	−0.0253814	+	0.246654i
$778$	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
$783$	298.720	+	94.9067i	0.381507	+	0.121209i
$784$	248.191	−	763.854i	0.316570	−	0.974303i
$785$	12.0233	−	3.90662i	0.0153164	−	0.00497659i
$786$	1617.05	−	347.397i	2.05731	−	0.441981i
$787$	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
$789$	−60.5138	−	54.2487i	−0.0766969	−	0.0687563i
$790$	−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
$795$	−168.443	+	187.896i	−0.211878	+	0.236348i
$796$	1067.05	+	3284.04i	1.34051	+	4.12567i
$797$	491.864	+	676.992i	0.617144	+	0.849426i	0.997141	−	0.0755619i	$-0.0240751\pi$
$797$	491.864	+	676.992i	0.617144	+	0.849426i	−0.379997	+	0.924988i	$0.624075\pi$
$798$	−211.675	−	985.297i	−0.265257	−	1.23471i
$799$	173.943	+	535.341i	0.217701	+	0.670014i
$800$	−542.587	−	176.297i	−0.678234	−	0.220372i
$801$	667.215	−	73.0668i	0.832977	−	0.0912195i
$802$	−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
$807$	426.292	+	43.8667i	0.528243	+	0.0543577i
$808$	−180.790	+	131.352i	−0.223750	+	0.162564i
$809$	−304.962	−	419.745i	−0.376962	−	0.518844i	0.577814	−	0.816168i	$-0.303906\pi$
$809$	−304.962	−	419.745i	−0.376962	−	0.518844i	−0.954777	+	0.297324i	$0.903906\pi$
$810$	591.874	−	131.206i	0.730708	−	0.161983i
$811$	−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
$816$	876.087	−	508.356i	1.07364	−	0.622986i
$817$	−51.7314	+	159.213i	−0.0633187	+	0.194875i
$818$	406.889	−	132.206i	0.497419	−	0.161621i
$819$	128.452	+	26.7191i	0.156840	+	0.0326240i
$820$	−581.965	+	422.822i	−0.709714	+	0.515637i
$821$	−524.622	+	170.460i	−0.639004	+	0.207625i	−0.610560	−	0.791970i	$-0.709055\pi$
$821$	−524.622	+	170.460i	−0.639004	+	0.207625i	−0.0284445	+	0.999595i	$0.509055\pi$
$822$	579.296	−	646.198i	0.704740	−	0.786129i
$823$	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	−0.966505	−	0.256646i	$-0.917382\pi$
$827$	−350.444	+	482.345i	−0.423753	+	0.583247i	0.542752	+	0.839893i	$0.317382\pi$
$828$	−666.708	−	1480.07i	−0.805203	−	1.78752i
$829$	−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
$831$	−718.368	+	154.330i	−0.864462	+	0.185716i
$832$	4.87182	+	14.9939i	0.00585555	+	0.0180215i
$833$	−349.184	−	113.457i	−0.419189	−	0.136203i
$834$	−1972.81	+	1144.74i	−2.36548	+	1.37259i
$835$	−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	$-0.939642\pi$
$839$	−1583.51	−	514.515i	−1.88738	−	0.613247i	−0.905305	−	0.424761i	$-0.860358\pi$
$840$	−99.1751	+	963.775i	−0.118066	+	1.14735i
$841$	−571.359	+	415.117i	−0.679381	+	0.493599i
$842$	1275.55	+	1755.64i	1.51490	+	2.08509i
$843$	194.308	+	19.9949i	0.230496	+	0.0237187i
$844$	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
$849$	237.255	+	408.878i	0.279452	+	0.481600i
$850$	−284.346	+	875.127i	−0.334525	+	1.02956i
$851$	−140.153	+	45.5386i	−0.164693	+	0.0535119i
$852$	57.0706	+	265.650i	0.0669843	+	0.311796i
$853$	−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
$855$	81.4841	+	180.892i	0.0953031	+	0.211569i
$856$	2602.90	+	1891.12i	3.04078	+	2.20925i
$857$		−	551.421i		−	0.643431i	−0.946836	−	0.321716i	$-0.895740\pi$
$857$		−	551.421i		−	0.643431i	0.946836	−	0.321716i	$-0.104260\pi$
$858$		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
$861$	−769.693	−	690.005i	−0.893952	−	0.801400i
$862$	491.544	+	1512.82i	0.570237	+	1.75501i
$863$	421.079	+	579.565i	0.487924	+	0.671570i	0.980003	−	0.198980i	$-0.0637630\pi$
$863$	421.079	+	579.565i	0.487924	+	0.671570i	−0.492079	+	0.870550i	$0.663763\pi$
$864$	434.567	−	606.423i	0.502971	−	0.701879i
$865$	24.7704	+	76.2355i	0.0286363	+	0.0881335i
$866$	−747.094	−	242.745i	−0.862695	−	0.280307i
$867$	202.747	+	349.408i	0.233848	+	0.403008i
$868$	−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
$873$	344.632	−	602.970i	0.394767	−	0.690688i
$874$	623.624	−	453.089i	0.713528	−	0.518409i
$875$	−496.145	−	682.885i	−0.567023	−	0.780440i
$876$	−203.227	+	1974.94i	−0.231994	+	2.25450i
$877$	−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	$-0.747272\pi$
$881$		−	1256.55i		−	1.42628i	0.701021	−	0.713140i	$-0.252728\pi$
$882$	−948.469	+	103.867i	−1.07536	+	0.117763i
$883$	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
$885$	692.620	−	148.798i	0.782622	−	0.168134i
$886$	−1719.65	+	1249.40i	−1.94091	+	1.41015i
$887$	1116.54	−	362.787i	1.25879	−	0.409005i	0.397725	−	0.917505i	$-0.369800\pi$
$887$	1116.54	−	362.787i	1.25879	−	0.409005i	0.861062	+	0.508500i	$0.169800\pi$
$888$	−282.684	−	253.418i	−0.318338	−	0.285380i
$889$	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
$894$	−1625.87	+	1813.64i	−1.81864	+	2.02868i
$895$	−87.7825	−	270.167i	−0.0980810	−	0.301862i
$896$	−754.921	−	1039.06i	−0.842546	−	1.15966i
$897$	21.0787	+	98.1164i	0.0234991	+	0.109383i
$898$	−483.460	−	1487.94i	−0.538374	−	1.65695i
$899$	258.218	+	83.9001i	0.287228	+	0.0933260i
$900$	179.398	+	1638.18i	0.199331	+	1.82020i
$901$	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
$906$	2919.64	+	300.439i	3.22256	+	0.331611i
$907$	−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
$909$	99.9802	+	57.1444i	0.109989	+	0.0628651i
$910$	33.7163	−	103.768i	0.0370509	−	0.114031i
$911$	632.867	−	871.067i	0.694695	−	0.956166i	−0.305297	−	0.952257i	$-0.598756\pi$
$911$	632.867	−	871.067i	0.694695	−	0.956166i	0.999992	−	0.00390866i	$-0.00124417\pi$
$912$	787.712	+	348.658i	0.863719	+	0.382301i
$913$		0			0
$914$			855.714i			0.936230i
$915$	−419.655	+	243.508i	−0.458639	+	0.266129i
$916$	1010.21	−	3109.11i	1.10285	−	3.39422i
$917$	1295.46	−	420.920i	1.41271	−	0.459018i
$918$	−978.087	−	700.904i	−1.06545	−	0.763512i
$919$	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
$921$	774.323	−	863.749i	0.840742	−	0.937838i
$922$	−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
$927$	579.041	−	260.834i	0.624639	−	0.281374i
$928$	−99.1224	−	305.067i	−0.106813	−	0.328736i
$929$	−657.526	−	905.007i	−0.707778	−	0.974173i	−0.999842	−	0.0177741i	$-0.994342\pi$
$929$	−657.526	−	905.007i	−0.707778	−	0.974173i	0.292064	−	0.956399i	$-0.405658\pi$
$930$	513.431	−	110.302i	0.552077	−	0.118605i
$931$	−96.4904	−	296.967i	−0.103642	−	0.318976i
$932$	1472.16	+	478.333i	1.57957	+	0.513233i
$933$	−239.350	+	138.885i	−0.256538	+	0.148858i
$934$	−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
$939$	−22.8466	+	222.021i	−0.0243307	+	0.236444i
$940$	678.245	−	492.774i	0.721538	−	0.524228i
$941$	188.418	+	259.335i	0.200231	+	0.275595i	0.897311	−	0.441399i	$-0.145518\pi$
$941$	188.418	+	259.335i	0.200231	+	0.275595i	−0.697080	+	0.716994i	$0.745518\pi$
$942$	−64.8666	−	6.67496i	−0.0688605	−	0.00708594i
$943$	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	$0.118691\pi$
$947$			689.980i			0.728596i	−0.931283	+	0.364298i	$0.881309\pi$
$948$	1152.52	+	1986.23i	1.21574	+	2.09518i
$949$	37.9284	−	116.732i	0.0399667	−	0.123005i
$950$	−744.259	+	241.824i	−0.783430	+	0.254552i
$951$	330.046	+	1536.28i	0.347052	+	1.61544i
$952$	1555.78	−	1130.34i	1.63422	−	1.18733i
$953$	−1276.39	+	414.726i	−1.33934	+	0.435179i	−0.889094	−	0.457724i	$-0.848665\pi$
$953$	−1276.39	+	414.726i	−1.33934	+	0.435179i	−0.450249	+	0.892903i	$0.648665\pi$
$954$	1186.77	−	534.592i	1.24400	−	0.560369i
$955$	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
$960$	44.6719	+	40.0470i	0.0465333	+	0.0417156i
$961$	−127.930	−	393.727i	−0.133122	−	0.409706i
$962$	25.1299	+	34.5884i	0.0261226	+	0.0359547i
$963$	337.646	−	1623.24i	0.350619	−	1.68560i
$964$	−716.504	−	2205.17i	−0.743261	−	2.28752i
$965$	290.518	+	94.3950i	0.301055	+	0.0978187i
$966$	−973.589	−	1677.86i	−1.00786	−	1.73691i
$967$	−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	0.694454	−	0.719537i	$-0.255646\pi$
$971$	809.179	+	262.918i	0.833346	+	0.270770i	0.138892	+	0.990308i	$0.455646\pi$
$972$	−2112.72	−	425.081i	−2.17358	−	0.437326i
$973$	−1519.69	+	1104.12i	−1.56186	+	1.13476i
$974$	−1044.78	−	1438.02i	−1.07267	−	1.47640i
$975$	10.4287	−	101.346i	0.0106961	−	0.103944i
$976$	−650.988	+	2003.54i	−0.666996	+	2.05280i
$977$	712.767	−	981.039i	0.729546	−	1.00413i	−0.269606	−	0.962971i	$-0.586893\pi$
$977$	712.767	−	981.039i	0.729546	−	1.00413i	0.999152	−	0.0411637i	$-0.0131065\pi$
$978$	−705.322	+	1593.51i	−0.721188	+	1.62936i
$979$		0			0
$980$			546.831i			0.557991i
$981$	−57.3530	−	523.723i	−0.0584639	−	0.533867i
$982$	366.090	−	1126.71i	0.372801	−	1.14736i
$983$	−432.404	+	140.496i	−0.439882	+	0.142926i	−0.520581	−	0.853812i	$-0.674285\pi$
$983$	−432.404	+	140.496i	−0.439882	+	0.142926i	0.0806993	+	0.996738i	$0.474285\pi$
$984$	1991.49	−	427.839i	2.02387	−	0.434796i
$985$	387.310	−	281.397i	0.393208	−	0.285682i
$986$	−492.036	+	159.872i	−0.499022	+	0.162142i
$987$	897.030	+	804.159i	0.908845	+	0.814751i
$988$	−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
$993$	−504.049	+	562.261i	−0.507602	+	0.566225i
$994$	100.337	+	308.807i	0.100943	+	0.310671i
$995$	−477.490	−	657.209i	−0.479890	−	0.660512i
$996$	65.9881	+	307.159i	0.0662531	+	0.308392i
$997$	−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
$999$	−59.2391	+	186.456i	−0.0592984	+	0.186642i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.1	✓	16	11.8	odd	10
33.3.h.b.14.4	yes	16	33.8	even	10
33.3.h.b.26.1	yes	16	33.32	even	2
33.3.h.b.26.4	yes	16	11.10	odd	2
363.3.b.l.122.1		8	11.5	even	5
363.3.b.l.122.8		8	33.5	odd	10
363.3.b.m.122.1		8	33.17	even	10
363.3.b.m.122.8		8	11.6	odd	10
363.3.h.j.245.1		16	33.14	odd	10	inner
363.3.h.j.245.4		16	11.3	even	5	inner
363.3.h.j.323.1		16	1.1	even	1	trivial
363.3.h.j.323.4		16	3.2	odd	2	inner
363.3.h.n.251.1		16	11.4	even	5
363.3.h.n.251.4		16	33.26	odd	10
363.3.h.n.269.1		16	33.20	odd	10
363.3.h.n.269.4		16	11.9	even	5
363.3.h.o.251.1		16	33.29	even	10
363.3.h.o.251.4		16	11.7	odd	10
363.3.h.o.269.1		16	11.2	odd	10
363.3.h.o.269.4		16	33.2	even	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} +(-2.00253 + 2.23380i) q^{3} +(-2.74053 - 8.43448i) q^{4} +(1.22635 + 1.68793i) q^{5} +(-2.26043 - 10.5218i) q^{6} +(-2.73883 - 8.42924i) q^{7} +(16.6100 + 5.39692i) q^{8} +(-0.979734 - 8.94651i) q^{9} -7.48447 q^{10} +(24.3290 + 10.7685i) q^{12} +(-1.33068 - 0.966792i) q^{13} +(30.2380 + 9.82492i) q^{14} +(-6.22630 - 0.640704i) q^{15} +(-21.9865 + 15.9742i) q^{16} +(7.30235 + 10.0508i) q^{17} +(28.0301 + 16.0208i) q^{18} +(-3.26497 + 10.0485i) q^{19} +(10.8759 - 14.9695i) q^{20} +(24.3138 + 10.7618i) q^{21} +20.3378i q^{23} +(-45.3177 + 26.2959i) q^{24} +(6.38026 - 19.6364i) q^{25} +(5.61158 - 1.82331i) q^{26} +(21.9467 + 15.7271i) q^{27} +(-63.5904 + 46.2012i) q^{28} +(11.0405 - 3.58727i) q^{29} +(14.9879 - 16.7188i) q^{30} +(18.9215 + 13.7473i) q^{31} -27.6317i q^{32} -44.5665 q^{34} +(10.8692 - 14.9601i) q^{35} +(-72.7742 + 32.7817i) q^{36} +(2.23911 + 6.89128i) q^{37} +(-22.2782 - 30.6633i) q^{38} +(4.82434 - 1.03643i) q^{39} +(11.2601 + 34.6550i) q^{40} +(-36.9741 - 12.0136i) q^{41} +(-82.4995 + 47.8710i) q^{42} +15.8444 q^{43} +(13.8996 - 12.6253i) q^{45} +(-59.0236 - 42.8832i) q^{46} +(43.0910 + 14.0011i) q^{47} +(8.34565 - 81.1023i) q^{48} +(-23.9091 + 17.3709i) q^{49} +(43.5351 + 59.9209i) q^{50} +(-37.0747 - 3.81509i) q^{51} +(-4.50764 + 13.8731i) q^{52} +(23.6972 - 32.6164i) q^{53} +(-91.9184 + 30.5315i) q^{54} -154.791i q^{56} +(-15.9082 - 27.4158i) q^{57} +(-12.8685 + 39.6053i) q^{58} +(-107.642 + 34.9750i) q^{59} +(11.6594 + 54.2715i) q^{60} +(62.7118 - 45.5628i) q^{61} +(-79.7937 + 25.9266i) q^{62} +(-72.7290 + 32.7614i) q^{63} +(-7.75446 - 5.63395i) q^{64} -3.43171i q^{65} +62.9082 q^{67} +(64.7612 - 89.1361i) q^{68} +(-45.4306 - 40.7270i) q^{69} +(20.4987 + 63.0884i) q^{70} +(6.00278 + 8.26212i) q^{71} +(32.0102 - 153.889i) q^{72} +(23.0595 + 70.9699i) q^{73} +(-24.7209 - 8.03232i) q^{74} +(31.0872 + 53.5748i) q^{75} +93.7020 q^{76} +(-7.16445 + 16.1864i) q^{78} +(69.8281 + 50.7331i) q^{79} +(-53.9264 - 17.5218i) q^{80} +(-79.0802 + 17.5304i) q^{81} +(112.827 - 81.9736i) q^{82} +(6.94074 + 9.55311i) q^{83} +(24.1377 - 234.568i) q^{84} +(-8.00981 + 24.6517i) q^{85} +(-33.4086 + 45.9830i) q^{86} +(-14.0957 + 31.8459i) q^{87} +74.5782i q^{89} +(7.33279 + 66.9599i) q^{90} +(-4.50483 + 13.8645i) q^{91} +(171.539 - 55.7363i) q^{92} +(-68.5996 + 14.7375i) q^{93} +(-131.493 + 95.5353i) q^{94} +(-20.9652 + 6.81201i) q^{95} +(61.7236 + 55.3333i) 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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