LMFDB - Embedded newform 16.3.f.a.11.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,3,Mod(3,16)] 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("16.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.435968422976$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.1
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.3.f.a.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55139 + 1.26222i) q^{2} +(2.10278 + 2.10278i) q^{3} +(0.813607 - 3.91638i) q^{4} +(-4.62721 - 4.62721i) q^{5} +(-5.91638 - 0.608056i) q^{6} +3.04888 q^{7} +(3.68111 + 7.10278i) q^{8} -0.156674i q^{9} +(13.0192 + 1.33804i) q^{10} +(-9.15165 + 9.15165i) q^{11} +(9.94610 - 6.52444i) q^{12} +(-5.78389 + 5.78389i) q^{13} +(-4.72999 + 3.84835i) q^{14} -19.4600i q^{15} +(-14.6761 - 6.37279i) q^{16} +17.6655 q^{17} +(0.197757 + 0.243062i) q^{18} +(-1.15165 - 1.15165i) q^{19} +(-21.8867 + 14.3572i) q^{20} +(6.41110 + 6.41110i) q^{21} +(2.64637 - 25.7491i) q^{22} -3.45998 q^{23} +(-7.19499 + 22.6761i) q^{24} +17.8222i q^{25} +(1.67252 - 16.2736i) q^{26} +(19.2544 - 19.2544i) q^{27} +(2.48059 - 11.9406i) q^{28} +(12.1950 - 12.1950i) q^{29} +(24.5628 + 30.1900i) q^{30} +38.5089i q^{31} +(30.8122 - 8.63778i) q^{32} -38.4877 q^{33} +(-27.4061 + 22.2978i) q^{34} +(-14.1078 - 14.1078i) q^{35} +(-0.613596 - 0.127471i) q^{36} +(-0.0972356 - 0.0972356i) q^{37} +(3.24029 + 0.333021i) q^{38} -24.3244 q^{39} +(15.8328 - 49.8993i) q^{40} -51.5266i q^{41} +(-18.0383 - 1.85389i) q^{42} +(-1.70172 + 1.70172i) q^{43} +(28.3955 + 43.2872i) q^{44} +(-0.724965 + 0.724965i) q^{45} +(5.36776 - 4.36725i) q^{46} +24.1533i q^{47} +(-17.4600 - 44.2611i) q^{48} -39.7044 q^{49} +(-22.4955 - 27.6491i) q^{50} +(37.1466 + 37.1466i) q^{51} +(17.9461 + 27.3577i) q^{52} +(27.0383 + 27.0383i) q^{53} +(-5.56777 + 54.1744i) q^{54} +84.6933 q^{55} +(11.2233 + 21.6555i) q^{56} -4.84333i q^{57} +(-3.52641 + 34.3119i) q^{58} +(19.5939 - 19.5939i) q^{59} +(-76.2127 - 15.8328i) q^{60} +(16.7250 - 16.7250i) q^{61} +(-48.6066 - 59.7422i) q^{62} -0.477680i q^{63} +(-36.8988 + 52.2922i) q^{64} +53.5266 q^{65} +(59.7094 - 48.5799i) q^{66} +(-75.8560 - 75.8560i) q^{67} +(14.3728 - 69.1849i) q^{68} +(-7.27555 - 7.27555i) q^{69} +(39.6938 + 4.07953i) q^{70} -134.749 q^{71} +(1.11282 - 0.576735i) q^{72} +112.210i q^{73} +(0.273583 + 0.0281175i) q^{74} +(-37.4761 + 37.4761i) q^{75} +(-5.44730 + 3.57331i) q^{76} +(-27.9022 + 27.9022i) q^{77} +(37.7366 - 30.7028i) q^{78} -135.915i q^{79} +(38.4211 + 97.3976i) q^{80} +79.5654 q^{81} +(65.0378 + 79.9377i) q^{82} +(74.9250 + 74.9250i) q^{83} +(30.3244 - 19.8922i) q^{84} +(-81.7422 - 81.7422i) q^{85} +(0.492084 - 4.78797i) q^{86} +51.2866 q^{87} +(-98.6904 - 31.3139i) q^{88} -31.4278i q^{89} +(0.209637 - 2.03977i) q^{90} +(-17.6344 + 17.6344i) q^{91} +(-2.81506 + 13.5506i) q^{92} +(-80.9755 + 80.9755i) q^{93} +(-30.4867 - 37.4711i) q^{94} +10.6579i q^{95} +(82.9543 + 46.6277i) q^{96} +31.5456 q^{97} +(61.5968 - 50.1156i) q^{98} +(1.43383 + 1.43383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21}+ \cdots - 226 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8 + 36 * q^10 - 18 * q^11 + 52 * q^12 - 2 * q^13 + 12 * q^14 - 40 * q^16 - 4 * q^17 - 74 * q^18 + 30 * q^19 - 84 * q^20 - 20 * q^21 - 52 * q^22 + 60 * q^23 + 48 * q^24 + 96 * q^26 + 64 * q^27 + 56 * q^28 - 18 * q^29 + 52 * q^30 + 8 * q^32 - 4 * q^33 - 76 * q^34 - 100 * q^35 - 52 * q^36 + 46 * q^37 + 40 * q^38 - 196 * q^39 + 40 * q^40 - 24 * q^42 - 114 * q^43 + 20 * q^44 + 66 * q^45 + 28 * q^46 - 24 * q^48 - 46 * q^49 + 46 * q^50 + 156 * q^51 + 100 * q^52 + 78 * q^53 + 32 * q^54 + 252 * q^55 - 168 * q^56 - 176 * q^58 + 206 * q^59 - 160 * q^60 + 30 * q^61 - 144 * q^62 + 64 * q^64 + 12 * q^65 + 196 * q^66 - 226 * q^67 + 112 * q^68 - 116 * q^69 - 16 * q^70 - 260 * q^71 + 52 * q^72 - 92 * q^74 - 238 * q^75 - 188 * q^76 - 212 * q^77 - 84 * q^78 + 232 * q^80 + 86 * q^81 + 304 * q^82 + 318 * q^83 + 232 * q^84 - 212 * q^85 + 268 * q^86 + 444 * q^87 - 8 * q^88 - 160 * q^90 + 188 * q^91 - 168 * q^92 - 32 * q^93 + 48 * q^94 - 80 * q^96 - 4 * q^97 + 10 * q^98 - 226 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.55139	+	1.26222i	−0.775694	+	0.631109i
$2$	−1.55139	+	1.26222i	−0.775694	+	0.631109i
$3$	2.10278	+	2.10278i	0.700925	+	0.700925i	0.964609	−	0.263684i	$-0.0849376\pi$
$3$	2.10278	+	2.10278i	0.700925	+	0.700925i	−0.263684	+	0.964609i	$0.584938\pi$
$4$	0.813607	−	3.91638i	0.203402	−	0.979095i
$5$	−4.62721	−	4.62721i	−0.925443	−	0.925443i	0.0719646	−	0.997407i	$-0.477073\pi$
$5$	−4.62721	−	4.62721i	−0.925443	−	0.925443i	−0.997407	+	0.0719646i	$0.977073\pi$
$6$	−5.91638	−	0.608056i	−0.986064	−	0.101343i
$7$	3.04888			0.435554			0.217777	−	0.975999i	$-0.430119\pi$
$7$	3.04888			0.435554			0.217777	+	0.975999i	$0.430119\pi$
$8$	3.68111	+	7.10278i	0.460139	+	0.887847i
$9$		−	0.156674i		−	0.0174082i
$10$	13.0192	+	1.33804i	1.30192	+	0.133804i
$11$	−9.15165	+	9.15165i	−0.831968	+	0.831968i	−0.987786	−	0.155818i	$-0.950199\pi$
$11$	−9.15165	+	9.15165i	−0.831968	+	0.831968i	0.155818	+	0.987786i	$0.450199\pi$
$12$	9.94610	−	6.52444i	0.828842	−	0.543703i
$13$	−5.78389	+	5.78389i	−0.444914	+	0.444914i	−0.893660	−	0.448745i	$-0.851871\pi$
$13$	−5.78389	+	5.78389i	−0.444914	+	0.444914i	0.448745	+	0.893660i	$0.351871\pi$
$14$	−4.72999	+	3.84835i	−0.337856	+	0.274882i
$15$		−	19.4600i		−	1.29733i
$16$	−14.6761	−	6.37279i	−0.917256	−	0.398299i
$17$	17.6655			1.03915			0.519574	−	0.854425i	$-0.326091\pi$
$17$	17.6655			1.03915			0.519574	+	0.854425i	$0.326091\pi$
$18$	0.197757	+	0.243062i	0.0109865	+	0.0135035i
$19$	−1.15165	−	1.15165i	−0.0606132	−	0.0606132i	0.676150	−	0.736764i	$-0.263647\pi$
$19$	−1.15165	−	1.15165i	−0.0606132	−	0.0606132i	−0.736764	+	0.676150i	$0.763647\pi$
$20$	−21.8867	+	14.3572i	−1.09433	+	0.717860i
$21$	6.41110	+	6.41110i	0.305290	+	0.305290i
$22$	2.64637	−	25.7491i	0.120290	−	1.17042i
$23$	−3.45998			−0.150434			−0.0752169	−	0.997167i	$-0.523965\pi$
$23$	−3.45998			−0.150434			−0.0752169	+	0.997167i	$0.523965\pi$
$24$	−7.19499	+	22.6761i	−0.299791	+	0.944837i
$25$			17.8222i			0.712888i
$26$	1.67252	−	16.2736i	0.0643276	−	0.625907i
$27$	19.2544	−	19.2544i	0.713127	−	0.713127i
$28$	2.48059	−	11.9406i	0.0885923	−	0.426449i
$29$	12.1950	−	12.1950i	0.420517	−	0.420517i	−0.464865	−	0.885382i	$-0.653897\pi$
$29$	12.1950	−	12.1950i	0.420517	−	0.420517i	0.885382	+	0.464865i	$0.153897\pi$
$30$	24.5628	+	30.1900i	0.818758	+	1.00633i
$31$			38.5089i			1.24222i	0.783723	+	0.621111i	$0.213318\pi$
$31$			38.5089i			1.24222i	−0.783723	+	0.621111i	$0.786682\pi$
$32$	30.8122	−	8.63778i	0.962880	−	0.269930i
$33$	−38.4877			−1.16629
$34$	−27.4061	+	22.2978i	−0.806061	+	0.655817i
$35$	−14.1078	−	14.1078i	−0.403080	−	0.403080i
$36$	−0.613596	−	0.127471i	−0.0170443	−	0.00354086i
$37$	−0.0972356	−	0.0972356i	−0.00262799	−	0.00262799i	0.705792	−	0.708420i	$-0.250592\pi$
$37$	−0.0972356	−	0.0972356i	−0.00262799	−	0.00262799i	−0.708420	+	0.705792i	$0.750592\pi$
$38$	3.24029	+	0.333021i	0.0852709	+	0.00876372i
$39$	−24.3244			−0.623703
$40$	15.8328	−	49.8993i	0.395819	−	1.24748i
$41$		−	51.5266i		−	1.25675i	−0.777912	−	0.628373i	$-0.783721\pi$
$41$		−	51.5266i		−	1.25675i	0.777912	−	0.628373i	$-0.216279\pi$
$42$	−18.0383	−	1.85389i	−0.429484	−	0.0441402i
$43$	−1.70172	+	1.70172i	−0.0395749	+	0.0395749i	−0.726617	−	0.687042i	$-0.758909\pi$
$43$	−1.70172	+	1.70172i	−0.0395749	+	0.0395749i	0.687042	+	0.726617i	$0.258909\pi$
$44$	28.3955	+	43.2872i	0.645353	+	0.983800i
$45$	−0.724965	+	0.724965i	−0.0161103	+	0.0161103i
$46$	5.36776	−	4.36725i	0.116691	−	0.0949402i
$47$			24.1533i			0.513899i	0.966425	+	0.256949i	$0.0827174\pi$
$47$			24.1533i			0.513899i	−0.966425	+	0.256949i	$0.917283\pi$
$48$	−17.4600	−	44.2611i	−0.363750	−	0.922105i
$49$	−39.7044			−0.810293
$50$	−22.4955	−	27.6491i	−0.449910	−	0.552983i
$51$	37.1466	+	37.1466i	0.728365	+	0.728365i
$52$	17.9461	+	27.3577i	0.345117	+	0.526110i
$53$	27.0383	+	27.0383i	0.510157	+	0.510157i	0.914574	−	0.404418i	$-0.132526\pi$
$53$	27.0383	+	27.0383i	0.510157	+	0.510157i	−0.404418	+	0.914574i	$0.632526\pi$
$54$	−5.56777	+	54.1744i	−0.103107	+	1.00323i
$55$	84.6933			1.53988
$56$	11.2233	+	21.6555i	0.200415	+	0.386705i
$57$		−	4.84333i		−	0.0849706i
$58$	−3.52641	+	34.3119i	−0.0608001	+	0.591584i
$59$	19.5939	−	19.5939i	0.332100	−	0.332100i	−0.521283	−	0.853384i	$-0.674547\pi$
$59$	19.5939	−	19.5939i	0.332100	−	0.332100i	0.853384	+	0.521283i	$0.174547\pi$
$60$	−76.2127	−	15.8328i	−1.27021	−	0.263879i
$61$	16.7250	−	16.7250i	0.274180	−	0.274180i	−0.556601	−	0.830780i	$-0.687895\pi$
$61$	16.7250	−	16.7250i	0.274180	−	0.274180i	0.830780	+	0.556601i	$0.187895\pi$
$62$	−48.6066	−	59.7422i	−0.783977	−	0.963583i
$63$		−	0.477680i		−	0.00758222i
$64$	−36.8988	+	52.2922i	−0.576544	+	0.817066i
$65$	53.5266			0.823485
$66$	59.7094	−	48.5799i	0.904688	−	0.736060i
$67$	−75.8560	−	75.8560i	−1.13218	−	1.13218i	−0.989814	−	0.142365i	$-0.954529\pi$
$67$	−75.8560	−	75.8560i	−1.13218	−	1.13218i	−0.142365	−	0.989814i	$-0.545471\pi$
$68$	14.3728	−	69.1849i	0.211365	−	1.01743i
$69$	−7.27555	−	7.27555i	−0.105443	−	0.105443i
$70$	39.6938	+	4.07953i	0.567054	+	0.0582790i
$71$	−134.749			−1.89787			−0.948935	−	0.315471i	$-0.897837\pi$
$71$	−134.749			−1.89787			−0.948935	+	0.315471i	$0.897837\pi$
$72$	1.11282	−	0.576735i	0.0154559	−	0.00801021i
$73$			112.210i			1.53712i	0.639777	+	0.768560i	$0.279026\pi$
$73$			112.210i			1.53712i	−0.639777	+	0.768560i	$0.720974\pi$
$74$	0.273583	+	0.0281175i	0.00369706	+	0.000379966i
$75$	−37.4761	+	37.4761i	−0.499681	+	0.499681i
$76$	−5.44730	+	3.57331i	−0.0716749	+	0.0470173i
$77$	−27.9022	+	27.9022i	−0.362367	+	0.362367i
$78$	37.7366	−	30.7028i	0.483803	−	0.393625i
$79$		−	135.915i		−	1.72045i	−0.509915	−	0.860225i	$-0.670323\pi$
$79$		−	135.915i		−	1.72045i	0.509915	−	0.860225i	$-0.329677\pi$
$80$	38.4211	+	97.3976i	0.480264	+	1.21747i
$81$	79.5654			0.982289
$82$	65.0378	+	79.9377i	0.793144	+	0.974849i
$83$	74.9250	+	74.9250i	0.902711	+	0.902711i	0.995670	−	0.0929594i	$-0.0296327\pi$
$83$	74.9250	+	74.9250i	0.902711	+	0.902711i	−0.0929594	+	0.995670i	$0.529633\pi$
$84$	30.3244	−	19.8922i	0.361005	−	0.236812i
$85$	−81.7422	−	81.7422i	−0.961672	−	0.961672i
$86$	0.492084	−	4.78797i	0.00572191	−	0.0556741i
$87$	51.2866			0.589501
$88$	−98.6904	−	31.3139i	−1.12148	−	0.355839i
$89$		−	31.4278i		−	0.353121i	−0.984290	−	0.176561i	$-0.943503\pi$
$89$		−	31.4278i		−	0.353121i	0.984290	−	0.176561i	$-0.0564971\pi$
$90$	0.209637	−	2.03977i	0.00232930	−	0.0226641i
$91$	−17.6344	+	17.6344i	−0.193784	+	0.193784i
$92$	−2.81506	+	13.5506i	−0.0305985	+	0.147289i
$93$	−80.9755	+	80.9755i	−0.870704	+	0.870704i
$94$	−30.4867	−	37.4711i	−0.324327	−	0.398628i
$95$			10.6579i			0.112188i
$96$	82.9543	+	46.6277i	0.864108	+	0.485706i
$97$	31.5456			0.325213			0.162606	−	0.986691i	$-0.448010\pi$
$97$	31.5456			0.325213			0.162606	+	0.986691i	$0.448010\pi$
$98$	61.5968	−	50.1156i	0.628539	−	0.511384i
$99$	1.43383	+	1.43383i	0.0144831	+	0.0144831i
$100$	69.7985	+	14.5003i	0.697985	+	0.145003i
$101$	27.4695	+	27.4695i	0.271975	+	0.271975i	0.829895	−	0.557920i	$-0.188400\pi$
$101$	27.4695	+	27.4695i	0.271975	+	0.271975i	−0.557920	+	0.829895i	$0.688400\pi$
$102$	−104.516	−	10.7416i	−1.02467	−	0.105310i
$103$	102.882			0.998854			0.499427	−	0.866356i	$-0.333544\pi$
$103$	102.882			0.998854			0.499427	+	0.866356i	$0.333544\pi$
$104$	−62.3728	−	19.7905i	−0.599738	−	0.190293i
$105$		−	59.3311i		−	0.565058i
$106$	−76.0752	−	7.81863i	−0.717690	−	0.0737607i
$107$	−79.6605	+	79.6605i	−0.744491	+	0.744491i	−0.973439	−	0.228948i	$-0.926471\pi$
$107$	−79.6605	+	79.6605i	−0.744491	+	0.744491i	0.228948	+	0.973439i	$0.426471\pi$
$108$	−59.7422	−	91.0732i	−0.553168	−	0.843270i
$109$	125.408	−	125.408i	1.15053	−	1.15053i	0.164088	−	0.986446i	$-0.447532\pi$
$109$	125.408	−	125.408i	1.15053	−	1.15053i	0.986446	−	0.164088i	$-0.0524682\pi$
$110$	−131.392	+	106.901i	−1.19447	+	0.971831i
$111$		−	0.408929i		−	0.00368405i
$112$	−44.7456	−	19.4298i	−0.399514	−	0.173481i
$113$	−96.6199			−0.855043			−0.427521	−	0.904005i	$-0.640613\pi$
$113$	−96.6199			−0.855043			−0.427521	+	0.904005i	$0.640613\pi$
$114$	6.11334	+	7.51388i	0.0536258	+	0.0659112i
$115$	16.0100	+	16.0100i	0.139218	+	0.139218i
$116$	−37.8383	−	57.6821i	−0.326192	−	0.497260i
$117$	0.906186	+	0.906186i	0.00774518	+	0.00774518i
$118$	−5.66595	+	55.1296i	−0.0480165	+	0.467200i
$119$	53.8600			0.452605
$120$	138.220	−	71.6344i	1.15183	−	0.596953i
$121$		−	46.5054i		−	0.384342i
$122$	−4.83633	+	47.0575i	−0.0396421	+	0.385717i
$123$	108.349	−	108.349i	0.880884	−	0.880884i
$124$	150.815	+	31.3311i	1.21625	+	0.252670i
$125$	−33.2132	+	33.2132i	−0.265706	+	0.265706i
$126$	0.602937	+	0.741067i	0.00478521	+	0.00588148i
$127$			196.309i			1.54574i	0.634566	+	0.772868i	$0.281179\pi$
$127$			196.309i			1.54574i	−0.634566	+	0.772868i	$0.718821\pi$
$128$	−8.75986	−	127.700i	−0.0684364	−	0.997655i
$129$	−7.15667			−0.0554781
$130$	−83.0404	+	67.5622i	−0.638773	+	0.519709i
$131$	17.9437	+	17.9437i	0.136975	+	0.136975i	0.772270	−	0.635295i	$-0.219121\pi$
$131$	17.9437	+	17.9437i	0.136975	+	0.136975i	−0.635295	+	0.772270i	$0.719121\pi$
$132$	−31.3139	+	150.733i	−0.237226	+	1.14191i
$133$	−3.51124	−	3.51124i	−0.0264003	−	0.0264003i
$134$	213.429	+	21.9352i	1.59275	+	0.163695i
$135$	−178.189			−1.31992
$136$	65.0288	+	125.474i	0.478153	+	0.922605i
$137$			51.7200i			0.377518i	0.982023	+	0.188759i	$0.0604465\pi$
$137$			51.7200i			0.377518i	−0.982023	+	0.188759i	$0.939553\pi$
$138$	20.4705	+	2.10386i	0.148337	+	0.0152454i
$139$	−17.4640	+	17.4640i	−0.125640	+	0.125640i	−0.767131	−	0.641491i	$-0.778316\pi$
$139$	−17.4640	+	17.4640i	−0.125640	+	0.125640i	0.641491	+	0.767131i	$0.278316\pi$
$140$	−66.7297	+	43.7733i	−0.476641	+	0.312667i
$141$	−50.7889	+	50.7889i	−0.360205	+	0.360205i
$142$	209.048	−	170.082i	1.47217	−	1.19776i
$143$		−	105.864i		−	0.740309i
$144$	−0.998451	+	2.29936i	−0.00693369	+	0.0159678i
$145$	−112.858			−0.778328
$146$	−141.633	−	174.081i	−0.970091	−	1.19233i
$147$	−83.4893	−	83.4893i	−0.567955	−	0.567955i
$148$	−0.459923	+	0.301700i	−0.00310759	+	0.00203851i
$149$	11.9170	+	11.9170i	0.0799802	+	0.0799802i	0.745965	−	0.665985i	$-0.231989\pi$
$149$	11.9170	+	11.9170i	0.0799802	+	0.0799802i	−0.665985	+	0.745965i	$0.731989\pi$
$150$	10.8369	−	105.443i	0.0722460	−	0.702953i
$151$	−132.548			−0.877805			−0.438902	−	0.898535i	$-0.644633\pi$
$151$	−132.548			−0.877805			−0.438902	+	0.898535i	$0.644633\pi$
$152$	3.94056	−	12.4193i	0.0259247	−	0.0817058i
$153$		−	2.76773i		−	0.0180898i
$154$	8.06845	−	78.5059i	0.0523925	−	0.509779i
$155$	178.189	−	178.189i	1.14960	−	1.14960i
$156$	−19.7905	+	95.2637i	−0.126862	+	0.610665i
$157$	106.091	−	106.091i	0.675742	−	0.675742i	−0.283292	−	0.959034i	$-0.591427\pi$
$157$	106.091	−	106.091i	0.675742	−	0.675742i	0.959034	+	0.283292i	$0.0914266\pi$
$158$	171.555	+	210.858i	1.08579	+	1.33454i
$159$			113.711i			0.715163i
$160$	−182.543	−	102.606i	−1.14090	−	0.641285i
$161$	−10.5490			−0.0655220
$162$	−123.437	+	100.429i	−0.761955	+	0.619932i
$163$	−105.577	−	105.577i	−0.647712	−	0.647712i	0.304728	−	0.952440i	$-0.401435\pi$
$163$	−105.577	−	105.577i	−0.647712	−	0.647712i	−0.952440	+	0.304728i	$0.901435\pi$
$164$	−201.798	−	41.9223i	−1.23047	−	0.255624i
$165$	178.091	+	178.091i	1.07934	+	1.07934i
$166$	−210.809	−	21.6659i	−1.26994	−	0.130518i
$167$	111.591			0.668210			0.334105	−	0.942536i	$-0.391566\pi$
$167$	111.591			0.668210			0.334105	+	0.942536i	$0.391566\pi$
$168$	−21.9366	+	69.1366i	−0.130575	+	0.411527i
$169$			102.093i			0.604102i
$170$	229.990	+	23.6373i	1.35288	+	0.139043i
$171$	−0.180434	+	0.180434i	−0.00105517	+	0.00105517i
$172$	5.28006	+	8.04912i	0.0306980	+	0.0467972i
$173$	14.5363	−	14.5363i	0.0840249	−	0.0840249i	−0.663845	−	0.747870i	$-0.731077\pi$
$173$	14.5363	−	14.5363i	0.0840249	−	0.0840249i	0.747870	+	0.663845i	$0.231077\pi$
$174$	−79.5654	+	64.7350i	−0.457273	+	0.372040i
$175$			54.3377i			0.310501i
$176$	192.632	−	75.9889i	1.09450	−	0.431755i
$177$	82.4032			0.465555
$178$	39.6687	+	48.7567i	0.222858	+	0.273914i
$179$	−19.7371	−	19.7371i	−0.110263	−	0.110263i	0.649823	−	0.760086i	$-0.274843\pi$
$179$	−19.7371	−	19.7371i	−0.110263	−	0.110263i	−0.760086	+	0.649823i	$0.774843\pi$
$180$	2.24940	+	3.42907i	0.0124967	+	0.0190504i
$181$	168.153	+	168.153i	0.929021	+	0.929021i	0.997643	−	0.0686221i	$-0.0218603\pi$
$181$	168.153	+	168.153i	0.929021	+	0.929021i	−0.0686221	+	0.997643i	$0.521860\pi$
$182$	5.09930	−	49.6161i	0.0280181	−	0.272616i
$183$	70.3377			0.384359
$184$	−12.7366	−	24.5754i	−0.0692204	−	0.133562i
$185$			0.899859i			0.00486410i
$186$	23.4156	−	227.833i	0.125890	−	1.22491i
$187$	−161.669	+	161.669i	−0.864539	+	0.864539i
$188$	94.5934	+	19.6512i	0.503156	+	0.104528i
$189$	58.7044	−	58.7044i	0.310605	−	0.310605i
$190$	−13.4526	−	16.5345i	−0.0708030	−	0.0870236i
$191$		−	196.309i		−	1.02779i	−0.857852	−	0.513897i	$-0.828201\pi$
$191$		−	196.309i		−	1.02779i	0.857852	−	0.513897i	$-0.171799\pi$
$192$	−187.549	+	32.3688i	−0.976816	+	0.168588i
$193$	−40.3699			−0.209170			−0.104585	−	0.994516i	$-0.533351\pi$
$193$	−40.3699			−0.209170			−0.104585	+	0.994516i	$0.533351\pi$
$194$	−48.9395	+	39.8175i	−0.252265	+	0.205245i
$195$	112.554	+	112.554i	0.577202	+	0.577202i
$196$	−32.3037	+	155.497i	−0.164815	+	0.793354i
$197$	−230.578	−	230.578i	−1.17045	−	1.17045i	−0.982103	−	0.188344i	$-0.939688\pi$
$197$	−230.578	−	230.578i	−1.17045	−	1.17045i	−0.188344	−	0.982103i	$-0.560312\pi$
$198$	−4.03423	−	0.414618i	−0.0203749	−	0.00209403i
$199$	61.5598			0.309346			0.154673	−	0.987966i	$-0.450568\pi$
$199$	61.5598			0.309346			0.154673	+	0.987966i	$0.450568\pi$
$200$	−126.587	+	65.6055i	−0.632935	+	0.328028i
$201$		−	319.016i		−	1.58715i
$202$	−77.2884	−	7.94332i	−0.382616	−	0.0393234i
$203$	37.1810	−	37.1810i	0.183158	−	0.183158i
$204$	175.703	−	115.258i	0.861290	−	0.564988i
$205$	−238.424	+	238.424i	−1.16305	+	1.16305i
$206$	−159.610	+	129.860i	−0.774805	+	0.630386i
$207$			0.542089i			0.00261879i
$208$	121.744	−	48.0254i	0.585309	−	0.230891i
$209$	21.0790			0.100857
$210$	74.8888	+	92.0455i	0.356613	+	0.438312i
$211$	151.149	+	151.149i	0.716346	+	0.716346i	0.967855	−	0.251509i	$-0.0809267\pi$
$211$	151.149	+	151.149i	0.716346	+	0.716346i	−0.251509	+	0.967855i	$0.580927\pi$
$212$	127.891	−	83.8938i	0.603259	−	0.395725i
$213$	−283.346	−	283.346i	−1.33026	−	1.33026i
$214$	23.0353	−	224.133i	0.107642	−	1.04735i
$215$	15.7485			0.0732486
$216$	207.638	+	65.8822i	0.961285	+	0.305010i
$217$			117.409i			0.541054i
$218$	−36.2641	+	352.849i	−0.166349	+	1.61857i
$219$	−235.952	+	235.952i	−1.07741	+	1.07741i
$220$	68.9070	−	331.691i	0.313214	−	1.50769i
$221$	−102.175	+	102.175i	−0.462332	+	0.462332i
$222$	0.516158	+	0.634407i	0.00232504	+	0.00285769i
$223$		−	115.527i		−	0.518056i	−0.965870	−	0.259028i	$-0.916598\pi$
$223$		−	115.527i		−	0.518056i	0.965870	−	0.259028i	$-0.0834022\pi$
$224$	93.9424	−	26.3355i	0.419386	−	0.117569i
$225$	2.79228			0.0124101
$226$	149.895	−	121.955i	0.663251	−	0.539626i
$227$	25.2363	+	25.2363i	0.111173	+	0.111173i	0.760505	−	0.649332i	$-0.224951\pi$
$227$	25.2363	+	25.2363i	0.111173	+	0.111173i	−0.649332	+	0.760505i	$0.724951\pi$
$228$	−18.9683	−	3.94056i	−0.0831944	−	0.0172832i
$229$	−155.318	−	155.318i	−0.678244	−	0.678244i	0.281359	−	0.959603i	$-0.409215\pi$
$229$	−155.318	−	155.318i	−0.678244	−	0.678244i	−0.959603	+	0.281359i	$0.909215\pi$
$230$	−45.0460	−	4.62960i	−0.195852	−	0.0201287i
$231$	−117.344			−0.507984
$232$	131.509	+	41.7271i	0.566851	+	0.179858i
$233$			119.738i			0.513899i	0.966425	+	0.256949i	$0.0827174\pi$
$233$			119.738i			0.513899i	−0.966425	+	0.256949i	$0.917283\pi$
$234$	−2.54965	−	0.262040i	−0.0108959	−	0.00111983i
$235$	111.762	−	111.762i	0.475584	−	0.475584i
$236$	−60.7955	−	92.6790i	−0.257608	−	0.392708i
$237$	285.800	−	285.800i	1.20591	−	1.20591i
$238$	−83.5577	+	67.9831i	−0.351083	+	0.285643i
$239$			245.409i			1.02681i	0.858145	+	0.513407i	$0.171617\pi$
$239$			245.409i			1.02681i	−0.858145	+	0.513407i	$0.828383\pi$
$240$	−124.014	+	285.596i	−0.516726	+	1.18998i
$241$	431.216			1.78928			0.894639	−	0.446790i	$-0.147433\pi$
$241$	431.216			1.78928			0.894639	+	0.446790i	$0.147433\pi$
$242$	58.7000	+	72.1479i	0.242562	+	0.298132i
$243$	−5.98173	−	5.98173i	−0.0246162	−	0.0246162i
$244$	−51.8938	−	79.1089i	−0.212680	−	0.324217i
$245$	183.721	+	183.721i	0.749880	+	0.749880i
$246$	−31.3311	+	304.851i	−0.127362	+	1.23923i
$247$	13.3220			0.0539354
$248$	−273.520	+	141.755i	−1.10290	+	0.571594i
$249$			315.101i			1.26546i
$250$	9.60421	−	93.4489i	0.0384169	−	0.373796i
$251$	−24.0171	+	24.0171i	−0.0956858	+	0.0956858i	−0.753329	−	0.657643i	$-0.771553\pi$
$251$	−24.0171	+	24.0171i	−0.0956858	+	0.0956858i	0.657643	+	0.753329i	$0.271553\pi$
$252$	−1.87078	−	0.388644i	−0.00742372	−	0.00154224i
$253$	31.6645	−	31.6645i	0.125156	−	0.125156i
$254$	−247.784	−	304.551i	−0.975529	−	1.19902i
$255$		−	343.771i		−	1.34812i
$256$	174.775	+	187.055i	0.682716	+	0.730684i
$257$	−100.860			−0.392450			−0.196225	−	0.980559i	$-0.562868\pi$
$257$	−100.860			−0.392450			−0.196225	+	0.980559i	$0.562868\pi$
$258$	11.1028	−	9.03329i	0.0430340	−	0.0350128i
$259$	−0.296459	−	0.296459i	−0.00114463	−	0.00114463i
$260$	43.5496	−	209.630i	0.167498	−	0.806271i
$261$	−1.91064	−	1.91064i	−0.00732046	−	0.00732046i
$262$	−50.4865	−	5.18876i	−0.192697	−	0.0198044i
$263$	216.776			0.824242			0.412121	−	0.911129i	$-0.364788\pi$
$263$	216.776			0.824242			0.412121	+	0.911129i	$0.364788\pi$
$264$	−141.678	−	273.370i	−0.536658	−	1.03549i
$265$		−	250.224i		−	0.944242i
$266$	9.87925	+	1.01534i	0.0371400	+	0.00381707i
$267$	66.0855	−	66.0855i	0.247511	−	0.247511i
$268$	−358.798	+	235.364i	−1.33880	+	0.878224i
$269$	−256.778	+	256.778i	−0.954567	+	0.954567i	−0.999012	−	0.0444453i	$-0.985848\pi$
$269$	−256.778	+	256.778i	−0.954567	+	0.954567i	0.0444453	+	0.999012i	$0.485848\pi$
$270$	276.440	−	224.913i	1.02385	−	0.833012i
$271$			12.8603i			0.0474551i	0.999718	+	0.0237275i	$0.00755342\pi$
$271$			12.8603i			0.0474551i	−0.999718	+	0.0237275i	$0.992447\pi$
$272$	−259.261	−	112.579i	−0.953165	−	0.413892i
$273$	−74.1622			−0.271656
$274$	−65.2820	−	80.2378i	−0.238255	−	0.292839i
$275$	−163.103	−	163.103i	−0.593100	−	0.593100i
$276$	−34.4133	+	22.5744i	−0.124686	+	0.0817913i
$277$	77.1023	+	77.1023i	0.278348	+	0.278348i	0.832449	−	0.554102i	$-0.186938\pi$
$277$	77.1023	+	77.1023i	0.278348	+	0.278348i	−0.554102	+	0.832449i	$0.686938\pi$
$278$	5.05003	−	49.1367i	0.0181656	−	0.176751i
$279$	6.03334			0.0216249
$280$	48.2721	−	152.137i	0.172400	−	0.543346i
$281$		−	189.034i		−	0.672719i	−0.941734	−	0.336360i	$-0.890804\pi$
$281$		−	189.034i		−	0.672719i	0.941734	−	0.336360i	$-0.109196\pi$
$282$	14.6865	−	142.900i	0.0520799	−	0.506737i
$283$	−69.4317	+	69.4317i	−0.245342	+	0.245342i	−0.819056	−	0.573714i	$-0.805502\pi$
$283$	−69.4317	+	69.4317i	−0.245342	+	0.245342i	0.573714	+	0.819056i	$0.305502\pi$
$284$	−109.632	+	527.728i	−0.386030	+	1.85820i
$285$	−22.4111	+	22.4111i	−0.0786354	+	0.0786354i
$286$	133.624	+	164.236i	0.467216	+	0.574253i
$287$		−	157.098i		−	0.547380i
$288$	−1.35332	−	4.82747i	−0.00469902	−	0.0167620i
$289$	23.0708			0.0798298
$290$	175.086	−	142.451i	0.603744	−	0.491210i
$291$	66.3333	+	66.3333i	0.227950	+	0.227950i
$292$	439.456	+	91.2946i	1.50499	+	0.312653i
$293$	239.919	+	239.919i	0.818837	+	0.818837i	0.985939	−	0.167103i	$-0.0534412\pi$
$293$	239.919	+	239.919i	0.818837	+	0.818837i	−0.167103	+	0.985939i	$0.553441\pi$
$294$	234.906	+	24.1425i	0.799000	+	0.0821173i
$295$	−181.331			−0.614680
$296$	0.332707	−	1.04858i	0.00112401	−	0.00354249i
$297$			352.420i			1.18660i
$298$	−33.5299	−	3.44604i	−0.112516	−	0.0115639i
$299$	20.0121	−	20.0121i	0.0669301	−	0.0669301i
$300$	116.280	+	177.261i	0.387599	+	0.590871i
$301$	−5.18834	+	5.18834i	−0.0172370	+	0.0172370i
$302$	205.634	−	167.305i	0.680908	−	0.553991i
$303$			115.524i			0.381269i
$304$	9.56251	+	24.2410i	0.0314556	+	0.0797400i
$305$	−154.780			−0.507475
$306$	3.49348	+	4.29382i	0.0114166	+	0.0140321i
$307$	−231.185	−	231.185i	−0.753046	−	0.753046i	0.222001	−	0.975046i	$-0.428741\pi$
$307$	−231.185	−	231.185i	−0.753046	−	0.753046i	−0.975046	+	0.222001i	$0.928741\pi$
$308$	86.5744	+	131.977i	0.281086	+	0.428498i
$309$	216.338	+	216.338i	0.700122	+	0.700122i
$310$	−51.5266	+	501.353i	−0.166215	+	1.61727i
$311$	−513.328			−1.65057			−0.825287	−	0.564714i	$-0.808987\pi$
$311$	−513.328			−1.65057			−0.825287	+	0.564714i	$0.808987\pi$
$312$	−89.5409	−	172.771i	−0.286990	−	0.553753i
$313$		−	345.242i		−	1.10301i	−0.834172	−	0.551504i	$-0.814054\pi$
$313$		−	345.242i		−	1.10301i	0.834172	−	0.551504i	$-0.185946\pi$
$314$	−30.6783	+	298.500i	−0.0977016	+	0.950635i
$315$	−2.21033	+	2.21033i	−0.00701691	+	0.00701691i
$316$	−532.297	−	110.582i	−1.68448	−	0.349942i
$317$	345.632	−	345.632i	1.09032	−	1.09032i	0.0948290	−	0.995494i	$-0.469770\pi$
$317$	345.632	−	345.632i	1.09032	−	1.09032i	0.995494	−	0.0948290i	$-0.0302304\pi$
$318$	−143.528	−	176.410i	−0.451346	−	0.554748i
$319$			223.209i			0.699713i
$320$	412.706	−	71.2285i	1.28971	−	0.222589i
$321$	−335.016			−1.04366
$322$	16.3656	−	13.3152i	0.0508250	−	0.0413515i
$323$	−20.3445	−	20.3445i	−0.0629861	−	0.0629861i
$324$	64.7349	−	311.608i	0.199799	−	0.961754i
$325$	−103.082	−	103.082i	−0.317174	−	0.317174i
$326$	297.052	+	30.5296i	0.911203	+	0.0936489i
$327$	527.410			1.61288
$328$	365.982	−	189.675i	1.11580	−	0.578278i
$329$			73.6403i			0.223831i
$330$	−501.078	−	51.4983i	−1.51842	−	0.156055i
$331$	425.968	−	425.968i	1.28691	−	1.28691i	0.350261	−	0.936652i	$-0.386093\pi$
$331$	425.968	−	425.968i	1.28691	−	1.28691i	0.936652	−	0.350261i	$-0.113907\pi$
$332$	354.394	−	232.475i	1.06745	−	0.700227i
$333$	−0.0152343	+	0.0152343i	−4.57487e−5	+	4.57487e-5i
$334$	−173.121	+	140.852i	−0.518326	+	0.421714i
$335$			702.004i			2.09553i
$336$	−53.2333	−	134.946i	−0.158432	−	0.401626i
$337$	−467.297			−1.38664			−0.693319	−	0.720631i	$-0.743852\pi$
$337$	−467.297			−1.38664			−0.693319	+	0.720631i	$0.743852\pi$
$338$	−128.864	−	158.386i	−0.381255	−	0.468598i
$339$	−203.170	−	203.170i	−0.599321	−	0.599321i
$340$	−386.639	+	253.628i	−1.13717	+	0.745963i
$341$	−352.420	−	352.420i	−1.03349	−	1.03349i
$342$	0.0521758	−	0.507670i	0.000152561	−	0.00148442i
$343$	−270.449			−0.788480
$344$	−18.3512	−	5.82272i	−0.0533464	−	0.0169265i
$345$			67.3311i			0.195162i
$346$	−4.20344	+	40.8994i	−0.0121487	+	0.118206i
$347$	−22.0463	+	22.0463i	−0.0635341	+	0.0635341i	−0.738160	−	0.674626i	$-0.764305\pi$
$347$	−22.0463	+	22.0463i	−0.0635341	+	0.0635341i	0.674626	+	0.738160i	$0.264305\pi$
$348$	41.7271	−	200.858i	0.119906	−	0.577178i
$349$	−158.622	+	158.622i	−0.454506	+	0.454506i	−0.896847	−	0.442341i	$-0.854148\pi$
$349$	−158.622	+	158.622i	−0.454506	+	0.454506i	0.442341	+	0.896847i	$0.354148\pi$
$350$	−68.5860	−	84.2988i	−0.195960	−	0.240854i
$351$			222.731i			0.634561i
$352$	−202.932	+	361.032i	−0.576512	+	1.02566i
$353$	404.451			1.14575			0.572877	−	0.819642i	$-0.305827\pi$
$353$	404.451			1.14575			0.572877	+	0.819642i	$0.305827\pi$
$354$	−127.839	+	104.011i	−0.361128	+	0.293816i
$355$	623.511	+	623.511i	1.75637	+	1.75637i
$356$	−123.083	−	25.5698i	−0.345739	−	0.0718254i
$357$	113.255	+	113.255i	0.317242	+	0.317242i
$358$	55.5325	+	5.70736i	0.155119	+	0.0159423i
$359$	423.833			1.18059			0.590297	−	0.807186i	$-0.299011\pi$
$359$	423.833			1.18059			0.590297	+	0.807186i	$0.299011\pi$
$360$	−7.81794	−	2.48059i	−0.0217165	−	0.00689051i
$361$		−	358.347i		−	0.992652i
$362$	−473.116	−	48.6245i	−1.30695	−	0.134322i
$363$	97.7905	−	97.7905i	0.269395	−	0.269395i
$364$	54.7154	+	83.4103i	0.150317	+	0.229149i
$365$	519.219	−	519.219i	1.42252	−	1.42252i
$366$	−109.121	+	88.7816i	−0.298145	+	0.242573i
$367$		−	477.144i		−	1.30012i	−0.759883	−	0.650059i	$-0.774744\pi$
$367$		−	477.144i		−	1.30012i	0.759883	−	0.650059i	$-0.225256\pi$
$368$	50.7789	+	22.0497i	0.137986	+	0.0599176i
$369$	−8.07288			−0.0218777
$370$	−1.13582	−	1.39603i	−0.00306978	−	0.00377306i
$371$	82.4365	+	82.4365i	0.222201	+	0.222201i
$372$	251.249	+	383.013i	0.675400	+	1.02960i
$373$	112.221	+	112.221i	0.300860	+	0.300860i	0.841350	−	0.540490i	$-0.181761\pi$
$373$	112.221	+	112.221i	0.300860	+	0.300860i	−0.540490	+	0.841350i	$0.681761\pi$
$374$	46.7495	−	454.872i	0.124999	−	1.21624i
$375$	−139.680			−0.372479
$376$	−171.555	+	88.9108i	−0.456264	+	0.236465i
$377$			141.069i			0.374188i
$378$	−16.9755	+	165.171i	−0.0449086	+	0.436960i
$379$	52.2069	−	52.2069i	0.137749	−	0.137749i	−0.634870	−	0.772619i	$-0.718946\pi$
$379$	52.2069	−	52.2069i	0.137749	−	0.137749i	0.772619	+	0.634870i	$0.218946\pi$
$380$	41.7403	+	8.67131i	0.109843	+	0.0228192i
$381$	−412.793	+	412.793i	−1.08345	+	1.08345i
$382$	247.784	+	304.551i	0.648650	+	0.797253i
$383$		−	74.8407i		−	0.195406i	−0.995216	−	0.0977032i	$-0.968850\pi$
$383$		−	74.8407i		−	0.195406i	0.995216	−	0.0977032i	$-0.0311496\pi$
$384$	250.104	−	286.944i	0.651313	−	0.747250i
$385$	258.219			0.670699
$386$	62.6293	−	50.9556i	0.162252	−	0.132009i
$387$	0.266616	+	0.266616i	0.000688930	+	0.000688930i
$388$	25.6657	−	123.545i	0.0661488	−	0.318414i
$389$	−57.0441	−	57.0441i	−0.146643	−	0.146643i	0.629974	−	0.776617i	$-0.283066\pi$
$389$	−57.0441	−	57.0441i	−0.146643	−	0.146643i	−0.776617	+	0.629974i	$0.783066\pi$
$390$	−316.684	−	32.5472i	−0.812009	−	0.0834543i
$391$	−61.1223			−0.156323
$392$	−146.156	−	282.011i	−0.372847	−	0.719416i
$393$			75.4632i			0.192018i
$394$	648.756	+	66.6759i	1.64659	+	0.169228i
$395$	−628.910	+	628.910i	−1.59218	+	1.59218i
$396$	6.78199	−	4.44884i	0.0171262	−	0.0112345i
$397$	−355.874	+	355.874i	−0.896407	+	0.896407i	−0.995116	−	0.0987089i	$-0.968529\pi$
$397$	−355.874	+	355.874i	−0.896407	+	0.896407i	0.0987089	+	0.995116i	$0.468529\pi$
$398$	−95.5031	+	77.7019i	−0.239958	+	0.195231i
$399$		−	14.7667i		−	0.0370093i
$400$	113.577	−	261.560i	0.283943	−	0.653900i
$401$	113.892			0.284019			0.142010	−	0.989865i	$-0.454644\pi$
$401$	113.892			0.284019			0.142010	+	0.989865i	$0.454644\pi$
$402$	402.668	+	494.918i	1.00166	+	1.23114i
$403$	−222.731	−	222.731i	−0.552682	−	0.552682i
$404$	129.930	−	85.2317i	0.321610	−	0.210970i
$405$	−368.166	−	368.166i	−0.909052	−	0.909052i
$406$	−10.7516	+	104.613i	−0.0264817	+	0.257667i
$407$	1.77973			0.00437281
$408$	−127.103	+	400.585i	−0.311528	+	0.981826i
$409$		−	139.909i		−	0.342077i	−0.985264	−	0.171038i	$-0.945288\pi$
$409$		−	139.909i		−	0.342077i	0.985264	−	0.171038i	$-0.0547122\pi$
$410$	68.9448	−	670.832i	0.168158	−	1.63618i
$411$	−108.756	+	108.756i	−0.264612	+	0.264612i
$412$	83.7054	−	402.925i	0.203168	−	0.977973i
$413$	59.7394	−	59.7394i	0.144648	−	0.144648i
$414$	−0.684235	−	0.840990i	−0.00165274	−	0.00203138i
$415$		−	693.388i		−	1.67081i
$416$	−128.254	+	228.174i	−0.308303	+	0.548495i
$417$	−73.4456			−0.176129
$418$	−32.7017	+	26.6063i	−0.0782338	+	0.0636515i
$419$	−370.978	−	370.978i	−0.885389	−	0.885389i	0.108687	−	0.994076i	$-0.465335\pi$
$419$	−370.978	−	370.978i	−0.885389	−	0.885389i	−0.994076	+	0.108687i	$0.965335\pi$
$420$	−232.363	−	48.2721i	−0.553245	−	0.114934i
$421$	465.112	+	465.112i	1.10478	+	1.10478i	0.993825	+	0.110955i	$0.0353908\pi$
$421$	465.112	+	465.112i	1.10478	+	1.10478i	0.110955	+	0.993825i	$0.464609\pi$
$422$	−425.274	−	43.7075i	−1.00776	−	0.103572i
$423$	3.78419			0.00894608
$424$	−92.5160	+	291.578i	−0.218198	+	0.687684i
$425$			314.839i			0.740797i
$426$	797.225	+	81.9349i	1.87142	+	0.192335i
$427$	50.9923	−	50.9923i	0.119420	−	0.119420i
$428$	247.169	+	376.793i	0.577497	+	0.880358i
$429$	222.609	−	222.609i	0.518901	−	0.518901i
$430$	−24.4320	+	19.8780i	−0.0568185	+	0.0462279i
$431$		−	409.924i		−	0.951099i	−0.879689	−	0.475549i	$-0.842249\pi$
$431$		−	409.924i		−	0.951099i	0.879689	−	0.475549i	$-0.157751\pi$
$432$	−405.284	+	159.875i	−0.938157	+	0.370082i
$433$	−20.6859			−0.0477735			−0.0238868	−	0.999715i	$-0.507604\pi$
$433$	−20.6859			−0.0477735			−0.0238868	+	0.999715i	$0.507604\pi$
$434$	−148.196	−	182.146i	−0.341464	−	0.419692i
$435$	−237.314	−	237.314i	−0.545550	−	0.545550i
$436$	−389.113	−	593.179i	−0.892462	−	1.36050i
$437$	3.98468	+	3.98468i	0.00911827	+	0.00911827i
$438$	68.2299	−	663.876i	0.155776	−	1.51570i
$439$	−63.2889			−0.144166			−0.0720830	−	0.997399i	$-0.522965\pi$
$439$	−63.2889			−0.144166			−0.0720830	+	0.997399i	$0.522965\pi$
$440$	311.765	+	601.557i	0.708558	+	1.36718i
$441$			6.22065i			0.0141058i
$442$	29.5459	−	287.481i	0.0668460	−	0.650410i
$443$	−297.084	+	297.084i	−0.670619	+	0.670619i	−0.957859	−	0.287240i	$-0.907262\pi$
$443$	−297.084	+	297.084i	−0.670619	+	0.670619i	0.287240	+	0.957859i	$0.407262\pi$
$444$	−1.60152	−	0.332707i	−0.00360703	−	0.000749341i
$445$	−145.423	+	145.423i	−0.326793	+	0.326793i
$446$	145.820	+	179.226i	0.326950	+	0.401853i
$447$			50.1177i			0.112120i
$448$	−112.500	+	159.432i	−0.251116	+	0.355876i
$449$	364.701			0.812251			0.406126	−	0.913817i	$-0.366880\pi$
$449$	364.701			0.812251			0.406126	+	0.913817i	$0.366880\pi$
$450$	−4.33191	+	3.52447i	−0.00962646	+	0.00783215i
$451$	471.553	+	471.553i	1.04557	+	1.04557i
$452$	−78.6105	+	378.400i	−0.173917	+	0.837169i
$453$	−278.720	−	278.720i	−0.615275	−	0.615275i
$454$	−71.0049	−	7.29753i	−0.156398	−	0.0160739i
$455$	163.196			0.358672
$456$	34.4011	−	17.8288i	0.0754409	−	0.0390983i
$457$			640.046i			1.40054i	0.713879	+	0.700269i	$0.246936\pi$
$457$			640.046i			1.40054i	−0.713879	+	0.700269i	$0.753064\pi$
$458$	437.003	+	44.9130i	0.954156	+	0.0980634i
$459$	340.140	−	340.140i	0.741045	−	0.741045i
$460$	75.7273	−	49.6756i	0.164625	−	0.107990i
$461$	−239.416	+	239.416i	−0.519341	+	0.519341i	−0.917372	−	0.398031i	$-0.869694\pi$
$461$	−239.416	+	239.416i	−0.519341	+	0.519341i	0.398031	+	0.917372i	$0.369694\pi$
$462$	182.046	−	148.114i	0.394040	−	0.320594i
$463$			479.413i			1.03545i	0.855548	+	0.517724i	$0.173221\pi$
$463$			479.413i			1.03545i	−0.855548	+	0.517724i	$0.826779\pi$
$464$	−256.691	+	101.259i	−0.553213	+	0.218230i
$465$	749.381			1.61157
$466$	−151.136	−	185.761i	−0.324326	−	0.398628i
$467$	403.375	+	403.375i	0.863758	+	0.863758i	0.991772	−	0.128015i	$-0.0408605\pi$
$467$	403.375	+	403.375i	0.863758	+	0.863758i	−0.128015	+	0.991772i	$0.540860\pi$
$468$	4.28625	−	2.81169i	0.00915865	−	0.00600789i
$469$	−231.276	−	231.276i	−0.493125	−	0.493125i
$470$	−32.3181	+	314.455i	−0.0687620	+	0.669053i
$471$	446.173			0.947288
$472$	211.299	+	67.0438i	0.447667	+	0.142042i
$473$		−	31.1471i		−	0.0658501i
$474$	−82.6443	+	804.128i	−0.174355	+	1.69647i
$475$	20.5250	−	20.5250i	0.0432104	−	0.0432104i
$476$	43.8208	−	210.936i	0.0920606	−	0.443143i
$477$	4.23621	−	4.23621i	0.00888093	−	0.00888093i
$478$	−309.760	−	380.724i	−0.648032	−	0.796494i
$479$		−	460.611i		−	0.961609i	−0.876828	−	0.480805i	$-0.840345\pi$
$479$		−	460.611i		−	0.961609i	0.876828	−	0.480805i	$-0.159655\pi$
$480$	−168.091	−	599.604i	−0.350189	−	1.24917i
$481$	1.12480			0.00233846
$482$	−668.983	+	544.289i	−1.38793	+	1.12923i
$483$	−22.1823	−	22.1823i	−0.0459260	−	0.0459260i
$484$	−182.133	−	37.8371i	−0.376308	−	0.0781759i
$485$	−145.968	−	145.968i	−0.300966	−	0.300966i
$486$	16.8302	+	1.72973i	0.0346301	+	0.00355911i
$487$	−575.128			−1.18096			−0.590481	−	0.807052i	$-0.701062\pi$
$487$	−575.128			−1.18096			−0.590481	+	0.807052i	$0.701062\pi$
$488$	180.360	+	57.2272i	0.369590	+	0.117269i
$489$		−	444.010i		−	0.907995i
$490$	−516.917	−	53.1262i	−1.05493	−	0.108421i
$491$	271.375	−	271.375i	0.552699	−	0.552699i	−0.374520	−	0.927219i	$-0.622192\pi$
$491$	271.375	−	271.375i	0.552699	−	0.552699i	0.927219	+	0.374520i	$0.122192\pi$
$492$	−336.182	−	512.488i	−0.683296	−	1.04164i
$493$	215.431	−	215.431i	0.436979	−	0.436979i
$494$	−20.6676	+	16.8153i	−0.0418373	+	0.0340391i
$495$		−	13.2693i		−	0.0268066i
$496$	245.409	−	565.159i	0.494776	−	1.13943i
$497$	−410.832			−0.826624
$498$	−397.726	−	488.843i	−0.798647	−	0.981613i
$499$	268.082	+	268.082i	0.537239	+	0.537239i	0.922717	−	0.385478i	$-0.125963\pi$
$499$	268.082	+	268.082i	0.537239	+	0.537239i	−0.385478	+	0.922717i	$0.625963\pi$
$500$	103.053	+	157.098i	0.206106	+	0.314196i
$501$	234.651	+	234.651i	0.468365	+	0.468365i
$502$	6.94500	−	67.5748i	0.0138347	−	0.134611i
$503$	−368.002			−0.731615			−0.365807	−	0.930691i	$-0.619207\pi$
$503$	−368.002			−0.731615			−0.365807	+	0.930691i	$0.619207\pi$
$504$	3.39285	−	1.75839i	0.00673185	−	0.00348888i
$505$		−	254.215i		−	0.503395i
$506$	−9.15638	+	89.0914i	−0.0180956	+	0.176070i
$507$	−214.679	+	214.679i	−0.423430	+	0.423430i
$508$	768.819	+	159.718i	1.51342	+	0.314405i
$509$	297.809	−	297.809i	0.585087	−	0.585087i	−0.351210	−	0.936297i	$-0.614230\pi$
$509$	297.809	−	297.809i	0.585087	−	0.585087i	0.936297	+	0.351210i	$0.114230\pi$
$510$	433.914	+	533.322i	0.850812	+	1.04573i
$511$			342.114i			0.669498i
$512$	−507.249	−	69.5905i	−0.990720	−	0.135919i
$513$	−44.3488			−0.0864498
$514$	156.472	−	127.307i	0.304421	−	0.247679i
$515$	−476.057	−	476.057i	−0.924382	−	0.924382i
$516$	−5.82272	+	28.0283i	−0.0112843	+	0.0543183i
$517$	−221.042	−	221.042i	−0.427548	−	0.427548i
$518$	0.834119	+	0.0857267i	0.00161027	+	0.000165495i
$519$	61.1332			0.117790
$520$	197.037	+	380.187i	0.378918	+	0.731129i
$521$		−	95.5605i		−	0.183418i	−0.995786	−	0.0917088i	$-0.970767\pi$
$521$		−	95.5605i		−	0.183418i	0.995786	−	0.0917088i	$-0.0292329\pi$
$522$	5.37579	+	0.552497i	0.0102984	+	0.00105842i
$523$	−250.389	+	250.389i	−0.478756	+	0.478756i	−0.904734	−	0.425978i	$-0.859930\pi$
$523$	−250.389	+	250.389i	−0.478756	+	0.478756i	0.425978	+	0.904734i	$0.359930\pi$
$524$	84.8735	−	55.6753i	0.161972	−	0.106251i
$525$	−114.260	+	114.260i	−0.217638	+	0.217638i
$526$	−336.303	+	273.618i	−0.639360	+	0.520187i
$527$			680.279i			1.29085i
$528$	564.849	+	245.274i	1.06979	+	0.464534i
$529$	−517.029			−0.977370
$530$	315.838	+	388.194i	0.595920	+	0.732442i
$531$	−3.06986	−	3.06986i	−0.00578128	−	0.00578128i
$532$	−16.6081	+	10.8946i	−0.0312183	+	0.0204786i
$533$	298.024	+	298.024i	0.559144	+	0.559144i
$534$	−19.1099	+	185.939i	−0.0357863	+	0.348200i
$535$	737.212			1.37797
$536$	259.554	−	818.023i	0.484242	−	1.52616i
$537$		−	83.0055i		−	0.154573i
$538$	74.2522	−	722.473i	0.138015	−	1.34289i
$539$	363.360	−	363.360i	0.674138	−	0.674138i
$540$	−144.975	+	697.855i	−0.268473	+	1.29232i
$541$	−81.7015	+	81.7015i	−0.151019	+	0.151019i	−0.778573	−	0.627554i	$-0.784056\pi$
$541$	−81.7015	+	81.7015i	−0.151019	+	0.151019i	0.627554	+	0.778573i	$0.284056\pi$
$542$	−16.2325	−	19.9513i	−0.0299493	−	0.0368106i
$543$			707.175i			1.30235i
$544$	544.313	−	152.591i	1.00058	−	0.280498i
$545$	−1160.58			−2.12951
$546$	115.054	−	93.6089i	0.210722	−	0.171445i
$547$	−381.162	−	381.162i	−0.696823	−	0.696823i	0.266901	−	0.963724i	$-0.414000\pi$
$547$	−381.162	−	381.162i	−0.696823	−	0.696823i	−0.963724	+	0.266901i	$0.914000\pi$
$548$	202.555	+	42.0797i	0.369626	+	0.0767878i
$549$	−2.62037	−	2.62037i	−0.00477299	−	0.00477299i
$550$	458.906	+	47.1641i	0.834375	+	0.0857530i
$551$	−28.0887			−0.0509777
$552$	24.8945	−	78.4587i	0.0450987	−	0.142135i
$553$		−	414.389i		−	0.749348i
$554$	−216.935	−	22.2956i	−0.391580	−	0.0402447i
$555$	−1.89220	+	1.89220i	−0.00340937	+	0.00340937i
$556$	54.1868	+	82.6044i	0.0974582	+	0.148569i
$557$	−63.7634	+	63.7634i	−0.114476	+	0.114476i	−0.762025	−	0.647548i	$-0.775794\pi$
$557$	−63.7634	+	63.7634i	−0.114476	+	0.114476i	0.647548	+	0.762025i	$0.275794\pi$
$558$	−9.36005	+	7.61540i	−0.0167743	+	0.0136477i
$559$		−	19.6851i		−	0.0352149i
$560$	117.141	+	296.953i	0.209181	+	0.530274i
$561$	−679.906			−1.21195
$562$	238.602	+	293.265i	0.424559	+	0.521824i
$563$	333.679	+	333.679i	0.592681	+	0.592681i	0.938355	−	0.345674i	$-0.112350\pi$
$563$	333.679	+	333.679i	0.592681	+	0.592681i	−0.345674	+	0.938355i	$0.612350\pi$
$564$	157.586	+	240.231i	0.279409	+	0.425941i
$565$	447.081	+	447.081i	0.791293	+	0.791293i
$566$	20.0775	−	195.353i	0.0354725	−	0.345147i
$567$	242.585			0.427839
$568$	−496.025	−	957.090i	−0.873284	−	1.68502i
$569$		−	93.3114i		−	0.163992i	−0.996633	−	0.0819960i	$-0.973871\pi$
$569$		−	93.3114i		−	0.163992i	0.996633	−	0.0819960i	$-0.0261295\pi$
$570$	6.48059	−	63.0560i	0.0113694	−	0.110625i
$571$	196.999	−	196.999i	0.345007	−	0.345007i	−0.513239	−	0.858246i	$-0.671555\pi$
$571$	196.999	−	196.999i	0.345007	−	0.345007i	0.858246	+	0.513239i	$0.171555\pi$
$572$	−414.605	−	86.1318i	−0.724833	−	0.150580i
$573$	412.793	−	412.793i	0.720406	−	0.720406i
$574$	198.292	+	243.720i	0.345457	+	0.424599i
$575$		−	61.6644i		−	0.107242i
$576$	8.19284	+	5.78109i	0.0142237	+	0.0100366i
$577$	370.057			0.641347			0.320673	−	0.947190i	$-0.396091\pi$
$577$	370.057			0.641347			0.320673	+	0.947190i	$0.396091\pi$
$578$	−35.7918	+	29.1204i	−0.0619235	+	0.0503814i
$579$	−84.8888	−	84.8888i	−0.146613	−	0.146613i
$580$	−91.8217	+	441.993i	−0.158313	+	0.762058i
$581$	228.437	+	228.437i	0.393179	+	0.393179i
$582$	−186.636	−	19.1815i	−0.320680	−	0.0329579i
$583$	−494.890			−0.848869
$584$	−797.001	+	413.057i	−1.36473	+	0.707289i
$585$		−	8.38623i		−	0.0143354i
$586$	−675.038	−	69.3771i	−1.15194	−	0.118391i
$587$	328.063	−	328.063i	0.558880	−	0.558880i	−0.370108	−	0.928989i	$-0.620679\pi$
$587$	328.063	−	328.063i	0.558880	−	0.558880i	0.928989	+	0.370108i	$0.120679\pi$
$588$	−394.904	+	259.049i	−0.671605	+	0.440559i
$589$	44.3488	−	44.3488i	0.0752950	−	0.0752950i
$590$	281.314	−	228.879i	0.476803	−	0.387930i
$591$		−	969.708i		−	1.64079i
$592$	0.807376	+	2.04670i	0.00136381	+	0.00345726i
$593$	1088.78			1.83605			0.918024	−	0.396525i	$-0.129784\pi$
$593$	1088.78			1.83605			0.918024	+	0.396525i	$0.129784\pi$
$594$	−444.831	−	546.739i	−0.748873	−	0.920437i
$595$	−249.222	−	249.222i	−0.418860	−	0.418860i
$596$	56.3675	−	36.9759i	0.0945763	−	0.0620401i
$597$	129.446	+	129.446i	0.216828	+	0.216828i
$598$	−5.78687	+	56.3062i	−0.00967705	+	0.0941575i
$599$	−350.354			−0.584899			−0.292449	−	0.956281i	$-0.594470\pi$
$599$	−350.354			−0.584899			−0.292449	+	0.956281i	$0.594470\pi$
$600$	−404.138	−	128.231i	−0.673563	−	0.213718i
$601$			1021.45i			1.69958i	0.527123	+	0.849789i	$0.323271\pi$
$601$			1021.45i			1.69958i	−0.527123	+	0.849789i	$0.676729\pi$
$602$	1.50030	−	14.5979i	0.00249220	−	0.0242491i
$603$	−11.8847	+	11.8847i	−0.0197093	+	0.0197093i
$604$	−107.842	+	519.110i	−0.178547	+	0.859454i
$605$	−215.191	+	215.191i	−0.355687	+	0.355687i
$606$	−145.817	−	179.223i	−0.240622	−	0.295748i
$607$			394.204i			0.649431i	0.945812	+	0.324715i	$0.105268\pi$
$607$			394.204i			0.649431i	−0.945812	+	0.324715i	$0.894732\pi$
$608$	−45.4325	−	25.5371i	−0.0747246	−	0.0420019i
$609$	156.367			0.256760
$610$	240.124	−	195.366i	0.393645	−	0.320272i
$611$	−139.700	−	139.700i	−0.228641	−	0.228641i
$612$	−10.8395	−	2.25184i	−0.0177116	−	0.00367948i
$613$	157.606	+	157.606i	0.257106	+	0.257106i	0.823876	−	0.566770i	$-0.191807\pi$
$613$	157.606	+	157.606i	0.257106	+	0.257106i	−0.566770	+	0.823876i	$0.691807\pi$
$614$	650.464	+	66.8514i	1.05939	+	0.108879i
$615$	−1002.71			−1.63042
$616$	−300.895	−	95.4721i	−0.488465	−	0.154987i
$617$		−	609.080i		−	0.987164i	−0.869699	−	0.493582i	$-0.835687\pi$
$617$		−	609.080i		−	0.987164i	0.869699	−	0.493582i	$-0.164313\pi$
$618$	−608.689	−	62.5580i	−0.984933	−	0.101227i
$619$	−497.519	+	497.519i	−0.803747	+	0.803747i	−0.983679	−	0.179932i	$-0.942412\pi$
$619$	−497.519	+	497.519i	−0.803747	+	0.803747i	0.179932	+	0.983679i	$0.442412\pi$
$620$	−552.879	−	842.830i	−0.891741	−	1.35940i
$621$	−66.6199	+	66.6199i	−0.107278	+	0.107278i
$622$	796.371	−	647.933i	1.28034	−	1.04169i
$623$		−	95.8194i		−	0.153803i
$624$	356.987	+	155.014i	0.572095	+	0.248421i
$625$	752.924			1.20468
$626$	435.771	+	535.604i	0.696119	+	0.855597i
$627$	44.3244	+	44.3244i	0.0706929	+	0.0706929i
$628$	−329.178	−	501.811i	−0.524169	−	0.799062i
$629$	−1.71772	−	1.71772i	−0.00273087	−	0.00273087i
$630$	0.639157	−	6.21899i	0.00101454	−	0.00987142i
$631$	668.065			1.05874			0.529370	−	0.848391i	$-0.322428\pi$
$631$	668.065			1.05874			0.529370	+	0.848391i	$0.322428\pi$
$632$	965.377	−	500.320i	1.52750	−	0.791646i
$633$			635.665i			1.00421i
$634$	−99.9460	+	972.473i	−0.157644	+	1.53387i
$635$	908.362	−	908.362i	1.43049	−	1.43049i
$636$	445.336	+	92.5160i	0.700213	+	0.145465i
$637$	229.646	−	229.646i	0.360511	−	0.360511i
$638$	−281.738	−	346.283i	−0.441596	−	0.542763i
$639$			21.1117i			0.0330386i
$640$	−550.361	+	631.428i	−0.859939	+	0.986607i
$641$	−419.792			−0.654902			−0.327451	−	0.944868i	$-0.606190\pi$
$641$	−419.792			−0.654902			−0.327451	+	0.944868i	$0.606190\pi$
$642$	519.740	−	422.864i	0.809564	−	0.658666i
$643$	−138.767	−	138.767i	−0.215813	−	0.215813i	0.590919	−	0.806731i	$-0.298765\pi$
$643$	−138.767	−	138.767i	−0.215813	−	0.215813i	−0.806731	+	0.590919i	$0.798765\pi$
$644$	−8.58277	+	41.3141i	−0.0133273	+	0.0641523i
$645$	33.1155	+	33.1155i	0.0513418	+	0.0513418i
$646$	57.2415	+	5.88300i	0.0886091	+	0.00910680i
$647$	647.036			1.00006			0.500028	−	0.866009i	$-0.333323\pi$
$647$	647.036			1.00006			0.500028	+	0.866009i	$0.333323\pi$
$648$	292.889	+	565.135i	0.451989	+	0.872122i
$649$			358.633i			0.552594i
$650$	290.031	+	29.8080i	0.446202	+	0.0458584i
$651$	−246.884	+	246.884i	−0.379238	+	0.379238i
$652$	−499.378	+	327.582i	−0.765917	+	0.502426i
$653$	−452.293	+	452.293i	−0.692639	+	0.692639i	−0.962812	−	0.270173i	$-0.912919\pi$
$653$	−452.293	+	452.293i	−0.692639	+	0.692639i	0.270173	+	0.962812i	$0.412919\pi$
$654$	−818.218	+	665.707i	−1.25110	+	1.01790i
$655$		−	166.059i		−	0.253525i
$656$	−328.368	+	756.208i	−0.500561	+	1.15276i
$657$	17.5804			0.0267586
$658$	−92.9501	−	114.245i	−0.141262	−	0.173624i
$659$	382.858	+	382.858i	0.580969	+	0.580969i	0.935169	−	0.354201i	$-0.115247\pi$
$659$	382.858	+	382.858i	0.580969	+	0.580969i	−0.354201	+	0.935169i	$0.615247\pi$
$660$	842.368	−	552.576i	1.27631	−	0.837236i
$661$	−841.606	−	841.606i	−1.27323	−	1.27323i	−0.944383	−	0.328849i	$-0.893339\pi$
$661$	−841.606	−	841.606i	−1.27323	−	1.27323i	−0.328849	−	0.944383i	$-0.606661\pi$
$662$	−123.177	+	1198.51i	−0.186067	+	1.81043i
$663$	−429.704			−0.648120
$664$	−256.368	+	807.982i	−0.386096	+	1.21684i
$665$			32.4945i			0.0488639i
$666$	0.00440528	−	0.0428633i	6.61454e−6	−	6.43594e-5i
$667$	−42.1944	+	42.1944i	−0.0632599	+	0.0632599i
$668$	90.7912	−	437.033i	0.135915	−	0.654241i
$669$	242.926	−	242.926i	0.363119	−	0.363119i
$670$	−886.083	−	1089.08i	−1.32251	−	1.62549i
$671$			306.122i			0.456218i
$672$	252.917	+	142.162i	0.376365	+	0.211551i
$673$	−506.103			−0.752010			−0.376005	−	0.926618i	$-0.622703\pi$
$673$	−506.103			−0.752010			−0.376005	+	0.926618i	$0.622703\pi$
$674$	724.958	−	589.831i	1.07561	−	0.875120i
$675$	343.156	+	343.156i	0.508380	+	0.508380i
$676$	399.836	+	83.0638i	0.591474	+	0.122875i
$677$	−430.816	−	430.816i	−0.636361	−	0.636361i	0.313295	−	0.949656i	$-0.398567\pi$
$677$	−430.816	−	430.816i	−0.636361	−	0.636361i	−0.949656	+	0.313295i	$0.898567\pi$
$678$	571.640	+	58.7503i	0.843127	+	0.0866524i
$679$	96.1787			0.141648
$680$	279.694	−	881.498i	0.411315	−	1.29632i
$681$			106.132i			0.155848i
$682$	991.570	+	101.909i	1.45391	+	0.149426i
$683$	−910.083	+	910.083i	−1.33248	+	1.33248i	−0.429333	+	0.903146i	$0.641251\pi$
$683$	−910.083	+	910.083i	−1.33248	+	1.33248i	−0.903146	+	0.429333i	$0.858749\pi$
$684$	0.559846	+	0.853451i	0.000818488	+	0.00124773i
$685$	239.319	−	239.319i	0.349371	−	0.349371i
$686$	419.571	−	341.365i	0.611619	−	0.497617i
$687$		−	653.197i		−	0.950796i
$688$	35.8193	−	14.1299i	0.0520630	−	0.0205377i
$689$	−312.773			−0.453952
$690$	−84.9865	−	104.457i	−0.123169	−	0.151386i
$691$	−601.836	−	601.836i	−0.870964	−	0.870964i	0.121614	−	0.992577i	$-0.461193\pi$
$691$	−601.836	−	601.836i	−0.870964	−	0.870964i	−0.992577	+	0.121614i	$0.961193\pi$
$692$	−45.1029	−	68.7565i	−0.0651776	−	0.0993592i
$693$	4.37156	+	4.37156i	0.00630817	+	0.00630817i
$694$	6.37511	−	62.0297i	0.00918604	−	0.0893800i
$695$	161.619			0.232545
$696$	188.792	+	364.277i	0.271253	+	0.523387i
$697$		−	910.244i		−	1.30595i
$698$	45.8686	−	446.301i	0.0657144	−	0.639400i
$699$	−251.783	+	251.783i	−0.360204	+	0.360204i
$700$	212.807	+	44.2095i	0.304010	+	0.0631564i
$701$	−555.343	+	555.343i	−0.792215	+	0.792215i	−0.981854	−	0.189639i	$-0.939268\pi$
$701$	−555.343	+	555.343i	−0.792215	+	0.792215i	0.189639	+	0.981854i	$0.439268\pi$
$702$	−281.135	−	345.542i	−0.400477	−	0.492225i
$703$			0.223963i			0.000318582i
$704$	−140.875	−	816.245i	−0.200107	−	1.15944i
$705$	470.022			0.666697
$706$	−627.460	+	510.506i	−0.888754	+	0.723096i
$707$	83.7511	+	83.7511i	0.118460	+	0.118460i
$708$	67.0438	−	322.722i	0.0946946	−	0.455823i
$709$	−412.979	−	412.979i	−0.582480	−	0.582480i	0.353104	−	0.935584i	$-0.385126\pi$
$709$	−412.979	−	412.979i	−0.582480	−	0.582480i	−0.935584	+	0.353104i	$0.885126\pi$
$710$	−1754.32	−	180.300i	−2.47087	−	0.253943i
$711$	−21.2945			−0.0299500
$712$	223.224	−	115.689i	0.313517	−	0.162485i
$713$		−	133.240i		−	0.186872i
$714$	−318.656	−	32.7499i	−0.446297	−	0.0458682i
$715$	−489.856	+	489.856i	−0.685114	+	0.685114i
$716$	−93.3564	+	61.2399i	−0.130386	+	0.0855305i
$717$	−516.039	+	516.039i	−0.719720	+	0.719720i
$718$	−657.529	+	534.970i	−0.915779	+	0.745084i
$719$		−	1173.98i		−	1.63279i	−0.577495	−	0.816394i	$-0.695970\pi$
$719$		−	1173.98i		−	1.63279i	0.577495	−	0.816394i	$-0.304030\pi$
$720$	15.2597	−	6.01960i	0.0211940	−	0.00836056i
$721$	313.674			0.435054
$722$	452.313	+	555.936i	0.626472	+	0.769994i
$723$	906.750	+	906.750i	1.25415	+	1.25415i
$724$	795.360	−	521.740i	1.09856	−	0.720636i
$725$	217.342	+	217.342i	0.299781	+	0.299781i
$726$	−28.2779	+	275.144i	−0.0389503	+	0.378986i
$727$	678.813			0.933718			0.466859	−	0.884332i	$-0.345386\pi$
$727$	678.813			0.933718			0.466859	+	0.884332i	$0.345386\pi$
$728$	−190.167	−	60.3388i	−0.261218	−	0.0828830i
$729$		−	741.245i		−	1.01680i
$730$	−150.142	+	1460.88i	−0.205674	+	2.00120i
$731$	−30.0618	+	30.0618i	−0.0411242	+	0.0411242i
$732$	57.2272	−	275.469i	0.0781792	−	0.376324i
$733$	336.854	−	336.854i	0.459556	−	0.459556i	−0.438954	−	0.898510i	$-0.644651\pi$
$733$	336.854	−	336.854i	0.459556	−	0.459556i	0.898510	+	0.438954i	$0.144651\pi$
$734$	602.260	+	740.235i	0.820517	+	1.00849i
$735$			772.646i			1.05122i
$736$	−106.609	+	29.8865i	−0.144850	+	0.0406067i
$737$	1388.42			1.88387
$738$	12.5242	−	10.1897i	0.0169704	−	0.0138072i
$739$	178.478	+	178.478i	0.241513	+	0.241513i	0.817476	−	0.575963i	$-0.195373\pi$
$739$	178.478	+	178.478i	0.241513	+	0.241513i	−0.575963	+	0.817476i	$0.695373\pi$
$740$	3.52419	+	0.732131i	0.00476242	+	0.000989367i
$741$	28.0133	+	28.0133i	0.0378047	+	0.0378047i
$742$	−231.944	−	23.8380i	−0.312593	−	0.0321267i
$743$	795.320			1.07042			0.535208	−	0.844720i	$-0.320233\pi$
$743$	795.320			1.07042			0.535208	+	0.844720i	$0.320233\pi$
$744$	−873.230	−	277.071i	−1.17370	−	0.372407i
$745$		−	110.285i		−	0.148034i
$746$	−315.745	−	32.4508i	−0.423251	−	0.0434997i
$747$	11.7388	−	11.7388i	0.0157146	−	0.0157146i
$748$	501.622	+	764.691i	0.670617	+	1.02231i
$749$	−242.875	+	242.875i	−0.324266	+	0.324266i
$750$	216.698	−	176.307i	0.288930	−	0.235075i
$751$		−	102.850i		−	0.136951i	−0.997653	−	0.0684755i	$-0.978186\pi$
$751$		−	102.850i		−	0.136951i	0.997653	−	0.0684755i	$-0.0218135\pi$
$752$	153.924	−	354.475i	0.204686	−	0.471377i
$753$	−101.005			−0.134137
$754$	−178.060	−	218.852i	−0.236154	−	0.290255i
$755$	613.330	+	613.330i	0.812358	+	0.812358i
$756$	−182.146	−	277.671i	−0.240934	−	0.367290i
$757$	48.6324	+	48.6324i	0.0642436	+	0.0642436i	0.738499	−	0.674255i	$-0.235535\pi$
$757$	48.6324	+	48.6324i	0.0642436	+	0.0642436i	−0.674255	+	0.738499i	$0.735535\pi$
$758$	−15.0966	+	146.890i	−0.0199164	+	0.193786i
$759$	133.167			0.175450
$760$	−75.7004	+	39.2328i	−0.0996058	+	0.0516221i
$761$			947.802i			1.24547i	0.782433	+	0.622734i	$0.213978\pi$
$761$			947.802i			1.24547i	−0.782433	+	0.622734i	$0.786022\pi$
$762$	119.367	−	1161.44i	0.156649	−	1.52419i
$763$	382.354	−	382.354i	0.501119	−	0.501119i
$764$	−768.819	−	159.718i	−1.00631	−	0.209055i
$765$	−12.8069	+	12.8069i	−0.0167410	+	0.0167410i
$766$	94.4653	+	116.107i	0.123323	+	0.151576i
$767$			226.658i			0.295512i
$768$	−25.8221	+	760.848i	−0.0336225	+	0.990687i
$769$	−183.427			−0.238527			−0.119263	−	0.992863i	$-0.538053\pi$
$769$	−183.427			−0.238527			−0.119263	+	0.992863i	$0.538053\pi$
$770$	−400.598	+	325.929i	−0.520257	+	0.423285i
$771$	−212.085	−	212.085i	−0.275078	−	0.275078i
$772$	−32.8452	+	158.104i	−0.0425456	+	0.204798i
$773$	−178.338	−	178.338i	−0.230710	−	0.230710i	0.582279	−	0.812989i	$-0.302161\pi$
$773$	−178.338	−	178.338i	−0.230710	−	0.230710i	−0.812989	+	0.582279i	$0.802161\pi$
$774$	−0.750152	−	0.0770969i	−0.000969189	−	9.96084e-5i
$775$	−686.312			−0.885564
$776$	116.123	+	224.061i	0.149643	+	0.288739i
$777$		−	1.24677i		−	0.00160460i
$778$	160.500	+	16.4954i	0.206298	+	0.0212023i
$779$	−59.3406	+	59.3406i	−0.0761754	+	0.0761754i
$780$	532.381	−	349.231i	0.682539	−	0.447732i
$781$	1233.17	−	1233.17i	1.57897	−	1.57897i
$782$	94.8244	−	77.1497i	0.121259	−	0.0986569i
$783$		−	469.615i		−	0.599764i
$784$	582.705	+	253.027i	0.743246	+	0.322739i
$785$	−981.815			−1.25072
$786$	−95.2511	−	117.073i	−0.121185	−	0.148947i
$787$	−480.981	−	480.981i	−0.611158	−	0.611158i	0.332090	−	0.943248i	$-0.392246\pi$
$787$	−480.981	−	480.981i	−0.611158	−	0.611158i	−0.943248	+	0.332090i	$0.892246\pi$
$788$	−1090.63	+	715.432i	−1.38405	+	0.907909i
$789$	455.831	+	455.831i	0.577732	+	0.577732i
$790$	181.861	−	1769.51i	0.230204	−	2.23988i
$791$	−294.582			−0.372417
$792$	−4.90607	+	15.4622i	−0.00619454	+	0.0195230i
$793$			193.471i			0.243973i
$794$	102.907	−	1001.29i	0.129606	−	1.26107i
$795$	526.165	−	526.165i	0.661843	−	0.661843i
$796$	50.0854	−	241.092i	0.0629214	−	0.302879i
$797$	−558.478	+	558.478i	−0.700725	+	0.700725i	−0.964566	−	0.263841i	$-0.915011\pi$
$797$	−558.478	+	558.478i	−0.700725	+	0.700725i	0.263841	+	0.964566i	$0.415011\pi$
$798$	18.6388	+	22.9089i	0.0233569	+	0.0287079i
$799$			426.680i			0.534017i
$800$	153.944	+	549.140i	0.192430	+	0.686425i
$801$	−4.92392			−0.00614722
$802$	−176.690	+	143.756i	−0.220312	+	0.179247i
$803$	−1026.90	−	1026.90i	−1.27884	−	1.27884i
$804$	−1249.39	−	259.554i	−1.55397	−	0.322828i
$805$	48.8126	+	48.8126i	0.0606368	+	0.0606368i
$806$	626.677	+	64.4068i	0.777515	+	0.0799091i
$807$	−1079.89			−1.33816
$808$	−93.9914	+	296.228i	−0.116326	+	0.366619i
$809$			1152.43i			1.42451i	0.701918	+	0.712257i	$0.252327\pi$
$809$			1152.43i			1.42451i	−0.701918	+	0.712257i	$0.747673\pi$
$810$	1035.87	+	106.462i	1.27886	+	0.131435i
$811$	364.890	−	364.890i	0.449926	−	0.449926i	−0.445404	−	0.895330i	$-0.646940\pi$
$811$	364.890	−	364.890i	0.449926	−	0.449926i	0.895330	+	0.445404i	$0.146940\pi$
$812$	−115.364	−	175.866i	−0.142074	−	0.216583i
$813$	−27.0424	+	27.0424i	−0.0332624	+	0.0332624i
$814$	−2.76105	+	2.24641i	−0.00339196	+	0.00275972i
$815$			977.055i			1.19884i
$816$	−308.440	−	781.895i	−0.377990	−	0.958204i
$817$	3.91958			0.00479753
$818$	176.596	+	217.054i	0.215888	+	0.265347i
$819$	2.76285	+	2.76285i	0.00337344	+	0.00337344i
$820$	739.777	+	1127.74i	0.902167	+	1.37530i
$821$	−618.975	−	618.975i	−0.753928	−	0.753928i	0.221282	−	0.975210i	$-0.428976\pi$
$821$	−618.975	−	618.975i	−0.753928	−	0.753928i	−0.975210	+	0.221282i	$0.928976\pi$
$822$	31.4487	−	305.995i	0.0382587	−	0.372257i
$823$	626.066			0.760712			0.380356	−	0.924840i	$-0.375801\pi$
$823$	626.066			0.760712			0.380356	+	0.924840i	$0.375801\pi$
$824$	378.720	+	730.747i	0.459612	+	0.886829i
$825$		−	685.936i		−	0.831438i
$826$	−17.2748	+	168.083i	−0.0209138	+	0.203491i
$827$	375.666	−	375.666i	0.454252	−	0.454252i	−0.442511	−	0.896763i	$-0.645912\pi$
$827$	375.666	−	375.666i	0.454252	−	0.454252i	0.896763	+	0.442511i	$0.145912\pi$
$828$	2.12303	+	0.441047i	0.00256404	+	0.000532666i
$829$	−299.648	+	299.648i	−0.361457	+	0.361457i	−0.864349	−	0.502892i	$-0.832269\pi$
$829$	−299.648	+	299.648i	−0.361457	+	0.361457i	0.502892	+	0.864349i	$0.332269\pi$
$830$	875.207	+	1075.71i	1.05447	+	1.29604i
$831$			324.258i			0.390202i
$832$	−89.0337	−	515.871i	−0.107012	−	0.620037i
$833$	−701.398			−0.842015
$834$	113.943	−	92.7044i	0.136622	−	0.111156i
$835$	−516.356	−	516.356i	−0.618390	−	0.618390i
$836$	17.1500	−	82.5535i	0.0205144	−	0.0987482i
$837$	741.466	+	741.466i	0.885861	+	0.885861i
$838$	1043.79	+	107.275i	1.24557	+	0.128013i
$839$	−1477.80			−1.76138			−0.880689	−	0.473694i	$-0.842920\pi$
$839$	−1477.80			−1.76138			−0.880689	+	0.473694i	$0.842920\pi$
$840$	421.415	−	218.404i	0.501685	−	0.260005i
$841$			543.565i			0.646331i
$842$	−1308.64	−	134.496i	−1.55421	−	0.159734i
$843$	397.496	−	397.496i	0.471526	−	0.471526i
$844$	714.933	−	468.981i	0.847077	−	0.555665i
$845$	472.407	−	472.407i	0.559062	−	0.559062i
$846$	−5.87075	+	4.77648i	−0.00693942	+	0.00564596i
$847$		−	141.789i		−	0.167402i
$848$	−224.507	−	569.126i	−0.264749	−	0.671139i
$849$	−291.998			−0.343932
$850$	−397.395	−	488.437i	−0.467524	−	0.574631i
$851$	0.336433	+	0.336433i	0.000395338	+	0.000395338i
$852$	−1340.22	+	879.160i	−1.57303	+	1.03188i
$853$	404.051	+	404.051i	0.473682	+	0.473682i	0.903104	−	0.429422i	$-0.141283\pi$
$853$	404.051	+	404.051i	0.473682	+	0.473682i	−0.429422	+	0.903104i	$0.641283\pi$
$854$	−14.7454	+	143.472i	−0.0172663	+	0.168000i
$855$	1.66981			0.00195300
$856$	−859.050	−	272.571i	−1.00356	−	0.318425i
$857$		−	892.363i		−	1.04126i	−0.853781	−	0.520632i	$-0.825696\pi$
$857$		−	892.363i		−	1.04126i	0.853781	−	0.520632i	$-0.174304\pi$
$858$	−64.3714	+	626.333i	−0.0750250	+	0.729992i
$859$	−378.424	+	378.424i	−0.440540	+	0.440540i	−0.892193	−	0.451654i	$-0.850834\pi$
$859$	−378.424	+	378.424i	−0.440540	+	0.440540i	0.451654	+	0.892193i	$0.350834\pi$
$860$	12.8130	−	61.6770i	0.0148989	−	0.0717174i
$861$	330.342	−	330.342i	0.383672	−	0.383672i
$862$	517.413	+	635.950i	0.600247	+	0.737761i
$863$		−	1457.30i		−	1.68865i	−0.535833	−	0.844324i	$-0.680002\pi$
$863$		−	1457.30i		−	1.68865i	0.535833	−	0.844324i	$-0.319998\pi$
$864$	426.955	−	759.586i	0.494161	−	0.879150i
$865$	−134.525			−0.155520
$866$	32.0919	−	26.1102i	0.0370576	−	0.0301503i
$867$	48.5127	+	48.5127i	0.0559547	+	0.0559547i
$868$	459.817	+	95.5245i	0.529743	+	0.110051i
$869$	1243.85	+	1243.85i	1.43136	+	1.43136i
$870$	667.709	+	68.6238i	0.767481	+	0.0788779i
$871$	877.485			1.00745
$872$	1352.39	+	429.105i	1.55090	+	0.492092i
$873$		−	4.94238i		−	0.00566138i
$874$	−11.2113	−	1.15225i	−0.0128276	−	0.00131836i
$875$	−101.263	+	101.263i	−0.115729	+	0.115729i
$876$	732.106	+	1116.05i	0.835737	+	1.27403i
$877$	−571.322	+	571.322i	−0.651450	+	0.651450i	−0.953342	−	0.301892i	$-0.902382\pi$
$877$	−571.322	+	571.322i	−0.651450	+	0.651450i	0.301892	+	0.953342i	$0.402382\pi$
$878$	98.1856	−	79.8845i	0.111829	−	0.0909846i
$879$			1008.99i			1.14789i
$880$	−1242.97	−	539.732i	−1.41246	−	0.613332i
$881$	994.662			1.12901			0.564507	−	0.825428i	$-0.309066\pi$
$881$	994.662			1.12901			0.564507	+	0.825428i	$0.309066\pi$
$882$	−7.85182	−	9.65064i	−0.00890229	−	0.0109418i
$883$	74.0725	+	74.0725i	0.0838873	+	0.0838873i	0.747805	−	0.663918i	$-0.231108\pi$
$883$	74.0725	+	74.0725i	0.0838873	+	0.0838873i	−0.663918	+	0.747805i	$0.731108\pi$
$884$	317.027	+	483.288i	0.358628	+	0.546706i
$885$	−381.297	−	381.297i	−0.430844	−	0.430844i
$886$	85.9074	−	835.878i	0.0969609	−	0.943429i
$887$	−522.759			−0.589356			−0.294678	−	0.955597i	$-0.595212\pi$
$887$	−522.759			−0.589356			−0.294678	+	0.955597i	$0.595212\pi$
$888$	2.90453	−	1.50531i	0.00327087	−	0.00169517i
$889$			598.520i			0.673251i
$890$	42.0518	−	409.163i	0.0472492	−	0.459734i
$891$	−728.155	+	728.155i	−0.817233	+	0.817233i
$892$	−452.446	−	93.9932i	−0.507227	−	0.105373i
$893$	27.8161	−	27.8161i	0.0311491	−	0.0311491i
$894$	−63.2596	−	77.7520i	−0.0707601	−	0.0869710i
$895$			182.656i			0.204085i
$896$	−26.7077	−	389.341i	−0.0298077	−	0.434533i
$897$	84.1619			0.0938260
$898$	−565.792	+	460.332i	−0.630058	+	0.512619i
$899$	469.615	+	469.615i	0.522375	+	0.522375i
$900$	2.27182	−	10.9356i	0.00252424	−	0.0121507i
$901$	477.646	+	477.646i	0.530129	+	0.530129i
$902$	−1326.76	−	136.358i	−1.47091	−	0.151173i
$903$	−21.8198			−0.0241637
$904$	−355.669	−	686.269i	−0.393439	−	0.759147i
$905$		−	1556.16i		−	1.71951i
$906$	784.207	+	80.5970i	0.865571	+	0.0889591i
$907$	442.760	−	442.760i	0.488159	−	0.488159i	−0.419566	−	0.907725i	$-0.637818\pi$
$907$	442.760	−	442.760i	0.488159	−	0.488159i	0.907725	+	0.419566i	$0.137818\pi$
$908$	119.367	−	78.3024i	0.131462	−	0.0862362i
$909$	4.30376	−	4.30376i	0.00473461	−	0.00473461i
$910$	−253.180	+	205.989i	−0.278220	+	0.226361i
$911$			835.738i			0.917385i	0.888595	+	0.458692i	$0.151682\pi$
$911$			835.738i			0.917385i	−0.888595	+	0.458692i	$0.848318\pi$
$912$	−30.8655	+	71.0811i	−0.0338437	+	0.0779398i
$913$	−1371.37			−1.50205
$914$	−807.878	−	992.959i	−0.883892	−	1.08639i
$915$	−325.467	−	325.467i	−0.355702	−	0.355702i
$916$	−734.652	+	481.916i	−0.802022	+	0.526110i
$917$	54.7082	+	54.7082i	0.0596599	+	0.0596599i
$918$	−98.3577	+	957.019i	−0.107143	+	1.04250i
$919$	776.423			0.844856			0.422428	−	0.906396i	$-0.361178\pi$
$919$	776.423			0.844856			0.422428	+	0.906396i	$0.361178\pi$
$920$	−54.7810	+	172.651i	−0.0595445	+	0.187664i
$921$		−	972.260i		−	1.05566i
$922$	69.2316	−	673.623i	0.0750885	−	0.730610i
$923$	779.372	−	779.372i	0.844390	−	0.844390i
$924$	−95.4721	+	459.565i	−0.103325	+	0.497365i
$925$	1.73295	−	1.73295i	0.00187346	−	0.00187346i
$926$	−605.124	−	743.755i	−0.653481	−	0.803191i
$927$		−	16.1189i		−	0.0173883i
$928$	270.416	−	481.091i	0.291397	−	0.518417i
$929$	−144.945			−0.156022			−0.0780112	−	0.996952i	$-0.524857\pi$
$929$	−144.945			−0.156022			−0.0780112	+	0.996952i	$0.524857\pi$
$930$	−1162.58	+	945.883i	−1.25009	+	1.01708i
$931$	45.7256	+	45.7256i	0.0491145	+	0.0491145i
$932$	468.941	+	97.4199i	0.503156	+	0.104528i
$933$	−1079.41	−	1079.41i	−1.15693	−	1.15693i
$934$	−1134.94	−	116.643i	−1.21514	−	0.124886i
$935$	1496.15			1.60016
$936$	−3.10066	+	9.77221i	−0.00331267	+	0.0104404i
$937$			851.499i			0.908750i	0.890811	+	0.454375i	$0.150137\pi$
$937$			851.499i			0.908750i	−0.890811	+	0.454375i	$0.849863\pi$
$938$	650.718	+	66.8776i	0.693730	+	0.0712981i
$939$	725.966	−	725.966i	0.773127	−	0.773127i
$940$	−346.773	−	528.634i	−0.368908	−	0.562377i
$941$	1251.60	−	1251.60i	1.33008	−	1.33008i	0.424778	−	0.905297i	$-0.360352\pi$
$941$	1251.60	−	1251.60i	1.33008	−	1.33008i	0.905297	−	0.424778i	$-0.139648\pi$
$942$	−692.187	+	563.168i	−0.734806	+	0.597843i
$943$			178.281i			0.189057i
$944$	−412.430	+	162.694i	−0.436896	+	0.172346i
$945$	−543.275			−0.574894
$946$	39.3145	+	48.3213i	0.0415587	+	0.0510795i
$947$	919.818	+	919.818i	0.971296	+	0.971296i	0.999599	−	0.0283032i	$-0.00901039\pi$
$947$	919.818	+	919.818i	0.971296	+	0.971296i	−0.0283032	+	0.999599i	$0.509010\pi$
$948$	−886.772	−	1351.83i	−0.935414	−	1.42598i
$949$	−649.009	−	649.009i	−0.683887	−	0.683887i
$950$	−5.93517	+	57.7491i	−0.00624755	+	0.0607886i
$951$	1453.57			1.52847
$952$	198.265	+	382.555i	0.208261	+	0.401844i
$953$		−	489.450i		−	0.513589i	−0.966466	−	0.256794i	$-0.917334\pi$
$953$		−	489.450i		−	0.513589i	0.966466	−	0.256794i	$-0.0826663\pi$
$954$	−1.22498	+	11.9190i	−0.00128404	+	0.0124937i
$955$	−908.362	+	908.362i	−0.951164	+	0.951164i
$956$	961.114	+	199.666i	1.00535	+	0.208856i
$957$	−469.357	+	469.357i	−0.490447	+	0.490447i
$958$	581.392	+	714.586i	0.606881	+	0.745914i
$959$			157.688i			0.164429i
$960$	1017.61	+	718.050i	1.06001	+	0.747969i
$961$	−521.932			−0.543113
$962$	−1.74500	+	1.41974i	−0.00181393	+	0.00147582i
$963$	12.4807	+	12.4807i	0.0129603	+	0.0129603i
$964$	350.840	−	1688.81i	0.363942	−	1.75187i
$965$	186.800	+	186.800i	0.193575	+	0.193575i
$966$	62.4121	+	6.41441i	0.0646088	+	0.00664018i
$967$	−1368.49			−1.41519			−0.707594	−	0.706619i	$-0.750220\pi$
$967$	−1368.49			−1.41519			−0.707594	+	0.706619i	$0.750220\pi$
$968$	330.318	−	171.192i	0.341237	−	0.176851i
$969$		−	85.5599i		−	0.0882971i
$970$	410.697	+	42.2094i	0.423399	+	0.0435149i
$971$	−1013.79	+	1013.79i	−1.04407	+	1.04407i	−0.0450900	+	0.998983i	$0.514357\pi$
$971$	−1013.79	+	1013.79i	−1.04407	+	1.04407i	−0.998983	+	0.0450900i	$0.985643\pi$
$972$	−28.2935	+	18.5600i	−0.0291085	+	0.0190946i
$973$	−53.2455	+	53.2455i	−0.0547230	+	0.0547230i
$974$	892.247	−	725.938i	0.916064	−	0.745316i
$975$		−	433.515i		−	0.444631i
$976$	−352.042	+	138.872i	−0.360698	+	0.142287i
$977$	−5.19534			−0.00531765			−0.00265882	−	0.999996i	$-0.500846\pi$
$977$	−5.19534			−0.00531765			−0.00265882	+	0.999996i	$0.500846\pi$
$978$	560.437	+	688.831i	0.573044	+	0.704326i
$979$	287.616	+	287.616i	0.293785	+	0.293785i
$980$	868.996	−	570.043i	0.886730	−	0.581677i
$981$	−19.6482	−	19.6482i	−0.0200288	−	0.0200288i
$982$	−78.4732	+	763.543i	−0.0799116	+	0.777539i
$983$	−1591.90			−1.61943			−0.809714	−	0.586825i	$-0.800378\pi$
$983$	−1591.90			−1.61943			−0.809714	+	0.586825i	$0.800378\pi$
$984$	1168.42	+	370.733i	1.18742	+	0.376761i
$985$			2133.87i			2.16636i
$986$	−62.2958	+	606.138i	−0.0631804	+	0.614744i
$987$	−154.849	+	154.849i	−0.156888	+	0.156888i
$988$	10.8389	−	52.1742i	0.0109705	−	0.0528079i
$989$	5.88792	−	5.88792i	0.00595340	−	0.00595340i
$990$	16.7487	+	20.5857i	0.0169179	+	0.0207937i
$991$			622.896i			0.628553i	0.949331	+	0.314277i	$0.101762\pi$
$991$			622.896i			0.628553i	−0.949331	+	0.314277i	$0.898238\pi$
$992$	332.631	+	1186.54i	0.335313	+	1.19611i
$993$	1791.43			1.80406
$994$	637.360	−	518.560i	0.641207	−	0.521690i
$995$	−284.850	−	284.850i	−0.286282	−	0.286282i
$996$	1234.05	+	256.368i	1.23901	+	0.257398i
$997$	−635.503	−	635.503i	−0.637415	−	0.637415i	0.312502	−	0.949917i	$-0.398833\pi$
$997$	−635.503	−	635.503i	−0.637415	−	0.637415i	−0.949917	+	0.312502i	$0.898833\pi$
$998$	−754.278	−	77.5210i	−0.755790	−	0.0776763i
$999$	−3.74443			−0.00374818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.3.f.a.11.1	yes	6
3.2	odd	2		144.3.m.a.91.3		6
4.3	odd	2		64.3.f.a.15.1		6
5.2	odd	4		400.3.k.c.299.2		6
5.3	odd	4		400.3.k.d.299.2		6
5.4	even	2		400.3.r.c.251.3		6
8.3	odd	2		128.3.f.a.31.3		6
8.5	even	2		128.3.f.b.31.1		6
12.11	even	2		576.3.m.a.271.3		6
16.3	odd	4	inner	16.3.f.a.3.1	✓	6
16.5	even	4		128.3.f.a.95.3		6
16.11	odd	4		128.3.f.b.95.1		6
16.13	even	4		64.3.f.a.47.1		6
24.5	odd	2		1152.3.m.a.415.1		6
24.11	even	2		1152.3.m.b.415.1		6
32.3	odd	8		1024.3.c.j.1023.4		12
32.5	even	8		1024.3.d.k.511.3		12
32.11	odd	8		1024.3.d.k.511.4		12
32.13	even	8		1024.3.c.j.1023.3		12
32.19	odd	8		1024.3.c.j.1023.9		12
32.21	even	8		1024.3.d.k.511.10		12
32.27	odd	8		1024.3.d.k.511.9		12
32.29	even	8		1024.3.c.j.1023.10		12
48.5	odd	4		1152.3.m.b.991.1		6
48.11	even	4		1152.3.m.a.991.1		6
48.29	odd	4		576.3.m.a.559.3		6
48.35	even	4		144.3.m.a.19.3		6
80.3	even	4		400.3.k.c.99.2		6
80.19	odd	4		400.3.r.c.51.3		6
80.67	even	4		400.3.k.d.99.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.1	✓	6	16.3	odd	4	inner
16.3.f.a.11.1	yes	6	1.1	even	1	trivial
64.3.f.a.15.1		6	4.3	odd	2
64.3.f.a.47.1		6	16.13	even	4
128.3.f.a.31.3		6	8.3	odd	2
128.3.f.a.95.3		6	16.5	even	4
128.3.f.b.31.1		6	8.5	even	2
128.3.f.b.95.1		6	16.11	odd	4
144.3.m.a.19.3		6	48.35	even	4
144.3.m.a.91.3		6	3.2	odd	2
400.3.k.c.99.2		6	80.3	even	4
400.3.k.c.299.2		6	5.2	odd	4
400.3.k.d.99.2		6	80.67	even	4
400.3.k.d.299.2		6	5.3	odd	4
400.3.r.c.51.3		6	80.19	odd	4
400.3.r.c.251.3		6	5.4	even	2
576.3.m.a.271.3		6	12.11	even	2
576.3.m.a.559.3		6	48.29	odd	4
1024.3.c.j.1023.3		12	32.13	even	8
1024.3.c.j.1023.4		12	32.3	odd	8
1024.3.c.j.1023.9		12	32.19	odd	8
1024.3.c.j.1023.10		12	32.29	even	8
1024.3.d.k.511.3		12	32.5	even	8
1024.3.d.k.511.4		12	32.11	odd	8
1024.3.d.k.511.9		12	32.27	odd	8
1024.3.d.k.511.10		12	32.21	even	8
1152.3.m.a.415.1		6	24.5	odd	2
1152.3.m.a.991.1		6	48.11	even	4
1152.3.m.b.415.1		6	24.11	even	2
1152.3.m.b.991.1		6	48.5	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55139 + 1.26222i) q^{2} +(2.10278 + 2.10278i) q^{3} +(0.813607 - 3.91638i) q^{4} +(-4.62721 - 4.62721i) q^{5} +(-5.91638 - 0.608056i) q^{6} +3.04888 q^{7} +(3.68111 + 7.10278i) q^{8} -0.156674i q^{9} +(13.0192 + 1.33804i) q^{10} +(-9.15165 + 9.15165i) q^{11} +(9.94610 - 6.52444i) q^{12} +(-5.78389 + 5.78389i) q^{13} +(-4.72999 + 3.84835i) q^{14} -19.4600i q^{15} +(-14.6761 - 6.37279i) q^{16} +17.6655 q^{17} +(0.197757 + 0.243062i) q^{18} +(-1.15165 - 1.15165i) q^{19} +(-21.8867 + 14.3572i) q^{20} +(6.41110 + 6.41110i) q^{21} +(2.64637 - 25.7491i) q^{22} -3.45998 q^{23} +(-7.19499 + 22.6761i) q^{24} +17.8222i q^{25} +(1.67252 - 16.2736i) q^{26} +(19.2544 - 19.2544i) q^{27} +(2.48059 - 11.9406i) q^{28} +(12.1950 - 12.1950i) q^{29} +(24.5628 + 30.1900i) q^{30} +38.5089i q^{31} +(30.8122 - 8.63778i) q^{32} -38.4877 q^{33} +(-27.4061 + 22.2978i) q^{34} +(-14.1078 - 14.1078i) q^{35} +(-0.613596 - 0.127471i) q^{36} +(-0.0972356 - 0.0972356i) q^{37} +(3.24029 + 0.333021i) q^{38} -24.3244 q^{39} +(15.8328 - 49.8993i) q^{40} -51.5266i q^{41} +(-18.0383 - 1.85389i) q^{42} +(-1.70172 + 1.70172i) q^{43} +(28.3955 + 43.2872i) q^{44} +(-0.724965 + 0.724965i) q^{45} +(5.36776 - 4.36725i) q^{46} +24.1533i q^{47} +(-17.4600 - 44.2611i) q^{48} -39.7044 q^{49} +(-22.4955 - 27.6491i) q^{50} +(37.1466 + 37.1466i) q^{51} +(17.9461 + 27.3577i) q^{52} +(27.0383 + 27.0383i) q^{53} +(-5.56777 + 54.1744i) q^{54} +84.6933 q^{55} +(11.2233 + 21.6555i) q^{56} -4.84333i q^{57} +(-3.52641 + 34.3119i) q^{58} +(19.5939 - 19.5939i) q^{59} +(-76.2127 - 15.8328i) q^{60} +(16.7250 - 16.7250i) q^{61} +(-48.6066 - 59.7422i) q^{62} -0.477680i q^{63} +(-36.8988 + 52.2922i) q^{64} +53.5266 q^{65} +(59.7094 - 48.5799i) q^{66} +(-75.8560 - 75.8560i) q^{67} +(14.3728 - 69.1849i) q^{68} +(-7.27555 - 7.27555i) q^{69} +(39.6938 + 4.07953i) q^{70} -134.749 q^{71} +(1.11282 - 0.576735i) q^{72} +112.210i q^{73} +(0.273583 + 0.0281175i) q^{74} +(-37.4761 + 37.4761i) q^{75} +(-5.44730 + 3.57331i) q^{76} +(-27.9022 + 27.9022i) q^{77} +(37.7366 - 30.7028i) q^{78} -135.915i q^{79} +(38.4211 + 97.3976i) q^{80} +79.5654 q^{81} +(65.0378 + 79.9377i) q^{82} +(74.9250 + 74.9250i) q^{83} +(30.3244 - 19.8922i) q^{84} +(-81.7422 - 81.7422i) q^{85} +(0.492084 - 4.78797i) q^{86} +51.2866 q^{87} +(-98.6904 - 31.3139i) q^{88} -31.4278i q^{89} +(0.209637 - 2.03977i) q^{90} +(-17.6344 + 17.6344i) q^{91} +(-2.81506 + 13.5506i) q^{92} +(-80.9755 + 80.9755i) q^{93} +(-30.4867 - 37.4711i) q^{94} +10.6579i q^{95} +(82.9543 + 46.6277i) q^{96} +31.5456 q^{97} +(61.5968 - 50.1156i) q^{98} +(1.43383 + 1.43383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21}+ \cdots - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8 + 36 * q^10 - 18 * q^11 + 52 * q^12 - 2 * q^13 + 12 * q^14 - 40 * q^16 - 4 * q^17 - 74 * q^18 + 30 * q^19 - 84 * q^20 - 20 * q^21 - 52 * q^22 + 60 * q^23 + 48 * q^24 + 96 * q^26 + 64 * q^27 + 56 * q^28 - 18 * q^29 + 52 * q^30 + 8 * q^32 - 4 * q^33 - 76 * q^34 - 100 * q^35 - 52 * q^36 + 46 * q^37 + 40 * q^38 - 196 * q^39 + 40 * q^40 - 24 * q^42 - 114 * q^43 + 20 * q^44 + 66 * q^45 + 28 * q^46 - 24 * q^48 - 46 * q^49 + 46 * q^50 + 156 * q^51 + 100 * q^52 + 78 * q^53 + 32 * q^54 + 252 * q^55 - 168 * q^56 - 176 * q^58 + 206 * q^59 - 160 * q^60 + 30 * q^61 - 144 * q^62 + 64 * q^64 + 12 * q^65 + 196 * q^66 - 226 * q^67 + 112 * q^68 - 116 * q^69 - 16 * q^70 - 260 * q^71 + 52 * q^72 - 92 * q^74 - 238 * q^75 - 188 * q^76 - 212 * q^77 - 84 * q^78 + 232 * q^80 + 86 * q^81 + 304 * q^82 + 318 * q^83 + 232 * q^84 - 212 * q^85 + 268 * q^86 + 444 * q^87 - 8 * q^88 - 160 * q^90 + 188 * q^91 - 168 * q^92 - 32 * q^93 + 48 * q^94 - 80 * q^96 - 4 * q^97 + 10 * q^98 - 226 * q^99

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