LMFDB - Embedded newform 16.3.f.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,3,Mod(3,16)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55139 - 1.26222i) q^{2} +(2.10278 - 2.10278i) q^{3} +(0.813607 + 3.91638i) q^{4} +(-4.62721 + 4.62721i) q^{5} +(-5.91638 + 0.608056i) q^{6} +3.04888 q^{7} +(3.68111 - 7.10278i) q^{8} +0.156674i q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 96 q^{26} + 64 q^{27} + 56 q^{28} - 18 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} + 46 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 66 q^{45} + 28 q^{46} - 24 q^{48} - 46 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 78 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 30 q^{61} - 144 q^{62} + 64 q^{64} + 12 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 86 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 212 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} - 4 q^{97} + 10 q^{98} - 226 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.263684	−	0.964609i	$-0.584938\pi$
$3$	2.10278	−	2.10278i	0.700925	−	0.700925i	0.964609	+	0.263684i	$0.0849376\pi$
$4$	0.813607	+	3.91638i	0.203402	+	0.979095i
$5$	−4.62721	+	4.62721i	−0.925443	+	0.925443i	−0.997407	−	0.0719646i	$-0.977073\pi$
$5$	−4.62721	+	4.62721i	−0.925443	+	0.925443i	0.0719646	+	0.997407i	$0.477073\pi$
$6$	−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	0.155818	−	0.987786i	$-0.450199\pi$
$11$	−9.15165	−	9.15165i	−0.831968	−	0.831968i	−0.987786	+	0.155818i	$0.950199\pi$
$12$	9.94610	+	6.52444i	0.828842	+	0.543703i
$13$	−5.78389	−	5.78389i	−0.444914	−	0.444914i	0.448745	−	0.893660i	$-0.351871\pi$
$13$	−5.78389	−	5.78389i	−0.444914	−	0.444914i	−0.893660	+	0.448745i	$0.851871\pi$
$14$	−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	−0.736764	−	0.676150i	$-0.763647\pi$
$19$	−1.15165	+	1.15165i	−0.0606132	+	0.0606132i	0.676150	+	0.736764i	$0.263647\pi$
$20$	−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	0.885382	−	0.464865i	$-0.153897\pi$
$29$	12.1950	+	12.1950i	0.420517	+	0.420517i	−0.464865	+	0.885382i	$0.653897\pi$
$30$	24.5628	−	30.1900i	0.818758	−	1.00633i
$31$		−	38.5089i		−	1.24222i	−0.783723	−	0.621111i	$-0.786682\pi$
$31$		−	38.5089i		−	1.24222i	0.783723	−	0.621111i	$-0.213318\pi$
$32$	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	−0.708420	−	0.705792i	$-0.750592\pi$
$37$	−0.0972356	+	0.0972356i	−0.00262799	+	0.00262799i	0.705792	+	0.708420i	$0.250592\pi$
$38$	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	$0.216279\pi$
$41$			51.5266i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$42$	−18.0383	+	1.85389i	−0.429484	+	0.0441402i
$43$	−1.70172	−	1.70172i	−0.0395749	−	0.0395749i	0.687042	−	0.726617i	$-0.258909\pi$
$43$	−1.70172	−	1.70172i	−0.0395749	−	0.0395749i	−0.726617	+	0.687042i	$0.758909\pi$
$44$	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	$-0.917283\pi$
$47$		−	24.1533i		−	0.513899i	0.966425	−	0.256949i	$-0.0827174\pi$
$48$	−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	−0.404418	−	0.914574i	$-0.632526\pi$
$53$	27.0383	−	27.0383i	0.510157	−	0.510157i	0.914574	+	0.404418i	$0.132526\pi$
$54$	−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	0.853384	−	0.521283i	$-0.174547\pi$
$59$	19.5939	+	19.5939i	0.332100	+	0.332100i	−0.521283	+	0.853384i	$0.674547\pi$
$60$	−76.2127	+	15.8328i	−1.27021	+	0.263879i
$61$	16.7250	+	16.7250i	0.274180	+	0.274180i	0.830780	−	0.556601i	$-0.187895\pi$
$61$	16.7250	+	16.7250i	0.274180	+	0.274180i	−0.556601	+	0.830780i	$0.687895\pi$
$62$	−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	−0.142365	+	0.989814i	$0.545471\pi$
$67$	−75.8560	+	75.8560i	−1.13218	+	1.13218i	−0.989814	+	0.142365i	$0.954529\pi$
$68$	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	$-0.720974\pi$
$73$		−	112.210i		−	1.53712i	0.639777	−	0.768560i	$-0.279026\pi$
$74$	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	$0.329677\pi$
$79$			135.915i			1.72045i	−0.509915	+	0.860225i	$0.670323\pi$
$80$	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	−0.0929594	−	0.995670i	$-0.529633\pi$
$83$	74.9250	−	74.9250i	0.902711	−	0.902711i	0.995670	+	0.0929594i	$0.0296327\pi$
$84$	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	$0.0564971\pi$
$89$			31.4278i			0.353121i	−0.984290	+	0.176561i	$0.943503\pi$
$90$	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	−0.557920	−	0.829895i	$-0.688400\pi$
$101$	27.4695	−	27.4695i	0.271975	−	0.271975i	0.829895	+	0.557920i	$0.188400\pi$
$102$	−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	0.228948	−	0.973439i	$-0.426471\pi$
$107$	−79.6605	−	79.6605i	−0.744491	−	0.744491i	−0.973439	+	0.228948i	$0.926471\pi$
$108$	−59.7422	+	91.0732i	−0.553168	+	0.843270i
$109$	125.408	+	125.408i	1.15053	+	1.15053i	0.986446	+	0.164088i	$0.0524682\pi$
$109$	125.408	+	125.408i	1.15053	+	1.15053i	0.164088	+	0.986446i	$0.447532\pi$
$110$	−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	$-0.718821\pi$
$127$		−	196.309i		−	1.54574i	0.634566	−	0.772868i	$-0.281179\pi$
$128$	−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	−0.635295	−	0.772270i	$-0.719121\pi$
$131$	17.9437	−	17.9437i	0.136975	−	0.136975i	0.772270	+	0.635295i	$0.219121\pi$
$132$	−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	$-0.939553\pi$
$137$		−	51.7200i		−	0.377518i	0.982023	−	0.188759i	$-0.0604465\pi$
$138$	20.4705	−	2.10386i	0.148337	−	0.0152454i
$139$	−17.4640	−	17.4640i	−0.125640	−	0.125640i	0.641491	−	0.767131i	$-0.278316\pi$
$139$	−17.4640	−	17.4640i	−0.125640	−	0.125640i	−0.767131	+	0.641491i	$0.778316\pi$
$140$	−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	−0.665985	−	0.745965i	$-0.731989\pi$
$149$	11.9170	−	11.9170i	0.0799802	−	0.0799802i	0.745965	+	0.665985i	$0.231989\pi$
$150$	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	0.959034	−	0.283292i	$-0.0914266\pi$
$157$	106.091	+	106.091i	0.675742	+	0.675742i	−0.283292	+	0.959034i	$0.591427\pi$
$158$	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	−0.952440	−	0.304728i	$-0.901435\pi$
$163$	−105.577	+	105.577i	−0.647712	+	0.647712i	0.304728	+	0.952440i	$0.401435\pi$
$164$	−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	0.747870	−	0.663845i	$-0.231077\pi$
$173$	14.5363	+	14.5363i	0.0840249	+	0.0840249i	−0.663845	+	0.747870i	$0.731077\pi$
$174$	−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	−0.760086	−	0.649823i	$-0.774843\pi$
$179$	−19.7371	+	19.7371i	−0.110263	+	0.110263i	0.649823	+	0.760086i	$0.274843\pi$
$180$	2.24940	−	3.42907i	0.0124967	−	0.0190504i
$181$	168.153	−	168.153i	0.929021	−	0.929021i	−0.0686221	−	0.997643i	$-0.521860\pi$
$181$	168.153	−	168.153i	0.929021	−	0.929021i	0.997643	+	0.0686221i	$0.0218603\pi$
$182$	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	$0.171799\pi$
$191$			196.309i			1.02779i	−0.857852	+	0.513897i	$0.828201\pi$
$192$	−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	−0.188344	+	0.982103i	$0.560312\pi$
$197$	−230.578	+	230.578i	−1.17045	+	1.17045i	−0.982103	+	0.188344i	$0.939688\pi$
$198$	−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	−0.251509	−	0.967855i	$-0.580927\pi$
$211$	151.149	−	151.149i	0.716346	−	0.716346i	0.967855	+	0.251509i	$0.0809267\pi$
$212$	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	$0.0834022\pi$
$223$			115.527i			0.518056i	−0.965870	+	0.259028i	$0.916598\pi$
$224$	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	−0.649332	−	0.760505i	$-0.724951\pi$
$227$	25.2363	−	25.2363i	0.111173	−	0.111173i	0.760505	+	0.649332i	$0.224951\pi$
$228$	−18.9683	+	3.94056i	−0.0831944	+	0.0172832i
$229$	−155.318	+	155.318i	−0.678244	+	0.678244i	−0.959603	−	0.281359i	$-0.909215\pi$
$229$	−155.318	+	155.318i	−0.678244	+	0.678244i	0.281359	+	0.959603i	$0.409215\pi$
$230$	−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	$-0.917283\pi$
$233$		−	119.738i		−	0.513899i	0.966425	−	0.256949i	$-0.0827174\pi$
$234$	−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	$-0.828383\pi$
$239$		−	245.409i		−	1.02681i	0.858145	−	0.513407i	$-0.171617\pi$
$240$	−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	0.657643	−	0.753329i	$-0.271553\pi$
$251$	−24.0171	−	24.0171i	−0.0956858	−	0.0956858i	−0.753329	+	0.657643i	$0.771553\pi$
$252$	−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	0.0444453	−	0.999012i	$-0.485848\pi$
$269$	−256.778	−	256.778i	−0.954567	−	0.954567i	−0.999012	+	0.0444453i	$0.985848\pi$
$270$	276.440	+	224.913i	1.02385	+	0.833012i
$271$		−	12.8603i		−	0.0474551i	−0.999718	−	0.0237275i	$-0.992447\pi$
$271$		−	12.8603i		−	0.0474551i	0.999718	−	0.0237275i	$-0.00755342\pi$
$272$	−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	−0.554102	−	0.832449i	$-0.686938\pi$
$277$	77.1023	−	77.1023i	0.278348	−	0.278348i	0.832449	+	0.554102i	$0.186938\pi$
$278$	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	$0.109196\pi$
$281$			189.034i			0.672719i	−0.941734	+	0.336360i	$0.890804\pi$
$282$	14.6865	+	142.900i	0.0520799	+	0.506737i
$283$	−69.4317	−	69.4317i	−0.245342	−	0.245342i	0.573714	−	0.819056i	$-0.305502\pi$
$283$	−69.4317	−	69.4317i	−0.245342	−	0.245342i	−0.819056	+	0.573714i	$0.805502\pi$
$284$	−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	−0.167103	−	0.985939i	$-0.553441\pi$
$293$	239.919	−	239.919i	0.818837	−	0.818837i	0.985939	+	0.167103i	$0.0534412\pi$
$294$	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	−0.975046	−	0.222001i	$-0.928741\pi$
$307$	−231.185	+	231.185i	−0.753046	+	0.753046i	0.222001	+	0.975046i	$0.428741\pi$
$308$	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	$0.185946\pi$
$313$			345.242i			1.10301i	−0.834172	+	0.551504i	$0.814054\pi$
$314$	−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	0.995494	+	0.0948290i	$0.0302304\pi$
$317$	345.632	+	345.632i	1.09032	+	1.09032i	0.0948290	+	0.995494i	$0.469770\pi$
$318$	−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	0.936652	+	0.350261i	$0.113907\pi$
$331$	425.968	+	425.968i	1.28691	+	1.28691i	0.350261	+	0.936652i	$0.386093\pi$
$332$	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	0.674626	−	0.738160i	$-0.264305\pi$
$347$	−22.0463	−	22.0463i	−0.0635341	−	0.0635341i	−0.738160	+	0.674626i	$0.764305\pi$
$348$	41.7271	+	200.858i	0.119906	+	0.577178i
$349$	−158.622	−	158.622i	−0.454506	−	0.454506i	0.442341	−	0.896847i	$-0.354148\pi$
$349$	−158.622	−	158.622i	−0.454506	−	0.454506i	−0.896847	+	0.442341i	$0.854148\pi$
$350$	−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	$0.225256\pi$
$367$			477.144i			1.30012i	−0.759883	+	0.650059i	$0.774744\pi$
$368$	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	−0.540490	−	0.841350i	$-0.681761\pi$
$373$	112.221	−	112.221i	0.300860	−	0.300860i	0.841350	+	0.540490i	$0.181761\pi$
$374$	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	0.772619	−	0.634870i	$-0.218946\pi$
$379$	52.2069	+	52.2069i	0.137749	+	0.137749i	−0.634870	+	0.772619i	$0.718946\pi$
$380$	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	$0.0311496\pi$
$383$			74.8407i			0.195406i	−0.995216	+	0.0977032i	$0.968850\pi$
$384$	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	−0.776617	−	0.629974i	$-0.783066\pi$
$389$	−57.0441	+	57.0441i	−0.146643	+	0.146643i	0.629974	+	0.776617i	$0.283066\pi$
$390$	−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	0.0987089	−	0.995116i	$-0.468529\pi$
$397$	−355.874	−	355.874i	−0.896407	−	0.896407i	−0.995116	+	0.0987089i	$0.968529\pi$
$398$	−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	$0.0547122\pi$
$409$			139.909i			0.342077i	−0.985264	+	0.171038i	$0.945288\pi$
$410$	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	−0.994076	−	0.108687i	$-0.965335\pi$
$419$	−370.978	+	370.978i	−0.885389	+	0.885389i	0.108687	+	0.994076i	$0.465335\pi$
$420$	−232.363	+	48.2721i	−0.553245	+	0.114934i
$421$	465.112	−	465.112i	1.10478	−	1.10478i	0.110955	−	0.993825i	$-0.464609\pi$
$421$	465.112	−	465.112i	1.10478	−	1.10478i	0.993825	−	0.110955i	$-0.0353908\pi$
$422$	−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	$0.157751\pi$
$431$			409.924i			0.951099i	−0.879689	+	0.475549i	$0.842249\pi$
$432$	−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	0.287240	−	0.957859i	$-0.407262\pi$
$443$	−297.084	−	297.084i	−0.670619	−	0.670619i	−0.957859	+	0.287240i	$0.907262\pi$
$444$	−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	$-0.753064\pi$
$457$		−	640.046i		−	1.40054i	0.713879	−	0.700269i	$-0.246936\pi$
$458$	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	0.398031	−	0.917372i	$-0.369694\pi$
$461$	−239.416	−	239.416i	−0.519341	−	0.519341i	−0.917372	+	0.398031i	$0.869694\pi$
$462$	182.046	+	148.114i	0.394040	+	0.320594i
$463$		−	479.413i		−	1.03545i	−0.855548	−	0.517724i	$-0.826779\pi$
$463$		−	479.413i		−	1.03545i	0.855548	−	0.517724i	$-0.173221\pi$
$464$	−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	−0.128015	−	0.991772i	$-0.540860\pi$
$467$	403.375	−	403.375i	0.863758	−	0.863758i	0.991772	+	0.128015i	$0.0408605\pi$
$468$	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	$0.159655\pi$
$479$			460.611i			0.961609i	−0.876828	+	0.480805i	$0.840345\pi$
$480$	−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	0.927219	−	0.374520i	$-0.122192\pi$
$491$	271.375	+	271.375i	0.552699	+	0.552699i	−0.374520	+	0.927219i	$0.622192\pi$
$492$	−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	−0.385478	−	0.922717i	$-0.625963\pi$
$499$	268.082	−	268.082i	0.537239	−	0.537239i	0.922717	+	0.385478i	$0.125963\pi$
$500$	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	0.936297	−	0.351210i	$-0.114230\pi$
$509$	297.809	+	297.809i	0.585087	+	0.585087i	−0.351210	+	0.936297i	$0.614230\pi$
$510$	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	$0.0292329\pi$
$521$			95.5605i			0.183418i	−0.995786	+	0.0917088i	$0.970767\pi$
$522$	5.37579	−	0.552497i	0.0102984	−	0.00105842i
$523$	−250.389	−	250.389i	−0.478756	−	0.478756i	0.425978	−	0.904734i	$-0.359930\pi$
$523$	−250.389	−	250.389i	−0.478756	−	0.478756i	−0.904734	+	0.425978i	$0.859930\pi$
$524$	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	0.627554	−	0.778573i	$-0.284056\pi$
$541$	−81.7015	−	81.7015i	−0.151019	−	0.151019i	−0.778573	+	0.627554i	$0.784056\pi$
$542$	−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	−0.963724	−	0.266901i	$-0.914000\pi$
$547$	−381.162	+	381.162i	−0.696823	+	0.696823i	0.266901	+	0.963724i	$0.414000\pi$
$548$	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	0.647548	−	0.762025i	$-0.275794\pi$
$557$	−63.7634	−	63.7634i	−0.114476	−	0.114476i	−0.762025	+	0.647548i	$0.775794\pi$
$558$	−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	−0.345674	−	0.938355i	$-0.612350\pi$
$563$	333.679	−	333.679i	0.592681	−	0.592681i	0.938355	+	0.345674i	$0.112350\pi$
$564$	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	$0.0261295\pi$
$569$			93.3114i			0.163992i	−0.996633	+	0.0819960i	$0.973871\pi$
$570$	6.48059	+	63.0560i	0.0113694	+	0.110625i
$571$	196.999	+	196.999i	0.345007	+	0.345007i	0.858246	−	0.513239i	$-0.171555\pi$
$571$	196.999	+	196.999i	0.345007	+	0.345007i	−0.513239	+	0.858246i	$0.671555\pi$
$572$	−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	0.928989	−	0.370108i	$-0.120679\pi$
$587$	328.063	+	328.063i	0.558880	+	0.558880i	−0.370108	+	0.928989i	$0.620679\pi$
$588$	−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	$-0.676729\pi$
$601$		−	1021.45i		−	1.69958i	0.527123	−	0.849789i	$-0.323271\pi$
$602$	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	$-0.894732\pi$
$607$		−	394.204i		−	0.649431i	0.945812	−	0.324715i	$-0.105268\pi$
$608$	−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	−0.566770	−	0.823876i	$-0.691807\pi$
$613$	157.606	−	157.606i	0.257106	−	0.257106i	0.823876	+	0.566770i	$0.191807\pi$
$614$	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	$0.164313\pi$
$617$			609.080i			0.987164i	−0.869699	+	0.493582i	$0.835687\pi$
$618$	−608.689	+	62.5580i	−0.984933	+	0.101227i
$619$	−497.519	−	497.519i	−0.803747	−	0.803747i	0.179932	−	0.983679i	$-0.442412\pi$
$619$	−497.519	−	497.519i	−0.803747	−	0.803747i	−0.983679	+	0.179932i	$0.942412\pi$
$620$	−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	−0.806731	−	0.590919i	$-0.798765\pi$
$643$	−138.767	+	138.767i	−0.215813	+	0.215813i	0.590919	+	0.806731i	$0.298765\pi$
$644$	−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	0.270173	−	0.962812i	$-0.412919\pi$
$653$	−452.293	−	452.293i	−0.692639	−	0.692639i	−0.962812	+	0.270173i	$0.912919\pi$
$654$	−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	−0.354201	−	0.935169i	$-0.615247\pi$
$659$	382.858	−	382.858i	0.580969	−	0.580969i	0.935169	+	0.354201i	$0.115247\pi$
$660$	842.368	+	552.576i	1.27631	+	0.837236i
$661$	−841.606	+	841.606i	−1.27323	+	1.27323i	−0.328849	+	0.944383i	$0.606661\pi$
$661$	−841.606	+	841.606i	−1.27323	+	1.27323i	−0.944383	+	0.328849i	$0.893339\pi$
$662$	−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	−0.949656	−	0.313295i	$-0.898567\pi$
$677$	−430.816	+	430.816i	−0.636361	+	0.636361i	0.313295	+	0.949656i	$0.398567\pi$
$678$	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	−0.903146	−	0.429333i	$-0.858749\pi$
$683$	−910.083	−	910.083i	−1.33248	−	1.33248i	−0.429333	−	0.903146i	$-0.641251\pi$
$684$	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	−0.992577	−	0.121614i	$-0.961193\pi$
$691$	−601.836	+	601.836i	−0.870964	+	0.870964i	0.121614	+	0.992577i	$0.461193\pi$
$692$	−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	0.189639	−	0.981854i	$-0.439268\pi$
$701$	−555.343	−	555.343i	−0.792215	−	0.792215i	−0.981854	+	0.189639i	$0.939268\pi$
$702$	−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	−0.935584	−	0.353104i	$-0.885126\pi$
$709$	−412.979	+	412.979i	−0.582480	+	0.582480i	0.353104	+	0.935584i	$0.385126\pi$
$710$	−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	$0.304030\pi$
$719$			1173.98i			1.63279i	−0.577495	+	0.816394i	$0.695970\pi$
$720$	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	0.898510	−	0.438954i	$-0.144651\pi$
$733$	336.854	+	336.854i	0.459556	+	0.459556i	−0.438954	+	0.898510i	$0.644651\pi$
$734$	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	−0.575963	−	0.817476i	$-0.695373\pi$
$739$	178.478	−	178.478i	0.241513	−	0.241513i	0.817476	+	0.575963i	$0.195373\pi$
$740$	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	$0.0218135\pi$
$751$			102.850i			0.136951i	−0.997653	+	0.0684755i	$0.978186\pi$
$752$	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	−0.674255	−	0.738499i	$-0.735535\pi$
$757$	48.6324	−	48.6324i	0.0642436	−	0.0642436i	0.738499	+	0.674255i	$0.235535\pi$
$758$	−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	$-0.786022\pi$
$761$		−	947.802i		−	1.24547i	0.782433	−	0.622734i	$-0.213978\pi$
$762$	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	−0.812989	−	0.582279i	$-0.802161\pi$
$773$	−178.338	+	178.338i	−0.230710	+	0.230710i	0.582279	+	0.812989i	$0.302161\pi$
$774$	−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	−0.943248	−	0.332090i	$-0.892246\pi$
$787$	−480.981	+	480.981i	−0.611158	+	0.611158i	0.332090	+	0.943248i	$0.392246\pi$
$788$	−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	0.263841	−	0.964566i	$-0.415011\pi$
$797$	−558.478	−	558.478i	−0.700725	−	0.700725i	−0.964566	+	0.263841i	$0.915011\pi$
$798$	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	$-0.747673\pi$
$809$		−	1152.43i		−	1.42451i	0.701918	−	0.712257i	$-0.252327\pi$
$810$	1035.87	−	106.462i	1.27886	−	0.131435i
$811$	364.890	+	364.890i	0.449926	+	0.449926i	0.895330	−	0.445404i	$-0.146940\pi$
$811$	364.890	+	364.890i	0.449926	+	0.449926i	−0.445404	+	0.895330i	$0.646940\pi$
$812$	−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	−0.975210	−	0.221282i	$-0.928976\pi$
$821$	−618.975	+	618.975i	−0.753928	+	0.753928i	0.221282	+	0.975210i	$0.428976\pi$
$822$	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	0.896763	−	0.442511i	$-0.145912\pi$
$827$	375.666	+	375.666i	0.454252	+	0.454252i	−0.442511	+	0.896763i	$0.645912\pi$
$828$	2.12303	−	0.441047i	0.00256404	−	0.000532666i
$829$	−299.648	−	299.648i	−0.361457	−	0.361457i	0.502892	−	0.864349i	$-0.332269\pi$
$829$	−299.648	−	299.648i	−0.361457	−	0.361457i	−0.864349	+	0.502892i	$0.832269\pi$
$830$	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	−0.429422	−	0.903104i	$-0.641283\pi$
$853$	404.051	−	404.051i	0.473682	−	0.473682i	0.903104	+	0.429422i	$0.141283\pi$
$854$	−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	$0.174304\pi$
$857$			892.363i			1.04126i	−0.853781	+	0.520632i	$0.825696\pi$
$858$	−64.3714	−	626.333i	−0.0750250	−	0.729992i
$859$	−378.424	−	378.424i	−0.440540	−	0.440540i	0.451654	−	0.892193i	$-0.350834\pi$
$859$	−378.424	−	378.424i	−0.440540	−	0.440540i	−0.892193	+	0.451654i	$0.850834\pi$
$860$	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	$0.319998\pi$
$863$			1457.30i			1.68865i	−0.535833	+	0.844324i	$0.680002\pi$
$864$	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	0.301892	−	0.953342i	$-0.402382\pi$
$877$	−571.322	−	571.322i	−0.651450	−	0.651450i	−0.953342	+	0.301892i	$0.902382\pi$
$878$	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	−0.663918	−	0.747805i	$-0.731108\pi$
$883$	74.0725	−	74.0725i	0.0838873	−	0.0838873i	0.747805	+	0.663918i	$0.231108\pi$
$884$	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	0.907725	−	0.419566i	$-0.137818\pi$
$907$	442.760	+	442.760i	0.488159	+	0.488159i	−0.419566	+	0.907725i	$0.637818\pi$
$908$	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	$-0.848318\pi$
$911$		−	835.738i		−	0.917385i	0.888595	−	0.458692i	$-0.151682\pi$
$912$	−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	$-0.849863\pi$
$937$		−	851.499i		−	0.908750i	0.890811	−	0.454375i	$-0.150137\pi$
$938$	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	0.905297	+	0.424778i	$0.139648\pi$
$941$	1251.60	+	1251.60i	1.33008	+	1.33008i	0.424778	+	0.905297i	$0.360352\pi$
$942$	−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	−0.0283032	−	0.999599i	$-0.509010\pi$
$947$	919.818	−	919.818i	0.971296	−	0.971296i	0.999599	+	0.0283032i	$0.00901039\pi$
$948$	−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	$0.0826663\pi$
$953$			489.450i			0.513589i	−0.966466	+	0.256794i	$0.917334\pi$
$954$	−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	−0.998983	−	0.0450900i	$-0.985643\pi$
$971$	−1013.79	−	1013.79i	−1.04407	−	1.04407i	−0.0450900	−	0.998983i	$-0.514357\pi$
$972$	−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	$-0.898238\pi$
$991$		−	622.896i		−	0.628553i	0.949331	−	0.314277i	$-0.101762\pi$
$992$	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	−0.949917	−	0.312502i	$-0.898833\pi$
$997$	−635.503	+	635.503i	−0.637415	+	0.637415i	0.312502	+	0.949917i	$0.398833\pi$
$998$	−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.3.1	✓	6
3.2	odd	2		144.3.m.a.19.3		6
4.3	odd	2		64.3.f.a.47.1		6
5.2	odd	4		400.3.k.d.99.2		6
5.3	odd	4		400.3.k.c.99.2		6
5.4	even	2		400.3.r.c.51.3		6
8.3	odd	2		128.3.f.a.95.3		6
8.5	even	2		128.3.f.b.95.1		6
12.11	even	2		576.3.m.a.559.3		6
16.3	odd	4		128.3.f.b.31.1		6
16.5	even	4		64.3.f.a.15.1		6
16.11	odd	4	inner	16.3.f.a.11.1	yes	6
16.13	even	4		128.3.f.a.31.3		6
24.5	odd	2		1152.3.m.a.991.1		6
24.11	even	2		1152.3.m.b.991.1		6
32.3	odd	8		1024.3.d.k.511.3		12
32.5	even	8		1024.3.c.j.1023.9		12
32.11	odd	8		1024.3.c.j.1023.10		12
32.13	even	8		1024.3.d.k.511.4		12
32.19	odd	8		1024.3.d.k.511.10		12
32.21	even	8		1024.3.c.j.1023.4		12
32.27	odd	8		1024.3.c.j.1023.3		12
32.29	even	8		1024.3.d.k.511.9		12
48.5	odd	4		576.3.m.a.271.3		6
48.11	even	4		144.3.m.a.91.3		6
48.29	odd	4		1152.3.m.b.415.1		6
48.35	even	4		1152.3.m.a.415.1		6
80.27	even	4		400.3.k.c.299.2		6
80.43	even	4		400.3.k.d.299.2		6
80.59	odd	4		400.3.r.c.251.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.1	✓	6	1.1	even	1	trivial
16.3.f.a.11.1	yes	6	16.11	odd	4	inner
64.3.f.a.15.1		6	16.5	even	4
64.3.f.a.47.1		6	4.3	odd	2
128.3.f.a.31.3		6	16.13	even	4
128.3.f.a.95.3		6	8.3	odd	2
128.3.f.b.31.1		6	16.3	odd	4
128.3.f.b.95.1		6	8.5	even	2
144.3.m.a.19.3		6	3.2	odd	2
144.3.m.a.91.3		6	48.11	even	4
400.3.k.c.99.2		6	5.3	odd	4
400.3.k.c.299.2		6	80.27	even	4
400.3.k.d.99.2		6	5.2	odd	4
400.3.k.d.299.2		6	80.43	even	4
400.3.r.c.51.3		6	5.4	even	2
400.3.r.c.251.3		6	80.59	odd	4
576.3.m.a.271.3		6	48.5	odd	4
576.3.m.a.559.3		6	12.11	even	2
1024.3.c.j.1023.3		12	32.27	odd	8
1024.3.c.j.1023.4		12	32.21	even	8
1024.3.c.j.1023.9		12	32.5	even	8
1024.3.c.j.1023.10		12	32.11	odd	8
1024.3.d.k.511.3		12	32.3	odd	8
1024.3.d.k.511.4		12	32.13	even	8
1024.3.d.k.511.9		12	32.29	even	8
1024.3.d.k.511.10		12	32.19	odd	8
1152.3.m.a.415.1		6	48.35	even	4
1152.3.m.a.991.1		6	24.5	odd	2
1152.3.m.b.415.1		6	48.29	odd	4
1152.3.m.b.991.1		6	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.55139 - 1.26222i) q^{2} +(2.10278 - 2.10278i) q^{3} +(0.813607 + 3.91638i) q^{4} +(-4.62721 + 4.62721i) q^{5} +(-5.91638 + 0.608056i) q^{6} +3.04888 q^{7} +(3.68111 - 7.10278i) q^{8} +0.156674i q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 96 q^{26} + 64 q^{27} + 56 q^{28} - 18 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} + 46 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 66 q^{45} + 28 q^{46} - 24 q^{48} - 46 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 78 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 30 q^{61} - 144 q^{62} + 64 q^{64} + 12 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 86 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 212 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} - 4 q^{97} + 10 q^{98} - 226 q^{99}+O(q^{100}) \) 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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