LMFDB - Embedded newform 112.3.l.b.69.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(13,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("112.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.l (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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.5
Character	$\chi$	$=$	112.69
Dual form			112.3.l.b.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88371 + 0.672048i) q^{2} +(-0.746365 - 0.746365i) q^{3} +(3.09670 - 2.53188i) q^{4} +(0.822232 - 0.822232i) q^{5} +(1.90753 + 0.904340i) q^{6} +(-6.88091 + 1.28574i) q^{7} +(-4.13173 + 6.85046i) q^{8} -7.88588i q^{9} +O(q^{10})$	\(q+(-1.88371 + 0.672048i) q^{2} +(-0.746365 - 0.746365i) q^{3} +(3.09670 - 2.53188i) q^{4} +(0.822232 - 0.822232i) q^{5} +(1.90753 + 0.904340i) q^{6} +(-6.88091 + 1.28574i) q^{7} +(-4.13173 + 6.85046i) q^{8} -7.88588i q^{9} +(-0.996265 + 2.10142i) q^{10} +(2.57423 + 2.57423i) q^{11} +(-4.20098 - 0.421563i) q^{12} +(-14.9766 - 14.9766i) q^{13} +(12.0975 - 7.04626i) q^{14} -1.22737 q^{15} +(3.17914 - 15.6810i) q^{16} -20.7103i q^{17} +(5.29969 + 14.8547i) q^{18} +(-10.0977 - 10.0977i) q^{19} +(0.464414 - 4.62800i) q^{20} +(6.09530 + 4.17604i) q^{21} +(-6.57909 - 3.11909i) q^{22} -19.5800i q^{23} +(8.19673 - 2.02916i) q^{24} +23.6479i q^{25} +(38.2766 + 18.1466i) q^{26} +(-12.6030 + 12.6030i) q^{27} +(-18.0528 + 21.4032i) q^{28} +(7.24407 - 7.24407i) q^{29} +(2.31201 - 0.824852i) q^{30} +45.5117i q^{31} +(4.54980 + 31.6749i) q^{32} -3.84263i q^{33} +(13.9183 + 39.0122i) q^{34} +(-4.60052 + 6.71488i) q^{35} +(-19.9661 - 24.4202i) q^{36} +(-34.5793 - 34.5793i) q^{37} +(25.8073 + 12.2350i) q^{38} +22.3561i q^{39} +(2.23542 + 9.02991i) q^{40} +61.5837 q^{41} +(-14.2883 - 3.77009i) q^{42} +(-16.6424 - 16.6424i) q^{43} +(14.4893 + 1.45398i) q^{44} +(-6.48402 - 6.48402i) q^{45} +(13.1587 + 36.8830i) q^{46} +55.0421i q^{47} +(-14.0765 + 9.33094i) q^{48} +(45.6937 - 17.6941i) q^{49} +(-15.8925 - 44.5457i) q^{50} +(-15.4575 + 15.4575i) q^{51} +(-84.2973 - 8.45912i) q^{52} +(38.2187 + 38.2187i) q^{53} +(15.2706 - 32.2103i) q^{54} +4.23322 q^{55} +(19.6222 - 52.4497i) q^{56} +15.0732i q^{57} +(-8.77734 + 18.5141i) q^{58} +(32.2679 - 32.2679i) q^{59} +(-3.80080 + 3.10756i) q^{60} +(-32.0297 - 32.0297i) q^{61} +(-30.5861 - 85.7308i) q^{62} +(10.1392 + 54.2620i) q^{63} +(-29.8575 - 56.6085i) q^{64} -24.6286 q^{65} +(2.58243 + 7.23839i) q^{66} +(42.1559 - 42.1559i) q^{67} +(-52.4362 - 64.1338i) q^{68} +(-14.6139 + 14.6139i) q^{69} +(4.15332 - 15.7406i) q^{70} -15.7491i q^{71} +(54.0219 + 32.5824i) q^{72} +65.7339 q^{73} +(88.3762 + 41.8983i) q^{74} +(17.6500 - 17.6500i) q^{75} +(-56.8360 - 5.70341i) q^{76} +(-21.0228 - 14.4032i) q^{77} +(-15.0244 - 42.1123i) q^{78} -96.5103 q^{79} +(-10.2794 - 15.5074i) q^{80} -52.1600 q^{81} +(-116.006 + 41.3872i) q^{82} +(-31.6530 - 31.6530i) q^{83} +(29.4486 - 2.50064i) q^{84} +(-17.0287 - 17.0287i) q^{85} +(42.5340 + 20.1650i) q^{86} -10.8134 q^{87} +(-28.2707 + 6.99861i) q^{88} +89.3246 q^{89} +(16.5716 + 7.85642i) q^{90} +(122.309 + 83.7968i) q^{91} +(-49.5743 - 60.6335i) q^{92} +(33.9684 - 33.9684i) q^{93} +(-36.9909 - 103.683i) q^{94} -16.6054 q^{95} +(20.2452 - 27.0369i) q^{96} +47.6196i q^{97} +(-74.1823 + 64.0389i) q^{98} +(20.3000 - 20.3000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8}+O(q^{10}) $ 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8	$ 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8} + 40 q^{14} - 8 q^{15} + 48 q^{16} + 196 q^{18} - 20 q^{21} - 120 q^{22} - 96 q^{29} - 40 q^{30} - 184 q^{32} - 100 q^{35} + 160 q^{36} - 128 q^{37} - 144 q^{42} - 72 q^{43} - 448 q^{44} - 168 q^{46} + 192 q^{49} - 364 q^{50} - 128 q^{51} + 88 q^{53} + 56 q^{56} + 408 q^{58} + 504 q^{60} + 444 q^{63} + 256 q^{64} - 8 q^{65} + 440 q^{67} - 112 q^{70} + 592 q^{72} - 408 q^{74} + 12 q^{77} + 664 q^{78} - 8 q^{79} + 64 q^{81} - 576 q^{84} + 96 q^{85} + 256 q^{86} + 448 q^{88} - 388 q^{91} - 1192 q^{92} + 32 q^{93} - 776 q^{95} + 540 q^{98} + 8 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8 + 40 * q^14 - 8 * q^15 + 48 * q^16 + 196 * q^18 - 20 * q^21 - 120 * q^22 - 96 * q^29 - 40 * q^30 - 184 * q^32 - 100 * q^35 + 160 * q^36 - 128 * q^37 - 144 * q^42 - 72 * q^43 - 448 * q^44 - 168 * q^46 + 192 * q^49 - 364 * q^50 - 128 * q^51 + 88 * q^53 + 56 * q^56 + 408 * q^58 + 504 * q^60 + 444 * q^63 + 256 * q^64 - 8 * q^65 + 440 * q^67 - 112 * q^70 + 592 * q^72 - 408 * q^74 + 12 * q^77 + 664 * q^78 - 8 * q^79 + 64 * q^81 - 576 * q^84 + 96 * q^85 + 256 * q^86 + 448 * q^88 - 388 * q^91 - 1192 * q^92 + 32 * q^93 - 776 * q^95 + 540 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.88371	+	0.672048i	−0.941853	+	0.336024i
$2$	−1.88371	+	0.672048i	−0.941853	+	0.336024i
$3$	−0.746365	−	0.746365i	−0.248788	−	0.248788i	0.571685	−	0.820473i	$-0.306290\pi$
$3$	−0.746365	−	0.746365i	−0.248788	−	0.248788i	−0.820473	+	0.571685i	$0.806290\pi$
$4$	3.09670	−	2.53188i	0.774176	−	0.632971i
$5$	0.822232	−	0.822232i	0.164446	−	0.164446i	−0.620087	−	0.784533i	$-0.712903\pi$
$5$	0.822232	−	0.822232i	0.164446	−	0.164446i	0.784533	+	0.620087i	$0.212903\pi$
$6$	1.90753	+	0.904340i	0.317921	+	0.150723i
$7$	−6.88091	+	1.28574i	−0.982987	+	0.183677i
$7$	−6.88091	+	1.28574i	−0.982987	+	0.183677i
$8$	−4.13173	+	6.85046i	−0.516467	+	0.856307i
$9$		−	7.88588i		−	0.876209i
$10$	−0.996265	+	2.10142i	−0.0996265	+	0.210142i
$11$	2.57423	+	2.57423i	0.234021	+	0.234021i	0.814369	−	0.580348i	$-0.197083\pi$
$11$	2.57423	+	2.57423i	0.234021	+	0.234021i	−0.580348	+	0.814369i	$0.697083\pi$
$12$	−4.20098	−	0.421563i	−0.350082	−	0.0351302i
$13$	−14.9766	−	14.9766i	−1.15205	−	1.15205i	−0.986141	−	0.165909i	$-0.946944\pi$
$13$	−14.9766	−	14.9766i	−1.15205	−	1.15205i	−0.165909	−	0.986141i	$-0.553056\pi$
$14$	12.0975	−	7.04626i	0.864109	−	0.503304i
$15$	−1.22737			−0.0818247
$16$	3.17914	−	15.6810i	0.198696	−	0.980061i
$17$		−	20.7103i		−	1.21826i	−0.793072	−	0.609128i	$-0.791520\pi$
$17$		−	20.7103i		−	1.21826i	0.793072	−	0.609128i	$-0.208480\pi$
$18$	5.29969	+	14.8547i	0.294427	+	0.825260i
$19$	−10.0977	−	10.0977i	−0.531460	−	0.531460i	0.389547	−	0.921007i	$-0.372632\pi$
$19$	−10.0977	−	10.0977i	−0.531460	−	0.531460i	−0.921007	+	0.389547i	$0.872632\pi$
$20$	0.464414	−	4.62800i	0.0232207	−	0.231400i
$21$	6.09530	+	4.17604i	0.290253	+	0.198859i
$22$	−6.57909	−	3.11909i	−0.299050	−	0.141777i
$23$		−	19.5800i		−	0.851305i	−0.904887	−	0.425653i	$-0.860045\pi$
$23$		−	19.5800i		−	0.851305i	0.904887	−	0.425653i	$-0.139955\pi$
$24$	8.19673	−	2.02916i	0.341530	−	0.0845484i
$25$			23.6479i			0.945915i
$26$	38.2766	+	18.1466i	1.47218	+	0.697946i
$27$	−12.6030	+	12.6030i	−0.466779	+	0.466779i
$28$	−18.0528	+	21.4032i	−0.644742	+	0.764400i
$29$	7.24407	−	7.24407i	0.249795	−	0.249795i	−0.571091	−	0.820887i	$-0.693480\pi$
$29$	7.24407	−	7.24407i	0.249795	−	0.249795i	0.820887	+	0.571091i	$0.193480\pi$
$30$	2.31201	−	0.824852i	0.0770669	−	0.0274951i
$31$			45.5117i			1.46812i	0.679084	+	0.734060i	$0.262377\pi$
$31$			45.5117i			1.46812i	−0.679084	+	0.734060i	$0.737623\pi$
$32$	4.54980	+	31.6749i	0.142181	+	0.989841i
$33$		−	3.84263i		−	0.116443i
$34$	13.9183	+	39.0122i	0.409363	+	1.14742i
$35$	−4.60052	+	6.71488i	−0.131444	+	0.191854i
$36$	−19.9661	−	24.4202i	−0.554614	−	0.678339i
$37$	−34.5793	−	34.5793i	−0.934575	−	0.934575i	0.0634120	−	0.997987i	$-0.479802\pi$
$37$	−34.5793	−	34.5793i	−0.934575	−	0.934575i	−0.997987	+	0.0634120i	$0.979802\pi$
$38$	25.8073	+	12.2350i	0.679141	+	0.321974i
$39$			22.3561i			0.573233i
$40$	2.23542	+	9.02991i	0.0558855	+	0.225748i
$41$	61.5837			1.50204			0.751020	−	0.660279i	$-0.229562\pi$
$41$	61.5837			1.50204			0.751020	+	0.660279i	$0.229562\pi$
$42$	−14.2883	−	3.77009i	−0.340197	−	0.0897641i
$43$	−16.6424	−	16.6424i	−0.387034	−	0.387034i	0.486594	−	0.873628i	$-0.338239\pi$
$43$	−16.6424	−	16.6424i	−0.387034	−	0.387034i	−0.873628	+	0.486594i	$0.838239\pi$
$44$	14.4893	+	1.45398i	0.329301	+	0.0330449i
$45$	−6.48402	−	6.48402i	−0.144089	−	0.144089i
$46$	13.1587	+	36.8830i	0.286059	+	0.801805i
$47$			55.0421i			1.17111i	0.810633	+	0.585554i	$0.199123\pi$
$47$			55.0421i			1.17111i	−0.810633	+	0.585554i	$0.800877\pi$
$48$	−14.0765	+	9.33094i	−0.293261	+	0.194395i
$49$	45.6937	−	17.6941i	0.932525	−	0.361105i
$50$	−15.8925	−	44.5457i	−0.317850	−	0.890913i
$51$	−15.4575	+	15.4575i	−0.303088	+	0.303088i
$52$	−84.2973	−	8.45912i	−1.62110	−	0.162675i
$53$	38.2187	+	38.2187i	0.721107	+	0.721107i	0.968831	−	0.247724i	$-0.0796826\pi$
$53$	38.2187	+	38.2187i	0.721107	+	0.721107i	−0.247724	+	0.968831i	$0.579683\pi$
$54$	15.2706	−	32.2103i	0.282789	−	0.596486i
$55$	4.23322			0.0769677
$56$	19.6222	−	52.4497i	0.350396	−	0.936602i
$57$			15.0732i			0.264442i
$58$	−8.77734	+	18.5141i	−0.151333	+	0.319208i
$59$	32.2679	−	32.2679i	0.546914	−	0.546914i	−0.378633	−	0.925547i	$-0.623606\pi$
$59$	32.2679	−	32.2679i	0.546914	−	0.546914i	0.925547	+	0.378633i	$0.123606\pi$
$60$	−3.80080	+	3.10756i	−0.0633467	+	0.0517926i
$61$	−32.0297	−	32.0297i	−0.525078	−	0.525078i	0.394023	−	0.919101i	$-0.371083\pi$
$61$	−32.0297	−	32.0297i	−0.525078	−	0.525078i	−0.919101	+	0.394023i	$0.871083\pi$
$62$	−30.5861	−	85.7308i	−0.493324	−	1.38275i
$63$	10.1392	+	54.2620i	0.160940	+	0.861301i
$64$	−29.8575	−	56.6085i	−0.466524	−	0.884509i
$65$	−24.6286			−0.378901
$66$	2.58243	+	7.23839i	0.0391277	+	0.109673i
$67$	42.1559	−	42.1559i	0.629192	−	0.629192i	−0.318673	−	0.947865i	$-0.603237\pi$
$67$	42.1559	−	42.1559i	0.629192	−	0.629192i	0.947865	+	0.318673i	$0.103237\pi$
$68$	−52.4362	−	64.1338i	−0.771120	−	0.943144i
$69$	−14.6139	+	14.6139i	−0.211795	+	0.211795i
$70$	4.15332	−	15.7406i	0.0593331	−	0.224866i
$71$		−	15.7491i		−	0.221819i	−0.993831	−	0.110909i	$-0.964624\pi$
$71$		−	15.7491i		−	0.221819i	0.993831	−	0.110909i	$-0.0353763\pi$
$72$	54.0219	+	32.5824i	0.750304	+	0.452533i
$73$	65.7339			0.900464			0.450232	−	0.892912i	$-0.351341\pi$
$73$	65.7339			0.900464			0.450232	+	0.892912i	$0.351341\pi$
$74$	88.3762	+	41.8983i	1.19427	+	0.566193i
$75$	17.6500	−	17.6500i	0.235333	−	0.235333i
$76$	−56.8360	−	5.70341i	−0.747842	−	0.0750449i
$77$	−21.0228	−	14.4032i	−0.273023	−	0.187055i
$78$	−15.0244	−	42.1123i	−0.192620	−	0.539902i
$79$	−96.5103			−1.22165			−0.610825	−	0.791766i	$-0.709162\pi$
$79$	−96.5103			−1.22165			−0.610825	+	0.791766i	$0.709162\pi$
$80$	−10.2794	−	15.5074i	−0.128493	−	0.193842i
$81$	−52.1600			−0.643950
$82$	−116.006	+	41.3872i	−1.41470	+	0.504722i
$83$	−31.6530	−	31.6530i	−0.381361	−	0.381361i	0.490231	−	0.871592i	$-0.336912\pi$
$83$	−31.6530	−	31.6530i	−0.381361	−	0.381361i	−0.871592	+	0.490231i	$0.836912\pi$
$84$	29.4486	−	2.50064i	0.350578	−	0.0297696i
$85$	−17.0287	−	17.0287i	−0.200338	−	0.200338i
$86$	42.5340	+	20.1650i	0.494582	+	0.234476i
$87$	−10.8134			−0.124292
$88$	−28.2707	+	6.99861i	−0.321258	+	0.0795297i
$89$	89.3246			1.00365			0.501824	−	0.864970i	$-0.332663\pi$
$89$	89.3246			1.00365			0.501824	+	0.864970i	$0.332663\pi$
$90$	16.5716	+	7.85642i	0.184128	+	0.0872936i
$91$	122.309	+	83.7968i	1.34406	+	0.920844i
$92$	−49.5743	−	60.6335i	−0.538851	−	0.659060i
$93$	33.9684	−	33.9684i	0.365252	−	0.365252i
$94$	−36.9909	−	103.683i	−0.393520	−	1.10301i
$95$	−16.6054			−0.174793
$96$	20.2452	−	27.0369i	0.210888	−	0.281634i
$97$			47.6196i			0.490923i	0.969406	+	0.245462i	$0.0789395\pi$
$97$			47.6196i			0.490923i	−0.969406	+	0.245462i	$0.921060\pi$
$98$	−74.1823	+	64.0389i	−0.756962	+	0.653459i
$99$	20.3000	−	20.3000i	0.205051	−	0.205051i
$100$	59.8736	+	73.2304i	0.598736	+	0.732304i
$101$	−57.7284	+	57.7284i	−0.571568	+	0.571568i	−0.932566	−	0.360999i	$-0.882436\pi$
$101$	−57.7284	+	57.7284i	−0.571568	+	0.571568i	0.360999	+	0.932566i	$0.382436\pi$
$102$	18.7292	−	39.5055i	0.183620	−	0.387309i
$103$	54.7987			0.532026			0.266013	−	0.963969i	$-0.414294\pi$
$103$	54.7987			0.532026			0.266013	+	0.963969i	$0.414294\pi$
$104$	164.476	−	40.7173i	1.58150	−	0.391513i
$105$	8.44542	−	1.57808i	0.0804326	−	0.0150294i
$106$	−97.6775	−	46.3080i	−0.921486	−	0.436868i
$107$	−53.0000	−	53.0000i	−0.495327	−	0.495327i	0.414653	−	0.909980i	$-0.363903\pi$
$107$	−53.0000	−	53.0000i	−0.495327	−	0.495327i	−0.909980	+	0.414653i	$0.863903\pi$
$108$	−7.11846	+	70.9373i	−0.0659116	+	0.656827i
$109$	−55.0097	+	55.0097i	−0.504676	+	0.504676i	−0.912888	−	0.408211i	$-0.866153\pi$
$109$	−55.0097	+	55.0097i	−0.504676	+	0.504676i	0.408211	+	0.912888i	$0.366153\pi$
$110$	−7.97415	+	2.84493i	−0.0724923	+	0.0258630i
$111$			51.6176i			0.465023i
$112$	−1.71369	+	111.987i	−0.0153008	+	0.999883i
$113$	6.79908			0.0601689			0.0300844	−	0.999547i	$-0.490422\pi$
$113$	6.79908			0.0601689			0.0300844	+	0.999547i	$0.490422\pi$
$114$	−10.1299	−	28.3935i	−0.0888589	−	0.249066i
$115$	−16.0993	−	16.0993i	−0.139994	−	0.139994i
$116$	4.09160	−	40.7738i	0.0352724	−	0.351499i
$117$	−118.104	+	118.104i	−1.00944	+	1.00944i
$118$	−39.0977	+	82.4689i	−0.331337	+	0.698889i
$119$	26.6282	+	142.506i	0.223766	+	1.19753i
$120$	5.07117	−	8.40805i	0.0422598	−	0.0700671i
$121$		−	107.747i		−	0.890469i
$122$	81.8602	+	38.8091i	0.670985	+	0.318108i
$123$	−45.9639	−	45.9639i	−0.373690	−	0.373690i
$124$	115.230	+	140.936i	0.929277	+	1.13658i
$125$	39.9998	+	39.9998i	0.319999	+	0.319999i
$126$	−55.5659	−	95.3996i	−0.440999	−	0.757140i
$127$	148.279			1.16755			0.583775	−	0.811916i	$-0.301575\pi$
$127$	148.279			1.16755			0.583775	+	0.811916i	$0.301575\pi$
$128$	94.2865	+	86.5682i	0.736613	+	0.676314i
$129$			24.8427i			0.192579i
$130$	46.3930	−	16.5516i	0.356869	−	0.127320i
$131$	−104.999	−	104.999i	−0.801520	−	0.801520i	0.181813	−	0.983333i	$-0.441803\pi$
$131$	−104.999	−	104.999i	−0.801520	−	0.801520i	−0.983333	+	0.181813i	$0.941803\pi$
$132$	−9.72908	−	11.8995i	−0.0737052	−	0.0901476i
$133$	82.4647	+	56.4985i	0.620035	+	0.424801i
$134$	−51.0785	+	107.740i	−0.381183	+	0.804030i
$135$			20.7252i			0.153520i
$136$	141.875	+	85.5697i	1.04320	+	0.629189i
$137$			19.9653i			0.145732i	0.997342	+	0.0728660i	$0.0232145\pi$
$137$			19.9653i			0.145732i	−0.997342	+	0.0728660i	$0.976785\pi$
$138$	17.7070	−	37.3494i	0.128312	−	0.270648i
$139$	166.512	−	166.512i	1.19793	−	1.19793i	0.223139	−	0.974787i	$-0.428370\pi$
$139$	166.512	−	166.512i	1.19793	−	1.19793i	0.974787	−	0.223139i	$-0.0716302\pi$
$140$	2.75483	+	32.4420i	0.0196774	+	0.231728i
$141$	41.0815	−	41.0815i	0.291358	−	0.291358i
$142$	10.5842	+	29.6667i	0.0745364	+	0.208921i
$143$		−	77.1066i		−	0.539207i
$144$	−123.658	−	25.0703i	−0.858738	−	0.174099i
$145$		−	11.9126i		−	0.0821559i
$146$	−123.823	+	44.1763i	−0.848105	+	0.302578i
$147$	−47.3105	−	20.8979i	−0.321840	−	0.142163i
$148$	−194.633	−	19.5311i	−1.31508	−	0.131967i
$149$	−128.482	−	128.482i	−0.862292	−	0.862292i	0.129312	−	0.991604i	$-0.458723\pi$
$149$	−128.482	−	128.482i	−0.862292	−	0.862292i	−0.991604	+	0.129312i	$0.958723\pi$
$150$	−21.3857	+	45.1090i	−0.142571	+	0.300726i
$151$		−	254.970i		−	1.68854i	−0.535915	−	0.844272i	$-0.680033\pi$
$151$		−	254.970i		−	1.68854i	0.535915	−	0.844272i	$-0.319967\pi$
$152$	110.895	−	27.4529i	0.729574	−	0.180611i
$153$	−163.319			−1.06745
$154$	49.2805	+	13.0031i	0.320003	+	0.0844359i
$155$	37.4212	+	37.4212i	0.241427	+	0.241427i
$156$	56.6030	+	69.2302i	0.362840	+	0.443783i
$157$	−106.743	−	106.743i	−0.679893	−	0.679893i	0.280083	−	0.959976i	$-0.409638\pi$
$157$	−106.743	−	106.743i	−0.679893	−	0.679893i	−0.959976	+	0.280083i	$0.909638\pi$
$158$	181.797	−	64.8595i	1.15061	−	0.410503i
$159$		−	57.0502i		−	0.358806i
$160$	29.7851	+	22.3031i	0.186157	+	0.139395i
$161$	25.1749	+	134.728i	0.156366	+	0.836822i
$162$	98.2541	−	35.0540i	0.606507	−	0.216383i
$163$	−121.521	+	121.521i	−0.745529	+	0.745529i	−0.973636	−	0.228107i	$-0.926746\pi$
$163$	−121.521	+	121.521i	−0.745529	+	0.745529i	0.228107	+	0.973636i	$0.426746\pi$
$164$	190.706	−	155.923i	1.16284	−	0.950748i
$165$	−3.15953	−	3.15953i	−0.0191487	−	0.0191487i
$166$	80.8973	+	38.3526i	0.487333	+	0.231040i
$167$	−168.178			−1.00705			−0.503527	−	0.863979i	$-0.667965\pi$
$167$	−168.178			−1.00705			−0.503527	+	0.863979i	$0.667965\pi$
$168$	−53.7919	+	24.5013i	−0.320190	+	0.145841i
$169$			279.600i			1.65444i
$170$	43.5212	+	20.6330i	0.256007	+	0.121370i
$171$	−79.6295	+	79.6295i	−0.465670	+	0.465670i
$172$	−93.6734	−	9.40000i	−0.544613	−	0.0546512i
$173$	80.3214	+	80.3214i	0.464285	+	0.464285i	0.900057	−	0.435772i	$-0.143525\pi$
$173$	80.3214	+	80.3214i	0.464285	+	0.464285i	−0.435772	+	0.900057i	$0.643525\pi$
$174$	20.3694	−	7.26715i	0.117065	−	0.0417652i
$175$	−30.4051	−	162.719i	−0.173743	−	0.929822i
$176$	48.5502	−	32.1826i	0.275854	−	0.182856i
$177$	−48.1673			−0.272132
$178$	−168.261	+	60.0304i	−0.945289	+	0.337250i
$179$	186.398	−	186.398i	1.04133	−	1.04133i	0.0422189	−	0.999108i	$-0.486557\pi$
$179$	186.398	−	186.398i	1.04133	−	1.04133i	0.999108	−	0.0422189i	$-0.0134427\pi$
$180$	−36.4959	−	3.66231i	−0.202755	−	0.0203462i
$181$	−14.9372	+	14.9372i	−0.0825261	+	0.0825261i	−0.747165	−	0.664639i	$-0.768585\pi$
$181$	−14.9372	+	14.9372i	−0.0825261	+	0.0825261i	0.664639	+	0.747165i	$0.268585\pi$
$182$	−286.710	−	75.6511i	−1.57533	−	0.415665i
$183$			47.8118i			0.261267i
$184$	134.132	+	80.8995i	0.728979	+	0.439671i
$185$	−56.8644			−0.307375
$186$	−41.1581	+	86.8149i	−0.221280	+	0.466747i
$187$	53.3131	−	53.3131i	0.285097	−	0.285097i
$188$	139.360	+	170.449i	0.741277	+	0.906643i
$189$	70.5161	−	102.925i	0.373101	−	0.544574i
$190$	31.2796	−	11.1596i	0.164630	−	0.0587347i
$191$	22.6772			0.118729			0.0593645	−	0.998236i	$-0.481093\pi$
$191$	22.6772			0.118729			0.0593645	+	0.998236i	$0.481093\pi$
$192$	−19.9660	+	64.5353i	−0.103990	+	0.336121i
$193$	−13.2053			−0.0684213			−0.0342107	−	0.999415i	$-0.510892\pi$
$193$	−13.2053			−0.0684213			−0.0342107	+	0.999415i	$0.510892\pi$
$194$	−32.0026	−	89.7013i	−0.164962	−	0.462378i
$195$	18.3819	+	18.3819i	0.0942662	+	0.0942662i
$196$	96.7005	−	170.485i	0.493370	−	0.869820i
$197$	44.3731	+	44.3731i	0.225244	+	0.225244i	0.810703	−	0.585458i	$-0.199085\pi$
$197$	44.3731	+	44.3731i	0.225244	+	0.225244i	−0.585458	+	0.810703i	$0.699085\pi$
$198$	−24.5967	+	51.8819i	−0.124226	+	0.262030i
$199$	116.110			0.583468			0.291734	−	0.956499i	$-0.405768\pi$
$199$	116.110			0.583468			0.291734	+	0.956499i	$0.405768\pi$
$200$	−161.999	−	97.7067i	−0.809994	−	0.488534i
$201$	−62.9274			−0.313071
$202$	69.9471	−	147.540i	0.346273	−	0.730394i
$203$	−40.5317	+	59.1597i	−0.199664	+	0.291427i
$204$	−8.73071	+	87.0038i	−0.0427976	+	0.426489i
$205$	50.6360	−	50.6360i	0.247005	−	0.247005i
$206$	−103.225	+	36.8273i	−0.501090	+	0.178773i
$207$	−154.406			−0.745921
$208$	−282.461	+	187.236i	−1.35799	+	0.900171i
$209$		−	51.9877i		−	0.248745i
$210$	−14.8482	+	8.64837i	−0.0707055	+	0.0411827i
$211$	−123.830	+	123.830i	−0.586873	+	0.586873i	−0.936783	−	0.349910i	$-0.886212\pi$
$211$	−123.830	+	123.830i	−0.586873	+	0.586873i	0.349910	+	0.936783i	$0.386212\pi$
$212$	215.117	+	21.5867i	1.01470	+	0.101824i
$213$	−11.7546	+	11.7546i	−0.0551859	+	0.0551859i
$214$	135.455	+	64.2179i	0.632967	+	0.300083i
$215$	−27.3679			−0.127293
$216$	−34.2642	−	138.409i	−0.158630	−	0.640782i
$217$	−58.5164	−	313.162i	−0.269661	−	1.44314i
$218$	66.6530	−	140.591i	0.305748	−	0.644914i
$219$	−49.0615	−	49.0615i	−0.224025	−	0.224025i
$220$	13.1090	−	10.7180i	0.0595865	−	0.0487183i
$221$	−310.172	+	310.172i	−1.40349	+	1.40349i
$222$	−34.6895	−	97.2324i	−0.156259	−	0.437984i
$223$		−	208.501i		−	0.934980i	−0.883998	−	0.467490i	$-0.845158\pi$
$223$		−	208.501i		−	0.934980i	0.883998	−	0.467490i	$-0.154842\pi$
$224$	−72.0325	−	212.102i	−0.321573	−	0.946885i
$225$	186.484			0.828819
$226$	−12.8075	+	4.56931i	−0.0566703	+	0.0202182i
$227$	38.5672	+	38.5672i	0.169900	+	0.169900i	0.786935	−	0.617036i	$-0.211667\pi$
$227$	38.5672	+	38.5672i	0.169900	+	0.169900i	−0.617036	+	0.786935i	$0.711667\pi$
$228$	38.1636	+	46.6772i	0.167384	+	0.204725i
$229$	239.869	−	239.869i	1.04746	−	1.04746i	0.0486463	−	0.998816i	$-0.484509\pi$
$229$	239.869	−	239.869i	1.04746	−	1.04746i	0.998816	−	0.0486463i	$-0.0154907\pi$
$230$	41.1459	+	19.5069i	0.178895	+	0.0848125i
$231$	4.94063	+	26.4408i	0.0213880	+	0.114462i
$232$	19.6946	+	79.5557i	0.0848905	+	0.342913i
$233$		−	187.643i		−	0.805335i	−0.915346	−	0.402667i	$-0.868083\pi$
$233$		−	187.643i		−	0.805335i	0.915346	−	0.402667i	$-0.131917\pi$
$234$	143.102	−	301.845i	0.611546	−	1.28994i
$235$	45.2573	+	45.2573i	0.192584	+	0.192584i
$236$	18.2256	−	181.623i	0.0772271	−	0.769588i
$237$	72.0320	+	72.0320i	0.303932	+	0.303932i
$238$	−145.930	−	250.544i	−0.613153	−	1.05271i
$239$	334.909			1.40129			0.700646	−	0.713509i	$-0.252895\pi$
$239$	334.909			1.40129			0.700646	+	0.713509i	$0.252895\pi$
$240$	−3.90199	+	19.2464i	−0.0162583	+	0.0801932i
$241$		−	20.7818i		−	0.0862314i	−0.999070	−	0.0431157i	$-0.986272\pi$
$241$		−	20.7818i		−	0.0862314i	0.999070	−	0.0431157i	$-0.0137284\pi$
$242$	72.4109	+	202.963i	0.299219	+	0.838691i
$243$	152.358	+	152.358i	0.626986	+	0.626986i
$244$	−180.282	−	18.0911i	−0.738861	−	0.0741437i
$245$	23.0222	−	52.1195i	0.0939680	−	0.212733i
$246$	117.472	+	55.6926i	0.477530	+	0.226393i
$247$			302.461i			1.22454i
$248$	−311.776	−	188.042i	−1.25716	−	0.758236i
$249$			47.2494i			0.189757i
$250$	−102.230	−	48.4662i	−0.408919	−	0.193865i
$251$	−331.900	+	331.900i	−1.32231	+	1.32231i	−0.410410	+	0.911901i	$0.634615\pi$
$251$	−331.900	+	331.900i	−1.32231	+	1.32231i	−0.911901	+	0.410410i	$0.865385\pi$
$252$	168.783	+	142.362i	0.669774	+	0.564929i
$253$	50.4034	−	50.4034i	0.199223	−	0.199223i
$254$	−279.314	+	99.6504i	−1.09966	+	0.392324i
$255$			25.4193i			0.0996834i
$256$	−235.786	−	99.7041i	−0.921039	−	0.389469i
$257$			4.98473i			0.0193958i	0.999953	+	0.00969792i	$0.00308699\pi$
$257$			4.98473i			0.0193958i	−0.999953	+	0.00969792i	$0.996913\pi$
$258$	−16.6955	−	46.7964i	−0.0647112	−	0.181381i
$259$	282.397	+	193.477i	1.09034	+	0.747015i
$260$	−76.2673	+	62.3566i	−0.293336	+	0.239833i
$261$	−57.1258	−	57.1258i	−0.218873	−	0.218873i
$262$	268.352	+	127.223i	1.02424	+	0.485584i
$263$		−	300.720i		−	1.14342i	−0.820455	−	0.571711i	$-0.806280\pi$
$263$		−	300.720i		−	1.14342i	0.820455	−	0.571711i	$-0.193720\pi$
$264$	26.3238	+	15.8767i	0.0997112	+	0.0601391i
$265$	62.8492			0.237167
$266$	−193.309	−	51.0064i	−0.726725	−	0.191753i
$267$	−66.6688	−	66.6688i	−0.249696	−	0.249696i
$268$	23.8105	−	237.278i	0.0888452	−	0.885365i
$269$	337.937	+	337.937i	1.25627	+	1.25627i	0.952860	+	0.303411i	$0.0981253\pi$
$269$	337.937	+	337.937i	1.25627	+	1.25627i	0.303411	+	0.952860i	$0.401875\pi$
$270$	−13.9284	−	39.0403i	−0.0515865	−	0.144594i
$271$			170.823i			0.630342i	0.949035	+	0.315171i	$0.102062\pi$
$271$			170.823i			0.630342i	−0.949035	+	0.315171i	$0.897938\pi$
$272$	−324.758	−	65.8411i	−1.19396	−	0.242063i
$273$	−28.7442	−	153.830i	−0.105290	−	0.563481i
$274$	−13.4176	−	37.6087i	−0.0489694	−	0.137258i
$275$	−60.8750	+	60.8750i	−0.221364	+	0.221364i
$276$	−8.25421	+	82.2553i	−0.0299066	+	0.298027i
$277$	177.959	+	177.959i	0.642451	+	0.642451i	0.951157	−	0.308707i	$-0.0998962\pi$
$277$	177.959	+	177.959i	0.642451	+	0.642451i	−0.308707	+	0.951157i	$0.599896\pi$
$278$	−201.755	+	425.563i	−0.725738	+	1.53080i
$279$	358.900			1.28638
$280$	−26.9918	−	59.2598i	−0.0963995	−	0.211642i
$281$			451.491i			1.60673i	0.595486	+	0.803366i	$0.296959\pi$
$281$			451.491i			1.60673i	−0.595486	+	0.803366i	$0.703041\pi$
$282$	−49.7768	+	104.994i	−0.176513	+	0.372320i
$283$	29.1197	−	29.1197i	0.102897	−	0.102897i	−0.653784	−	0.756681i	$-0.726820\pi$
$283$	29.1197	−	29.1197i	0.102897	−	0.102897i	0.756681	+	0.653784i	$0.226820\pi$
$284$	−39.8749	−	48.7704i	−0.140405	−	0.171727i
$285$	12.3937	+	12.3937i	0.0434866	+	0.0434866i
$286$	51.8193	+	145.246i	0.181186	+	0.507854i
$287$	−423.751	+	79.1807i	−1.47649	+	0.275891i
$288$	249.784	−	35.8791i	0.867307	−	0.124580i
$289$	−139.918			−0.484147
$290$	8.00584	+	22.4399i	0.0276063	+	0.0773788i
$291$	35.5416	−	35.5416i	0.122136	−	0.122136i
$292$	203.558	−	166.430i	0.697118	−	0.569967i
$293$	264.180	−	264.180i	0.901637	−	0.901637i	−0.0939410	−	0.995578i	$-0.529947\pi$
$293$	264.180	−	264.180i	0.901637	−	0.901637i	0.995578	+	0.0939410i	$0.0299465\pi$
$294$	103.164	+	7.57065i	0.350896	+	0.0257505i
$295$		−	53.0634i		−	0.179876i
$296$	379.756	−	94.0115i	1.28296	−	0.317606i
$297$	−64.8862			−0.218472
$298$	328.367	+	155.676i	1.10190	+	0.522402i
$299$	−293.243	+	293.243i	−0.980746	+	0.980746i
$300$	9.96906	−	99.3443i	0.0332302	−	0.331148i
$301$	135.913	+	93.1172i	0.451538	+	0.309360i
$302$	171.352	+	480.289i	0.567391	+	1.59036i
$303$	86.1729			0.284399
$304$	−190.445	+	126.240i	−0.626462	+	0.415264i
$305$	−52.6717			−0.172694
$306$	307.646	−	109.758i	1.00538	−	0.358687i
$307$	402.236	+	402.236i	1.31022	+	1.31022i	0.921254	+	0.388962i	$0.127166\pi$
$307$	402.236	+	402.236i	1.31022	+	1.31022i	0.388962	+	0.921254i	$0.372834\pi$
$308$	−101.569	+	8.62477i	−0.329768	+	0.0280025i
$309$	−40.8998	−	40.8998i	−0.132362	−	0.132362i
$310$	−95.6394	−	45.3417i	−0.308514	−	0.146264i
$311$	−352.364			−1.13300			−0.566502	−	0.824060i	$-0.691704\pi$
$311$	−352.364			−1.13300			−0.566502	+	0.824060i	$0.691704\pi$
$312$	−153.150	−	92.3695i	−0.490864	−	0.296056i
$313$	−290.355			−0.927652			−0.463826	−	0.885926i	$-0.653524\pi$
$313$	−290.355			−0.927652			−0.463826	+	0.885926i	$0.653524\pi$
$314$	272.809	+	129.336i	0.868820	+	0.411899i
$315$	52.9527	+	36.2792i	0.168104	+	0.115172i
$316$	−298.864	+	244.353i	−0.945771	+	0.773268i
$317$	334.727	−	334.727i	1.05592	−	1.05592i	0.0575804	−	0.998341i	$-0.481661\pi$
$317$	334.727	−	334.727i	1.05592	−	1.05592i	0.998341	−	0.0575804i	$-0.0183386\pi$
$318$	38.3404	+	107.466i	0.120567	+	0.337943i
$319$	37.2957			0.116915
$320$	−71.0952	−	21.9955i	−0.222172	−	0.0687361i
$321$			79.1147i			0.246463i
$322$	−137.966	−	236.870i	−0.428466	−	0.735621i
$323$	−209.128	+	209.128i	−0.647454	+	0.647454i
$324$	−161.524	+	132.063i	−0.498531	+	0.407601i
$325$	354.166	−	354.166i	1.08974	−	1.08974i
$326$	147.242	−	310.578i	0.451663	−	0.952694i
$327$	82.1147			0.251115
$328$	−254.447	+	421.876i	−0.775754	+	1.28621i
$329$	−70.7699	−	378.739i	−0.215106	−	1.15118i
$330$	8.07499	+	3.82828i	0.0244697	+	0.0116008i
$331$	33.5183	+	33.5183i	0.101264	+	0.101264i	0.755924	−	0.654660i	$-0.227188\pi$
$331$	33.5183	+	33.5183i	0.101264	+	0.101264i	−0.654660	+	0.755924i	$0.727188\pi$
$332$	−178.162	−	17.8783i	−0.536631	−	0.0538502i
$333$	−272.688	+	272.688i	−0.818883	+	0.818883i
$334$	316.798	−	113.024i	0.948497	−	0.338394i
$335$		−	69.3238i		−	0.206937i
$336$	84.8622	−	82.3041i	0.252566	−	0.244953i
$337$	−15.4008			−0.0456997			−0.0228499	−	0.999739i	$-0.507274\pi$
$337$	−15.4008			−0.0456997			−0.0228499	+	0.999739i	$0.507274\pi$
$338$	−187.905	−	526.684i	−0.555931	−	1.55824i
$339$	−5.07460	−	5.07460i	−0.0149693	−	0.0149693i
$340$	−95.8475	−	9.61817i	−0.281905	−	0.0282887i
$341$	−117.158	+	117.158i	−0.343571	+	0.343571i
$342$	96.4838	−	203.514i	0.282116	−	0.595069i
$343$	−291.664	+	180.502i	−0.850333	+	0.526245i
$344$	182.771	−	45.2462i	0.531310	−	0.131530i
$345$			24.0320i			0.0696578i
$346$	−205.282	−	97.3221i	−0.593300	−	0.281278i
$347$	−114.114	−	114.114i	−0.328859	−	0.328859i	0.523294	−	0.852153i	$-0.324703\pi$
$347$	−114.114	−	114.114i	−0.328859	−	0.328859i	−0.852153	+	0.523294i	$0.824703\pi$
$348$	−33.4860	+	27.3784i	−0.0962242	+	0.0786735i
$349$	−374.354	−	374.354i	−1.07265	−	1.07265i	−0.997146	−	0.0755012i	$-0.975944\pi$
$349$	−374.354	−	374.354i	−1.07265	−	1.07265i	−0.0755012	−	0.997146i	$-0.524056\pi$
$350$	166.629	+	286.081i	0.476083	+	0.817374i
$351$	377.502			1.07551
$352$	−69.8262	+	93.2506i	−0.198370	+	0.264917i
$353$		−	63.2575i		−	0.179200i	−0.995978	−	0.0895999i	$-0.971441\pi$
$353$		−	63.2575i		−	0.179200i	0.995978	−	0.0895999i	$-0.0285588\pi$
$354$	90.7331	−	32.3707i	0.256308	−	0.0914428i
$355$	−12.9494	−	12.9494i	−0.0364773	−	0.0364773i
$356$	276.612	−	226.159i	0.776999	−	0.635279i
$357$	86.4872	−	126.236i	0.242261	−	0.353602i
$358$	−225.850	+	476.387i	−0.630867	+	1.33069i
$359$			24.7880i			0.0690472i	0.999404	+	0.0345236i	$0.0109914\pi$
$359$			24.7880i			0.0690472i	−0.999404	+	0.0345236i	$0.989009\pi$
$360$	71.2088	−	17.6282i	0.197802	−	0.0489674i
$361$		−	157.071i		−	0.435101i
$362$	18.0988	−	38.1759i	0.0499968	−	0.105458i
$363$	−80.4184	+	80.4184i	−0.221538	+	0.221538i
$364$	590.918	−	50.1782i	1.62340	−	0.137852i
$365$	54.0485	−	54.0485i	0.148078	−	0.148078i
$366$	−32.1318	−	90.0634i	−0.0877918	−	0.246075i
$367$		−	150.362i		−	0.409705i	−0.978793	−	0.204852i	$-0.934329\pi$
$367$		−	150.362i		−	0.409705i	0.978793	−	0.204852i	$-0.0656715\pi$
$368$	−307.034	−	62.2477i	−0.834331	−	0.169151i
$369$		−	485.641i		−	1.31610i
$370$	107.116	−	38.2156i	0.289502	−	0.103285i
$371$	−312.118	−	213.840i	−0.841289	−	0.576387i
$372$	19.1861	−	191.194i	0.0515754	−	0.513962i
$373$	100.362	+	100.362i	0.269068	+	0.269068i	0.828724	−	0.559657i	$-0.189067\pi$
$373$	100.362	+	100.362i	0.269068	+	0.269068i	−0.559657	+	0.828724i	$0.689067\pi$
$374$	−64.5973	+	136.255i	−0.172720	+	0.364319i
$375$		−	59.7090i		−	0.159224i
$376$	−377.063	−	227.419i	−1.00283	−	0.604838i
$377$	−216.984			−0.575553
$378$	−63.6613	+	241.270i	−0.168416	+	0.638280i
$379$	−377.568	−	377.568i	−0.996222	−	0.996222i	0.00377077	−	0.999993i	$-0.498800\pi$
$379$	−377.568	−	377.568i	−0.996222	−	0.996222i	−0.999993	+	0.00377077i	$0.998800\pi$
$380$	−51.4219	+	42.0428i	−0.135321	+	0.110639i
$381$	−110.670	−	110.670i	−0.290473	−	0.290473i
$382$	−42.7173	+	15.2402i	−0.111825	+	0.0398958i
$383$		−	453.557i		−	1.18422i	−0.805856	−	0.592111i	$-0.798295\pi$
$383$		−	453.557i		−	1.18422i	0.805856	−	0.592111i	$-0.201705\pi$
$384$	−5.76065	−	134.984i	−0.0150017	−	0.351520i
$385$	−29.1284	+	5.44283i	−0.0756582	+	0.0141372i
$386$	24.8749	−	8.87461i	0.0644429	−	0.0229912i
$387$	−131.240	+	131.240i	−0.339122	+	0.339122i
$388$	120.567	+	147.464i	0.310740	+	0.380061i
$389$	406.780	+	406.780i	1.04571	+	1.04571i	0.998904	+	0.0468024i	$0.0149031\pi$
$389$	406.780	+	406.780i	1.04571	+	1.04571i	0.0468024	+	0.998904i	$0.485097\pi$
$390$	−46.9796	−	22.2726i	−0.120461	−	0.0571092i
$391$	−405.509			−1.03711
$392$	−67.5815	+	386.130i	−0.172402	+	0.985027i
$393$			156.735i			0.398818i
$394$	−113.407	−	53.7651i	−0.287835	−	0.136460i
$395$	−79.3538	+	79.3538i	−0.200896	+	0.200896i
$396$	11.4659	−	114.261i	0.0289543	−	0.288537i
$397$	−94.3830	−	94.3830i	−0.237741	−	0.237741i	0.578173	−	0.815914i	$-0.303766\pi$
$397$	−94.3830	−	94.3830i	−0.237741	−	0.237741i	−0.815914	+	0.578173i	$0.803766\pi$
$398$	−218.718	+	78.0316i	−0.549542	+	0.196059i
$399$	−19.3802	−	103.717i	−0.0485721	−	0.259943i
$400$	370.822	+	75.1799i	0.927054	+	0.187950i
$401$	703.081			1.75332			0.876660	−	0.481110i	$-0.159766\pi$
$401$	703.081			1.75332			0.876660	+	0.481110i	$0.159766\pi$
$402$	118.537	−	42.2902i	0.294867	−	0.105200i
$403$	681.613	−	681.613i	1.69135	−	1.69135i
$404$	−32.6062	+	324.929i	−0.0807083	+	0.804280i
$405$	−42.8876	+	42.8876i	−0.105895	+	0.105895i
$406$	36.5917	−	138.679i	0.0901274	−	0.341574i
$407$		−	178.030i		−	0.437420i
$408$	−42.0246	−	169.757i	−0.103001	−	0.416071i
$409$	−472.432			−1.15509			−0.577546	−	0.816358i	$-0.695989\pi$
$409$	−472.432			−1.15509			−0.577546	+	0.816358i	$0.695989\pi$
$410$	−61.3536	+	129.413i	−0.149643	+	0.315642i
$411$	14.9014	−	14.9014i	0.0362564	−	0.0362564i
$412$	169.695	−	138.744i	0.411882	−	0.336757i
$413$	−180.544	+	263.521i	−0.437153	+	0.638065i
$414$	290.855	−	103.768i	0.702548	−	0.250647i
$415$	−52.0522			−0.125427
$416$	406.243	−	542.525i	0.976546	−	1.30415i
$417$	−248.557			−0.596060
$418$	34.9383	+	97.9297i	0.0835843	+	0.234282i
$419$	−356.549	−	356.549i	−0.850953	−	0.850953i	0.139298	−	0.990251i	$-0.455515\pi$
$419$	−356.549	−	356.549i	−0.850953	−	0.850953i	−0.990251	+	0.139298i	$0.955515\pi$
$420$	22.1575	−	26.2697i	0.0527558	−	0.0625468i
$421$	−458.909	−	458.909i	−1.09004	−	1.09004i	−0.995523	−	0.0945219i	$-0.969868\pi$
$421$	−458.909	−	458.909i	−1.09004	−	1.09004i	−0.0945219	−	0.995523i	$-0.530132\pi$
$422$	150.040	−	316.479i	0.355545	−	0.749951i
$423$	434.055			1.02613
$424$	−419.725	+	103.906i	−0.989917	+	0.245061i
$425$	489.756			1.15237
$426$	14.2426	−	30.0419i	0.0334333	−	0.0705208i
$427$	261.576	+	179.212i	0.612589	+	0.419699i
$428$	−298.315	−	29.9355i	−0.696997	−	0.0699427i
$429$	−57.5497	+	57.5497i	−0.134148	+	0.134148i
$430$	51.5531	−	18.3925i	0.119891	−	0.0427734i
$431$	−509.215			−1.18147			−0.590736	−	0.806865i	$-0.701163\pi$
$431$	−509.215			−1.18147			−0.590736	+	0.806865i	$0.701163\pi$
$432$	157.561	+	237.695i	0.364725	+	0.550219i
$433$		−	105.687i		−	0.244081i	−0.992525	−	0.122041i	$-0.961056\pi$
$433$		−	105.687i		−	0.244081i	0.992525	−	0.122041i	$-0.0389438\pi$
$434$	320.688	+	550.580i	0.738911	+	1.26862i
$435$	−8.89116	+	8.89116i	−0.0204394	+	0.0204394i
$436$	−31.0706	+	309.627i	−0.0712629	+	0.710153i
$437$	−197.714	+	197.714i	−0.452435	+	0.452435i
$438$	125.389	+	59.4458i	0.286277	+	0.135721i
$439$	−129.713			−0.295473			−0.147736	−	0.989027i	$-0.547199\pi$
$439$	−129.713			−0.295473			−0.147736	+	0.989027i	$0.547199\pi$
$440$	−17.4906	+	28.9995i	−0.0397513	+	0.0659080i
$441$	−139.534	−	360.335i	−0.316403	−	0.817087i
$442$	375.822	−	792.722i	0.850276	−	1.79349i
$443$	446.226	+	446.226i	1.00728	+	1.00728i	0.999973	+	0.00730994i	$0.00232685\pi$
$443$	446.226	+	446.226i	1.00728	+	1.00728i	0.00730994	+	0.999973i	$0.497673\pi$
$444$	130.690	+	159.844i	0.294346	+	0.360010i
$445$	73.4455	−	73.4455i	0.165046	−	0.165046i
$446$	140.122	+	392.754i	0.314176	+	0.880614i
$447$			191.788i			0.429057i
$448$	278.231	+	351.129i	0.621051	+	0.783770i
$449$	−578.506			−1.28843			−0.644216	−	0.764843i	$-0.722816\pi$
$449$	−578.506			−1.28843			−0.644216	+	0.764843i	$0.722816\pi$
$450$	−351.282	+	125.326i	−0.780626	+	0.278503i
$451$	158.530	+	158.530i	0.351509	+	0.351509i
$452$	21.0547	−	17.2145i	0.0465813	−	0.0380851i
$453$	−190.301	+	190.301i	−0.420090	+	0.420090i
$454$	−98.5684	−	46.7303i	−0.217111	−	0.102930i
$455$	169.467	−	31.6660i	0.372454	−	0.0695955i
$456$	−103.258	−	62.2785i	−0.226444	−	0.136576i
$457$			432.070i			0.945450i	0.881210	+	0.472725i	$0.156730\pi$
$457$			432.070i			0.945450i	−0.881210	+	0.472725i	$0.843270\pi$
$458$	−290.639	+	613.046i	−0.634584	+	1.33853i
$459$	261.013	+	261.013i	0.568656	+	0.568656i
$460$	−90.6164	−	9.09323i	−0.196992	−	0.0197679i
$461$	434.353	+	434.353i	0.942198	+	0.942198i	0.998418	−	0.0562205i	$-0.0179050\pi$
$461$	434.353	+	434.353i	0.942198	+	0.942198i	−0.0562205	+	0.998418i	$0.517905\pi$
$462$	−27.0762	−	46.4863i	−0.0586064	−	0.100620i
$463$	93.7911			0.202573			0.101286	−	0.994857i	$-0.467704\pi$
$463$	93.7911			0.202573			0.101286	+	0.994857i	$0.467704\pi$
$464$	−90.5641	−	136.624i	−0.195181	−	0.294448i
$465$		−	55.8598i		−	0.120129i
$466$	126.105	+	353.464i	0.270612	+	0.758507i
$467$	67.8183	+	67.8183i	0.145221	+	0.145221i	0.775979	−	0.630758i	$-0.217256\pi$
$467$	67.8183	+	67.8183i	0.145221	+	0.145221i	−0.630758	+	0.775979i	$0.717256\pi$
$468$	−66.7076	+	664.759i	−0.142538	+	1.42042i
$469$	−235.869	+	344.272i	−0.502919	+	0.734056i
$470$	−115.667	−	54.8365i	−0.246099	−	0.116673i
$471$			159.339i			0.338299i
$472$	87.7275	+	354.373i	0.185863	+	0.750789i
$473$		−	85.6829i		−	0.181148i
$474$	−184.096	−	87.2782i	−0.388388	−	0.184131i
$475$	238.790	−	238.790i	0.502716	−	0.502716i
$476$	443.268	+	373.879i	0.931235	+	0.785461i
$477$	301.388	−	301.388i	0.631840	−	0.631840i
$478$	−630.870	+	225.075i	−1.31981	+	0.470868i
$479$			113.366i			0.236673i	0.992974	+	0.118337i	$0.0377562\pi$
$479$			113.366i			0.236673i	−0.992974	+	0.118337i	$0.962244\pi$
$480$	−5.58429	−	38.8769i	−0.0116339	−	0.0809934i
$481$			1035.76i			2.15335i
$482$	13.9663	+	39.1467i	0.0289758	+	0.0812173i
$483$	81.7669	−	119.346i	0.169290	−	0.247094i
$484$	−272.802	−	333.660i	−0.563640	−	0.689379i
$485$	39.1543	+	39.1543i	0.0807306	+	0.0807306i
$486$	−389.389	−	184.606i	−0.801212	−	0.379847i
$487$			132.462i			0.271996i	0.990709	+	0.135998i	$0.0434240\pi$
$487$			132.462i			0.271996i	−0.990709	+	0.135998i	$0.956576\pi$
$488$	351.757	−	87.0800i	0.720813	−	0.178443i
$489$	181.398			0.370958
$490$	−8.34019	+	113.650i	−0.0170208	+	0.231939i
$491$	−614.010	−	614.010i	−1.25053	−	1.25053i	−0.955483	−	0.295047i	$-0.904665\pi$
$491$	−614.010	−	614.010i	−1.25053	−	1.25053i	−0.295047	−	0.955483i	$-0.595335\pi$
$492$	−258.712	−	25.9614i	−0.525837	−	0.0527670i
$493$	−150.027	−	150.027i	−0.304315	−	0.304315i
$494$	−203.268	−	569.747i	−0.411474	−	1.15333i
$495$		−	33.3827i		−	0.0674398i
$496$	713.669	+	144.688i	1.43885	+	0.291710i
$497$	20.2493	+	108.368i	0.0407431	+	0.218045i
$498$	−31.7539	−	89.0040i	−0.0637628	−	0.178723i
$499$	−540.237	+	540.237i	−1.08264	+	1.08264i	−0.0863773	+	0.996262i	$0.527529\pi$
$499$	−540.237	+	540.237i	−1.08264	+	1.08264i	−0.996262	+	0.0863773i	$0.972471\pi$
$500$	225.142	+	22.5927i	0.450285	+	0.0451855i
$501$	125.522	+	125.522i	0.250543	+	0.250543i
$502$	402.150	−	848.255i	0.801095	−	1.68975i
$503$	417.128			0.829280			0.414640	−	0.909986i	$-0.363907\pi$
$503$	417.128			0.829280			0.414640	+	0.909986i	$0.363907\pi$
$504$	−413.612	−	154.738i	−0.820658	−	0.307020i
$505$			94.9322i			0.187985i
$506$	−61.0718	+	128.819i	−0.120695	+	0.254583i
$507$	208.684	−	208.684i	0.411605	−	0.411605i
$508$	459.175	−	375.424i	0.903888	−	0.739024i
$509$	−23.6510	−	23.6510i	−0.0464657	−	0.0464657i	0.683492	−	0.729958i	$-0.260460\pi$
$509$	−23.6510	−	23.6510i	−0.0464657	−	0.0464657i	−0.729958	+	0.683492i	$0.760460\pi$
$510$	−17.0830	−	47.8825i	−0.0334960	−	0.0938872i
$511$	−452.309	+	84.5168i	−0.885144	+	0.165395i
$512$	511.158	+	29.3538i	0.998355	+	0.0573316i
$513$	254.524			0.496149
$514$	−3.34998	−	9.38977i	−0.00651747	−	0.0182680i
$515$	45.0572	−	45.0572i	0.0874897	−	0.0874897i
$516$	62.8988	+	76.9305i	0.121897	+	0.149090i
$517$	−141.691	+	141.691i	−0.274063	+	0.274063i
$518$	−661.979	−	174.669i	−1.27795	−	0.337200i
$519$		−	119.898i		−	0.231018i
$520$	101.759	−	168.717i	0.195690	−	0.324456i
$521$	877.949			1.68512			0.842562	−	0.538600i	$-0.181047\pi$
$521$	877.949			1.68512			0.842562	+	0.538600i	$0.181047\pi$
$522$	146.000	+	69.2170i	0.279693	+	0.132600i
$523$	510.059	−	510.059i	0.975256	−	0.975256i	−0.0244456	−	0.999701i	$-0.507782\pi$
$523$	510.059	−	510.059i	0.975256	−	0.975256i	0.999701	+	0.0244456i	$0.00778204\pi$
$524$	−590.997	−	59.3057i	−1.12786	−	0.113179i
$525$	−98.7544	+	144.141i	−0.188104	+	0.274554i
$526$	202.098	+	566.468i	0.384217	+	1.07694i
$527$	942.564			1.78855
$528$	−60.2562	−	12.2163i	−0.114122	−	0.0231369i
$529$	145.623			0.275279
$530$	−118.389	+	42.2377i	−0.223376	+	0.0796937i
$531$	−254.461	−	254.461i	−0.479211	−	0.479211i
$532$	398.416	−	33.8317i	0.748903	−	0.0635935i
$533$	−922.317	−	922.317i	−1.73043	−	1.73043i
$534$	170.389	+	80.7798i	0.319081	+	0.151273i
$535$	−87.1565			−0.162909
$536$	114.610	+	462.964i	0.213825	+	0.863738i
$537$	−278.241			−0.518140
$538$	−863.683	−	409.464i	−1.60536	−	0.761086i
$539$	163.175	+	72.0773i	0.302736	+	0.133724i
$540$	52.4739	+	64.1799i	0.0971738	+	0.118852i
$541$	−63.2455	+	63.2455i	−0.116905	+	0.116905i	−0.763139	−	0.646234i	$-0.776343\pi$
$541$	−63.2455	+	63.2455i	−0.116905	+	0.116905i	0.646234	+	0.763139i	$0.276343\pi$
$542$	−114.801	−	321.780i	−0.211810	−	0.593690i
$543$	22.2973			0.0410631
$544$	655.998	−	94.2278i	1.20588	−	0.173213i
$545$			90.4615i			0.165984i
$546$	157.527	+	270.454i	0.288511	+	0.495336i
$547$	−323.315	+	323.315i	−0.591069	+	0.591069i	−0.937920	−	0.346851i	$-0.887251\pi$
$547$	−323.315	+	323.315i	−0.591069	+	0.591069i	0.346851	+	0.937920i	$0.387251\pi$
$548$	50.5497	+	61.8266i	0.0922441	+	0.112822i
$549$	−252.583	+	252.583i	−0.460078	+	0.460078i
$550$	73.7597	−	155.582i	0.134109	−	0.282876i
$551$	−146.297			−0.265512
$552$	−39.7310	−	160.492i	−0.0719765	−	0.290747i
$553$	664.078	−	124.087i	1.20086	−	0.224389i
$554$	−454.819	−	215.625i	−0.820973	−	0.389215i
$555$	42.4416	+	42.4416i	0.0764714	+	0.0764714i
$556$	94.0492	−	937.225i	0.169153	−	1.68566i
$557$	−234.582	+	234.582i	−0.421153	+	0.421153i	−0.885600	−	0.464448i	$-0.846253\pi$
$557$	−234.582	+	234.582i	−0.421153	+	0.421153i	0.464448	+	0.885600i	$0.346253\pi$
$558$	−676.063	+	241.198i	−1.21158	+	0.432255i
$559$			498.496i			0.891764i
$560$	90.6701	+	93.4882i	0.161911	+	0.166943i
$561$	−79.5822			−0.141858
$562$	−303.424	−	850.477i	−0.539900	−	1.51331i
$563$	−520.051	−	520.051i	−0.923714	−	0.923714i	0.0735757	−	0.997290i	$-0.476559\pi$
$563$	−520.051	−	520.051i	−0.923714	−	0.923714i	−0.997290	+	0.0735757i	$0.976559\pi$
$564$	23.2037	−	231.231i	0.0411413	−	0.409984i
$565$	5.59042	−	5.59042i	0.00989456	−	0.00989456i
$566$	−35.2832	+	74.4229i	−0.0623378	+	0.131489i
$567$	358.908	−	67.0642i	0.632994	−	0.118279i
$568$	107.889	+	65.0712i	0.189945	+	0.114562i
$569$			169.180i			0.297328i	0.988888	+	0.148664i	$0.0474973\pi$
$569$			169.180i			0.297328i	−0.988888	+	0.148664i	$0.952503\pi$
$570$	−31.6752	−	15.0169i	−0.0555705	−	0.0263454i
$571$	273.184	+	273.184i	0.478432	+	0.478432i	0.904630	−	0.426198i	$-0.140147\pi$
$571$	273.184	+	273.184i	0.478432	+	0.478432i	−0.426198	+	0.904630i	$0.640147\pi$
$572$	−195.225	−	238.776i	−0.341302	−	0.417441i
$573$	−16.9255	−	16.9255i	−0.0295384	−	0.0295384i
$574$	745.010	−	433.934i	1.29793	−	0.755983i
$575$	463.026			0.805262
$576$	−446.408	+	235.453i	−0.775014	+	0.408772i
$577$			1152.31i			1.99707i	0.0540701	+	0.998537i	$0.482781\pi$
$577$			1152.31i			1.99707i	−0.0540701	+	0.998537i	$0.517219\pi$
$578$	263.565	−	94.0319i	0.455995	−	0.162685i
$579$	9.85599	+	9.85599i	0.0170224	+	0.0170224i
$580$	−30.1613	−	36.8898i	−0.0520023	−	0.0636031i
$581$	258.499	+	177.104i	0.444921	+	0.304826i
$582$	−43.0643	+	90.8356i	−0.0739936	+	0.156075i
$583$			196.767i			0.337508i
$584$	−271.595	+	450.307i	−0.465060	+	0.771074i
$585$			194.218i			0.331996i
$586$	−320.096	+	675.178i	−0.546238	+	1.15218i
$587$	594.972	−	594.972i	1.01358	−	1.01358i	0.0136745	−	0.999906i	$-0.495647\pi$
$587$	594.972	−	594.972i	1.01358	−	1.01358i	0.999906	−	0.0136745i	$-0.00435287\pi$
$588$	−199.418	+	55.0700i	−0.339146	+	0.0936564i
$589$	459.566	−	459.566i	0.780247	−	0.780247i
$590$	35.6612	+	99.9559i	0.0604427	+	0.169417i
$591$		−	66.2371i		−	0.112076i
$592$	−652.170	+	432.305i	−1.10164	+	0.730244i
$593$		−	567.041i		−	0.956225i	−0.878299	−	0.478112i	$-0.841321\pi$
$593$		−	567.041i		−	0.956225i	0.878299	−	0.478112i	$-0.158679\pi$
$594$	122.227	−	43.6066i	0.205769	−	0.0734118i
$595$	139.067	+	95.2784i	0.233727	+	0.160132i
$596$	−723.169	−	72.5690i	−1.21337	−	0.121760i
$597$	−86.6606	−	86.6606i	−0.145160	−	0.145160i
$598$	355.311	−	749.458i	0.594165	−	1.25327i
$599$			353.024i			0.589355i	0.955597	+	0.294678i	$0.0952123\pi$
$599$			353.024i			0.589355i	−0.955597	+	0.294678i	$0.904788\pi$
$600$	47.9853	+	193.835i	0.0799755	+	0.323059i
$601$	30.5796			0.0508811			0.0254406	−	0.999676i	$-0.491901\pi$
$601$	30.5796			0.0508811			0.0254406	+	0.999676i	$0.491901\pi$
$602$	−318.600	−	84.0655i	−0.529235	−	0.139644i
$603$	−332.436	−	332.436i	−0.551303	−	0.551303i
$604$	−645.555	−	789.567i	−1.06880	−	1.30723i
$605$	−88.5928	−	88.5928i	−0.146434	−	0.146434i
$606$	−162.324	+	57.9123i	−0.267862	+	0.0955649i
$607$			622.168i			1.02499i	0.858691	+	0.512494i	$0.171278\pi$
$607$			622.168i			1.02499i	−0.858691	+	0.512494i	$0.828722\pi$
$608$	273.902	−	365.787i	0.450497	−	0.601624i
$609$	74.4063	−	13.9033i	0.122178	−	0.0228297i
$610$	99.2181	−	35.3979i	0.162653	−	0.0580294i
$611$	824.346	−	824.346i	1.34917	−	1.34917i
$612$	−505.751	+	413.505i	−0.826391	+	0.675662i
$613$	375.828	+	375.828i	0.613097	+	0.613097i	0.943752	−	0.330655i	$-0.107270\pi$
$613$	375.828	+	375.828i	0.613097	+	0.613097i	−0.330655	+	0.943752i	$0.607270\pi$
$614$	−1028.02	−	487.373i	−1.67430	−	0.793768i
$615$	−75.5860			−0.122904
$616$	185.529	−	84.5055i	0.301184	−	0.137184i
$617$			724.934i			1.17493i	0.809248	+	0.587467i	$0.199875\pi$
$617$			724.934i			1.17493i	−0.809248	+	0.587467i	$0.800125\pi$
$618$	104.530	+	49.5566i	0.169142	+	0.0801887i
$619$	67.3282	−	67.3282i	0.108769	−	0.108769i	−0.650628	−	0.759397i	$-0.725494\pi$
$619$	67.3282	−	67.3282i	0.108769	−	0.108769i	0.759397	+	0.650628i	$0.225494\pi$
$620$	210.628	+	21.1363i	0.339723	+	0.0340908i
$621$	246.768	+	246.768i	0.397372	+	0.397372i
$622$	663.751	−	236.806i	1.06712	−	0.380717i
$623$	−614.634	+	114.848i	−0.986572	+	0.184347i
$624$	350.566	+	71.0732i	0.561804	+	0.113899i
$625$	−525.418			−0.840670
$626$	546.944	−	195.132i	0.873712	−	0.311713i
$627$	−38.8019	+	38.8019i	−0.0618849	+	0.0618849i
$628$	−600.813	−	60.2908i	−0.956709	−	0.0960044i
$629$	−716.149	+	716.149i	−1.13855	+	1.13855i
$630$	−124.129	−	32.7525i	−0.197030	−	0.0519882i
$631$		−	941.200i		−	1.49160i	−0.666169	−	0.745801i	$-0.732067\pi$
$631$		−	941.200i		−	1.49160i	0.666169	−	0.745801i	$-0.267933\pi$
$632$	398.755	−	661.140i	0.630941	−	1.04611i
$633$	184.845			0.292014
$634$	−405.575	+	855.480i	−0.639708	+	1.34934i
$635$	121.919	−	121.919i	0.191999	−	0.191999i
$636$	−144.444	−	176.667i	−0.227114	−	0.277779i
$637$	−949.338	−	419.340i	−1.49033	−	0.658305i
$638$	−70.2543	+	25.0645i	−0.110116	+	0.0392861i
$639$	−124.196			−0.194359
$640$	148.705	−	6.34621i	0.232351	−	0.00991595i
$641$	28.5724			0.0445748			0.0222874	−	0.999752i	$-0.492905\pi$
$641$	28.5724			0.0445748			0.0222874	+	0.999752i	$0.492905\pi$
$642$	−53.1688	−	149.029i	−0.0828175	−	0.232132i
$643$	−30.2697	−	30.2697i	−0.0470758	−	0.0470758i	0.683177	−	0.730253i	$-0.260598\pi$
$643$	−30.2697	−	30.2697i	−0.0470758	−	0.0470758i	−0.730253	+	0.683177i	$0.760598\pi$
$644$	419.075	+	353.474i	0.650738	+	0.548872i
$645$	20.4265	+	20.4265i	0.0316689	+	0.0316689i
$646$	253.391	−	534.479i	0.392247	−	0.827367i
$647$	96.1146			0.148554			0.0742771	−	0.997238i	$-0.476335\pi$
$647$	96.1146			0.148554			0.0742771	+	0.997238i	$0.476335\pi$
$648$	215.511	−	357.320i	0.332579	−	0.551419i
$649$	166.130			0.255978
$650$	−429.128	+	905.161i	−0.660197	+	1.39256i
$651$	−190.059	+	277.408i	−0.291949	+	0.426126i
$652$	−68.6377	+	683.992i	−0.105273	+	1.04907i
$653$	299.672	−	299.672i	0.458916	−	0.458916i	−0.439383	−	0.898300i	$-0.644803\pi$
$653$	299.672	−	299.672i	0.458916	−	0.458916i	0.898300	+	0.439383i	$0.144803\pi$
$654$	−154.680	+	55.1850i	−0.236514	+	0.0843808i
$655$	−172.667			−0.263614
$656$	195.783	−	965.692i	0.298450	−	1.47209i
$657$		−	518.369i		−	0.788994i
$658$	387.841	+	665.873i	0.589424	+	1.01197i
$659$	−499.672	+	499.672i	−0.758228	+	0.758228i	−0.976000	−	0.217772i	$-0.930121\pi$
$659$	−499.672	+	499.672i	−0.758228	+	0.758228i	0.217772	+	0.976000i	$0.430121\pi$
$660$	−17.7837	−	1.78457i	−0.0269450	−	0.00270389i
$661$	−368.251	+	368.251i	−0.557112	+	0.557112i	−0.928484	−	0.371372i	$-0.878887\pi$
$661$	−368.251	+	368.251i	−0.557112	+	0.557112i	0.371372	+	0.928484i	$0.378887\pi$
$662$	−85.6646	−	40.6128i	−0.129403	−	0.0613486i
$663$	463.003			0.698345
$664$	347.619	−	86.0557i	0.523523	−	0.129602i
$665$	114.260	−	21.3502i	0.171819	−	0.0321056i
$666$	330.405	−	696.924i	0.496103	−	1.04643i
$667$	−141.839	−	141.839i	−0.212652	−	0.212652i
$668$	−520.797	+	425.807i	−0.779637	+	0.637436i
$669$	−155.618	+	155.618i	−0.232612	+	0.232612i
$670$	46.5889	+	130.586i	0.0695357	+	0.194904i
$671$		−	164.904i		−	0.245758i
$672$	−104.543	+	212.068i	−0.155570	+	0.315578i
$673$	360.905			0.536262			0.268131	−	0.963382i	$-0.413594\pi$
$673$	360.905			0.536262			0.268131	+	0.963382i	$0.413594\pi$
$674$	29.0106	−	10.3501i	0.0430424	−	0.0153562i
$675$	−298.035	−	298.035i	−0.441533	−	0.441533i
$676$	707.914	+	865.838i	1.04721	+	1.28083i
$677$	388.404	−	388.404i	0.573713	−	0.573713i	−0.359451	−	0.933164i	$-0.617036\pi$
$677$	388.404	−	388.404i	0.573713	−	0.573713i	0.933164	+	0.359451i	$0.117036\pi$
$678$	12.9694	+	6.14869i	0.0191290	+	0.00906886i
$679$	−61.2264	−	327.666i	−0.0901715	−	0.482571i
$680$	187.013	−	46.2963i	0.275018	−	0.0680828i
$681$		−	57.5705i		−	0.0845382i
$682$	141.955	−	299.426i	0.208145	−	0.439041i
$683$	614.349	+	614.349i	0.899486	+	0.899486i	0.995391	−	0.0959045i	$-0.0305744\pi$
$683$	614.349	+	614.349i	0.899486	+	0.899486i	−0.0959045	+	0.995391i	$0.530574\pi$
$684$	−44.9764	+	448.202i	−0.0657550	+	0.655265i
$685$	16.4161	+	16.4161i	0.0239651	+	0.0239651i
$686$	428.104	−	536.025i	0.624058	−	0.781378i
$687$	−358.060			−0.521193
$688$	−313.879	+	208.061i	−0.456219	+	0.302414i
$689$		−	1144.77i		−	1.66150i
$690$	−16.1506	−	45.2692i	−0.0234067	−	0.0656075i
$691$	−370.027	−	370.027i	−0.535496	−	0.535496i	0.386707	−	0.922203i	$-0.373612\pi$
$691$	−370.027	−	370.027i	−0.535496	−	0.535496i	−0.922203	+	0.386707i	$0.873612\pi$
$692$	452.096	+	45.3672i	0.653318	+	0.0655595i
$693$	−113.582	+	165.783i	−0.163899	+	0.239226i
$694$	291.648	+	138.267i	0.420241	+	0.199232i
$695$		−	273.822i		−	0.393989i
$696$	44.6783	−	74.0770i	0.0641929	−	0.106432i
$697$		−	1275.42i		−	1.82987i
$698$	956.756	+	453.589i	1.37071	+	0.649841i
$699$	−140.050	+	140.050i	−0.200358	+	0.200358i
$700$	−506.140	−	426.910i	−0.723057	−	0.609871i
$701$	12.8864	−	12.8864i	0.0183829	−	0.0183829i	−0.697856	−	0.716238i	$-0.745862\pi$
$701$	12.8864	−	12.8864i	0.0183829	−	0.0183829i	0.716238	+	0.697856i	$0.245862\pi$
$702$	−711.104	+	253.700i	−1.01297	+	0.361396i
$703$			698.345i			0.993379i
$704$	68.8632	−	222.583i	0.0978170	−	0.316170i
$705$		−	67.5570i		−	0.0958256i
$706$	42.5121	+	119.159i	0.0602154	+	0.168780i
$707$	323.000	−	471.447i	0.456859	−	0.666828i
$708$	−149.160	+	121.954i	−0.210678	+	0.172251i
$709$	−30.4271	−	30.4271i	−0.0429155	−	0.0429155i	0.685323	−	0.728239i	$-0.259661\pi$
$709$	−30.4271	−	30.4271i	−0.0429155	−	0.0429155i	−0.728239	+	0.685323i	$0.759661\pi$
$710$	33.0956	+	15.6903i	0.0466135	+	0.0220990i
$711$			761.068i			1.07042i
$712$	−369.066	+	611.914i	−0.518351	+	0.859430i
$713$	891.121			1.24982
$714$	−78.0800	+	295.915i	−0.109356	+	0.414447i
$715$	−63.3995	−	63.3995i	−0.0886706	−	0.0886706i
$716$	105.281	−	1049.15i	0.147041	−	1.46530i
$717$	−249.964	−	249.964i	−0.348625	−	0.348625i
$718$	−16.6587	−	46.6932i	−0.0232015	−	0.0650324i
$719$			317.738i			0.441916i	0.975283	+	0.220958i	$0.0709184\pi$
$719$			317.738i			0.441916i	−0.975283	+	0.220958i	$0.929082\pi$
$720$	−122.289	+	81.0621i	−0.169846	+	0.112586i
$721$	−377.064	+	70.4569i	−0.522974	+	0.0977211i
$722$	105.559	+	295.876i	0.146204	+	0.409801i
$723$	−15.5108	+	15.5108i	−0.0214534	+	0.0214534i
$724$	−8.43686	+	84.0755i	−0.0116531	+	0.116126i
$725$	171.307	+	171.307i	0.236285	+	0.236285i
$726$	97.4397	−	205.530i	0.134214	−	0.283099i
$727$	−803.482			−1.10520			−0.552601	−	0.833446i	$-0.686365\pi$
$727$	−803.482			−1.10520			−0.552601	+	0.833446i	$0.686365\pi$
$728$	−1079.39	+	491.646i	−1.48269	+	0.675339i
$729$			242.011i			0.331976i
$730$	−65.4883	+	138.135i	−0.0897101	+	0.189226i
$731$	−344.671	+	344.671i	−0.471506	+	0.471506i
$732$	121.054	+	148.059i	0.165374	+	0.202266i
$733$	−553.720	−	553.720i	−0.755416	−	0.755416i	0.220069	−	0.975484i	$-0.429372\pi$
$733$	−553.720	−	553.720i	−0.755416	−	0.755416i	−0.975484	+	0.220069i	$0.929372\pi$
$734$	101.050	+	283.237i	0.137671	+	0.385882i
$735$	−56.0832	+	21.7173i	−0.0763036	+	0.0295473i
$736$	620.195	−	89.0851i	0.842657	−	0.121040i
$737$	217.038			0.294488
$738$	326.374	+	914.806i	0.442241	+	1.23957i
$739$	82.0530	−	82.0530i	0.111032	−	0.111032i	−0.649408	−	0.760440i	$-0.724983\pi$
$739$	82.0530	−	82.0530i	0.111032	−	0.111032i	0.760440	+	0.649408i	$0.224983\pi$
$740$	−176.092	+	143.974i	−0.237962	+	0.194559i
$741$	225.746	−	225.746i	0.304651	−	0.304651i
$742$	731.650	+	193.053i	0.986051	+	0.260179i
$743$			1174.63i			1.58093i	0.612507	+	0.790465i	$0.290161\pi$
$743$			1174.63i			1.58093i	−0.612507	+	0.790465i	$0.709839\pi$
$744$	92.3506	+	373.047i	0.124127	+	0.501408i
$745$	−211.283			−0.283602
$746$	−256.501	−	121.605i	−0.343835	−	0.163009i
$747$	−249.612	+	249.612i	−0.334152	+	0.334152i
$748$	30.1124	−	300.078i	0.0402572	−	0.401173i
$749$	432.832	+	296.543i	0.577880	+	0.395919i
$750$	40.1273	+	112.474i	0.0535031	+	0.149966i
$751$	−40.2707			−0.0536227			−0.0268114	−	0.999641i	$-0.508535\pi$
$751$	−40.2707			−0.0536227			−0.0268114	+	0.999641i	$0.508535\pi$
$752$	863.113	+	174.987i	1.14776	+	0.232695i
$753$	495.438			0.657952
$754$	408.734	−	145.823i	0.542087	−	0.193400i
$755$	−209.645	−	209.645i	−0.277675	−	0.277675i
$756$	−42.2256	−	497.265i	−0.0558539	−	0.657758i
$757$	55.7299	+	55.7299i	0.0736195	+	0.0736195i	0.742958	−	0.669338i	$-0.233422\pi$
$757$	55.7299	+	55.7299i	0.0736195	+	0.0736195i	−0.669338	+	0.742958i	$0.733422\pi$
$758$	964.972	+	457.484i	1.27305	+	0.603541i
$759$	−75.2388			−0.0991288
$760$	68.6090	−	113.754i	0.0902750	−	0.149677i
$761$	−97.8619			−0.128596			−0.0642982	−	0.997931i	$-0.520481\pi$
$761$	−97.8619			−0.128596			−0.0642982	+	0.997931i	$0.520481\pi$
$762$	282.846	+	134.094i	0.371189	+	0.175977i
$763$	307.788	−	449.245i	0.403392	−	0.588788i
$764$	70.2247	−	57.4161i	0.0919171	−	0.0751520i
$765$	−134.286	+	134.286i	−0.175538	+	0.175538i
$766$	304.812	+	854.369i	0.397927	+	1.11536i
$767$	−966.531			−1.26014
$768$	101.567	+	250.398i	0.132249	+	0.326039i
$769$			659.680i			0.857841i	0.903342	+	0.428920i	$0.141106\pi$
$769$			659.680i			0.857841i	−0.903342	+	0.428920i	$0.858894\pi$
$770$	51.2116	−	29.8284i	0.0665085	−	0.0387382i
$771$	3.72043	−	3.72043i	0.00482546	−	0.00482546i
$772$	−40.8930	+	33.4343i	−0.0529701	+	0.0433087i
$773$	756.470	−	756.470i	0.978616	−	0.978616i	−0.0211604	−	0.999776i	$-0.506736\pi$
$773$	756.470	−	756.470i	0.978616	−	0.978616i	0.999776	+	0.0211604i	$0.00673606\pi$
$774$	159.018	−	335.418i	0.205450	−	0.433357i
$775$	−1076.26			−1.38872
$776$	−326.216	−	196.751i	−0.420381	−	0.253546i
$777$	−66.3669	−	355.176i	−0.0854142	−	0.457112i
$778$	−1039.63	−	492.878i	−1.33628	−	0.633520i
$779$	−621.856	−	621.856i	−0.798274	−	0.798274i
$780$	103.464	+	10.3825i	0.132646	+	0.0133109i
$781$	40.5418	−	40.5418i	0.0519101	−	0.0519101i
$782$	763.860	−	272.522i	0.976803	−	0.348493i
$783$			182.594i			0.233199i
$784$	−132.194	−	772.775i	−0.168615	−	0.985682i
$785$	−175.535			−0.223612
$786$	−105.334	−	295.244i	−0.134012	−	0.375628i
$787$	1017.48	+	1017.48i	1.29286	+	1.29286i	0.933009	+	0.359854i	$0.117173\pi$
$787$	1017.48	+	1017.48i	1.29286	+	1.29286i	0.359854	+	0.933009i	$0.382827\pi$
$788$	249.758	+	25.0629i	0.316952	+	0.0318057i
$789$	−224.447	+	224.447i	−0.284470	+	0.284470i
$790$	96.1498	−	202.809i	0.121709	−	0.256720i
$791$	−46.7839	+	8.74187i	−0.0591452	+	0.0110517i
$792$	55.1902	+	222.939i	0.0696846	+	0.281489i
$793$			959.396i			1.20983i
$794$	241.220	+	114.360i	0.303803	+	0.144030i
$795$	−46.9085	−	46.9085i	−0.0590044	−	0.0590044i
$796$	359.559	−	293.977i	0.451707	−	0.369318i
$797$	−871.234	−	871.234i	−1.09314	−	1.09314i	−0.995191	−	0.0979499i	$-0.968772\pi$
$797$	−871.234	−	871.234i	−1.09314	−	1.09314i	−0.0979499	−	0.995191i	$-0.531228\pi$
$798$	106.210	+	182.349i	0.133095	+	0.228507i
$799$	1139.94			1.42671
$800$	−749.044	+	107.593i	−0.936305	+	0.134491i
$801$		−	704.403i		−	0.879404i
$802$	−1324.40	+	472.504i	−1.65137	+	0.589157i
$803$	169.214	+	169.214i	0.210727	+	0.210727i
$804$	−194.867	+	159.325i	−0.242372	+	0.198165i
$805$	131.477	+	90.0783i	0.163326	+	0.111899i
$806$	−825.883	+	1742.04i	−1.02467	+	2.16134i
$807$		−	504.449i		−	0.625091i
$808$	−156.947	−	633.984i	−0.194242	−	0.784633i
$809$		−	678.651i		−	0.838876i	−0.907784	−	0.419438i	$-0.862227\pi$
$809$		−	678.651i		−	0.838876i	0.907784	−	0.419438i	$-0.137773\pi$
$810$	51.9651	−	109.610i	0.0641545	−	0.135321i
$811$	−733.218	+	733.218i	−0.904092	+	0.904092i	−0.995787	−	0.0916954i	$-0.970771\pi$
$811$	−733.218	+	733.218i	−0.904092	+	0.904092i	0.0916954	+	0.995787i	$0.470771\pi$
$812$	24.2707	+	285.822i	0.0298901	+	0.351997i
$813$	127.496	−	127.496i	0.156822	−	0.156822i
$814$	119.645	+	335.356i	0.146984	+	0.411985i
$815$			199.837i			0.245199i
$816$	193.247	+	291.530i	0.236822	+	0.357267i
$817$			336.102i			0.411386i
$818$	889.924	−	317.497i	1.08793	−	0.388138i
$819$	660.811	−	964.514i	0.806851	−	1.17767i
$820$	28.6003	−	285.009i	0.0348784	−	0.347572i
$821$	219.233	+	219.233i	0.267032	+	0.267032i	0.827903	−	0.560871i	$-0.189534\pi$
$821$	219.233	+	219.233i	0.267032	+	0.267032i	−0.560871	+	0.827903i	$0.689534\pi$
$822$	−18.0554	+	38.0843i	−0.0219652	+	0.0463313i
$823$		−	584.619i		−	0.710351i	−0.934800	−	0.355176i	$-0.884421\pi$
$823$		−	584.619i		−	0.710351i	0.934800	−	0.355176i	$-0.115579\pi$
$824$	−226.414	+	375.396i	−0.274774	+	0.455578i
$825$	90.8700			0.110145
$826$	162.994	−	617.730i	0.197329	−	0.747858i
$827$	377.082	+	377.082i	0.455964	+	0.455964i	0.897328	−	0.441364i	$-0.145505\pi$
$827$	377.082	+	377.082i	0.455964	+	0.455964i	−0.441364	+	0.897328i	$0.645505\pi$
$828$	−478.149	+	390.937i	−0.577474	+	0.472146i
$829$	−220.663	−	220.663i	−0.266179	−	0.266179i	0.561379	−	0.827559i	$-0.310271\pi$
$829$	−220.663	−	220.663i	−0.266179	−	0.266179i	−0.827559	+	0.561379i	$0.810271\pi$
$830$	98.0511	−	34.9816i	0.118134	−	0.0421465i
$831$		−	265.645i		−	0.319669i
$832$	−400.641	+	1294.97i	−0.481539	+	1.55646i
$833$	−366.452	−	946.333i	−0.439918	−	1.13605i
$834$	468.209	−	167.042i	0.561401	−	0.200290i
$835$	−138.281	+	138.281i	−0.165606	+	0.165606i
$836$	−131.627	−	160.991i	−0.157448	−	0.192573i
$837$	−573.586	−	573.586i	−0.685288	−	0.685288i
$838$	911.252	+	432.016i	1.08741	+	0.515532i
$839$	1453.30			1.73218			0.866090	−	0.499888i	$-0.166626\pi$
$839$	1453.30			1.73218			0.866090	+	0.499888i	$0.166626\pi$
$840$	−24.0837	+	64.3752i	−0.0286710	+	0.0766372i
$841$			736.047i			0.875205i
$842$	1172.86	+	556.041i	1.39294	+	0.660381i
$843$	336.978	−	336.978i	0.399736	−	0.399736i
$844$	−69.9418	+	696.989i	−0.0828695	+	0.825816i
$845$	229.896	+	229.896i	0.272066	+	0.272066i
$846$	−817.632	+	291.706i	−0.966469	+	0.344806i
$847$	138.534	+	741.395i	0.163559	+	0.875319i
$848$	720.808	−	477.803i	0.850010	−	0.563447i
$849$	−43.4679			−0.0511990
$850$	−922.556	+	329.139i	−1.08536	+	0.387223i
$851$	−677.063	+	677.063i	−0.795609	+	0.795609i
$852$	−6.63924	+	66.1618i	−0.00779254	+	0.0776547i
$853$	454.447	−	454.447i	0.532763	−	0.532763i	−0.388630	−	0.921394i	$-0.627052\pi$
$853$	454.447	−	454.447i	0.532763	−	0.532763i	0.921394	+	0.388630i	$0.127052\pi$
$854$	−613.171	−	161.791i	−0.717998	−	0.189451i
$855$			130.948i			0.153155i
$856$	582.056	−	144.092i	0.679972	−	0.168332i
$857$	−884.451			−1.03203			−0.516016	−	0.856579i	$-0.672585\pi$
$857$	−884.451			−1.03203			−0.516016	+	0.856579i	$0.672585\pi$
$858$	69.7306	−	147.083i	0.0812711	−	0.171425i
$859$	−496.836	+	496.836i	−0.578389	+	0.578389i	−0.934459	−	0.356071i	$-0.884116\pi$
$859$	−496.836	+	496.836i	−0.578389	+	0.578389i	0.356071	+	0.934459i	$0.384116\pi$
$860$	−84.7503	+	69.2923i	−0.0985468	+	0.0805725i
$861$	375.371	+	257.176i	0.435971	+	0.298694i
$862$	959.211	−	342.217i	1.11277	−	0.397003i
$863$	209.451			0.242701			0.121351	−	0.992610i	$-0.461277\pi$
$863$	209.451			0.242701			0.121351	+	0.992610i	$0.461277\pi$
$864$	−456.541	−	341.859i	−0.528404	−	0.395670i
$865$	132.086			0.152700
$866$	71.0268	+	199.083i	0.0820171	+	0.229889i
$867$	104.430	+	104.430i	0.120450	+	0.120450i
$868$	−974.097	−	821.613i	−1.12223	−	0.946559i
$869$	−248.439	−	248.439i	−0.285891	−	0.285891i
$870$	10.7730	−	22.7236i	0.0123828	−	0.0261191i
$871$	−1262.71			−1.44972
$872$	−149.556	−	604.127i	−0.171509	−	0.692807i
$873$	375.522			0.430151
$874$	239.562	−	505.308i	0.274098	−	0.578156i
$875$	−326.665	−	223.806i	−0.373331	−	0.255778i
$876$	−276.147	−	27.7110i	−0.315236	−	0.0316335i
$877$	−410.184	+	410.184i	−0.467713	+	0.467713i	−0.901173	−	0.433460i	$-0.857293\pi$
$877$	−410.184	+	410.184i	−0.467713	+	0.467713i	0.433460	+	0.901173i	$0.357293\pi$
$878$	244.340	−	87.1731i	0.278292	−	0.0992860i
$879$	−394.349			−0.448634
$880$	13.4580	−	66.3811i	0.0152932	−	0.0754331i
$881$		−	270.639i		−	0.307195i	−0.988134	−	0.153597i	$-0.950914\pi$
$881$		−	270.639i		−	0.307195i	0.988134	−	0.153597i	$-0.0490859\pi$
$882$	505.003	+	584.993i	0.572566	+	0.663257i
$883$	−455.994	+	455.994i	−0.516414	+	0.516414i	−0.916484	−	0.400070i	$-0.868986\pi$
$883$	−455.994	+	455.994i	−0.516414	+	0.516414i	0.400070	+	0.916484i	$0.368986\pi$
$884$	−175.191	+	1745.83i	−0.198180	+	1.97492i
$885$	−39.6047	+	39.6047i	−0.0447511	+	0.0447511i
$886$	−1140.45	−	540.674i	−1.28718	−	0.610242i
$887$	270.546			0.305013			0.152506	−	0.988303i	$-0.451266\pi$
$887$	270.546			0.305013			0.152506	+	0.988303i	$0.451266\pi$
$888$	−353.604	−	213.270i	−0.398203	−	0.240169i
$889$	−1020.29	+	190.648i	−1.14769	+	0.214452i
$890$	−88.9909	+	187.709i	−0.0999898	+	0.210909i
$891$	−134.272	−	134.272i	−0.150698	−	0.150698i
$892$	−527.899	−	645.664i	−0.591815	−	0.723839i
$893$	555.800	−	555.800i	0.622397	−	0.622397i
$894$	−128.891	−	361.273i	−0.144173	−	0.404108i
$895$		−	306.524i		−	0.342485i
$896$	−760.081	−	474.440i	−0.848305	−	0.529509i
$897$	437.733			0.487997
$898$	1089.74	−	388.784i	1.21351	−	0.432944i
$899$	329.690	+	329.690i	0.366730	+	0.366730i
$900$	577.486	−	472.156i	0.641651	−	0.524618i
$901$	791.522	−	791.522i	0.878492	−	0.878492i
$902$	−405.165	−	192.085i	−0.449185	−	0.212954i
$903$	−31.9413	−	170.940i	−0.0353724	−	0.189303i
$904$	−28.0920	+	46.5768i	−0.0310752	+	0.0515231i
$905$			24.5637i			0.0271422i
$906$	230.580	−	486.362i	0.254503	−	0.536824i
$907$	392.452	+	392.452i	0.432693	+	0.432693i	0.889543	−	0.456851i	$-0.151023\pi$
$907$	392.452	+	392.452i	0.432693	+	0.432693i	−0.456851	+	0.889543i	$0.651023\pi$
$908$	217.079	+	21.7836i	0.239074	+	0.0239907i
$909$	455.239	+	455.239i	0.500813	+	0.500813i
$910$	−297.945	+	173.539i	−0.327412	+	0.190702i
$911$	1096.68			1.20382			0.601911	−	0.798563i	$-0.294406\pi$
$911$	1096.68			1.20382			0.601911	+	0.798563i	$0.294406\pi$
$912$	236.363	+	47.9199i	0.259170	+	0.0525437i
$913$		−	162.964i		−	0.178493i
$914$	−290.372	−	813.894i	−0.317694	−	0.890475i
$915$	39.3124	+	39.3124i	0.0429643	+	0.0429643i
$916$	135.483	−	1350.12i	0.147907	−	1.47393i
$917$	857.491	+	587.487i	0.935105	+	0.640662i
$918$	−667.086	−	316.259i	−0.726673	−	0.344509i
$919$			141.891i			0.154397i	0.997016	+	0.0771984i	$0.0245975\pi$
$919$			141.891i			0.154397i	−0.997016	+	0.0771984i	$0.975403\pi$
$920$	176.806	−	43.7696i	0.192180	−	0.0475756i
$921$		−	600.431i		−	0.651933i
$922$	−1110.10	−	526.288i	−1.20401	−	0.570811i
$923$	−235.869	+	235.869i	−0.255546	+	0.255546i
$924$	82.2446	+	69.3701i	0.0890093	+	0.0750759i
$925$	817.727	−	817.727i	0.884029	−	0.884029i
$926$	−176.675	+	63.0321i	−0.190794	+	0.0680692i
$927$		−	432.136i		−	0.466166i
$928$	262.414	+	196.496i	0.282774	+	0.211741i
$929$			173.652i			0.186923i	0.995623	+	0.0934617i	$0.0297933\pi$
$929$			173.652i			0.186923i	−0.995623	+	0.0934617i	$0.970207\pi$
$930$	37.5405	+	105.223i	0.0403661	+	0.113144i
$931$	−640.074	−	282.733i	−0.687512	−	0.303687i
$932$	−475.090	−	581.075i	−0.509753	−	0.623471i
$933$	262.993	+	262.993i	0.281878	+	0.281878i
$934$	−173.327	−	82.1726i	−0.185575	−	0.0879793i
$935$		−	87.6715i		−	0.0937663i
$936$	−321.092	−	1297.04i	−0.343047	−	1.38573i
$937$	−374.767			−0.399965			−0.199982	−	0.979799i	$-0.564089\pi$
$937$	−374.767			−0.399965			−0.199982	+	0.979799i	$0.564089\pi$
$938$	212.941	−	807.023i	0.227016	−	0.860366i
$939$	216.711	+	216.711i	0.230789	+	0.230789i
$940$	254.735	+	25.5623i	0.270995	+	0.0271939i
$941$	834.839	+	834.839i	0.887182	+	0.887182i	0.994252	−	0.107069i	$-0.0341466\pi$
$941$	834.839	+	834.839i	0.887182	+	0.887182i	−0.107069	+	0.994252i	$0.534147\pi$
$942$	−107.083	−	300.148i	−0.113677	−	0.318628i
$943$		−	1205.81i		−	1.27870i
$944$	−403.408	−	608.577i	−0.427339	−	0.644679i
$945$	−26.6473	−	142.608i	−0.0281982	−	0.150908i
$946$	57.5830	+	161.401i	0.0608700	+	0.170615i
$947$	208.061	−	208.061i	0.219706	−	0.219706i	−0.588669	−	0.808374i	$-0.700348\pi$
$947$	208.061	−	208.061i	0.219706	−	0.219706i	0.808374	+	0.588669i	$0.200348\pi$
$948$	405.438	+	40.6851i	0.427677	+	0.0429168i
$949$	−984.473	−	984.473i	−1.03738	−	1.03738i
$950$	−289.332	+	610.289i	−0.304560	+	0.642409i
$951$	−499.657			−0.525402
$952$	−1086.25	−	406.382i	−1.14102	−	0.426872i
$953$			226.681i			0.237860i	0.992903	+	0.118930i	$0.0379464\pi$
$953$			226.681i			0.237860i	−0.992903	+	0.118930i	$0.962054\pi$
$954$	−365.179	+	770.273i	−0.382787	+	0.807414i
$955$	18.6459	−	18.6459i	0.0195245	−	0.0195245i
$956$	1037.11	−	847.950i	1.08485	−	0.886977i
$957$	−27.8363	−	27.8363i	−0.0290870	−	0.0290870i
$958$	−76.1876	−	213.549i	−0.0795278	−	0.222911i
$959$	−25.6702	−	137.379i	−0.0267677	−	0.143253i
$960$	36.6463	+	69.4797i	0.0381732	+	0.0723747i
$961$	−1110.32			−1.15538
$962$	−696.083	−	1951.08i	−0.723579	−	2.02814i
$963$	−417.951	+	417.951i	−0.434009	+	0.434009i
$964$	−52.6170	−	64.3549i	−0.0545819	−	0.0667582i
$965$	−10.8578	+	10.8578i	−0.0112516	+	0.0112516i
$966$	−73.8185	+	279.765i	−0.0764167	+	0.289611i
$967$			343.065i			0.354773i	0.984141	+	0.177386i	$0.0567643\pi$
$967$			343.065i			0.354773i	−0.984141	+	0.177386i	$0.943236\pi$
$968$	738.114	+	445.181i	0.762515	+	0.459898i
$969$	312.171			0.322158
$970$	−100.069	−	47.4417i	−0.103164	−	0.0489089i
$971$	−21.4880	+	21.4880i	−0.0221297	+	0.0221297i	−0.718085	−	0.695955i	$-0.754981\pi$
$971$	−21.4880	+	21.4880i	−0.0221297	+	0.0221297i	0.695955	+	0.718085i	$0.254981\pi$
$972$	857.558	+	86.0548i	0.882262	+	0.0885337i
$973$	−931.660	+	1359.84i	−0.957513	+	1.39758i
$974$	−89.0207	−	249.519i	−0.0913971	−	0.256180i
$975$	−528.674			−0.542230
$976$	−604.085	+	400.431i	−0.618939	+	0.410277i
$977$	291.470			0.298332			0.149166	−	0.988812i	$-0.452341\pi$
$977$	291.470			0.298332			0.149166	+	0.988812i	$0.452341\pi$
$978$	−341.701	+	121.908i	−0.349388	+	0.124651i
$979$	229.942	+	229.942i	0.234874	+	0.234874i
$980$	−60.6677	−	219.688i	−0.0619058	−	0.224172i
$981$	433.800	+	433.800i	0.442202	+	0.442202i
$982$	1569.26	+	743.971i	1.59802	+	0.757608i
$983$	1331.33			1.35435			0.677177	−	0.735820i	$-0.263203\pi$
$983$	1331.33			1.35435			0.677177	+	0.735820i	$0.263203\pi$
$984$	504.785	−	124.963i	0.512992	−	0.126995i
$985$	72.9700			0.0740812
$986$	383.432	+	181.782i	0.388877	+	0.184363i
$987$	−229.858	+	335.498i	−0.232885	+	0.339917i
$988$	765.795	+	936.631i	0.775096	+	0.948007i
$989$	−325.860	+	325.860i	−0.329484	+	0.329484i
$990$	22.4348	+	62.8832i	0.0226614	+	0.0635184i
$991$	−913.947			−0.922247			−0.461124	−	0.887336i	$-0.652554\pi$
$991$	−913.947			−0.922247			−0.461124	+	0.887336i	$0.652554\pi$
$992$	−1441.58	+	207.069i	−1.45321	+	0.208739i
$993$		−	50.0338i		−	0.0503865i
$994$	−110.972	−	190.525i	−0.111642	−	0.191676i
$995$	95.4695	−	95.4695i	0.0959493	−	0.0959493i
$996$	119.630	+	146.317i	0.120110	+	0.146905i
$997$	421.536	−	421.536i	0.422805	−	0.422805i	−0.463364	−	0.886168i	$-0.653358\pi$
$997$	421.536	−	421.536i	0.422805	−	0.422805i	0.886168	+	0.463364i	$0.153358\pi$
$998$	654.583	−	1380.71i	0.655895	−	1.38348i
$999$	871.608			0.872481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.l.b.69.5	yes	56
4.3	odd	2		448.3.l.b.433.15		56
7.6	odd	2	inner	112.3.l.b.69.6	yes	56
16.3	odd	4		448.3.l.b.209.14		56
16.13	even	4	inner	112.3.l.b.13.6	yes	56
28.27	even	2		448.3.l.b.433.14		56
112.13	odd	4	inner	112.3.l.b.13.5	✓	56
112.83	even	4		448.3.l.b.209.15		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.l.b.13.5	✓	56	112.13	odd	4	inner
112.3.l.b.13.6	yes	56	16.13	even	4	inner
112.3.l.b.69.5	yes	56	1.1	even	1	trivial
112.3.l.b.69.6	yes	56	7.6	odd	2	inner
448.3.l.b.209.14		56	16.3	odd	4
448.3.l.b.209.15		56	112.83	even	4
448.3.l.b.433.14		56	28.27	even	2
448.3.l.b.433.15		56	4.3	odd	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88371 + 0.672048i) q^{2} +(-0.746365 - 0.746365i) q^{3} +(3.09670 - 2.53188i) q^{4} +(0.822232 - 0.822232i) q^{5} +(1.90753 + 0.904340i) q^{6} +(-6.88091 + 1.28574i) q^{7} +(-4.13173 + 6.85046i) q^{8} -7.88588i q^{9} +O(q^{10})\)	\(q+(-1.88371 + 0.672048i) q^{2} +(-0.746365 - 0.746365i) q^{3} +(3.09670 - 2.53188i) q^{4} +(0.822232 - 0.822232i) q^{5} +(1.90753 + 0.904340i) q^{6} +(-6.88091 + 1.28574i) q^{7} +(-4.13173 + 6.85046i) q^{8} -7.88588i q^{9} +(-0.996265 + 2.10142i) q^{10} +(2.57423 + 2.57423i) q^{11} +(-4.20098 - 0.421563i) q^{12} +(-14.9766 - 14.9766i) q^{13} +(12.0975 - 7.04626i) q^{14} -1.22737 q^{15} +(3.17914 - 15.6810i) q^{16} -20.7103i q^{17} +(5.29969 + 14.8547i) q^{18} +(-10.0977 - 10.0977i) q^{19} +(0.464414 - 4.62800i) q^{20} +(6.09530 + 4.17604i) q^{21} +(-6.57909 - 3.11909i) q^{22} -19.5800i q^{23} +(8.19673 - 2.02916i) q^{24} +23.6479i q^{25} +(38.2766 + 18.1466i) q^{26} +(-12.6030 + 12.6030i) q^{27} +(-18.0528 + 21.4032i) q^{28} +(7.24407 - 7.24407i) q^{29} +(2.31201 - 0.824852i) q^{30} +45.5117i q^{31} +(4.54980 + 31.6749i) q^{32} -3.84263i q^{33} +(13.9183 + 39.0122i) q^{34} +(-4.60052 + 6.71488i) q^{35} +(-19.9661 - 24.4202i) q^{36} +(-34.5793 - 34.5793i) q^{37} +(25.8073 + 12.2350i) q^{38} +22.3561i q^{39} +(2.23542 + 9.02991i) q^{40} +61.5837 q^{41} +(-14.2883 - 3.77009i) q^{42} +(-16.6424 - 16.6424i) q^{43} +(14.4893 + 1.45398i) q^{44} +(-6.48402 - 6.48402i) q^{45} +(13.1587 + 36.8830i) q^{46} +55.0421i q^{47} +(-14.0765 + 9.33094i) q^{48} +(45.6937 - 17.6941i) q^{49} +(-15.8925 - 44.5457i) q^{50} +(-15.4575 + 15.4575i) q^{51} +(-84.2973 - 8.45912i) q^{52} +(38.2187 + 38.2187i) q^{53} +(15.2706 - 32.2103i) q^{54} +4.23322 q^{55} +(19.6222 - 52.4497i) q^{56} +15.0732i q^{57} +(-8.77734 + 18.5141i) q^{58} +(32.2679 - 32.2679i) q^{59} +(-3.80080 + 3.10756i) q^{60} +(-32.0297 - 32.0297i) q^{61} +(-30.5861 - 85.7308i) q^{62} +(10.1392 + 54.2620i) q^{63} +(-29.8575 - 56.6085i) q^{64} -24.6286 q^{65} +(2.58243 + 7.23839i) q^{66} +(42.1559 - 42.1559i) q^{67} +(-52.4362 - 64.1338i) q^{68} +(-14.6139 + 14.6139i) q^{69} +(4.15332 - 15.7406i) q^{70} -15.7491i q^{71} +(54.0219 + 32.5824i) q^{72} +65.7339 q^{73} +(88.3762 + 41.8983i) q^{74} +(17.6500 - 17.6500i) q^{75} +(-56.8360 - 5.70341i) q^{76} +(-21.0228 - 14.4032i) q^{77} +(-15.0244 - 42.1123i) q^{78} -96.5103 q^{79} +(-10.2794 - 15.5074i) q^{80} -52.1600 q^{81} +(-116.006 + 41.3872i) q^{82} +(-31.6530 - 31.6530i) q^{83} +(29.4486 - 2.50064i) q^{84} +(-17.0287 - 17.0287i) q^{85} +(42.5340 + 20.1650i) q^{86} -10.8134 q^{87} +(-28.2707 + 6.99861i) q^{88} +89.3246 q^{89} +(16.5716 + 7.85642i) q^{90} +(122.309 + 83.7968i) q^{91} +(-49.5743 - 60.6335i) q^{92} +(33.9684 - 33.9684i) q^{93} +(-36.9909 - 103.683i) q^{94} -16.6054 q^{95} +(20.2452 - 27.0369i) q^{96} +47.6196i q^{97} +(-74.1823 + 64.0389i) q^{98} +(20.3000 - 20.3000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8}+O(q^{10}) \) 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8	\( 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8} + 40 q^{14} - 8 q^{15} + 48 q^{16} + 196 q^{18} - 20 q^{21} - 120 q^{22} - 96 q^{29} - 40 q^{30} - 184 q^{32} - 100 q^{35} + 160 q^{36} - 128 q^{37} - 144 q^{42} - 72 q^{43} - 448 q^{44} - 168 q^{46} + 192 q^{49} - 364 q^{50} - 128 q^{51} + 88 q^{53} + 56 q^{56} + 408 q^{58} + 504 q^{60} + 444 q^{63} + 256 q^{64} - 8 q^{65} + 440 q^{67} - 112 q^{70} + 592 q^{72} - 408 q^{74} + 12 q^{77} + 664 q^{78} - 8 q^{79} + 64 q^{81} - 576 q^{84} + 96 q^{85} + 256 q^{86} + 448 q^{88} - 388 q^{91} - 1192 q^{92} + 32 q^{93} - 776 q^{95} + 540 q^{98} + 8 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8 + 40 * q^14 - 8 * q^15 + 48 * q^16 + 196 * q^18 - 20 * q^21 - 120 * q^22 - 96 * q^29 - 40 * q^30 - 184 * q^32 - 100 * q^35 + 160 * q^36 - 128 * q^37 - 144 * q^42 - 72 * q^43 - 448 * q^44 - 168 * q^46 + 192 * q^49 - 364 * q^50 - 128 * q^51 + 88 * q^53 + 56 * q^56 + 408 * q^58 + 504 * q^60 + 444 * q^63 + 256 * q^64 - 8 * q^65 + 440 * q^67 - 112 * q^70 + 592 * q^72 - 408 * q^74 + 12 * q^77 + 664 * q^78 - 8 * q^79 + 64 * q^81 - 576 * q^84 + 96 * q^85 + 256 * q^86 + 448 * q^88 - 388 * q^91 - 1192 * q^92 + 32 * q^93 - 776 * q^95 + 540 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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