LMFDB - Embedded newform 640.2.bm.a.461.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			461.35
Character	$\chi$	$=$	640.461
Dual form			640.2.bm.a.261.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.219023 - 1.39715i) q^{2} +(-2.20974 + 0.670316i) q^{3} +(-1.90406 - 0.612016i) q^{4} +(0.995185 - 0.0980171i) q^{5} +(0.452549 + 3.23415i) q^{6} +(1.02738 - 1.53758i) q^{7} +(-1.27211 + 2.52621i) q^{8} +(1.93920 - 1.29573i) q^{9} +O(q^{10})$	\(q+(0.219023 - 1.39715i) q^{2} +(-2.20974 + 0.670316i) q^{3} +(-1.90406 - 0.612016i) q^{4} +(0.995185 - 0.0980171i) q^{5} +(0.452549 + 3.23415i) q^{6} +(1.02738 - 1.53758i) q^{7} +(-1.27211 + 2.52621i) q^{8} +(1.93920 - 1.29573i) q^{9} +(0.0810236 - 1.41189i) q^{10} +(1.19733 + 2.24005i) q^{11} +(4.61771 + 0.0760732i) q^{12} +(0.654048 - 6.64066i) q^{13} +(-1.92321 - 1.77217i) q^{14} +(-2.13339 + 0.883680i) q^{15} +(3.25087 + 2.33063i) q^{16} +(-6.42807 - 2.66259i) q^{17} +(-1.38560 - 2.99315i) q^{18} +(-1.42040 - 1.73076i) q^{19} +(-1.95488 - 0.422439i) q^{20} +(-1.23957 + 4.08632i) q^{21} +(3.39193 - 1.18223i) q^{22} +(-1.43133 + 7.19578i) q^{23} +(1.11767 - 6.43497i) q^{24} +(0.980785 - 0.195090i) q^{25} +(-9.13474 - 2.36826i) q^{26} +(0.978193 - 1.19193i) q^{27} +(-2.89722 + 2.29887i) q^{28} +(-5.54292 - 2.96275i) q^{29} +(0.767372 + 3.17422i) q^{30} +(-4.44482 + 4.44482i) q^{31} +(3.96825 - 4.03150i) q^{32} +(-4.14733 - 4.14733i) q^{33} +(-5.12794 + 8.39781i) q^{34} +(0.871723 - 1.63088i) q^{35} +(-4.48536 + 1.28033i) q^{36} +(3.53891 + 2.90431i) q^{37} +(-2.72923 + 1.60543i) q^{38} +(3.00607 + 15.1125i) q^{39} +(-1.01837 + 2.63873i) q^{40} +(-10.3869 - 2.06608i) q^{41} +(5.43771 + 2.62687i) q^{42} +(-10.7916 - 3.27360i) q^{43} +(-0.908842 - 4.99797i) q^{44} +(1.80286 - 1.47957i) q^{45} +(9.74009 + 3.57582i) q^{46} +(0.240365 - 0.580292i) q^{47} +(-8.74583 - 2.97096i) q^{48} +(1.37013 + 3.30779i) q^{49} +(-0.0577560 - 1.41303i) q^{50} +(15.9891 + 1.57479i) q^{51} +(-5.30953 + 12.2439i) q^{52} +(2.18855 - 1.16981i) q^{53} +(-1.45106 - 1.62774i) q^{54} +(1.41113 + 2.11190i) q^{55} +(2.57731 + 4.55135i) q^{56} +(4.29885 + 2.87240i) q^{57} +(-5.35343 + 7.09538i) q^{58} +(0.446530 + 4.53370i) q^{59} +(4.60293 - 0.376908i) q^{60} +(-2.30386 - 7.59480i) q^{61} +(5.23657 + 7.18361i) q^{62} -4.31289i q^{63} +(-4.76347 - 6.42724i) q^{64} -6.67279i q^{65} +(-6.70280 + 4.88608i) q^{66} +(-3.38209 - 11.1493i) q^{67} +(10.6099 + 9.00381i) q^{68} +(-1.66059 - 16.8602i) q^{69} +(-2.08766 - 1.57513i) q^{70} +(-5.99584 - 4.00629i) q^{71} +(0.806413 + 6.54714i) q^{72} +(-5.20691 - 7.79269i) q^{73} +(4.83286 - 4.30828i) q^{74} +(-2.03650 + 1.08853i) q^{75} +(1.64527 + 4.16477i) q^{76} +(4.67438 + 0.460386i) q^{77} +(21.7728 - 0.889938i) q^{78} +(0.656292 + 1.58443i) q^{79} +(3.46366 + 2.00076i) q^{80} +(-4.04012 + 9.75372i) q^{81} +(-5.16158 + 14.0595i) q^{82} +(-3.46124 + 2.84056i) q^{83} +(4.86111 - 7.02195i) q^{84} +(-6.65810 - 2.01971i) q^{85} +(-6.93731 + 14.3605i) q^{86} +(14.2344 + 2.83139i) q^{87} +(-7.18197 + 0.175119i) q^{88} +(2.62909 + 13.2173i) q^{89} +(-1.67231 - 2.84292i) q^{90} +(-9.53860 - 7.82813i) q^{91} +(7.12927 - 12.8252i) q^{92} +(6.84245 - 12.8013i) q^{93} +(-0.758109 - 0.462923i) q^{94} +(-1.58320 - 1.58320i) q^{95} +(-6.06641 + 11.5685i) q^{96} +(9.89082 - 9.89082i) q^{97} +(4.92158 - 1.18980i) q^{98} +(5.22437 + 2.79248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{31}{32}\right)$	$1$

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 $

$2$	0.219023	−	1.39715i	0.154873	−	0.987934i
$2$	0.219023	−	1.39715i	0.154873	−	0.987934i
$3$	−2.20974	+	0.670316i	−1.27579	+	0.387007i	−0.854279	−	0.519815i	$-0.826001\pi$
$3$	−2.20974	+	0.670316i	−1.27579	+	0.387007i	−0.421513	+	0.906822i	$0.638501\pi$
$4$	−1.90406	−	0.612016i	−0.952029	−	0.306008i
$5$	0.995185	−	0.0980171i	0.445060	−	0.0438346i
$5$	0.995185	−	0.0980171i	0.445060	−	0.0438346i
$6$	0.452549	+	3.23415i	0.184752	+	1.32034i
$7$	1.02738	−	1.53758i	0.388313	−	0.581152i	−0.584886	−	0.811115i	$-0.698861\pi$
$7$	1.02738	−	1.53758i	0.388313	−	0.581152i	0.973199	+	0.229964i	$0.0738608\pi$
$8$	−1.27211	+	2.52621i	−0.449759	+	0.893150i
$9$	1.93920	−	1.29573i	0.646400	−	0.431910i
$10$	0.0810236	−	1.41189i	0.0256219	−	0.446479i
$11$	1.19733	+	2.24005i	0.361009	+	0.675400i	0.995209	−	0.0977685i	$-0.0311705\pi$
$11$	1.19733	+	2.24005i	0.361009	+	0.675400i	−0.634200	+	0.773169i	$0.718670\pi$
$12$	4.61771	+	0.0760732i	1.33302	+	0.0219604i
$13$	0.654048	−	6.64066i	0.181400	−	1.84179i	−0.286591	−	0.958053i	$-0.592522\pi$
$13$	0.654048	−	6.64066i	0.181400	−	1.84179i	0.467991	−	0.883733i	$-0.344978\pi$
$14$	−1.92321	−	1.77217i	−0.514001	−	0.473632i
$15$	−2.13339	+	0.883680i	−0.550840	+	0.228165i
$16$	3.25087	+	2.33063i	0.812718	+	0.582657i
$17$	−6.42807	−	2.66259i	−1.55904	−	0.645774i	−0.574114	−	0.818775i	$-0.694653\pi$
$17$	−6.42807	−	2.66259i	−1.55904	−	0.645774i	−0.984922	+	0.173001i	$0.944653\pi$
$18$	−1.38560	−	2.99315i	−0.326590	−	0.705492i
$19$	−1.42040	−	1.73076i	−0.325861	−	0.397063i	0.584151	−	0.811645i	$-0.301428\pi$
$19$	−1.42040	−	1.73076i	−0.325861	−	0.397063i	−0.910012	+	0.414582i	$0.863928\pi$
$20$	−1.95488	−	0.422439i	−0.437124	−	0.0944602i
$21$	−1.23957	+	4.08632i	−0.270497	+	0.891708i
$22$	3.39193	−	1.18223i	0.723162	−	0.252052i
$23$	−1.43133	+	7.19578i	−0.298453	+	1.50042i	0.482535	+	0.875877i	$0.339716\pi$
$23$	−1.43133	+	7.19578i	−0.298453	+	1.50042i	−0.780987	+	0.624547i	$0.785284\pi$
$24$	1.11767	−	6.43497i	0.228143	−	1.31353i
$25$	0.980785	−	0.195090i	0.196157	−	0.0390181i
$26$	−9.13474	−	2.36826i	−1.79147	−	0.464454i
$27$	0.978193	−	1.19193i	0.188253	−	0.229387i
$28$	−2.89722	+	2.29887i	−0.547522	+	0.434446i
$29$	−5.54292	−	2.96275i	−1.02929	−	0.550169i	−0.131837	−	0.991271i	$-0.542088\pi$
$29$	−5.54292	−	2.96275i	−1.02929	−	0.550169i	−0.897457	+	0.441102i	$0.854588\pi$
$30$	0.767372	+	3.17422i	0.140102	+	0.579530i
$31$	−4.44482	+	4.44482i	−0.798314	+	0.798314i	−0.982830	−	0.184516i	$-0.940928\pi$
$31$	−4.44482	+	4.44482i	−0.798314	+	0.798314i	0.184516	+	0.982830i	$0.440928\pi$
$32$	3.96825	−	4.03150i	0.701495	−	0.712675i
$33$	−4.14733	−	4.14733i	−0.721957	−	0.721957i
$34$	−5.12794	+	8.39781i	−0.879434	+	1.44021i
$35$	0.871723	−	1.63088i	0.147348	−	0.275669i
$36$	−4.48536	+	1.28033i	−0.747559	+	0.213388i
$37$	3.53891	+	2.90431i	0.581793	+	0.477465i	0.878656	−	0.477455i	$-0.158441\pi$
$37$	3.53891	+	2.90431i	0.581793	+	0.477465i	−0.296863	+	0.954920i	$0.595941\pi$
$38$	−2.72923	+	1.60543i	−0.442739	+	0.260435i
$39$	3.00607	+	15.1125i	0.481356	+	2.41994i
$40$	−1.01837	+	2.63873i	−0.161019	+	0.417220i
$41$	−10.3869	−	2.06608i	−1.62216	−	0.322667i	−0.701389	−	0.712779i	$-0.747436\pi$
$41$	−10.3869	−	2.06608i	−1.62216	−	0.322667i	−0.920768	+	0.390112i	$0.872436\pi$
$42$	5.43771	+	2.62687i	0.839057	+	0.405334i
$43$	−10.7916	−	3.27360i	−1.64570	−	0.499219i	−0.674661	−	0.738128i	$-0.735710\pi$
$43$	−10.7916	−	3.27360i	−1.64570	−	0.499219i	−0.971042	+	0.238909i	$0.923210\pi$
$44$	−0.908842	−	4.99797i	−0.137013	−	0.753472i
$45$	1.80286	−	1.47957i	0.268754	−	0.220561i
$46$	9.74009	+	3.57582i	1.43610	+	0.527226i
$47$	0.240365	−	0.580292i	0.0350608	−	0.0846443i	−0.905379	−	0.424604i	$-0.860413\pi$
$47$	0.240365	−	0.580292i	0.0350608	−	0.0846443i	0.940440	+	0.339960i	$0.110413\pi$
$48$	−8.74583	−	2.97096i	−1.26235	−	0.428821i
$49$	1.37013	+	3.30779i	0.195733	+	0.472542i
$50$	−0.0577560	−	1.41303i	−0.00816793	−	0.199833i
$51$	15.9891	+	1.57479i	2.23892	+	0.220515i
$52$	−5.30953	+	12.2439i	−0.736300	+	1.69792i
$53$	2.18855	−	1.16981i	0.300621	−	0.160685i	−0.314189	−	0.949360i	$-0.601733\pi$
$53$	2.18855	−	1.16981i	0.300621	−	0.160685i	0.614810	+	0.788675i	$0.289233\pi$
$54$	−1.45106	−	1.62774i	−0.197464	−	0.221508i
$55$	1.41113	+	2.11190i	0.190277	+	0.284769i
$56$	2.57731	+	4.55135i	0.344408	+	0.608200i
$57$	4.29885	+	2.87240i	0.569397	+	0.380459i
$58$	−5.35343	+	7.09538i	−0.702940	+	0.931669i
$59$	0.446530	+	4.53370i	0.0581333	+	0.590237i	0.979486	+	0.201510i	$0.0645850\pi$
$59$	0.446530	+	4.53370i	0.0581333	+	0.590237i	−0.921353	+	0.388727i	$0.872915\pi$
$60$	4.60293	−	0.376908i	0.594236	−	0.0486586i
$61$	−2.30386	−	7.59480i	−0.294979	−	0.972415i	−0.971709	−	0.236183i	$-0.924103\pi$
$61$	−2.30386	−	7.59480i	−0.294979	−	0.972415i	0.676730	−	0.736232i	$-0.263397\pi$
$62$	5.23657	+	7.18361i	0.665045	+	0.912319i
$63$		−	4.31289i		−	0.543373i
$64$	−4.76347	−	6.42724i	−0.595434	−	0.803405i
$65$		−	6.67279i		−	0.827657i
$66$	−6.70280	+	4.88608i	−0.825058	+	0.601435i
$67$	−3.38209	−	11.1493i	−0.413188	−	1.36210i	−0.878834	−	0.477128i	$-0.841678\pi$
$67$	−3.38209	−	11.1493i	−0.413188	−	1.36210i	0.465646	−	0.884971i	$-0.345822\pi$
$68$	10.6099	+	9.00381i	1.28664	+	1.09187i
$69$	−1.66059	−	16.8602i	−0.199911	−	2.02973i
$70$	−2.08766	−	1.57513i	−0.249523	−	0.188264i
$71$	−5.99584	−	4.00629i	−0.711576	−	0.475460i	0.146350	−	0.989233i	$-0.453247\pi$
$71$	−5.99584	−	4.00629i	−0.711576	−	0.475460i	−0.857926	+	0.513773i	$0.828247\pi$
$72$	0.806413	+	6.54714i	0.0950367	+	0.771588i
$73$	−5.20691	−	7.79269i	−0.609422	−	0.912065i	0.390541	−	0.920585i	$-0.372288\pi$
$73$	−5.20691	−	7.79269i	−0.609422	−	0.912065i	−0.999964	+	0.00852046i	$0.997288\pi$
$74$	4.83286	−	4.30828i	0.561808	−	0.500827i
$75$	−2.03650	+	1.08853i	−0.235155	+	0.125693i
$76$	1.64527	+	4.16477i	0.188725	+	0.477732i
$77$	4.67438	+	0.460386i	0.532694	+	0.0524658i
$78$	21.7728	−	0.889938i	2.46529	−	0.100766i
$79$	0.656292	+	1.58443i	0.0738386	+	0.178262i	0.956489	−	0.291767i	$-0.0942433\pi$
$79$	0.656292	+	1.58443i	0.0738386	+	0.178262i	−0.882651	+	0.470030i	$0.844243\pi$
$80$	3.46366	+	2.00076i	0.387249	+	0.223692i
$81$	−4.04012	+	9.75372i	−0.448903	+	1.08375i
$82$	−5.16158	+	14.0595i	−0.570001	+	1.55261i
$83$	−3.46124	+	2.84056i	−0.379920	+	0.311792i	−0.804900	−	0.593410i	$-0.797781\pi$
$83$	−3.46124	+	2.84056i	−0.379920	+	0.311792i	0.424980	+	0.905203i	$0.360281\pi$
$84$	4.86111	−	7.02195i	0.530390	−	0.766158i
$85$	−6.65810	−	2.01971i	−0.722172	−	0.219068i
$86$	−6.93731	+	14.3605i	−0.748070	+	1.54853i
$87$	14.2344	+	2.83139i	1.52608	+	0.303557i
$88$	−7.18197	+	0.175119i	−0.765601	+	0.0186677i
$89$	2.62909	+	13.2173i	0.278683	+	1.40103i	0.825793	+	0.563973i	$0.190728\pi$
$89$	2.62909	+	13.2173i	0.278683	+	1.40103i	−0.547110	+	0.837061i	$0.684272\pi$
$90$	−1.67231	−	2.84292i	−0.176277	−	0.299670i
$91$	−9.53860	−	7.82813i	−0.999917	−	0.820611i
$92$	7.12927	−	12.8252i	0.743277	−	1.33712i
$93$	6.84245	−	12.8013i	0.709529	−	1.32744i
$94$	−0.758109	−	0.462923i	−0.0781930	−	0.0477468i
$95$	−1.58320	−	1.58320i	−0.162433	−	0.162433i
$96$	−6.06641	+	11.5685i	−0.619151	+	1.18071i
$97$	9.89082	−	9.89082i	1.00426	−	1.00426i	0.00426992	−	0.999991i	$-0.498641\pi$
$97$	9.89082	−	9.89082i	1.00426	−	1.00426i	0.999991	−	0.00426992i	$-0.00135916\pi$
$98$	4.92158	−	1.18980i	0.497154	−	0.120188i
$99$	5.22437	+	2.79248i	0.525069	+	0.280655i
$100$	−1.98687	−	0.228793i	−0.198687	−	0.0228793i
$101$	11.2393	−	13.6951i	1.11835	−	1.36272i	0.194079	−	0.980986i	$-0.437828\pi$
$101$	11.2393	−	13.6951i	1.11835	−	1.36272i	0.924273	−	0.381731i	$-0.124672\pi$
$102$	5.70220	−	21.9943i	0.564602	−	2.17776i
$103$	−0.924775	+	0.183949i	−0.0911208	+	0.0181250i	−0.240440	−	0.970664i	$-0.577292\pi$
$103$	−0.924775	+	0.183949i	−0.0911208	+	0.0181250i	0.149319	+	0.988789i	$0.452292\pi$
$104$	15.9437	+	10.0999i	1.56341	+	0.990378i
$105$	−0.833073	+	4.18814i	−0.0812996	+	0.408721i
$106$	−1.15505	−	3.31395i	−0.112188	−	0.321879i
$107$	2.74149	−	9.03749i	0.265030	−	0.873687i	−0.718897	−	0.695117i	$-0.755353\pi$
$107$	2.74149	−	9.03749i	0.265030	−	0.873687i	0.983927	−	0.178570i	$-0.0571473\pi$
$108$	−2.59202	+	1.67084i	−0.249417	+	0.160776i
$109$	7.66578	+	9.34078i	0.734248	+	0.894684i	0.997545	−	0.0700308i	$-0.0223098\pi$
$109$	7.66578	+	9.34078i	0.734248	+	0.894684i	−0.263297	+	0.964715i	$0.584810\pi$
$110$	3.25972	−	1.50900i	0.310802	−	0.143878i
$111$	−9.76686	−	4.04557i	−0.927029	−	0.383988i
$112$	6.92341	−	2.60404i	0.654201	−	0.246059i
$113$	12.5558	−	5.20077i	1.18115	−	0.489248i	0.296285	−	0.955099i	$-0.404252\pi$
$113$	12.5558	−	5.20077i	1.18115	−	0.489248i	0.884863	+	0.465852i	$0.154252\pi$
$114$	4.95473	−	5.37702i	0.464053	−	0.503604i
$115$	−0.719128	+	7.30142i	−0.0670590	+	0.680861i
$116$	8.74078	+	9.03360i	0.811561	+	0.838749i
$117$	−7.33618	−	13.7250i	−0.678230	−	1.26888i
$118$	6.43206	+	0.369114i	0.592119	+	0.0339797i
$119$	−10.6980	+	7.14819i	−0.980686	+	0.655274i
$120$	0.481551	−	6.51354i	0.0439594	−	0.594602i
$121$	2.52705	−	3.78200i	0.229732	−	0.343818i
$122$	−11.1157	+	1.55540i	−1.00637	+	0.140819i
$123$	24.3372	−	2.39700i	2.19441	−	0.216130i
$124$	11.1835	−	5.74290i	1.00431	−	0.515728i
$125$	0.956940	−	0.290285i	0.0855913	−	0.0259639i
$126$	−6.02575	−	0.944621i	−0.536817	−	0.0841535i
$127$	3.18191			0.282348			0.141174	−	0.989985i	$-0.454912\pi$
$127$	3.18191			0.282348			0.141174	+	0.989985i	$0.454912\pi$
$128$	−10.0231	+	5.24757i	−0.885927	+	0.463824i
$129$	26.0409			2.29278
$130$	−9.32289	−	1.46149i	−0.817671	−	0.128181i
$131$	2.05423	−	0.623144i	0.179479	−	0.0544444i	−0.199266	−	0.979945i	$-0.563856\pi$
$131$	2.05423	−	0.623144i	0.179479	−	0.0544444i	0.378745	+	0.925501i	$0.376356\pi$
$132$	5.35852	+	10.4350i	0.466399	+	0.908249i
$133$	−4.12047	+	0.405831i	−0.357290	+	0.0351900i
$134$	−16.3179	+	2.28335i	−1.40966	+	0.197251i
$135$	0.856653	−	1.28207i	0.0737290	−	0.110343i
$136$	14.9035	−	12.8515i	1.27796	−	1.10201i
$137$	−6.84717	+	4.57513i	−0.584993	+	0.390880i	−0.812556	−	0.582884i	$-0.801924\pi$
$137$	−6.84717	+	4.57513i	−0.584993	+	0.390880i	0.227563	+	0.973763i	$0.426924\pi$
$138$	−23.9200	−	1.37269i	−2.03620	−	0.116851i
$139$	−1.20463	−	2.25370i	−0.102175	−	0.191156i	0.825639	−	0.564198i	$-0.190815\pi$
$139$	−1.20463	−	2.25370i	−0.102175	−	0.191156i	−0.927814	+	0.373042i	$0.878315\pi$
$140$	−2.65794	+	2.57178i	−0.224637	+	0.217355i
$141$	−0.142164	+	1.44341i	−0.0119723	+	0.121557i
$142$	−6.91062	+	7.49962i	−0.579926	+	0.629354i
$143$	15.6585	−	6.48597i	1.30943	−	0.542384i
$144$	9.32396	+	0.307293i	0.776996	+	0.0256078i
$145$	−5.80663	−	2.40518i	−0.482214	−	0.199740i
$146$	−12.0280	+	5.56805i	−0.995443	+	0.460815i
$147$	−5.24490	−	6.39093i	−0.432592	−	0.527115i
$148$	−4.96081	−	7.69584i	−0.407776	−	0.632594i
$149$	−4.47228	+	14.7431i	−0.366384	+	1.20781i	0.559126	+	0.829083i	$0.311137\pi$
$149$	−4.47228	+	14.7431i	−0.366384	+	1.20781i	−0.925510	+	0.378723i	$0.876363\pi$
$150$	1.07480	+	3.08372i	0.0877574	+	0.251784i
$151$	−1.17539	+	5.90910i	−0.0956521	+	0.480876i	0.903031	+	0.429575i	$0.141337\pi$
$151$	−1.17539	+	5.90910i	−0.0956521	+	0.480876i	−0.998683	+	0.0513006i	$0.983663\pi$
$152$	6.17916	−	1.38650i	0.501196	−	0.112460i
$153$	−15.9153	+	3.16575i	−1.28668	+	0.255936i
$154$	1.66702	−	6.42997i	0.134333	−	0.518142i
$155$	−3.98775	+	4.85909i	−0.320304	+	0.390291i
$156$	3.52538	−	30.6149i	0.282256	−	2.45115i
$157$	−6.20264	−	3.31538i	−0.495024	−	0.264596i	0.204939	−	0.978775i	$-0.434300\pi$
$157$	−6.20264	−	3.31538i	−0.495024	−	0.264596i	−0.699963	+	0.714179i	$0.746800\pi$
$158$	2.35743	−	0.569912i	0.187547	−	0.0453398i
$159$	−4.05198	+	4.05198i	−0.321343	+	0.321343i
$160$	3.55399	−	4.40104i	0.280968	−	0.347933i
$161$	9.59358	+	9.59358i	0.756080	+	0.756080i
$162$	12.7425	+	7.78095i	1.00115	+	0.611329i
$163$	−3.00042	+	5.61339i	−0.235011	+	0.439675i	−0.971588	−	0.236679i	$-0.923941\pi$
$163$	−3.00042	+	5.61339i	−0.235011	+	0.439675i	0.736577	+	0.676354i	$0.236441\pi$
$164$	18.5127	+	10.2909i	1.44560	+	0.803581i
$165$	−4.53387	−	3.72085i	−0.352961	−	0.289668i
$166$	3.21060	+	5.45802i	0.249191	+	0.423624i
$167$	−0.738896	−	3.71468i	−0.0571775	−	0.287451i	0.941609	−	0.336710i	$-0.109314\pi$
$167$	−0.738896	−	3.71468i	−0.0571775	−	0.287451i	−0.998786	+	0.0492589i	$0.984314\pi$
$168$	−8.74603	−	8.32967i	−0.674771	−	0.642648i
$169$	−30.9203	−	6.15044i	−2.37849	−	0.473110i
$170$	−4.28012	+	8.86000i	−0.328270	+	0.679531i
$171$	−4.99703	−	1.51583i	−0.382132	−	0.115919i
$172$	18.5443	+	12.8377i	1.41399	+	0.978869i
$173$	−2.99735	+	2.45986i	−0.227884	+	0.187020i	−0.741406	−	0.671057i	$-0.765841\pi$
$173$	−2.99735	+	2.45986i	−0.227884	+	0.187020i	0.513522	+	0.858077i	$0.328341\pi$
$174$	7.07353	−	19.2674i	0.536243	−	1.46066i
$175$	0.707671	−	1.70847i	0.0534949	−	0.129148i
$176$	−1.32835	+	10.0727i	−0.100128	+	0.759255i
$177$	−4.02572	−	9.71895i	−0.302592	−	0.730521i
$178$	19.0424	−	0.778335i	1.42729	−	0.0583387i
$179$	−4.17177	−	0.410884i	−0.311813	−	0.0307109i	−0.0590996	−	0.998252i	$-0.518823\pi$
$179$	−4.17177	−	0.410884i	−0.311813	−	0.0307109i	−0.252713	+	0.967541i	$0.581323\pi$
$180$	−4.33826	+	1.71380i	−0.323355	+	0.127739i
$181$	−10.2918	+	5.50106i	−0.764980	+	0.408890i	−0.807245	−	0.590216i	$-0.799043\pi$
$181$	−10.2918	+	5.50106i	−0.764980	+	0.408890i	0.0422653	+	0.999106i	$0.486543\pi$
$182$	−13.0262	+	11.6123i	−0.965569	+	0.860762i
$183$	10.1818	+	15.2382i	0.752663	+	1.12644i
$184$	−16.3572	−	12.7697i	−1.20587	−	0.941392i
$185$	3.80654	+	2.54345i	0.279862	+	0.186998i
$186$	−16.3867	−	12.3637i	−1.20153	−	0.906552i
$187$	−1.73219	−	17.5872i	−0.126670	−	1.28610i
$188$	−0.812816	+	0.957802i	−0.0592807	+	0.0698549i
$189$	−0.827718	−	2.72862i	−0.0602076	−	0.198478i
$190$	−2.55873	+	1.86521i	−0.185630	+	0.135317i
$191$		−	15.0823i		−	1.09132i	−0.838008	−	0.545658i	$-0.816280\pi$
$191$		−	15.0823i		−	1.09132i	0.838008	−	0.545658i	$-0.183720\pi$
$192$	14.8343	+	11.0095i	1.07057	+	0.794540i
$193$			6.68619i			0.481282i	0.970614	+	0.240641i	$0.0773577\pi$
$193$			6.68619i			0.481282i	−0.970614	+	0.240641i	$0.922642\pi$
$194$	−11.6526	−	15.9853i	−0.836611	−	1.14768i
$195$	4.47288	+	14.7451i	0.320309	+	1.05592i
$196$	−0.584390	−	7.13678i	−0.0417421	−	0.509770i
$197$	−0.444551	−	4.51360i	−0.0316729	−	0.321581i	−0.997946	−	0.0640610i	$-0.979595\pi$
$197$	−0.444551	−	4.51360i	−0.0316729	−	0.321581i	0.966273	−	0.257520i	$-0.0829052\pi$
$198$	5.04577	−	6.68761i	0.358588	−	0.475268i
$199$	15.9296	+	10.6438i	1.12922	+	0.754520i	0.972449	−	0.233115i	$-0.0748920\pi$
$199$	15.9296	+	10.6438i	1.12922	+	0.754520i	0.156770	+	0.987635i	$0.449892\pi$
$200$	−0.754829	+	2.72585i	−0.0533744	+	0.192746i
$201$	14.9471	+	22.3698i	1.05428	+	1.57785i
$202$	−16.6725	−	18.7026i	−1.17307	−	1.31591i
$203$	−10.2502	+	5.47882i	−0.719420	+	0.384538i
$204$	−29.4804	−	12.7841i	−2.06404	−	0.895065i
$205$	−10.5394	−	1.03804i	−0.736101	−	0.0724996i
$206$	0.0544577	+	1.33234i	0.00379425	+	0.0928284i
$207$	6.54816	+	15.8087i	0.455129	+	1.09878i
$208$	17.6031	−	20.0636i	1.22056	−	1.39116i
$209$	2.17630	−	5.25405i	0.150538	−	0.363430i
$210$	5.66900	+	2.08123i	0.391198	+	0.143618i
$211$	12.5320	−	10.2847i	0.862735	−	0.708028i	−0.0950627	−	0.995471i	$-0.530305\pi$
$211$	12.5320	−	10.2847i	0.862735	−	0.708028i	0.957798	+	0.287443i	$0.0928051\pi$
$212$	−4.88307	+	0.887949i	−0.335371	+	0.0609846i
$213$	15.9347	+	4.83374i	1.09183	+	0.331202i
$214$	−12.0263	−	5.80969i	−0.822100	−	0.397143i
$215$	−11.0605	−	2.20007i	−0.754320	−	0.150044i
$216$	1.76670	+	3.98739i	0.120209	+	0.271308i
$217$	2.26776	+	11.4008i	0.153946	+	0.773937i
$218$	14.7295	−	8.66440i	0.997604	−	0.586827i
$219$	16.7294	+	13.7295i	1.13047	+	0.927754i
$220$	−1.39435	−	4.88482i	−0.0940072	−	0.329335i
$221$	−21.8856	+	40.9451i	−1.47219	+	2.75427i
$222$	−7.79143	+	12.7597i	−0.522926	+	0.856375i
$223$	−18.7667	−	18.7667i	−1.25671	−	1.25671i	−0.952654	−	0.304057i	$-0.901659\pi$
$223$	−18.7667	−	18.7667i	−1.25671	−	1.25671i	−0.304057	−	0.952654i	$-0.598341\pi$
$224$	−2.12186	−	10.2434i	−0.141772	−	0.684416i
$225$	1.64915	−	1.64915i	0.109944	−	0.109944i
$226$	−4.51626	−	18.6814i	−0.300417	−	1.24267i
$227$	17.8639	+	9.54845i	1.18567	+	0.633753i	0.941839	−	0.336066i	$-0.109096\pi$
$227$	17.8639	+	9.54845i	1.18567	+	0.633753i	0.243829	+	0.969818i	$0.421596\pi$
$228$	−6.42731	−	8.10019i	−0.425659	−	0.536448i
$229$	0.356896	−	0.434879i	0.0235843	−	0.0287376i	−0.761085	−	0.648652i	$-0.775333\pi$
$229$	0.356896	−	0.434879i	0.0235843	−	0.0287376i	0.784669	+	0.619915i	$0.212833\pi$
$230$	10.0437	+	2.60391i	0.662261	+	0.171697i
$231$	−10.6377	+	2.11598i	−0.699912	+	0.139221i
$232$	14.5357	−	10.2336i	0.954318	−	0.671870i
$233$	−2.39683	+	12.0497i	−0.157021	+	0.789399i	0.819349	+	0.573295i	$0.194335\pi$
$233$	−2.39683	+	12.0497i	−0.157021	+	0.789399i	−0.976370	+	0.216104i	$0.930665\pi$
$234$	−20.7827	+	7.24365i	−1.35861	+	0.473532i
$235$	0.182329	−	0.601057i	0.0118938	−	0.0392087i
$236$	1.92448	−	8.90570i	0.125273	−	0.579712i
$237$	−2.51230	−	3.06125i	−0.163191	−	0.198849i
$238$	7.64398	+	16.5124i	0.495486	+	1.07034i
$239$	5.99362	+	2.48264i	0.387695	+	0.160589i	0.568013	−	0.823020i	$-0.307713\pi$
$239$	5.99362	+	2.48264i	0.387695	+	0.160589i	−0.180317	+	0.983608i	$0.557713\pi$
$240$	−8.99492	−	2.09941i	−0.580619	−	0.135516i
$241$	22.2349	−	9.20999i	1.43227	−	0.593267i	0.474362	−	0.880330i	$-0.342679\pi$
$241$	22.2349	−	9.20999i	1.43227	−	0.593267i	0.957912	+	0.287062i	$0.0926787\pi$
$242$	−4.73054	−	4.35902i	−0.304091	−	0.280208i
$243$	1.93612	−	19.6578i	0.124202	−	1.26105i
$244$	−0.261462	+	15.8709i	−0.0167384	+	1.01603i
$245$	1.68776	+	3.15757i	0.107827	+	0.201730i
$246$	1.98143	−	34.5277i	0.126331	−	2.20140i
$247$	−12.4224	+	8.30036i	−0.790417	+	0.528140i
$248$	−5.57425	−	16.8829i	−0.353965	−	1.07206i
$249$	5.74434	−	8.59701i	0.364033	−	0.544814i
$250$	−0.195979	−	1.40057i	−0.0123948	−	0.0885797i
$251$	14.8674	−	1.46431i	0.938422	−	0.0924265i	0.382772	−	0.923843i	$-0.374969\pi$
$251$	14.8674	−	1.46431i	0.938422	−	0.0924265i	0.555650	+	0.831416i	$0.312469\pi$
$252$	−2.63956	+	8.21199i	−0.166276	+	0.517306i
$253$	−17.8327	+	5.40948i	−1.12113	+	0.340091i
$254$	0.696910	−	4.44560i	0.0437280	−	0.278942i
$255$	16.0665			1.00612
$256$	5.13635	+	15.1531i	0.321022	+	0.947072i
$257$	−7.04635			−0.439539			−0.219769	−	0.975552i	$-0.570531\pi$
$257$	−7.04635			−0.439539			−0.219769	+	0.975552i	$0.570531\pi$
$258$	5.70356	−	36.3831i	0.355088	−	2.26511i
$259$	8.10142	−	2.45754i	0.503398	−	0.152704i
$260$	−4.08385	+	12.7054i	−0.253270	+	0.787954i
$261$	−14.5877	+	1.43677i	−0.902959	+	0.0889337i
$262$	−0.420702	−	3.00655i	−0.0259911	−	0.185745i
$263$	−6.13479	+	9.18137i	−0.378288	+	0.566147i	−0.970944	−	0.239308i	$-0.923079\pi$
$263$	−6.13479	+	9.18137i	−0.378288	+	0.566147i	0.592656	+	0.805456i	$0.298079\pi$
$264$	15.7529	−	5.20116i	0.969523	−	0.320109i
$265$	2.06335	−	1.37869i	0.126751	−	0.0846922i
$266$	−0.335471	+	5.84580i	−0.0205690	+	0.358429i
$267$	−14.6694	−	27.4445i	−0.897751	−	1.67957i
$268$	−0.383829	+	23.2987i	−0.0234461	+	1.42320i
$269$	2.54212	−	25.8106i	0.154996	−	1.57370i	−0.531814	−	0.846861i	$-0.678490\pi$
$269$	2.54212	−	25.8106i	0.154996	−	1.57370i	0.686810	−	0.726837i	$-0.259010\pi$
$270$	−1.60362	−	1.47768i	−0.0975933	−	0.0899285i
$271$	−25.1001	+	10.3968i	−1.52472	+	0.631560i	−0.978531	−	0.206100i	$-0.933923\pi$
$271$	−25.1001	+	10.3968i	−1.52472	+	0.631560i	−0.546191	+	0.837661i	$0.683923\pi$
$272$	−14.6913	−	23.6372i	−0.890792	−	1.43322i
$273$	26.3251	+	10.9042i	1.59327	+	0.659953i
$274$	4.89246	+	10.5686i	0.295564	+	0.638471i
$275$	1.61134	+	1.96342i	0.0971673	+	0.118399i
$276$	−7.15687	+	33.1191i	−0.430793	+	1.99354i
$277$	1.32422	−	4.36537i	0.0795647	−	0.262290i	−0.908129	−	0.418691i	$-0.862489\pi$
$277$	1.32422	−	4.36537i	0.0795647	−	0.262290i	0.987694	+	0.156401i	$0.0499892\pi$
$278$	−3.41260	+	1.18943i	−0.204674	+	0.0713375i
$279$	−2.86010	+	14.3787i	−0.171230	+	0.860830i
$280$	3.01101	+	4.27681i	0.179943	+	0.255589i
$281$	10.2046	−	2.02983i	0.608757	−	0.121089i	0.118921	−	0.992904i	$-0.462057\pi$
$281$	10.2046	−	2.02983i	0.608757	−	0.121089i	0.489836	+	0.871814i	$0.337057\pi$
$282$	1.98553	+	0.514764i	0.118236	+	0.0306538i
$283$	5.63875	−	6.87084i	0.335189	−	0.408429i	−0.577953	−	0.816070i	$-0.696148\pi$
$283$	5.63875	−	6.87084i	0.335189	−	0.408429i	0.913142	+	0.407641i	$0.133648\pi$
$284$	8.96451	+	11.2978i	0.531946	+	0.670399i
$285$	4.55970	+	2.43721i	0.270093	+	0.144368i
$286$	−5.63230	−	23.2979i	−0.333045	−	1.37763i
$287$	−13.8480	+	13.8480i	−0.817423	+	0.817423i
$288$	2.47150	−	12.9597i	0.145634	−	0.763656i
$289$	22.2099	+	22.2099i	1.30646	+	1.30646i
$290$	−4.63219	+	7.58594i	−0.272011	+	0.445462i
$291$	−15.2261	+	28.4861i	−0.892571	+	1.66988i
$292$	5.14500	+	18.0244i	0.301088	+	1.05480i
$293$	8.77123	+	7.19836i	0.512420	+	0.420533i	0.854744	−	0.519049i	$-0.173714\pi$
$293$	8.77123	+	7.19836i	0.512420	+	0.420533i	−0.342324	+	0.939582i	$0.611214\pi$
$294$	−10.0778	+	5.92815i	−0.587752	+	0.345737i
$295$	0.888760	+	4.46810i	0.0517456	+	0.260143i
$296$	−11.8388	+	5.24543i	−0.688115	+	0.304884i
$297$	3.84121	+	0.764064i	0.222890	+	0.0443355i
$298$	19.6189	+	9.47754i	1.13649	+	0.549019i
$299$	46.8485	+	14.2113i	2.70932	+	0.821864i
$300$	4.54382	−	0.826259i	0.262338	−	0.0477041i
$301$	−16.1205	+	13.2297i	−0.929170	+	0.762550i
$302$	7.99846	+	2.93643i	0.460260	+	0.168973i
$303$	−15.6558	+	37.7965i	−0.899404	+	2.17135i
$304$	−0.583775	−	8.93689i	−0.0334818	−	0.512566i
$305$	−3.03719	−	7.33241i	−0.173909	−	0.419853i
$306$	0.937213	+	22.9295i	0.0535769	+	1.31079i
$307$	6.96746	+	0.686235i	0.397654	+	0.0391655i	0.294868	−	0.955538i	$-0.404724\pi$
$307$	6.96746	+	0.686235i	0.397654	+	0.0391655i	0.102786	+	0.994703i	$0.467224\pi$
$308$	−8.61852	−	3.73739i	−0.491086	−	0.212958i
$309$	1.92020	−	1.02637i	0.109237	−	0.0583882i
$310$	5.91547	+	6.63574i	0.335976	+	0.376885i
$311$	0.367077	+	0.549370i	0.0208150	+	0.0311519i	0.841731	−	0.539897i	$-0.181537\pi$
$311$	0.367077	+	0.549370i	0.0208150	+	0.0311519i	−0.820916	+	0.571049i	$0.806537\pi$
$312$	−42.0014	−	11.6308i	−2.37786	−	0.658467i
$313$	12.4408	+	8.31270i	0.703197	+	0.469861i	0.855053	−	0.518541i	$-0.173525\pi$
$313$	12.4408	+	8.31270i	0.703197	+	0.469861i	−0.151855	+	0.988403i	$0.548525\pi$
$314$	−5.99060	+	7.93987i	−0.338069	+	0.448073i
$315$	−0.422737	−	4.29212i	−0.0238185	−	0.241834i
$316$	−0.279922	−	3.41851i	−0.0157468	−	0.192306i
$317$	2.12266	+	6.99747i	0.119220	+	0.393017i	0.996157	−	0.0875898i	$-0.0279165\pi$
$317$	2.12266	+	6.99747i	0.119220	+	0.393017i	−0.876936	+	0.480607i	$0.840416\pi$
$318$	4.77375	+	6.54871i	0.267699	+	0.367233i
$319$		−	15.9638i		−	0.893802i
$320$	−5.37051	−	5.92939i	−0.300221	−	0.331463i
$321$			21.8081i			1.21721i
$322$	15.5049	−	11.3025i	0.864054	−	0.629862i
$323$	4.52210	+	14.9074i	0.251616	+	0.829468i
$324$	13.6621	−	16.0990i	0.759003	−	0.894391i
$325$	−0.654048	−	6.64066i	−0.0362800	−	0.368357i
$326$	7.18559	+	5.42150i	0.397973	+	0.300269i
$327$	−23.2006	−	15.5022i	−1.28300	−	0.857271i
$328$	18.4326	−	23.6111i	1.01777	−	1.30371i
$329$	−0.645301	−	0.965760i	−0.0355766	−	0.0532441i
$330$	−6.19160	+	5.51954i	−0.340837	+	0.303841i
$331$	12.6228	−	6.74701i	0.693810	−	0.370849i	−0.0864918	−	0.996253i	$-0.527566\pi$
$331$	12.6228	−	6.74701i	0.693810	−	0.370849i	0.780301	+	0.625404i	$0.215066\pi$
$332$	8.32886	−	3.29026i	0.457106	−	0.180577i
$333$	10.6259	+	1.04656i	0.582293	+	0.0573509i
$334$	−5.35180	+	0.218748i	−0.292838	+	0.0119694i
$335$	−4.45862	−	10.7641i	−0.243601	−	0.588104i
$336$	−13.5534	+	10.3951i	−0.739397	+	0.567101i
$337$	3.41135	−	8.23572i	0.185828	−	0.448628i	−0.803321	−	0.595547i	$-0.796935\pi$
$337$	3.41135	−	8.23572i	0.185828	−	0.448628i	0.989149	+	0.146918i	$0.0469355\pi$
$338$	−15.3653	+	41.8533i	−0.835765	+	2.27652i
$339$	−24.2588	+	19.9087i	−1.31756	+	1.08129i
$340$	11.4413	+	7.92051i	0.620492	+	0.429550i
$341$	−15.2786	−	4.63470i	−0.827380	−	0.250983i
$342$	−3.21231	+	6.64960i	−0.173702	+	0.359569i
$343$	19.1896	+	3.81704i	1.03614	+	0.206101i
$344$	21.9979	−	23.0975i	1.18605	−	1.24533i
$345$	−3.30518	−	16.6163i	−0.177945	−	0.894589i
$346$	2.78030	+	4.72651i	0.149470	+	0.254099i
$347$	−8.11220	−	6.65751i	−0.435486	−	0.357394i	0.390963	−	0.920407i	$-0.372142\pi$
$347$	−8.11220	−	6.65751i	−0.435486	−	0.357394i	−0.826448	+	0.563013i	$0.809642\pi$
$348$	−25.3702	−	14.1028i	−1.35998	−	0.755989i
$349$	13.4439	−	25.1518i	0.719637	−	1.34635i	−0.209938	−	0.977715i	$-0.567326\pi$
$349$	13.4439	−	25.1518i	0.719637	−	1.34635i	0.929575	−	0.368632i	$-0.120174\pi$
$350$	−2.23199	−	1.36292i	−0.119305	−	0.0728510i
$351$	−7.27543	−	7.27543i	−0.388333	−	0.388333i
$352$	13.7821	+	4.06205i	0.734587	+	0.216508i
$353$	−9.91676	+	9.91676i	−0.527816	+	0.527816i	−0.919921	−	0.392105i	$-0.871747\pi$
$353$	−9.91676	+	9.91676i	−0.527816	+	0.527816i	0.392105	+	0.919921i	$0.371747\pi$
$354$	−14.4606	+	3.49587i	−0.768570	+	0.185803i
$355$	−6.35966	−	3.39931i	−0.337535	−	0.180416i
$356$	3.08328	−	26.7756i	0.163413	−	1.41910i
$357$	18.8483	−	22.9667i	0.997556	−	1.21553i
$358$	−1.48778	+	5.73860i	−0.0786316	+	0.303294i
$359$	11.8491	−	2.35693i	0.625370	−	0.124394i	0.127775	−	0.991803i	$-0.459217\pi$
$359$	11.8491	−	2.35693i	0.625370	−	0.124394i	0.497595	+	0.867409i	$0.334217\pi$
$360$	1.44426	+	6.43657i	0.0761193	+	0.339237i
$361$	2.72872	−	13.7182i	0.143617	−	0.722010i
$362$	5.43167	+	15.5840i	0.285482	+	0.819076i
$363$	−3.04898	+	10.0511i	−0.160030	+	0.527548i
$364$	13.3711	+	20.7430i	0.700836	+	1.08723i
$365$	−5.94565	−	7.24480i	−0.311210	−	0.379210i
$366$	23.5201	−	10.8880i	1.22942	−	0.569127i
$367$	−14.7560	−	6.11215i	−0.770259	−	0.319052i	−0.0372818	−	0.999305i	$-0.511870\pi$
$367$	−14.7560	−	6.11215i	−0.770259	−	0.319052i	−0.732977	+	0.680253i	$0.761870\pi$
$368$	−21.4238	+	20.0567i	−1.11679	+	1.04553i
$369$	−22.8193	+	9.45206i	−1.18792	+	0.492055i
$370$	4.38730	−	4.76124i	0.228085	−	0.247525i
$371$	0.449802	−	4.56691i	0.0233525	−	0.237102i
$372$	−20.8630	+	20.1868i	−1.08170	+	1.04664i
$373$	0.886316	+	1.65818i	0.0458917	+	0.0858573i	0.903822	−	0.427909i	$-0.140750\pi$
$373$	0.886316	+	1.65818i	0.0458917	+	0.0858573i	−0.857930	+	0.513767i	$0.828250\pi$
$374$	−24.9514	−	1.43187i	−1.29020	−	0.0740404i
$375$	−1.92000	+	1.28290i	−0.0991485	+	0.0662489i
$376$	1.16017	+	1.34541i	0.0598311	+	0.0693841i
$377$	−23.2999	+	34.8708i	−1.20001	+	1.79594i
$378$	−3.99358	+	0.558816i	−0.205408	+	0.0287424i
$379$	−18.9045	+	1.86193i	−0.971060	+	0.0956411i	−0.571090	−	0.820887i	$-0.693479\pi$
$379$	−18.9045	+	1.86193i	−0.971060	+	0.0956411i	−0.399970	+	0.916528i	$0.630979\pi$
$380$	2.04556	+	3.98345i	0.104935	+	0.204347i
$381$	−7.03117	+	2.13288i	−0.360218	+	0.109271i
$382$	−21.0722	−	3.30337i	−1.07815	−	0.169015i
$383$	−15.3516			−0.784431			−0.392216	−	0.919873i	$-0.628291\pi$
$383$	−15.3516			−0.784431			−0.392216	+	0.919873i	$0.628291\pi$
$384$	18.6309	−	18.3144i	0.950755	−	0.934603i
$385$	4.69699			0.239381
$386$	9.34161	+	1.46443i	0.475475	+	0.0745374i
$387$	−25.1688	+	7.63486i	−1.27940	+	0.388102i
$388$	−24.8860	+	12.7794i	−1.26340	+	0.648773i
$389$	3.67940	−	0.362389i	0.186553	−	0.0183739i	−0.00430913	−	0.999991i	$-0.501372\pi$
$389$	3.67940	−	0.362389i	0.186553	−	0.0183739i	0.190862	+	0.981617i	$0.438872\pi$
$390$	21.5808	−	3.01977i	1.09279	−	0.152912i
$391$	28.3601	−	42.4439i	1.43423	−	2.14648i
$392$	−10.0991	−	0.746637i	−0.510084	−	0.0377109i
$393$	−4.12160	+	2.75397i	−0.207907	+	0.138919i
$394$	−6.40354	−	0.367478i	−0.322606	−	0.0185133i
$395$	0.808433	+	1.51247i	0.0406767	+	0.0761007i
$396$	−8.23845	−	8.51444i	−0.413998	−	0.427867i
$397$	1.10694	−	11.2390i	0.0555558	−	0.564067i	−0.926607	−	0.376032i	$-0.877288\pi$
$397$	1.10694	−	11.2390i	0.0555558	−	0.564067i	0.982162	−	0.188035i	$-0.0602118\pi$
$398$	18.3599	−	19.9248i	0.920301	−	0.998740i
$399$	8.83311	−	3.65879i	0.442209	−	0.183169i
$400$	3.64309	+	1.65163i	0.182155	+	0.0825816i
$401$	−0.387877	−	0.160664i	−0.0193696	−	0.00802316i	0.372978	−	0.927840i	$-0.378337\pi$
$401$	−0.387877	−	0.160664i	−0.0193696	−	0.00802316i	−0.392347	+	0.919817i	$0.628337\pi$
$402$	34.5278	−	15.9838i	1.72209	−	0.797198i
$403$	26.6094	+	32.4237i	1.32551	+	1.61514i
$404$	−29.7819	+	19.1977i	−1.48171	+	0.955121i
$405$	−3.06464	+	10.1028i	−0.152283	+	0.502010i
$406$	5.40972	+	15.5210i	0.268480	+	0.770294i
$407$	−2.26855	+	11.4048i	−0.112448	+	0.565313i
$408$	−24.3182	+	38.3885i	−1.20393	+	1.90052i
$409$	−15.6451	+	3.11201i	−0.773601	+	0.153879i	−0.566079	−	0.824351i	$-0.691540\pi$
$409$	−15.6451	+	3.11201i	−0.773601	+	0.153879i	−0.207523	+	0.978230i	$0.566540\pi$
$410$	−3.75866	+	14.4977i	−0.185627	+	0.715992i
$411$	12.0636	−	14.6996i	0.595056	−	0.725078i
$412$	1.87340	+	0.215727i	0.0922960	+	0.0106281i
$413$	7.42969	+	3.97125i	0.365591	+	0.195412i
$414$	23.5213	−	5.68631i	1.15601	−	0.279467i
$415$	−3.16615	+	3.16615i	−0.155420	+	0.155420i
$416$	−24.1764	−	28.9886i	−1.18534	−	1.42128i
$417$	4.17260	+	4.17260i	0.204333	+	0.204333i
$418$	−6.86404	−	4.19137i	−0.335731	−	0.205007i
$419$	1.70670	−	3.19302i	0.0833780	−	0.155989i	−0.836777	−	0.547544i	$-0.815563\pi$
$419$	1.70670	−	3.19302i	0.0833780	−	0.155989i	0.920155	+	0.391555i	$0.128063\pi$
$420$	4.14943	−	7.46461i	0.202471	−	0.364236i
$421$	−12.4157	−	10.1893i	−0.605102	−	0.496594i	0.281233	−	0.959640i	$-0.409257\pi$
$421$	−12.4157	−	10.1893i	−0.605102	−	0.496594i	−0.886335	+	0.463045i	$0.846757\pi$
$422$	−11.6245	−	19.7616i	−0.565872	−	0.961980i
$423$	−0.285787	−	1.43675i	−0.0138955	−	0.0698571i
$424$	0.171093	+	7.01686i	0.00830901	+	0.340769i
$425$	−6.82400	−	1.35738i	−0.331013	−	0.0658425i
$426$	10.2435	−	21.2045i	0.496301	−	1.02736i
$427$	−14.0446	−	4.26037i	−0.679665	−	0.206174i
$428$	−10.7510	+	15.5301i	−0.519672	+	0.750674i
$429$	−30.2535	+	24.8284i	−1.46065	+	1.19873i
$430$	−5.49633	+	14.9713i	−0.265057	+	0.721981i
$431$	−5.73826	+	13.8534i	−0.276402	+	0.667294i	−0.999731	−	0.0232104i	$-0.992611\pi$
$431$	−5.73826	+	13.8534i	−0.276402	+	0.667294i	0.723329	+	0.690504i	$0.242611\pi$
$432$	5.95793	−	1.59501i	0.286651	−	0.0767402i
$433$	−3.33922	−	8.06160i	−0.160473	−	0.387416i	0.823108	−	0.567885i	$-0.192238\pi$
$433$	−3.33922	−	8.06160i	−0.160473	−	0.387416i	−0.983581	+	0.180469i	$0.942238\pi$
$434$	16.4253	−	0.671365i	0.788441	−	0.0322265i
$435$	14.4433	+	1.42255i	0.692505	+	0.0682058i
$436$	−8.87938	−	22.4770i	−0.425245	−	1.07645i
$437$	14.4872	−	7.74357i	0.693017	−	0.370425i
$438$	22.8463	−	20.3665i	1.09164	−	0.973148i
$439$	6.30844	+	9.44124i	0.301085	+	0.450606i	0.950905	−	0.309482i	$-0.100156\pi$
$439$	6.30844	+	9.44124i	0.301085	+	0.450606i	−0.649820	+	0.760088i	$0.725156\pi$
$440$	−7.13023	+	0.878232i	−0.339920	+	0.0418681i
$441$	6.94298	+	4.63915i	0.330618	+	0.220912i
$442$	52.4131	+	39.5454i	2.49303	+	1.88098i
$443$	0.423572	+	4.30059i	0.0201245	+	0.204327i	0.999989	+	0.00466440i	$0.00148473\pi$
$443$	0.423572	+	4.30059i	0.0201245	+	0.204327i	−0.979865	+	0.199663i	$0.936015\pi$
$444$	16.1207	+	13.6805i	0.765055	+	0.649246i
$445$	3.91195	+	12.8960i	0.185444	+	0.611328i
$446$	−30.3302	+	22.1096i	−1.43618	+	1.04692i
$447$		−	35.5763i		−	1.68270i
$448$	−14.7763	+	0.721013i	−0.698114	+	0.0340646i
$449$		−	23.1886i		−	1.09434i	−0.837022	−	0.547169i	$-0.815706\pi$
$449$		−	23.1886i		−	1.09434i	0.837022	−	0.547169i	$-0.184294\pi$
$450$	−1.94291	−	2.66532i	−0.0915898	−	0.125644i
$451$	−7.80841	−	25.7409i	−0.367684	−	1.21209i
$452$	−27.0899	+	2.21824i	−1.27420	+	0.104337i
$453$	−1.36366	−	13.8454i	−0.0640702	−	0.650515i
$454$	17.2532	−	22.8672i	0.809734	−	1.07321i
$455$	−10.2600	−	6.85549i	−0.480994	−	0.321390i
$456$	−12.7249	+	7.20579i	−0.595899	+	0.337442i
$457$	5.07406	+	7.59386i	0.237354	+	0.355226i	0.930955	−	0.365134i	$-0.118977\pi$
$457$	5.07406	+	7.59386i	0.237354	+	0.355226i	−0.693601	+	0.720360i	$0.743977\pi$
$458$	−0.529422	−	0.593885i	−0.0247383	−	0.0277504i
$459$	−9.46152	+	5.05729i	−0.441626	+	0.236054i
$460$	5.83785	−	13.4622i	0.272191	−	0.627679i
$461$	−0.499393	−	0.0491859i	−0.0232590	−	0.00229082i	0.0863809	−	0.996262i	$-0.472470\pi$
$461$	−0.499393	−	0.0491859i	−0.0232590	−	0.00229082i	−0.109640	+	0.993971i	$0.534970\pi$
$462$	0.626430	+	15.3260i	0.0291441	+	0.713028i
$463$	−13.5518	−	32.7169i	−0.629805	−	1.52048i	−0.839865	−	0.542795i	$-0.817366\pi$
$463$	−13.5518	−	32.7169i	−0.629805	−	1.52048i	0.210060	−	0.977688i	$-0.432634\pi$
$464$	−11.1142	−	22.5500i	−0.515966	−	1.04686i
$465$	5.55475	−	13.4104i	0.257595	−	0.621890i
$466$	16.3102	+	5.98788i	0.755556	+	0.277383i
$467$	5.56714	−	4.56883i	0.257616	−	0.211420i	−0.496716	−	0.867913i	$-0.665461\pi$
$467$	5.56714	−	4.56883i	0.257616	−	0.211420i	0.754332	+	0.656493i	$0.227961\pi$
$468$	5.56857	+	30.6231i	0.257407	+	1.41555i
$469$	−20.6176	−	6.25428i	−0.952032	−	0.288796i
$470$	−0.799833	−	0.386386i	−0.0368936	−	0.0178227i
$471$	15.9285	+	3.16838i	0.733948	+	0.145991i
$472$	−12.0211	−	4.63934i	−0.553316	−	0.213543i
$473$	−5.58810	−	28.0933i	−0.256941	−	1.29173i
$474$	−4.82727	+	2.83958i	−0.221724	+	0.130426i
$475$	−1.73076	−	1.42040i	−0.0794126	−	0.0651722i
$476$	24.7445	−	7.06321i	1.13416	−	0.323742i
$477$	2.72829	−	5.10426i	0.124920	−	0.233708i
$478$	4.78136	−	7.83023i	0.218694	−	0.358147i
$479$	−21.9632	−	21.9632i	−1.00352	−	1.00352i	−0.999994	−	0.00352958i	$-0.998876\pi$
$479$	−21.9632	−	21.9632i	−1.00352	−	1.00352i	−0.00352958	−	0.999994i	$-0.501124\pi$
$480$	−4.90329	+	12.1074i	−0.223803	+	0.552626i
$481$	21.6011	−	21.6011i	0.984927	−	0.984927i
$482$	−7.99779	−	33.0827i	−0.364289	−	1.50687i
$483$	−27.6300	−	14.7686i	−1.25721	−	0.671992i
$484$	−7.12630	+	5.65455i	−0.323923	+	0.257025i
$485$	8.87372	−	10.8127i	0.402935	−	0.490978i
$486$	−27.0408	−	7.01056i	−1.22660	−	0.318005i
$487$	−16.9483	+	3.37124i	−0.768003	+	0.152765i	−0.563517	−	0.826104i	$-0.690552\pi$
$487$	−16.9483	+	3.37124i	−0.768003	+	0.152765i	−0.204486	+	0.978870i	$0.565552\pi$
$488$	22.1168	+	3.84140i	1.00118	+	0.173892i
$489$	2.86739	−	14.4153i	0.129668	−	0.651885i
$490$	4.78126	−	1.66647i	0.215995	−	0.0752834i
$491$	−5.85726	+	19.3088i	−0.264335	+	0.871394i	0.719832	+	0.694148i	$0.244219\pi$
$491$	−5.85726	+	19.3088i	−0.264335	+	0.871394i	−0.984167	+	0.177246i	$0.943281\pi$
$492$	−47.8064	−	10.3307i	−2.15528	−	0.465744i
$493$	27.7417	+	33.8033i	1.24942	+	1.52242i
$494$	8.87607	+	19.1739i	0.399353	+	0.862674i
$495$	5.47292	+	2.26696i	0.245990	+	0.101892i
$496$	−24.8088	+	4.09033i	−1.11395	+	0.183661i
$497$	−12.3200	+	5.10312i	−0.552628	+	0.228906i
$498$	−10.7532	−	9.90865i	−0.481861	−	0.444017i
$499$	2.97910	−	30.2473i	0.133363	−	1.35406i	−0.662719	−	0.748868i	$-0.730598\pi$
$499$	2.97910	−	30.2473i	0.133363	−	1.35406i	0.796082	−	0.605189i	$-0.206902\pi$
$500$	−1.99973	−	0.0329440i	−0.0894306	−	0.00147330i
$501$	4.12277	+	7.71317i	0.184192	+	0.344599i
$502$	1.21044	−	21.0927i	0.0540246	−	0.941414i
$503$	18.6736	−	12.4773i	0.832616	−	0.556336i	−0.0646083	−	0.997911i	$-0.520580\pi$
$503$	18.6736	−	12.4773i	0.832616	−	0.556336i	0.897225	+	0.441574i	$0.145580\pi$
$504$	10.8953	+	5.48647i	0.485313	+	0.244387i
$505$	9.84283	−	14.7308i	0.438000	−	0.655514i
$506$	3.65210	+	26.0997i	0.162355	+	1.16027i
$507$	72.4485	−	7.13555i	3.21755	−	0.316901i
$508$	−6.05853	−	1.94738i	−0.268804	−	0.0864009i
$509$	17.5264	−	5.31659i	0.776846	−	0.235654i	0.123127	−	0.992391i	$-0.460708\pi$
$509$	17.5264	−	5.31659i	0.776846	−	0.235654i	0.653719	+	0.756737i	$0.273208\pi$
$510$	3.51893	−	22.4473i	0.155821	−	0.993982i
$511$	−17.3314			−0.766694
$512$	22.2962	−	3.85736i	0.985362	−	0.170473i
$513$	−3.45237			−0.152426
$514$	−1.54331	+	9.84480i	−0.0680726	+	0.434236i
$515$	−0.902292	+	0.273707i	−0.0397597	+	0.0120610i
$516$	−49.5834	−	15.9375i	−2.18279	−	0.701608i
$517$	1.58768	−	0.156373i	0.0698260	−	0.00687726i
$518$	−1.65915	−	11.8572i	−0.0728990	−	0.520973i
$519$	4.97446	−	7.44481i	0.218355	−	0.326791i
$520$	16.8569	+	8.48852i	0.739222	+	0.372246i
$521$	33.6126	−	22.4593i	1.47260	−	0.983958i	0.478199	−	0.878251i	$-0.341290\pi$
$521$	33.6126	−	22.4593i	1.47260	−	0.983958i	0.994397	−	0.105706i	$-0.0337103\pi$
$522$	−1.18767	+	20.6960i	−0.0519830	+	0.905838i
$523$	−5.90297	−	11.0437i	−0.258119	−	0.482906i	0.719166	−	0.694839i	$-0.244524\pi$
$523$	−5.90297	−	11.0437i	−0.258119	−	0.482906i	−0.977284	+	0.211933i	$0.932024\pi$
$524$	−4.29275	−	0.0707197i	−0.187530	−	0.00308941i
$525$	−0.418552	+	4.24963i	−0.0182671	+	0.185469i
$526$	11.4841	+	10.5822i	0.500730	+	0.461404i
$527$	40.4064	−	16.7369i	1.76013	−	0.729070i
$528$	−3.81656	−	23.1483i	−0.166094	−	1.00740i
$529$	−28.4813	−	11.7973i	−1.23832	−	0.512928i
$530$	−1.47431	−	3.18478i	−0.0640401	−	0.138338i
$531$	6.74036	+	8.21316i	0.292507	+	0.356421i
$532$	8.09399	+	1.74907i	0.350919	+	0.0758317i
$533$	−20.5136	+	67.6243i	−0.888543	+	2.92913i
$534$	−41.5570	+	14.4844i	−1.79835	+	0.626799i
$535$	1.84246	−	9.26268i	0.0796566	−	0.400461i
$536$	32.4678	+	5.63922i	1.40239	+	0.243577i
$537$	9.49394	−	1.88846i	0.409694	−	0.0814931i
$538$	−35.5045	−	9.20483i	−1.53071	−	0.396848i
$539$	−5.76912	+	7.02969i	−0.248494	+	0.302790i
$540$	−2.41577	+	1.91685i	−0.103958	+	0.0824883i
$541$	−25.7611	−	13.7696i	−1.10756	−	0.592001i	−0.186902	−	0.982379i	$-0.559845\pi$
$541$	−25.7611	−	13.7696i	−1.10756	−	0.592001i	−0.920655	+	0.390377i	$0.872345\pi$
$542$	9.02839	+	37.3457i	0.387803	+	1.60414i
$543$	19.0546	−	19.0546i	0.817712	−	0.817712i
$544$	−36.2424	+	15.3489i	−1.55388	+	0.658078i
$545$	8.54442	+	8.54442i	0.366003	+	0.366003i
$546$	21.0006	−	34.3919i	0.898744	−	1.47184i
$547$	−20.1046	+	37.6131i	−0.859611	+	1.60822i	−0.0675995	+	0.997713i	$0.521534\pi$
$547$	−20.1046	+	37.6131i	−0.859611	+	1.60822i	−0.792011	+	0.610506i	$0.790966\pi$
$548$	15.8375	−	4.52074i	0.676543	−	0.193116i
$549$	−14.3085	−	11.7427i	−0.610670	−	0.501164i
$550$	3.09611	−	1.82125i	0.132019	−	0.0776582i
$551$	2.74533	+	13.8017i	0.116955	+	0.587973i
$552$	44.7049	+	17.2531i	1.90277	+	0.734339i
$553$	3.11045	+	0.618707i	0.132270	+	0.0263101i
$554$	−5.80904	−	2.80625i	−0.246803	−	0.119226i
$555$	−10.1164	−	3.06877i	−0.429416	−	0.130262i
$556$	0.914381	+	5.02843i	0.0387784	+	0.213253i
$557$	−14.9684	+	12.2842i	−0.634231	+	0.520500i	−0.895670	−	0.444720i	$-0.853303\pi$
$557$	−14.9684	+	12.2842i	−0.634231	+	0.520500i	0.261439	+	0.965220i	$0.415803\pi$
$558$	19.4628	+	7.14526i	0.823925	+	0.302483i
$559$	−28.7970	+	69.5222i	−1.21798	+	2.94048i
$560$	6.63483	−	3.27012i	0.280373	−	0.138188i
$561$	15.6167	+	37.7020i	0.659336	+	1.59178i
$562$	−0.600925	−	14.7020i	−0.0253485	−	0.620165i
$563$	−11.3407	−	1.11696i	−0.477955	−	0.0470744i	−0.143828	−	0.989603i	$-0.545941\pi$
$563$	−11.3407	−	1.11696i	−0.477955	−	0.0470744i	−0.334127	+	0.942528i	$0.608441\pi$
$564$	1.15408	−	2.66133i	0.0485955	−	0.112062i
$565$	11.9856	−	6.40641i	0.504236	−	0.269520i
$566$	−8.36458	−	9.38306i	−0.351590	−	0.394399i
$567$	10.8464	+	16.2328i	0.455506	+	0.681713i
$568$	17.7481	−	10.0503i	0.744694	−	0.421701i
$569$	11.3815	+	7.60489i	0.477138	+	0.318814i	0.770779	−	0.637102i	$-0.219867\pi$
$569$	11.3815	+	7.60489i	0.477138	+	0.318814i	−0.293641	+	0.955916i	$0.594867\pi$
$570$	4.40383	−	5.83678i	0.184456	−	0.244476i
$571$	−4.40034	−	44.6774i	−0.184149	−	1.86969i	−0.433331	−	0.901235i	$-0.642662\pi$
$571$	−4.40034	−	44.6774i	−0.184149	−	1.86969i	0.249182	−	0.968457i	$-0.419838\pi$
$572$	−33.7842	+	2.76640i	−1.41259	+	0.115669i
$573$	10.1099	+	33.3279i	0.422347	+	1.39229i
$574$	16.3147	+	22.3808i	0.680964	+	0.934157i
$575$			7.33675i			0.305964i
$576$	−17.5653	−	6.29152i	−0.731887	−	0.262146i
$577$			9.35242i			0.389347i	0.980868	+	0.194673i	$0.0623646\pi$
$577$			9.35242i			0.389347i	−0.980868	+	0.194673i	$0.937635\pi$
$578$	35.8950	−	26.1660i	1.49303	−	1.08836i
$579$	−4.48186	−	14.7747i	−0.186260	−	0.614016i
$580$	9.58414	+	8.13336i	0.397960	+	0.337719i
$581$	0.811596	+	8.24027i	0.0336707	+	0.341864i
$582$	36.4645	+	27.5123i	1.51150	+	1.14042i
$583$	5.24085	+	3.50182i	0.217054	+	0.145031i
$584$	26.3097	−	3.24058i	1.08870	−	0.134096i
$585$	−8.64614	−	12.9399i	−0.357474	−	0.534998i
$586$	11.9783	−	10.6781i	0.494819	−	0.441109i
$587$	−10.8111	+	5.77867i	−0.446223	+	0.238511i	−0.679174	−	0.733977i	$-0.737662\pi$
$587$	−10.8111	+	5.77867i	−0.446223	+	0.238511i	0.232951	+	0.972489i	$0.425162\pi$
$588$	6.07524	+	15.3787i	0.250539	+	0.634205i
$589$	14.0063	+	1.37950i	0.577121	+	0.0568414i
$590$	6.43726	−	0.263115i	0.265018	−	0.0108323i
$591$	4.00788	+	9.67587i	0.164862	+	0.398012i
$592$	4.73568	+	17.6894i	0.194635	+	0.727031i
$593$	−0.412052	+	0.994781i	−0.0169209	+	0.0408508i	−0.932114	−	0.362165i	$-0.882038\pi$
$593$	−0.412052	+	0.994781i	−0.0169209	+	0.0408508i	0.915193	+	0.403015i	$0.132038\pi$
$594$	1.90883	−	5.19940i	0.0783200	−	0.213334i
$595$	−9.94587	+	8.16236i	−0.407741	+	0.334624i
$596$	17.5385	−	25.3347i	0.718406	−	1.03775i
$597$	−42.3349	−	12.8422i	−1.73265	−	0.525594i
$598$	30.1163	−	62.3418i	1.23155	−	2.54935i
$599$	4.54360	+	0.903778i	0.185646	+	0.0369274i	0.287038	−	0.957919i	$-0.407329\pi$
$599$	4.54360	+	0.903778i	0.185646	+	0.0369274i	−0.101391	+	0.994847i	$0.532329\pi$
$600$	−0.159206	−	6.52937i	−0.00649957	−	0.266560i
$601$	1.28386	+	6.45440i	0.0523698	+	0.263281i	0.998096	−	0.0616848i	$-0.0196473\pi$
$601$	1.28386	+	6.45440i	0.0523698	+	0.263281i	−0.945726	+	0.324965i	$0.894647\pi$
$602$	14.9532	+	25.4204i	0.609446	+	1.03606i
$603$	−21.0050	−	17.2384i	−0.855390	−	0.702000i
$604$	5.85448	−	10.5319i	0.238215	−	0.428537i
$605$	2.14418	−	4.01148i	0.0871734	−	0.163090i
$606$	49.3784	+	30.1519i	2.00586	+	1.22484i
$607$	3.34050	+	3.34050i	0.135587	+	0.135587i	0.771643	−	0.636056i	$-0.219435\pi$
$607$	3.34050	+	3.34050i	0.135587	+	0.135587i	−0.636056	+	0.771643i	$0.719435\pi$
$608$	−12.6140	−	1.14176i	−0.511567	−	0.0463046i
$609$	18.9776	−	18.9776i	0.769011	−	0.769011i
$610$	−10.9097	+	2.63744i	−0.441721	+	0.106787i
$611$	−3.69631	−	1.97572i	−0.149537	−	0.0799290i
$612$	32.2412	+	3.71265i	1.30327	+	0.150075i
$613$	4.00937	−	4.88543i	0.161937	−	0.197321i	−0.685720	−	0.727865i	$-0.740513\pi$
$613$	4.00937	−	4.88543i	0.161937	−	0.197321i	0.847657	+	0.530545i	$0.178013\pi$
$614$	2.48481	−	9.58429i	0.100279	−	0.386790i
$615$	23.9850	−	4.77092i	0.967169	−	0.192382i
$616$	−7.10935	+	11.2228i	−0.286444	+	0.452179i
$617$	−1.68018	+	8.44685i	−0.0676416	+	0.340057i	−0.999756	−	0.0221078i	$-0.992962\pi$
$617$	−1.68018	+	8.44685i	−0.0676416	+	0.340057i	0.932114	+	0.362165i	$0.117962\pi$
$618$	−1.01342	−	2.90761i	−0.0407659	−	0.116961i
$619$	−5.10356	+	16.8242i	−0.205129	+	0.676220i	0.792654	+	0.609672i	$0.208699\pi$
$619$	−5.10356	+	16.8242i	−0.205129	+	0.676220i	−0.997783	+	0.0665487i	$0.978801\pi$
$620$	10.5668	−	6.81142i	0.424371	−	0.273553i
$621$	7.17676	+	8.74491i	0.287994	+	0.350921i
$622$	0.847951	−	0.392538i	0.0339997	−	0.0157393i
$623$	23.0238	+	9.53677i	0.922429	+	0.382083i
$624$	−25.4493	+	56.1349i	−1.01879	+	2.24719i
$625$	0.923880	−	0.382683i	0.0369552	−	0.0153073i
$626$	14.3389	−	15.5610i	0.573098	−	0.621944i
$627$	−1.28717	+	13.0689i	−0.0514047	+	0.521920i
$628$	9.78112	+	10.1088i	0.390309	+	0.403385i
$629$	−15.0154	−	28.0918i	−0.598702	−	1.12009i
$630$	−6.08932	−	0.349446i	−0.242604	−	0.0139223i
$631$	4.18118	−	2.79378i	0.166450	−	0.111218i	−0.469555	−	0.882903i	$-0.655586\pi$
$631$	4.18118	−	2.79378i	0.166450	−	0.111218i	0.636005	+	0.771685i	$0.280586\pi$
$632$	−4.83748	−	0.357638i	−0.192425	−	0.0142261i
$633$	−20.7983	+	31.1268i	−0.826658	+	1.23718i
$634$	10.2414	−	1.43307i	0.406739	−	0.0569144i
$635$	3.16658	−	0.311881i	0.125662	−	0.0123766i
$636$	10.1951	−	5.23533i	0.404262	−	0.207594i
$637$	22.8621	−	6.93513i	0.905828	−	0.274780i
$638$	−22.3038	−	3.49644i	−0.883017	−	0.138425i
$639$	−16.8182			−0.665318
$640$	−9.46051	+	6.20474i	−0.373959	+	0.245264i
$641$	9.93148			0.392270			0.196135	−	0.980577i	$-0.437161\pi$
$641$	9.93148			0.392270			0.196135	+	0.980577i	$0.437161\pi$
$642$	30.4692	+	4.77648i	1.20252	+	0.188513i
$643$	9.79479	−	2.97122i	0.386269	−	0.117173i	−0.0911766	−	0.995835i	$-0.529063\pi$
$643$	9.79479	−	2.97122i	0.386269	−	0.117173i	0.477446	+	0.878661i	$0.341563\pi$
$644$	−12.3953	−	24.1382i	−0.488444	−	0.951177i
$645$	25.9155	−	2.55246i	1.02042	−	0.100503i
$646$	21.8183	−	3.05300i	0.858429	−	0.120119i
$647$	−3.36905	+	5.04214i	−0.132451	+	0.198227i	−0.891767	−	0.452495i	$-0.850534\pi$
$647$	−3.36905	+	5.04214i	−0.132451	+	0.198227i	0.759316	+	0.650723i	$0.225534\pi$
$648$	−19.5005	−	22.6140i	−0.766050	−	0.888362i
$649$	−9.62106	+	6.42859i	−0.377660	+	0.252344i
$650$	−9.42125	−	0.540654i	−0.369532	−	0.0212062i
$651$	−12.6533	−	23.6726i	−0.495922	−	0.927804i
$652$	9.14846	−	8.85192i	0.358282	−	0.346668i
$653$	−2.21876	+	22.5274i	−0.0868266	+	0.881566i	0.848833	+	0.528661i	$0.177306\pi$
$653$	−2.21876	+	22.5274i	−0.0868266	+	0.881566i	−0.935659	+	0.352904i	$0.885194\pi$
$654$	−26.7403	+	29.0194i	−1.04563	+	1.13475i
$655$	1.98326	−	0.821494i	0.0774924	−	0.0320984i
$656$	−28.9511	−	30.9245i	−1.13035	−	1.20740i
$657$	−20.1945	−	8.36482i	−0.787861	−	0.326343i
$658$	−1.49065	+	0.690058i	−0.0581115	+	0.0269013i
$659$	−3.29150	−	4.01070i	−0.128218	−	0.156235i	0.704944	−	0.709263i	$-0.250972\pi$
$659$	−3.29150	−	4.01070i	−0.128218	−	0.156235i	−0.833162	+	0.553028i	$0.813472\pi$
$660$	6.35552	+	9.85951i	0.247388	+	0.383781i
$661$	3.05623	−	10.0750i	0.118873	−	0.391873i	−0.877229	−	0.480071i	$-0.840611\pi$
$661$	3.05623	−	10.0750i	0.118873	−	0.391873i	0.996103	+	0.0881979i	$0.0281108\pi$
$662$	−6.66191	−	19.1136i	−0.258922	−	0.742873i
$663$	20.9153	−	105.148i	0.812282	−	4.08362i
$664$	−2.77278	−	12.3573i	−0.107605	−	0.479557i
$665$	−4.06085	+	0.807753i	−0.157473	+	0.0313233i
$666$	3.78950	−	14.6167i	0.146840	−	0.566385i
$667$	29.2530	−	35.6449i	1.13268	−	1.38018i
$668$	−0.866543	+	7.52518i	−0.0335276	+	0.291158i
$669$	54.0490	+	28.8898i	2.08966	+	1.11694i
$670$	−16.0156	+	3.87179i	−0.618735	+	0.149580i
$671$	14.2543	−	14.2543i	0.550279	−	0.550279i
$672$	11.5551	+	21.2129i	0.445746	+	0.818305i
$673$	30.6164	+	30.6164i	1.18018	+	1.18018i	0.979699	+	0.200477i	$0.0642490\pi$
$673$	30.6164	+	30.6164i	1.18018	+	1.18018i	0.200477	+	0.979699i	$0.435751\pi$
$674$	−10.7594	−	6.56998i	−0.414436	−	0.253066i
$675$	0.726863	−	1.35987i	0.0279770	−	0.0523412i
$676$	55.1099	+	30.6345i	2.11961	+	1.17825i
$677$	−26.8426	−	22.0292i	−1.03165	−	0.846650i	−0.0433285	−	0.999061i	$-0.513796\pi$
$677$	−26.8426	−	22.0292i	−1.03165	−	0.846650i	−0.988317	+	0.152411i	$0.951296\pi$
$678$	22.5022	+	38.2536i	0.864191	+	1.46912i
$679$	−5.04632	−	25.3696i	−0.193660	−	0.973595i
$680$	13.5720	−	14.2504i	0.520464	−	0.546480i
$681$	−45.8749	−	9.12509i	−1.75793	−	0.349674i
$682$	−9.82173	+	20.3313i	−0.376093	+	0.778527i
$683$	−34.7844	−	10.5517i	−1.33099	−	0.403751i	−0.456901	−	0.889518i	$-0.651041\pi$
$683$	−34.7844	−	10.5517i	−1.33099	−	0.403751i	−0.874089	+	0.485766i	$0.838541\pi$
$684$	8.58692	+	5.94449i	0.328329	+	0.227293i
$685$	−6.36576	+	5.22424i	−0.243223	+	0.199608i
$686$	9.53594	−	25.9747i	0.364084	−	0.991718i
$687$	−0.497139	+	1.20020i	−0.0189670	+	0.0457905i
$688$	−27.4526	−	35.7932i	−1.04662	−	1.36460i
$689$	−6.33686	−	15.2985i	−0.241415	−	0.582828i
$690$	−23.9393	+	0.978490i	−0.911354	+	0.0372505i
$691$	33.9991	+	3.34862i	1.29339	+	0.127387i	0.721195	−	0.692732i	$-0.243593\pi$
$691$	33.9991	+	3.34862i	1.29339	+	0.127387i	0.572192	+	0.820120i	$0.306093\pi$
$692$	7.21259	−	2.84929i	0.274182	−	0.108314i
$693$	9.66108	−	5.16396i	0.366994	−	0.196162i
$694$	−11.0783	+	9.87581i	−0.420526	+	0.374881i
$695$	−1.41973	−	2.12477i	−0.0538534	−	0.0805973i
$696$	−25.2604	+	32.3571i	−0.957492	+	1.22649i
$697$	61.2664	+	40.9369i	2.32063	+	1.55060i
$698$	−32.1964	−	24.2920i	−1.21865	−	0.919467i
$699$	−2.78073	−	28.2332i	−0.105177	−	1.06788i
$700$	−2.39306	+	2.81992i	−0.0904491	+	0.106583i
$701$	8.60717	+	28.3741i	0.325089	+	1.07167i	0.955396	+	0.295328i	$0.0954288\pi$
$701$	8.60717	+	28.3741i	0.325089	+	1.07167i	−0.630308	+	0.776346i	$0.717071\pi$
$702$	−11.7583	+	8.57138i	−0.443790	+	0.323506i
$703$		−	10.2503i		−	0.386596i
$704$	8.69388	−	18.3659i	0.327663	−	0.692192i
$705$			1.45040i			0.0546251i
$706$	11.6832	+	16.0272i	0.439703	+	0.603192i
$707$	−9.51036	−	31.3515i	−0.357674	−	1.17909i
$708$	1.71705	+	20.9693i	0.0645308	+	0.788073i
$709$	2.07121	+	21.0294i	0.0777860	+	0.789775i	0.952379	+	0.304917i	$0.0986287\pi$
$709$	2.07121	+	21.0294i	0.0777860	+	0.789775i	−0.874593	+	0.484858i	$0.838871\pi$
$710$	−6.14225	+	8.14087i	−0.230515	+	0.305521i
$711$	3.32568	+	2.22215i	0.124723	+	0.0833370i
$712$	−36.7342	−	10.1723i	−1.37667	−	0.381222i
$713$	−25.6220	−	38.3460i	−0.959550	−	1.43607i
$714$	−27.9597	−	31.3641i	−1.04637	−	1.17377i
$715$	14.9474	−	7.98954i	0.559000	−	0.298792i
$716$	7.69183	+	3.33554i	0.287457	+	0.124655i
$717$	−14.9085	−	1.46836i	−0.556767	−	0.0548368i
$718$	−0.697762	−	17.0712i	−0.0260403	−	0.637090i
$719$	10.0161	+	24.1809i	0.373536	+	0.901796i	0.993145	+	0.116886i	$0.0372911\pi$
$719$	10.0161	+	24.1809i	0.373536	+	0.901796i	−0.619609	+	0.784910i	$0.712709\pi$
$720$	9.30918	−	0.608094i	0.346933	−	0.0226623i
$721$	−0.667258	+	1.61090i	−0.0248500	+	0.0599932i
$722$	−18.5687	−	6.81703i	−0.691057	−	0.253704i
$723$	−42.9596	+	35.2560i	−1.59768	+	1.31119i
$724$	22.9628	−	4.17561i	0.853407	−	0.155185i
$725$	−6.01442	−	1.82445i	−0.223370	−	0.0677585i
$726$	13.3752	+	6.46132i	0.496399	+	0.239802i
$727$	−40.0266	−	7.96178i	−1.48450	−	0.295286i	−0.614730	−	0.788738i	$-0.710735\pi$
$727$	−40.0266	−	7.96178i	−1.48450	−	0.295286i	−0.869773	+	0.493451i	$0.835735\pi$
$728$	31.9096	−	14.1383i	1.18265	−	0.523999i
$729$	2.71969	+	13.6728i	0.100729	+	0.506400i
$730$	−11.4243	+	6.72019i	−0.422832	+	0.248725i
$731$	60.6529	+	49.7765i	2.24333	+	1.84105i
$732$	−10.0608	−	35.2459i	−0.371857	−	1.30272i
$733$	−18.2497	+	34.1428i	−0.674069	+	1.26109i	0.279566	+	0.960127i	$0.409809\pi$
$733$	−18.2497	+	34.1428i	−0.674069	+	1.26109i	−0.953634	+	0.300967i	$0.902691\pi$
$734$	−11.7715	+	19.2777i	−0.434494	+	0.711553i
$735$	−5.84607	−	5.84607i	−0.215635	−	0.215635i
$736$	23.3299	+	34.3251i	0.859951	+	1.26524i
$737$	20.9254	−	20.9254i	0.770798	−	0.770798i
$738$	8.20800	+	33.9522i	0.302141	+	1.24980i
$739$	−7.60864	−	4.06690i	−0.279888	−	0.149603i	0.325480	−	0.945549i	$-0.394474\pi$
$739$	−7.60864	−	4.06690i	−0.279888	−	0.149603i	−0.605368	+	0.795945i	$0.706974\pi$
$740$	−5.69124	−	7.17254i	−0.209214	−	0.263668i
$741$	21.8863	−	26.6685i	0.804013	−	0.979693i
$742$	−6.28215	−	1.62870i	−0.230625	−	0.0597915i
$743$	−39.4850	+	7.85406i	−1.44857	+	0.288138i	−0.855829	−	0.517259i	$-0.826952\pi$
$743$	−39.4850	+	7.85406i	−1.44857	+	0.288138i	−0.592736	+	0.805396i	$0.701952\pi$
$744$	23.6345	+	33.5702i	0.866482	+	1.23074i
$745$	−3.00567	+	15.1105i	−0.110119	+	0.553606i
$746$	2.51085	−	0.875137i	0.0919288	−	0.0320410i
$747$	−3.03142	+	9.99325i	−0.110914	+	0.365634i
$748$	−7.46546	+	34.5472i	−0.272964	+	1.26317i
$749$	−11.0793	−	13.5002i	−0.404830	−	0.493287i
$750$	1.37189	+	2.96352i	0.0500942	+	0.108212i
$751$	−25.3072	−	10.4826i	−0.923472	−	0.382515i	−0.130274	−	0.991478i	$-0.541586\pi$
$751$	−25.3072	−	10.4826i	−0.923472	−	0.382515i	−0.793198	+	0.608964i	$0.791586\pi$
$752$	2.13384	−	1.32625i	0.0778131	−	0.0483635i
$753$	−31.8715	+	13.2016i	−1.16146	+	0.481093i
$754$	43.6166	+	40.1910i	1.58842	+	1.46367i
$755$	−0.590540	+	5.99586i	−0.0214920	+	0.218212i
$756$	−0.0939365	+	5.70203i	−0.00341644	+	0.207381i
$757$	3.67473	+	6.87494i	0.133560	+	0.249874i	0.939807	−	0.341706i	$-0.111005\pi$
$757$	3.67473	+	6.87494i	0.133560	+	0.249874i	−0.806247	+	0.591580i	$0.798505\pi$
$758$	−1.53912	+	26.8203i	−0.0559035	+	0.974156i
$759$	35.7794	−	23.9071i	1.29871	−	0.867771i
$760$	6.01350	−	1.98549i	0.218133	−	0.0720213i
$761$	13.0986	−	19.6034i	0.474824	−	0.710624i	−0.514316	−	0.857601i	$-0.671954\pi$
$761$	13.0986	−	19.6034i	0.474824	−	0.710624i	0.989140	+	0.146977i	$0.0469542\pi$
$762$	1.43997	+	10.2908i	0.0521646	+	0.372795i
$763$	22.2379	−	2.19024i	0.805065	−	0.0792920i
$764$	−9.23060	+	28.7176i	−0.333951	+	1.03896i
$765$	−15.5284	+	4.71048i	−0.561430	+	0.170308i
$766$	−3.36236	+	21.4485i	−0.121487	+	0.774967i
$767$	30.3988			1.09764
$768$	−21.5074	−	30.0415i	−0.776080	−	1.08403i
$769$	−20.7978			−0.749987			−0.374994	−	0.927027i	$-0.622355\pi$
$769$	−20.7978			−0.749987			−0.374994	+	0.927027i	$0.622355\pi$
$770$	1.02875	−	6.56240i	0.0370735	−	0.236493i
$771$	15.5706	−	4.72328i	0.560760	−	0.170105i
$772$	4.09205	−	12.7309i	0.147276	−	0.458195i
$773$	3.43977	−	0.338788i	0.123720	−	0.0121854i	−0.0359676	−	0.999353i	$-0.511451\pi$
$773$	3.43977	−	0.338788i	0.123720	−	0.0121854i	0.159688	+	0.987168i	$0.448951\pi$
$774$	5.15451	+	36.8367i	0.185275	+	1.32407i
$775$	−3.49228	+	5.22656i	−0.125446	+	0.187744i
$776$	12.4041	+	37.5685i	0.445280	+	1.34863i
$777$	−16.2547	+	10.8610i	−0.583133	+	0.389637i
$778$	0.299561	−	5.22005i	0.0107398	−	0.187148i
$779$	11.1776	+	20.9118i	0.400479	+	0.749243i
$780$	0.507620	−	30.8130i	0.0181757	−	1.10328i
$781$	1.79529	−	18.2278i	0.0642404	−	0.652244i
$782$	−53.0890	−	48.9195i	−1.89846	−	1.74936i
$783$	−8.95344	+	3.70864i	−0.319970	+	0.132536i
$784$	−3.25511	+	13.9465i	−0.116254	+	0.498089i
$785$	−6.49773	−	2.69145i	−0.231914	−	0.0960620i
$786$	2.94498	+	6.36168i	0.105044	+	0.226914i
$787$	−6.94825	−	8.46647i	−0.247678	−	0.301797i	0.634300	−	0.773087i	$-0.281288\pi$
$787$	−6.94825	−	8.46647i	−0.247678	−	0.301797i	−0.881978	+	0.471290i	$0.843788\pi$
$788$	−1.91594	+	8.86623i	−0.0682527	+	0.315846i
$789$	7.40186	−	24.4006i	0.263513	−	0.868686i
$790$	2.29022	−	0.798237i	0.0814822	−	0.0284000i
$791$	4.90293	−	24.6487i	0.174328	−	0.876407i
$792$	−13.7004	+	9.64550i	−0.486821	+	0.342738i
$793$	−51.9413	+	10.3318i	−1.84449	+	0.366892i
$794$	−15.4601	−	4.00815i	−0.548657	−	0.142244i
$795$	−3.63531	+	4.42964i	−0.128931	+	0.157103i
$796$	−23.8167	−	30.0156i	−0.844160	−	1.06387i
$797$	20.1075	+	10.7477i	0.712244	+	0.380702i	0.787378	−	0.616471i	$-0.211438\pi$
$797$	20.1075	+	10.7477i	0.712244	+	0.380702i	−0.0751335	+	0.997173i	$0.523938\pi$
$798$	−3.17723	−	13.1425i	−0.112473	−	0.465241i
$799$	−3.09016	+	3.09016i	−0.109322	+	0.109322i
$800$	3.10550	−	4.72820i	0.109796	−	0.167167i
$801$	22.2244	+	22.2244i	0.785262	+	0.785262i
$802$	−0.309425	+	0.506733i	−0.0109262	+	0.0178934i
$803$	11.2216	−	20.9942i	0.396002	−	0.740868i
$804$	−14.7694	−	51.7413i	−0.520875	−	1.82478i
$805$	10.4877	+	8.60705i	0.369644	+	0.303359i
$806$	51.1288	−	30.0758i	1.80094	−	1.05938i
$807$	11.6838	+	58.7385i	0.411290	+	2.06769i
$808$	20.2991	+	45.8146i	0.714121	+	1.61175i
$809$	−0.187508	−	0.0372977i	−0.00659244	−	0.00131132i	0.191793	−	0.981435i	$-0.438570\pi$
$809$	−0.187508	−	0.0372977i	−0.00659244	−	0.00131132i	−0.198385	+	0.980124i	$0.563570\pi$
$810$	13.4438	+	6.49449i	0.472368	+	0.228193i
$811$	13.4534	+	4.08104i	0.472412	+	0.143305i	0.517509	−	0.855678i	$-0.326860\pi$
$811$	13.4534	+	4.08104i	0.472412	+	0.143305i	−0.0450967	+	0.998983i	$0.514360\pi$
$812$	22.8700	−	4.15873i	0.802580	−	0.145943i
$813$	48.4954	−	39.7992i	1.70081	−	1.39582i
$814$	15.4373	+	5.66740i	0.541077	+	0.198642i
$815$	−2.43577	+	5.88046i	−0.0853211	+	0.205983i
$816$	48.3083	+	42.3841i	1.69113	+	1.48374i
$817$	9.66254	+	23.3274i	0.338050	+	0.816124i
$818$	0.921302	+	22.5402i	0.0322126	+	0.788099i
$819$	−28.6404	−	2.82083i	−1.00078	−	0.0985679i
$820$	19.4323	+	8.42674i	0.678604	+	0.294275i
$821$	29.3245	−	15.6743i	1.02343	−	0.547036i	0.127786	−	0.991802i	$-0.459213\pi$
$821$	29.3245	−	15.6743i	1.02343	−	0.547036i	0.895647	+	0.444766i	$0.146713\pi$
$822$	−17.8953	−	20.0743i	−0.624171	−	0.700171i
$823$	−8.41756	−	12.5978i	−0.293418	−	0.439131i	0.655247	−	0.755415i	$-0.272565\pi$
$823$	−8.41756	−	12.5978i	−0.293418	−	0.439131i	−0.948664	+	0.316284i	$0.897565\pi$
$824$	0.711722	−	2.57018i	0.0247940	−	0.0895364i
$825$	−4.87674	−	3.25853i	−0.169786	−	0.113448i
$826$	7.17571	−	9.51060i	0.249675	−	0.330916i
$827$	−3.82144	−	38.7997i	−0.132884	−	1.34920i	−0.798090	−	0.602538i	$-0.794156\pi$
$827$	−3.82144	−	38.7997i	−0.132884	−	1.34920i	0.665206	−	0.746660i	$-0.268344\pi$
$828$	−2.79293	−	34.1082i	−0.0970609	−	1.18534i
$829$	10.0288	+	33.0606i	0.348316	+	1.14824i	0.939742	+	0.341884i	$0.111065\pi$
$829$	10.0288	+	33.0606i	0.348316	+	1.14824i	−0.591426	+	0.806359i	$0.701435\pi$
$830$	3.73012	+	5.11704i	0.129474	+	0.177615i
$831$			10.5340i			0.365419i
$832$	−45.7966	+	27.4288i	−1.58771	+	0.950924i
$833$		−	24.9108i		−	0.863110i
$834$	6.74365	−	4.91586i	0.233513	−	0.170222i
$835$	−1.09944	−	3.62437i	−0.0380477	−	0.125426i
$836$	−7.35936	+	8.67208i	−0.254529	+	0.299930i
$837$	0.950031	+	9.64582i	0.0328379	+	0.333408i
$838$	−4.08732	−	3.08387i	−0.141194	−	0.106530i
$839$	47.0948	+	31.4677i	1.62589	+	1.08639i	0.929562	+	0.368666i	$0.120185\pi$
$839$	47.0948	+	31.4677i	1.62589	+	1.08639i	0.696331	+	0.717721i	$0.254815\pi$
$840$	−9.52036	−	7.43230i	−0.328484	−	0.256439i
$841$	5.83450	+	8.73195i	0.201190	+	0.301102i
$842$	−16.9552	+	15.1148i	−0.584316	+	0.520892i
$843$	−21.1889	+	11.3257i	−0.729784	+	0.390078i
$844$	−30.1560	+	11.9129i	−1.03801	+	0.410060i
$845$	−31.3743	−	3.09010i	−1.07931	−	0.106303i
$846$	−2.06995	+	0.0846066i	−0.0711663	+	0.00290883i
$847$	−3.21890	−	7.77110i	−0.110603	−	0.267018i
$848$	9.84109	+	1.29781i	0.337944	+	0.0445670i
$849$	−7.85452	+	18.9625i	−0.269566	+	0.650791i
$850$	−3.39107	+	9.23686i	−0.116313	+	0.316822i
$851$	−25.9641	+	21.3082i	−0.890038	+	0.730435i
$852$	−27.3823	−	18.9560i	−0.938101	−	0.649423i
$853$	11.0220	+	3.34347i	0.377385	+	0.114478i	0.473278	−	0.880913i	$-0.343071\pi$
$853$	11.0220	+	3.34347i	0.377385	+	0.114478i	−0.0958931	+	0.995392i	$0.530571\pi$
$854$	−9.02847	+	18.6893i	−0.308948	+	0.639533i
$855$	−5.12154	−	1.01874i	−0.175153	−	0.0348401i
$856$	19.3431	+	18.4223i	0.661134	+	0.629660i
$857$	−8.78441	−	44.1622i	−0.300070	−	1.50855i	−0.776937	−	0.629578i	$-0.783228\pi$
$857$	−8.78441	−	44.1622i	−0.300070	−	1.50855i	0.476868	−	0.878975i	$-0.341772\pi$
$858$	28.0628	+	47.7067i	0.958049	+	1.62868i
$859$	−3.03321	−	2.48929i	−0.103492	−	0.0849335i	0.581224	−	0.813743i	$-0.302574\pi$
$859$	−3.03321	−	2.48929i	−0.103492	−	0.0849335i	−0.684716	+	0.728810i	$0.740074\pi$
$860$	19.7134	+	10.9583i	0.672220	+	0.373674i
$861$	21.3179	−	39.8830i	0.726513	−	1.35921i
$862$	18.0984	+	11.0514i	0.616435	+	0.376413i
$863$	−0.356833	−	0.356833i	−0.0121467	−	0.0121467i	0.701007	−	0.713154i	$-0.252734\pi$
$863$	−0.356833	−	0.356833i	−0.0121467	−	0.0121467i	−0.713154	+	0.701007i	$0.752734\pi$
$864$	−0.923551	−	8.67347i	−0.0314199	−	0.295077i
$865$	−2.74181	+	2.74181i	−0.0932242	+	0.0932242i
$866$	−11.9946	+	2.89972i	−0.407594	+	0.0985366i
$867$	−63.9655	−	34.1903i	−2.17238	−	1.16116i
$868$	2.65953	−	23.0957i	0.0902702	−	0.783919i
$869$	−2.76340	+	3.36721i	−0.0937420	+	0.114225i
$870$	5.15093	−	19.8680i	0.174633	−	0.673587i
$871$	−76.2504	+	15.1672i	−2.58365	+	0.513920i
$872$	−33.3485	+	7.48286i	−1.12932	+	0.253401i
$873$	6.36442	−	31.9961i	0.215403	−	1.08290i
$874$	−7.64590	−	21.9368i	−0.258627	−	0.742024i
$875$	0.536804	−	1.76961i	0.0181473	−	0.0598236i
$876$	−23.4512	−	36.3805i	−0.792341	−	1.22918i
$877$	1.19394	+	1.45482i	0.0403164	+	0.0491257i	0.792778	−	0.609510i	$-0.208634\pi$
$877$	1.19394	+	1.45482i	0.0403164	+	0.0491257i	−0.752462	+	0.658636i	$0.771134\pi$
$878$	14.5725	−	6.74599i	0.491799	−	0.227666i
$879$	−24.2073	−	10.0270i	−0.816491	−	0.338202i
$880$	−0.334661	+	10.1543i	−0.0112814	+	0.342303i
$881$	−31.9340	+	13.2275i	−1.07588	+	0.445646i	−0.849064	−	0.528291i	$-0.822833\pi$
$881$	−31.9340	+	13.2275i	−1.07588	+	0.445646i	−0.226821	+	0.973937i	$0.572833\pi$
$882$	8.00226	−	8.68430i	0.269450	−	0.292416i
$883$	5.04813	−	51.2546i	0.169883	−	1.72485i	−0.411660	−	0.911338i	$-0.635051\pi$
$883$	5.04813	−	51.2546i	0.169883	−	1.72485i	0.581543	−	0.813516i	$-0.302449\pi$
$884$	66.7306	−	64.5675i	2.24439	−	2.17164i
$885$	−4.95896	−	9.27757i	−0.166694	−	0.311862i
$886$	6.10135	+	0.350136i	0.204979	+	0.0117630i
$887$	−4.74655	+	3.17154i	−0.159373	+	0.106490i	−0.632700	−	0.774397i	$-0.718053\pi$
$887$	−4.74655	+	3.17154i	−0.159373	+	0.106490i	0.473326	+	0.880887i	$0.343053\pi$
$888$	22.6445	−	19.5267i	0.759899	−	0.655274i
$889$	3.26903	−	4.89244i	0.109640	−	0.164087i
$890$	18.8744	−	2.64107i	0.632673	−	0.0885289i
$891$	−26.6862	+	2.62836i	−0.894021	+	0.0880534i
$892$	24.2473	+	47.2184i	0.811861	+	1.58099i
$893$	−1.34576	+	0.408231i	−0.0450341	+	0.0136609i
$894$	−49.7054	−	7.79203i	−1.66240	−	0.260604i
$895$	−4.19196			−0.140122
$896$	−2.22899	+	20.8026i	−0.0744652	+	0.694967i
$897$	−113.049			−3.77460
$898$	−32.3980	−	5.07884i	−1.08113	−	0.169483i
$899$	37.8062	−	11.4684i	1.26091	−	0.382492i
$900$	−4.14939	+	2.13078i	−0.138313	+	0.0710258i
$901$	−17.1829	+	1.69237i	−0.572445	+	0.0563809i
$902$	−37.6741	+	5.27168i	−1.25441	+	0.175528i
$903$	26.7539	−	40.0401i	0.890314	−	1.33245i
$904$	−2.83410	+	38.3345i	−0.0942607	+	1.27499i
$905$	−9.70300	+	6.48334i	−0.322539	+	0.215513i
$906$	−19.6428	−	1.12724i	−0.652589	−	0.0374499i
$907$	25.3826	+	47.4875i	0.842816	+	1.57680i	0.816645	+	0.577140i	$0.195831\pi$
$907$	25.3826	+	47.4875i	0.842816	+	1.57680i	0.0261703	+	0.999657i	$0.491669\pi$
$908$	−28.1701	−	29.1138i	−0.934857	−	0.966175i
$909$	4.05004	−	41.1207i	0.134331	−	1.36389i
$910$	−11.8253	+	12.8332i	−0.392005	+	0.425416i
$911$	3.08444	−	1.27762i	0.102192	−	0.0423294i	−0.331002	−	0.943630i	$-0.607387\pi$
$911$	3.08444	−	1.27762i	0.102192	−	0.0423294i	0.433194	+	0.901301i	$0.357387\pi$
$912$	7.28053	+	19.3568i	0.241082	+	0.640969i
$913$	−10.5072	−	4.35225i	−0.347739	−	0.144038i
$914$	11.7211	−	5.42599i	0.387700	−	0.179476i
$915$	11.6264	+	14.1668i	0.384357	+	0.468341i
$916$	−0.945703	+	0.609608i	−0.0312469	+	0.0201420i
$917$	1.15234	−	3.79876i	0.0380536	−	0.125446i
$918$	4.99350	+	14.3268i	0.164810	+	0.472856i
$919$	−6.07289	+	30.5305i	−0.200326	+	1.00711i	0.741486	+	0.670968i	$0.234121\pi$
$919$	−6.07289	+	30.5305i	−0.200326	+	1.00711i	−0.941812	+	0.336139i	$0.890879\pi$
$920$	−17.5301	−	11.1049i	−0.577951	−	0.366117i
$921$	−15.8562	+	3.15400i	−0.522481	+	0.103928i
$922$	−0.178099	+	0.686954i	−0.00586537	+	0.0226236i
$923$	−30.5260	+	37.1960i	−1.00477	+	1.22432i
$924$	21.5499	+	2.48152i	0.708939	+	0.0816361i
$925$	4.03751	+	2.15810i	0.132753	+	0.0709577i
$926$	−48.6786	+	11.7681i	−1.59968	+	0.386725i
$927$	−1.55497	+	1.55497i	−0.0510720	+	0.0510720i
$928$	−33.9400	+	10.5893i	−1.11414	+	0.347611i
$929$	25.8770	+	25.8770i	0.848997	+	0.848997i	0.990008	−	0.141011i	$-0.0450352\pi$
$929$	25.8770	+	25.8770i	0.848997	+	0.848997i	−0.141011	+	0.990008i	$0.545035\pi$
$930$	−17.5197	−	10.6980i	−0.574493	−	0.350801i
$931$	3.77886	−	7.06975i	0.123847	−	0.231702i
$932$	11.9383	−	21.4763i	0.391051	−	0.703481i
$933$	−1.17940	−	0.967905i	−0.0386117	−	0.0316878i
$934$	−5.16401	−	8.77881i	−0.168972	−	0.287251i
$935$	−3.44769	−	17.3327i	−0.112752	−	0.566841i
$936$	44.0047	−	1.07297i	1.43834	−	0.0350712i
$937$	−26.3403	−	5.23942i	−0.860501	−	0.171164i	−0.254934	−	0.966958i	$-0.582054\pi$
$937$	−26.3403	−	5.23942i	−0.860501	−	0.171164i	−0.605567	+	0.795794i	$0.707054\pi$
$938$	−13.2539	+	27.4361i	−0.432755	+	0.895819i
$939$	−33.0631	−	10.0296i	−1.07897	−	0.327303i
$940$	−0.715021	+	1.03286i	−0.0233214	+	0.0336882i
$941$	12.5322	−	10.2849i	0.408537	−	0.335278i	−0.407574	−	0.913172i	$-0.633625\pi$
$941$	12.5322	−	10.2849i	0.408537	−	0.335278i	0.816112	+	0.577894i	$0.196125\pi$
$942$	7.91543	−	21.5606i	0.257898	−	0.702483i
$943$	29.7341	−	71.7844i	0.968274	−	2.33762i
$944$	−9.11475	+	15.7792i	−0.296660	+	0.513568i
$945$	−1.09118	−	2.63435i	−0.0354962	−	0.0856954i
$946$	−40.4745	+	1.65434i	−1.31594	+	0.0537874i
$947$	−9.23427	−	0.909496i	−0.300074	−	0.0295547i	−0.0531399	−	0.998587i	$-0.516923\pi$
$947$	−9.23427	−	0.909496i	−0.300074	−	0.0295547i	−0.246934	+	0.969032i	$0.579423\pi$
$948$	2.91003	+	7.36636i	0.0945135	+	0.239248i
$949$	−55.1541	+	29.4805i	−1.79038	+	0.956977i
$950$	−2.36358	+	2.10703i	−0.0766847	+	0.0683611i
$951$	−9.38103	−	14.0397i	−0.304201	−	0.455269i
$952$	−4.44876	−	36.1187i	−0.144185	−	1.17062i
$953$	24.1623	+	16.1447i	0.782694	+	0.522979i	0.881532	−	0.472124i	$-0.156513\pi$
$953$	24.1623	+	16.1447i	0.782694	+	0.522979i	−0.0988381	+	0.995104i	$0.531513\pi$
$954$	−6.53386	−	4.92978i	−0.211542	−	0.159607i
$955$	−1.47832	−	15.0097i	−0.0478374	−	0.485701i
$956$	−9.89278	−	8.39528i	−0.319956	−	0.271523i
$957$	10.7008	+	35.2758i	0.345908	+	1.14030i
$958$	−35.4963	+	25.8754i	−1.14683	+	0.835997i
$959$			15.2285i			0.491753i
$960$	15.8420	+	9.50244i	0.511297	+	0.306690i
$961$		−	8.51292i		−	0.274610i
$962$	−25.4489	−	34.9112i	−0.820505	−	1.12558i
$963$	−6.39386	−	21.0777i	−0.206039	−	0.679220i
$964$	−47.9731	+	3.92825i	−1.54511	+	0.126520i
$965$	0.655361	+	6.65399i	0.0210968	+	0.214200i
$966$	−26.6855	+	35.3686i	−0.858592	+	1.13797i
$967$	−6.20249	−	4.14437i	−0.199459	−	0.133274i	0.451830	−	0.892104i	$-0.350771\pi$
$967$	−6.20249	−	4.14437i	−0.199459	−	0.133274i	−0.651289	+	0.758830i	$0.725771\pi$
$968$	6.33944	+	11.1950i	0.203757	+	0.359821i
$969$	−19.9853	−	29.9101i	−0.642020	−	0.960851i
$970$	−13.1634	−	14.7661i	−0.422650	−	0.474112i
$971$	−31.8463	+	17.0222i	−1.02199	+	0.546268i	−0.895202	−	0.445662i	$-0.852968\pi$
$971$	−31.8463	+	17.0222i	−1.02199	+	0.546268i	−0.126793	+	0.991929i	$0.540468\pi$
$972$	−15.7174	+	36.2446i	−0.504135	+	1.16255i
$973$	−4.70286	−	0.463191i	−0.150767	−	0.0148492i
$974$	0.998046	+	24.4178i	0.0319795	+	0.782396i
$975$	5.89661	+	14.2357i	0.188843	+	0.455906i
$976$	10.2111	−	30.0592i	0.326850	−	0.962171i
$977$	−4.43511	+	10.7073i	−0.141892	+	0.342557i	−0.978810	−	0.204771i	$-0.934355\pi$
$977$	−4.43511	+	10.7073i	−0.141892	+	0.342557i	0.836918	+	0.547328i	$0.184355\pi$
$978$	−19.5124	−	7.16347i	−0.623937	−	0.229062i
$979$	−26.4596	+	21.7148i	−0.845652	+	0.694009i
$980$	−1.28110	−	7.04513i	−0.0409233	−	0.225048i
$981$	26.9686	+	8.18084i	0.861041	+	0.261194i
$982$	25.6944	+	12.4125i	0.819942	+	0.396100i
$983$	54.2330	+	10.7876i	1.72976	+	0.344072i	0.956882	−	0.290478i	$-0.0938142\pi$
$983$	54.2330	+	10.7876i	1.72976	+	0.344072i	0.772883	+	0.634549i	$0.218814\pi$
$984$	−24.9042	+	64.5300i	−0.793918	+	2.05714i
$985$	−0.884820	−	4.44829i	−0.0281927	−	0.141734i
$986$	53.3044	−	31.3556i	1.69756	−	0.998564i
$987$	2.07331	+	1.70152i	0.0659941	+	0.0541600i
$988$	28.7329	−	8.20168i	0.914115	−	0.260930i
$989$	39.0024	−	72.9684i	1.24020	−	2.32026i
$990$	4.36598	−	7.14998i	0.138760	−	0.227241i
$991$	31.5210	+	31.5210i	1.00130	+	1.00130i	0.999999	+	0.00129910i	$0.000413516\pi$
$991$	31.5210	+	31.5210i	1.00130	+	1.00130i	0.00129910	+	0.999999i	$0.499586\pi$
$992$	0.281107	+	35.5575i	0.00892515	+	1.12895i
$993$	−23.3703	+	23.3703i	−0.741635	+	0.741635i
$994$	4.43145	+	18.3306i	0.140557	+	0.581412i
$995$	16.8962	+	9.03119i	0.535644	+	0.286308i
$996$	−16.1991	+	12.8536i	−0.513287	+	0.407281i
$997$	11.4198	−	13.9151i	0.361669	−	0.440695i	−0.560106	−	0.828421i	$-0.689239\pi$
$997$	11.4198	−	13.9151i	0.361669	−	0.440695i	0.921775	+	0.387726i	$0.126739\pi$
$998$	−41.6076	−	10.7871i	−1.31706	−	0.341460i
$999$	6.92348	−	1.37716i	0.219049	−	0.0435716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.461.35	yes	1024
128.5	even	32	inner	640.2.bm.a.261.35	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.261.35	✓	1024	128.5	even	32	inner
640.2.bm.a.461.35	yes	1024	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.219023 - 1.39715i) q^{2} +(-2.20974 + 0.670316i) q^{3} +(-1.90406 - 0.612016i) q^{4} +(0.995185 - 0.0980171i) q^{5} +(0.452549 + 3.23415i) q^{6} +(1.02738 - 1.53758i) q^{7} +(-1.27211 + 2.52621i) q^{8} +(1.93920 - 1.29573i) q^{9} +O(q^{10})\)	\(q+(0.219023 - 1.39715i) q^{2} +(-2.20974 + 0.670316i) q^{3} +(-1.90406 - 0.612016i) q^{4} +(0.995185 - 0.0980171i) q^{5} +(0.452549 + 3.23415i) q^{6} +(1.02738 - 1.53758i) q^{7} +(-1.27211 + 2.52621i) q^{8} +(1.93920 - 1.29573i) q^{9} +(0.0810236 - 1.41189i) q^{10} +(1.19733 + 2.24005i) q^{11} +(4.61771 + 0.0760732i) q^{12} +(0.654048 - 6.64066i) q^{13} +(-1.92321 - 1.77217i) q^{14} +(-2.13339 + 0.883680i) q^{15} +(3.25087 + 2.33063i) q^{16} +(-6.42807 - 2.66259i) q^{17} +(-1.38560 - 2.99315i) q^{18} +(-1.42040 - 1.73076i) q^{19} +(-1.95488 - 0.422439i) q^{20} +(-1.23957 + 4.08632i) q^{21} +(3.39193 - 1.18223i) q^{22} +(-1.43133 + 7.19578i) q^{23} +(1.11767 - 6.43497i) q^{24} +(0.980785 - 0.195090i) q^{25} +(-9.13474 - 2.36826i) q^{26} +(0.978193 - 1.19193i) q^{27} +(-2.89722 + 2.29887i) q^{28} +(-5.54292 - 2.96275i) q^{29} +(0.767372 + 3.17422i) q^{30} +(-4.44482 + 4.44482i) q^{31} +(3.96825 - 4.03150i) q^{32} +(-4.14733 - 4.14733i) q^{33} +(-5.12794 + 8.39781i) q^{34} +(0.871723 - 1.63088i) q^{35} +(-4.48536 + 1.28033i) q^{36} +(3.53891 + 2.90431i) q^{37} +(-2.72923 + 1.60543i) q^{38} +(3.00607 + 15.1125i) q^{39} +(-1.01837 + 2.63873i) q^{40} +(-10.3869 - 2.06608i) q^{41} +(5.43771 + 2.62687i) q^{42} +(-10.7916 - 3.27360i) q^{43} +(-0.908842 - 4.99797i) q^{44} +(1.80286 - 1.47957i) q^{45} +(9.74009 + 3.57582i) q^{46} +(0.240365 - 0.580292i) q^{47} +(-8.74583 - 2.97096i) q^{48} +(1.37013 + 3.30779i) q^{49} +(-0.0577560 - 1.41303i) q^{50} +(15.9891 + 1.57479i) q^{51} +(-5.30953 + 12.2439i) q^{52} +(2.18855 - 1.16981i) q^{53} +(-1.45106 - 1.62774i) q^{54} +(1.41113 + 2.11190i) q^{55} +(2.57731 + 4.55135i) q^{56} +(4.29885 + 2.87240i) q^{57} +(-5.35343 + 7.09538i) q^{58} +(0.446530 + 4.53370i) q^{59} +(4.60293 - 0.376908i) q^{60} +(-2.30386 - 7.59480i) q^{61} +(5.23657 + 7.18361i) q^{62} -4.31289i q^{63} +(-4.76347 - 6.42724i) q^{64} -6.67279i q^{65} +(-6.70280 + 4.88608i) q^{66} +(-3.38209 - 11.1493i) q^{67} +(10.6099 + 9.00381i) q^{68} +(-1.66059 - 16.8602i) q^{69} +(-2.08766 - 1.57513i) q^{70} +(-5.99584 - 4.00629i) q^{71} +(0.806413 + 6.54714i) q^{72} +(-5.20691 - 7.79269i) q^{73} +(4.83286 - 4.30828i) q^{74} +(-2.03650 + 1.08853i) q^{75} +(1.64527 + 4.16477i) q^{76} +(4.67438 + 0.460386i) q^{77} +(21.7728 - 0.889938i) q^{78} +(0.656292 + 1.58443i) q^{79} +(3.46366 + 2.00076i) q^{80} +(-4.04012 + 9.75372i) q^{81} +(-5.16158 + 14.0595i) q^{82} +(-3.46124 + 2.84056i) q^{83} +(4.86111 - 7.02195i) q^{84} +(-6.65810 - 2.01971i) q^{85} +(-6.93731 + 14.3605i) q^{86} +(14.2344 + 2.83139i) q^{87} +(-7.18197 + 0.175119i) q^{88} +(2.62909 + 13.2173i) q^{89} +(-1.67231 - 2.84292i) q^{90} +(-9.53860 - 7.82813i) q^{91} +(7.12927 - 12.8252i) q^{92} +(6.84245 - 12.8013i) q^{93} +(-0.758109 - 0.462923i) q^{94} +(-1.58320 - 1.58320i) q^{95} +(-6.06641 + 11.5685i) q^{96} +(9.89082 - 9.89082i) q^{97} +(4.92158 - 1.18980i) q^{98} +(5.22437 + 2.79248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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