LMFDB - Embedded newform 889.2.f.c.128.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [889,2,Mod(128,889)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("889.128"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(889, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.09870073969$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			128.36
Character	$\chi$	$=$	889.128
Dual form			889.2.f.c.382.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24531 - 2.15694i) q^{2} +(-0.448739 - 0.777240i) q^{3} +(-2.10158 - 3.64005i) q^{4} +(0.262530 - 0.454716i) q^{5} -2.23528 q^{6} +(-2.22760 - 1.42751i) q^{7} -5.48724 q^{8} +(1.09727 - 1.90052i) q^{9} +(-0.653862 - 1.13252i) q^{10} +(-1.30679 - 2.26342i) q^{11} +(-1.88613 + 3.26687i) q^{12} +1.45191 q^{13} +(-5.85311 + 3.02710i) q^{14} -0.471231 q^{15} +(-2.63014 + 4.55553i) q^{16} +(2.27602 + 3.94218i) q^{17} +(-2.73287 - 4.73346i) q^{18} +(-0.100839 + 0.174659i) q^{19} -2.20692 q^{20} +(-0.109909 + 2.37196i) q^{21} -6.50942 q^{22} +(0.235477 - 0.407858i) q^{23} +(2.46234 + 4.26490i) q^{24} +(2.36216 + 4.09137i) q^{25} +(1.80807 - 3.13167i) q^{26} -4.66198 q^{27} +(-0.514735 + 11.1086i) q^{28} -1.50355 q^{29} +(-0.586827 + 1.01641i) q^{30} +(0.900011 + 1.55886i) q^{31} +(1.06342 + 1.84189i) q^{32} +(-1.17282 + 2.03138i) q^{33} +11.3374 q^{34} +(-1.23393 + 0.638159i) q^{35} -9.22398 q^{36} +(0.480992 - 0.833102i) q^{37} +(0.251152 + 0.435008i) q^{38} +(-0.651528 - 1.12848i) q^{39} +(-1.44057 + 2.49513i) q^{40} +1.83977 q^{41} +(4.97930 + 3.19089i) q^{42} -6.33513 q^{43} +(-5.49265 + 9.51355i) q^{44} +(-0.576131 - 0.997888i) q^{45} +(-0.586482 - 1.01582i) q^{46} +(-1.91960 + 3.32485i) q^{47} +4.72098 q^{48} +(2.92441 + 6.35986i) q^{49} +11.7664 q^{50} +(2.04268 - 3.53802i) q^{51} +(-3.05130 - 5.28501i) q^{52} +(-1.53772 - 2.66341i) q^{53} +(-5.80560 + 10.0556i) q^{54} -1.37229 q^{55} +(12.2234 + 7.83311i) q^{56} +0.181002 q^{57} +(-1.87238 + 3.24305i) q^{58} +(-4.68890 - 8.12141i) q^{59} +(0.990330 + 1.71530i) q^{60} +(6.89125 - 11.9360i) q^{61} +4.48316 q^{62} +(-5.15729 + 2.66724i) q^{63} -5.22342 q^{64} +(0.381169 - 0.660205i) q^{65} +(2.92103 + 5.05938i) q^{66} +(-6.69052 - 11.5883i) q^{67} +(9.56649 - 16.5696i) q^{68} -0.422671 q^{69} +(-0.160149 + 3.45620i) q^{70} +10.5072 q^{71} +(-6.02096 + 10.4286i) q^{72} +(1.47152 + 2.54876i) q^{73} +(-1.19797 - 2.07494i) q^{74} +(2.11999 - 3.67192i) q^{75} +0.847689 q^{76} +(-0.320068 + 6.90747i) q^{77} -3.24541 q^{78} +(1.76927 - 3.06446i) q^{79} +(1.38098 + 2.39193i) q^{80} +(-1.19978 - 2.07808i) q^{81} +(2.29108 - 3.96827i) q^{82} +17.4538 q^{83} +(8.86503 - 4.58480i) q^{84} +2.39010 q^{85} +(-7.88919 + 13.6645i) q^{86} +(0.674700 + 1.16861i) q^{87} +(7.17066 + 12.4200i) q^{88} +(2.83313 - 4.90713i) q^{89} -2.86984 q^{90} +(-3.23427 - 2.07262i) q^{91} -1.97950 q^{92} +(0.807741 - 1.39905i) q^{93} +(4.78099 + 8.28091i) q^{94} +(0.0529467 + 0.0917064i) q^{95} +(0.954394 - 1.65306i) q^{96} +6.82742 q^{97} +(17.3596 + 1.61223i) q^{98} -5.73558 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 2 q^{2} - 11 q^{3} - 38 q^{4} - 16 q^{5} + 22 q^{6} + 3 q^{7} - 47 q^{9} - 12 q^{10} + 2 q^{11} - 30 q^{12} + 42 q^{13} - 2 q^{14} + 14 q^{15} - 46 q^{16} - 58 q^{17} + 13 q^{18} - 17 q^{19} + 88 q^{20}+ \cdots + 32 q^{99}+O(q^{100}) $ 76 * q + 2 * q^2 - 11 * q^3 - 38 * q^4 - 16 * q^5 + 22 * q^6 + 3 * q^7 - 47 * q^9 - 12 * q^10 + 2 * q^11 - 30 * q^12 + 42 * q^13 - 2 * q^14 + 14 * q^15 - 46 * q^16 - 58 * q^17 + 13 * q^18 - 17 * q^19 + 88 * q^20 + q^21 + 42 * q^22 - 7 * q^23 - 21 * q^24 - 52 * q^25 - 49 * q^26 + 70 * q^27 - 26 * q^28 - 4 * q^29 - 6 * q^30 - 2 * q^31 + 22 * q^32 - 29 * q^33 + 74 * q^34 + 22 * q^35 + 50 * q^36 - 11 * q^37 - 40 * q^38 - 2 * q^39 + 8 * q^40 + 136 * q^41 + 14 * q^42 - 76 * q^43 - 43 * q^44 - 60 * q^45 + 28 * q^46 - 35 * q^47 + 132 * q^48 + 73 * q^49 - 50 * q^50 + 3 * q^51 - 32 * q^52 + 18 * q^53 + 68 * q^54 + 38 * q^55 + 45 * q^56 - 62 * q^57 - 55 * q^58 - 21 * q^59 + 11 * q^60 - 5 * q^61 + 76 * q^62 + 53 * q^63 + 36 * q^64 + 9 * q^65 - 20 * q^66 - 6 * q^67 - 74 * q^68 + 106 * q^69 + 193 * q^70 - 52 * q^71 - 24 * q^72 - 22 * q^73 + 2 * q^74 - 38 * q^75 + 78 * q^76 + 5 * q^77 - 228 * q^78 + 14 * q^79 - 140 * q^80 - 58 * q^81 + 8 * q^82 + 92 * q^83 + 149 * q^84 - 22 * q^85 - 51 * q^86 - 59 * q^87 + 4 * q^88 - 74 * q^89 + 2 * q^90 + 65 * q^91 - 162 * q^92 - 92 * q^93 + 36 * q^94 - 20 * q^95 + 108 * q^96 + 132 * q^97 - 11 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/889\mathbb{Z}\right)^\times$.

$n$	$255$	$638$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.24531	−	2.15694i	0.880566	−	1.52518i	0.0298523	−	0.999554i	$-0.490496\pi$
$2$	1.24531	−	2.15694i	0.880566	−	1.52518i	0.850713	−	0.525630i	$-0.176170\pi$
$3$	−0.448739	−	0.777240i	−0.259080	−	0.448739i	0.706916	−	0.707298i	$-0.250086\pi$
$3$	−0.448739	−	0.777240i	−0.259080	−	0.448739i	−0.965996	+	0.258558i	$0.916753\pi$
$4$	−2.10158	−	3.64005i	−1.05079	−	1.82002i
$5$	0.262530	−	0.454716i	0.117407	−	0.203355i	−0.801332	−	0.598219i	$-0.795875\pi$
$5$	0.262530	−	0.454716i	0.117407	−	0.203355i	0.918739	+	0.394864i	$0.129208\pi$
$6$	−2.23528			−0.912547
$7$	−2.22760	−	1.42751i	−0.841954	−	0.539550i
$7$	−2.22760	−	1.42751i	−0.841954	−	0.539550i
$8$	−5.48724			−1.94003
$9$	1.09727	−	1.90052i	0.365755	−	0.633507i
$10$	−0.653862	−	1.13252i	−0.206769	−	0.358135i
$11$	−1.30679	−	2.26342i	−0.394012	−	0.682448i	0.598963	−	0.800777i	$-0.295580\pi$
$11$	−1.30679	−	2.26342i	−0.394012	−	0.682448i	−0.992974	+	0.118329i	$0.962246\pi$
$12$	−1.88613	+	3.26687i	−0.544478	+	0.943063i
$13$	1.45191			0.402686			0.201343	−	0.979521i	$-0.435469\pi$
$13$	1.45191			0.402686			0.201343	+	0.979521i	$0.435469\pi$
$14$	−5.85311	+	3.02710i	−1.56431	+	0.809026i
$15$	−0.471231			−0.121671
$16$	−2.63014	+	4.55553i	−0.657534	+	1.13888i
$17$	2.27602	+	3.94218i	0.552016	+	0.956119i	0.998129	+	0.0611429i	$0.0194745\pi$
$17$	2.27602	+	3.94218i	0.552016	+	0.956119i	−0.446113	+	0.894977i	$0.647192\pi$
$18$	−2.73287	−	4.73346i	−0.644143	−	1.11569i
$19$	−0.100839	+	0.174659i	−0.0231341	+	0.0400695i	−0.877361	−	0.479831i	$-0.840698\pi$
$19$	−0.100839	+	0.174659i	−0.0231341	+	0.0400695i	0.854227	+	0.519901i	$0.174031\pi$
$20$	−2.20692			−0.493481
$21$	−0.109909	+	2.37196i	−0.0239840	+	0.517604i
$22$	−6.50942			−1.38781
$23$	0.235477	−	0.407858i	0.0491003	−	0.0850442i	−0.840431	−	0.541919i	$-0.817698\pi$
$23$	0.235477	−	0.407858i	0.0491003	−	0.0850442i	0.889531	+	0.456875i	$0.151031\pi$
$24$	2.46234	+	4.26490i	0.502623	+	0.870569i
$25$	2.36216	+	4.09137i	0.472431	+	0.818275i
$26$	1.80807	−	3.13167i	0.354592	−	0.614171i
$27$	−4.66198			−0.897199
$28$	−0.514735	+	11.1086i	−0.0972758	+	2.09933i
$29$	−1.50355			−0.279201			−0.139601	−	0.990208i	$-0.544582\pi$
$29$	−1.50355			−0.279201			−0.139601	+	0.990208i	$0.544582\pi$
$30$	−0.586827	+	1.01641i	−0.107140	+	0.185571i
$31$	0.900011	+	1.55886i	0.161647	+	0.279980i	0.935459	−	0.353434i	$-0.114986\pi$
$31$	0.900011	+	1.55886i	0.161647	+	0.279980i	−0.773813	+	0.633415i	$0.781653\pi$
$32$	1.06342	+	1.84189i	0.187987	+	0.325604i
$33$	−1.17282	+	2.03138i	−0.204161	+	0.353617i
$34$	11.3374			1.94434
$35$	−1.23393	+	0.638159i	−0.208571	+	0.107869i
$36$	−9.22398			−1.53733
$37$	0.480992	−	0.833102i	0.0790745	−	0.136961i	−0.823776	−	0.566915i	$-0.808137\pi$
$37$	0.480992	−	0.833102i	0.0790745	−	0.136961i	0.902851	+	0.429954i	$0.141470\pi$
$38$	0.251152	+	0.435008i	0.0407422	+	0.0705676i
$39$	−0.651528	−	1.12848i	−0.104328	−	0.180701i
$40$	−1.44057	+	2.49513i	−0.227773	+	0.394515i
$41$	1.83977			0.287324			0.143662	−	0.989627i	$-0.454112\pi$
$41$	1.83977			0.287324			0.143662	+	0.989627i	$0.454112\pi$
$42$	4.97930	+	3.19089i	0.768323	+	0.492365i
$43$	−6.33513			−0.966098			−0.483049	−	0.875593i	$-0.660471\pi$
$43$	−6.33513			−0.966098			−0.483049	+	0.875593i	$0.660471\pi$
$44$	−5.49265	+	9.51355i	−0.828048	+	1.43422i
$45$	−0.576131	−	0.997888i	−0.0858845	−	0.148756i
$46$	−0.586482	−	1.01582i	−0.0864721	−	0.149774i
$47$	−1.91960	+	3.32485i	−0.280003	+	0.484979i	−0.971385	−	0.237510i	$-0.923669\pi$
$47$	−1.91960	+	3.32485i	−0.280003	+	0.484979i	0.691382	+	0.722489i	$0.257002\pi$
$48$	4.72098			0.681415
$49$	2.92441	+	6.35986i	0.417772	+	0.908552i
$50$	11.7664			1.66403
$51$	2.04268	−	3.53802i	0.286032	−	0.495423i
$52$	−3.05130	−	5.28501i	−0.423139	−	0.732899i
$53$	−1.53772	−	2.66341i	−0.211222	−	0.365847i	0.740875	−	0.671643i	$-0.234411\pi$
$53$	−1.53772	−	2.66341i	−0.211222	−	0.365847i	−0.952097	+	0.305795i	$0.901078\pi$
$54$	−5.80560	+	10.0556i	−0.790043	+	1.36839i
$55$	−1.37229			−0.185039
$56$	12.2234	+	7.83311i	1.63342	+	1.04674i
$57$	0.181002			0.0239743
$58$	−1.87238	+	3.24305i	−0.245855	+	0.425834i
$59$	−4.68890	−	8.12141i	−0.610443	−	1.05732i	−0.991166	−	0.132629i	$-0.957658\pi$
$59$	−4.68890	−	8.12141i	−0.610443	−	1.05732i	0.380723	−	0.924689i	$-0.375675\pi$
$60$	0.990330	+	1.71530i	0.127851	+	0.221445i
$61$	6.89125	−	11.9360i	0.882334	−	1.52825i	0.0335958	−	0.999436i	$-0.489304\pi$
$61$	6.89125	−	11.9360i	0.882334	−	1.52825i	0.848739	−	0.528813i	$-0.177363\pi$
$62$	4.48316			0.569362
$63$	−5.15729	+	2.66724i	−0.649757	+	0.336040i
$64$	−5.22342			−0.652927
$65$	0.381169	−	0.660205i	0.0472782	−	0.0818883i
$66$	2.92103	+	5.05938i	0.359554	+	0.622766i
$67$	−6.69052	−	11.5883i	−0.817377	−	1.41574i	−0.907609	−	0.419817i	$-0.862094\pi$
$67$	−6.69052	−	11.5883i	−0.817377	−	1.41574i	0.0902317	−	0.995921i	$-0.471239\pi$
$68$	9.56649	−	16.5696i	1.16011	−	2.00936i
$69$	−0.422671			−0.0508836
$70$	−0.160149	+	3.45620i	−0.0191414	+	0.413095i
$71$	10.5072			1.24698			0.623490	−	0.781832i	$-0.285714\pi$
$71$	10.5072			1.24698			0.623490	+	0.781832i	$0.285714\pi$
$72$	−6.02096	+	10.4286i	−0.709577	+	1.22902i
$73$	1.47152	+	2.54876i	0.172229	+	0.298309i	0.939199	−	0.343374i	$-0.111570\pi$
$73$	1.47152	+	2.54876i	0.172229	+	0.298309i	−0.766970	+	0.641683i	$0.778236\pi$
$74$	−1.19797	−	2.07494i	−0.139261	−	0.241207i
$75$	2.11999	−	3.67192i	0.244795	−	0.423997i
$76$	0.847689			0.0972366
$77$	−0.320068	+	6.90747i	−0.0364752	+	0.787179i
$78$	−3.24541			−0.367470
$79$	1.76927	−	3.06446i	0.199058	−	0.344779i	−0.749165	−	0.662383i	$-0.769545\pi$
$79$	1.76927	−	3.06446i	0.199058	−	0.344779i	0.948223	+	0.317604i	$0.102878\pi$
$80$	1.38098	+	2.39193i	0.154398	+	0.267426i
$81$	−1.19978	−	2.07808i	−0.133309	−	0.230898i
$82$	2.29108	−	3.96827i	0.253008	−	0.438222i
$83$	17.4538			1.91580			0.957902	−	0.287094i	$-0.0926893\pi$
$83$	17.4538			1.91580			0.957902	+	0.287094i	$0.0926893\pi$
$84$	8.86503	−	4.58480i	0.967255	−	0.500243i
$85$	2.39010			0.259242
$86$	−7.88919	+	13.6645i	−0.850713	+	1.47348i
$87$	0.674700	+	1.16861i	0.0723354	+	0.125289i
$88$	7.17066	+	12.4200i	0.764395	+	1.32397i
$89$	2.83313	−	4.90713i	0.300312	−	0.520155i	−0.675895	−	0.736998i	$-0.736243\pi$
$89$	2.83313	−	4.90713i	0.300312	−	0.520155i	0.976206	+	0.216843i	$0.0695760\pi$
$90$	−2.86984			−0.302508
$91$	−3.23427	−	2.07262i	−0.339043	−	0.217269i
$92$	−1.97950			−0.206377
$93$	0.807741	−	1.39905i	0.0837588	−	0.145075i
$94$	4.78099	+	8.28091i	0.493121	+	0.854111i
$95$	0.0529467	+	0.0917064i	0.00543222	+	0.00940888i
$96$	0.954394	−	1.65306i	0.0974075	−	0.168715i
$97$	6.82742			0.693219			0.346610	−	0.938009i	$-0.387333\pi$
$97$	6.82742			0.693219			0.346610	+	0.938009i	$0.387333\pi$
$98$	17.3596	+	1.61223i	1.75358	+	0.162860i
$99$	−5.73558			−0.576447
$100$	9.92853	−	17.1967i	0.992853	−	1.71967i
$101$	−3.49520	−	6.05386i	−0.347785	−	0.602381i	0.638071	−	0.769978i	$-0.279733\pi$
$101$	−3.49520	−	6.05386i	−0.347785	−	0.602381i	−0.985856	+	0.167596i	$0.946399\pi$
$102$	−5.08753	−	8.81186i	−0.503740	−	0.872504i
$103$	−2.00406	+	3.47114i	−0.197466	+	0.342021i	−0.947706	−	0.319144i	$-0.896605\pi$
$103$	−2.00406	+	3.47114i	−0.197466	+	0.342021i	0.750240	+	0.661165i	$0.229938\pi$
$104$	−7.96696			−0.781224
$105$	1.04971	+	0.672689i	0.102442	+	0.0656477i
$106$	−7.65974			−0.743980
$107$	3.05688	−	5.29468i	0.295520	−	0.511856i	−0.679586	−	0.733596i	$-0.737840\pi$
$107$	3.05688	−	5.29468i	0.295520	−	0.511856i	0.975106	+	0.221740i	$0.0711737\pi$
$108$	9.79754	+	16.9698i	0.942769	+	1.63292i
$109$	2.24913	+	3.89561i	0.215428	+	0.373132i	0.953405	−	0.301694i	$-0.0975521\pi$
$109$	2.24913	+	3.89561i	0.215428	+	0.373132i	−0.737977	+	0.674826i	$0.764219\pi$
$110$	−1.70892	+	2.95993i	−0.162939	+	0.282219i
$111$	−0.863360			−0.0819465
$112$	12.3620	−	6.39334i	1.16810	−	0.604114i
$113$	−7.47274			−0.702977			−0.351488	−	0.936192i	$-0.614324\pi$
$113$	−7.47274			−0.702977			−0.351488	+	0.936192i	$0.614324\pi$
$114$	0.225404	−	0.390410i	0.0211110	−	0.0365653i
$115$	−0.123640	−	0.214150i	−0.0115294	−	0.0199696i
$116$	3.15983	+	5.47298i	0.293382	+	0.508153i
$117$	1.59313	−	2.75938i	0.147285	−	0.255105i
$118$	−23.3565			−2.15014
$119$	0.557459	−	12.0307i	0.0511022	−	1.10285i
$120$	2.58576			0.236046
$121$	2.08461	−	3.61064i	0.189510	−	0.328240i
$122$	−17.1635	−	29.7280i	−1.55391	−	2.69145i
$123$	−0.825579	−	1.42994i	−0.0744399	−	0.128934i
$124$	3.78290	−	6.55217i	0.339714	−	0.588402i
$125$	5.10585			0.456681
$126$	−0.669354	+	14.4455i	−0.0596308	+	1.28691i
$127$	1.00000			0.0887357
$127$	1.00000			0.0887357
$128$	−8.63159	+	14.9504i	−0.762932	+	1.32144i
$129$	2.84282	+	4.92391i	0.250297	+	0.433526i
$130$	−0.949346	−	1.64432i	−0.0832632	−	0.144216i
$131$	−0.00535191	+	0.00926978i	−0.000467599	+	0.000809905i	−0.866259	−	0.499595i	$-0.833482\pi$
$131$	−0.00535191	+	0.00926978i	−0.000467599	+	0.000809905i	0.865792	+	0.500405i	$0.166816\pi$
$132$	9.85908			0.858122
$133$	0.473958	−	0.245120i	0.0410973	−	0.0212546i
$134$	−33.3270			−2.87902
$135$	−1.22391	+	2.11988i	−0.105338	+	0.182450i
$136$	−12.4891	−	21.6317i	−1.07093	−	1.85490i
$137$	1.23789	+	2.14409i	0.105760	+	0.183182i	0.914048	−	0.405605i	$-0.132939\pi$
$137$	1.23789	+	2.14409i	0.105760	+	0.183182i	−0.808288	+	0.588787i	$0.799606\pi$
$138$	−0.526355	+	0.911674i	−0.0448063	+	0.0776069i
$139$	−5.74197			−0.487028			−0.243514	−	0.969897i	$-0.578300\pi$
$139$	−5.74197			−0.487028			−0.243514	+	0.969897i	$0.578300\pi$
$140$	4.91613	+	3.15040i	0.415489	+	0.266258i
$141$	3.44560			0.290172
$142$	13.0847	−	22.6634i	1.09805	−	1.90187i
$143$	−1.89734	−	3.28628i	−0.158663	−	0.274813i
$144$	5.77191	+	9.99725i	0.480993	+	0.833104i
$145$	−0.394726	+	0.683686i	−0.0327802	+	0.0567770i
$146$	7.33000			0.606635
$147$	3.63084	−	5.12688i	0.299467	−	0.422858i
$148$	−4.04338			−0.332363
$149$	−2.97753	+	5.15723i	−0.243928	+	0.422496i	−0.961830	−	0.273648i	$-0.911770\pi$
$149$	−2.97753	+	5.15723i	−0.243928	+	0.422496i	0.717901	+	0.696145i	$0.245103\pi$
$150$	−5.28007	−	9.14535i	−0.431116	−	0.746714i
$151$	−7.89503	−	13.6746i	−0.642488	−	1.11282i	−0.984875	−	0.173264i	$-0.944569\pi$
$151$	−7.89503	−	13.6746i	−0.642488	−	1.11282i	0.342387	−	0.939559i	$-0.388765\pi$
$152$	0.553329	−	0.958395i	0.0448809	−	0.0777361i
$153$	9.98959			0.807611
$154$	14.5004	+	9.29229i	1.16847	+	0.748794i
$155$	0.945120			0.0759139
$156$	−2.73848	+	4.74318i	−0.219254	+	0.379759i
$157$	3.27313	+	5.66923i	0.261224	+	0.452454i	0.966568	−	0.256412i	$-0.0825404\pi$
$157$	3.27313	+	5.66923i	0.261224	+	0.452454i	−0.705343	+	0.708866i	$0.749207\pi$
$158$	−4.40657	−	7.63239i	−0.350567	−	0.607201i
$159$	−1.38007	+	2.39035i	−0.109447	+	0.189567i
$160$	1.11672			0.0882842
$161$	−1.10677	+	0.572397i	−0.0872258	+	0.0451112i
$162$	−5.97639			−0.469549
$163$	−3.15013	+	5.45618i	−0.246737	+	0.427361i	−0.962619	−	0.270861i	$-0.912692\pi$
$163$	−3.15013	+	5.45618i	−0.246737	+	0.427361i	0.715882	+	0.698222i	$0.246025\pi$
$164$	−3.86643	−	6.69686i	−0.301918	−	0.522937i
$165$	0.615799	+	1.06660i	0.0479399	+	0.0830343i
$166$	21.7354	−	37.6468i	1.68699	−	2.92196i
$167$	16.4914			1.27614			0.638072	−	0.769976i	$-0.279732\pi$
$167$	16.4914			1.27614			0.638072	+	0.769976i	$0.279732\pi$
$168$	0.603094	−	13.0155i	0.0465297	−	1.00417i
$169$	−10.8920			−0.837844
$170$	2.97640	−	5.15528i	0.228280	−	0.395392i
$171$	0.221295	+	0.383294i	0.0169229	+	0.0293112i
$172$	13.3138	+	23.0602i	1.01517	+	1.75832i
$173$	−10.5980	+	18.3563i	−0.805751	+	1.39560i	0.110032	+	0.993928i	$0.464905\pi$
$173$	−10.5980	+	18.3563i	−0.805751	+	1.39560i	−0.915783	+	0.401673i	$0.868429\pi$
$174$	3.36084			0.254784
$175$	0.578556	−	12.4860i	0.0437348	−	0.943850i
$176$	13.7481			1.03630
$177$	−4.20819	+	7.28880i	−0.316307	+	0.547859i
$178$	−7.05625	−	12.2218i	−0.528888	−	0.916061i
$179$	3.12847	+	5.41868i	0.233833	+	0.405011i	0.958933	−	0.283633i	$-0.0915397\pi$
$179$	3.12847	+	5.41868i	0.233833	+	0.405011i	−0.725100	+	0.688644i	$0.758206\pi$
$180$	−2.42157	+	4.19429i	−0.180493	+	0.312624i
$181$	7.21573			0.536341			0.268171	−	0.963371i	$-0.413581\pi$
$181$	7.21573			0.536341			0.268171	+	0.963371i	$0.413581\pi$
$182$	−8.49816	+	4.39506i	−0.629926	+	0.325784i
$183$	−12.3695			−0.914380
$184$	−1.29212	+	2.23801i	−0.0952561	+	0.164988i
$185$	−0.252550	−	0.437429i	−0.0185678	−	0.0321604i
$186$	−2.01177	−	3.48449i	−0.147510	−	0.255495i
$187$	5.94855	−	10.3032i	0.435001	−	0.753444i
$188$	16.1368			1.17690
$189$	10.3850	+	6.65505i	0.755400	+	0.484083i
$190$	0.263740			0.0191337
$191$	−11.5057	+	19.9285i	−0.832524	+	1.44197i	0.0635070	+	0.997981i	$0.479771\pi$
$191$	−11.5057	+	19.9285i	−0.832524	+	1.44197i	−0.896031	+	0.443992i	$0.853562\pi$
$192$	2.34395	+	4.05984i	0.169160	+	0.292994i
$193$	−6.70506	−	11.6135i	−0.482641	−	0.835959i	0.517160	−	0.855888i	$-0.326989\pi$
$193$	−6.70506	−	11.6135i	−0.482641	−	0.835959i	−0.999801	+	0.0199298i	$0.993656\pi$
$194$	8.50223	−	14.7263i	0.610425	−	1.05729i
$195$	−0.684183			−0.0489954
$196$	17.0043	−	24.0108i	1.21459	−	1.71505i
$197$	4.15719			0.296187			0.148094	−	0.988973i	$-0.452686\pi$
$197$	4.15719			0.296187			0.148094	+	0.988973i	$0.452686\pi$
$198$	−7.14256	+	12.3713i	−0.507600	+	0.879188i
$199$	2.37768	+	4.11827i	0.168549	+	0.291936i	0.937910	−	0.346879i	$-0.112758\pi$
$199$	2.37768	+	4.11827i	0.168549	+	0.291936i	−0.769361	+	0.638815i	$0.779425\pi$
$200$	−12.9617	−	22.4503i	−0.916531	−	1.58748i
$201$	−6.00460	+	10.4003i	−0.423532	+	0.733579i
$202$	−17.4104			−1.22499
$203$	3.34930	+	2.14633i	0.235075	+	0.150643i
$204$	−17.1714			−1.20224
$205$	0.482996	−	0.836573i	0.0337339	−	0.0584288i
$206$	4.99135	+	8.64527i	0.347764	+	0.602344i
$207$	−0.516761	−	0.895057i	−0.0359174	−	0.0622107i
$208$	−3.81871	+	6.61420i	−0.264780	+	0.458612i
$209$	0.527103			0.0364605
$210$	2.75816	−	1.42646i	0.190331	−	0.0984352i
$211$	27.7227			1.90851			0.954254	−	0.298997i	$-0.0966520\pi$
$211$	27.7227			1.90851			0.954254	+	0.298997i	$0.0966520\pi$
$212$	−6.46329	+	11.1948i	−0.443901	+	0.768859i
$213$	−4.71501	−	8.16664i	−0.323067	−	0.559569i
$214$	−7.61352	−	13.1870i	−0.520450	−	0.901445i
$215$	−1.66316	+	2.88068i	−0.113427	+	0.196461i
$216$	25.5814			1.74059
$217$	0.220437	−	4.75731i	0.0149643	−	0.322947i
$218$	11.2034			0.758793
$219$	1.32066	−	2.28745i	0.0892421	−	0.154572i
$220$	2.88397	+	4.99519i	0.194437	+	0.336776i
$221$	3.30457	+	5.72368i	0.222289	+	0.385016i
$222$	−1.07515	+	1.86221i	−0.0721593	+	0.124983i
$223$	19.5825			1.31134			0.655671	−	0.755047i	$-0.272386\pi$
$223$	19.5825			1.31134			0.655671	+	0.755047i	$0.272386\pi$
$224$	0.260460	−	5.62104i	0.0174027	−	0.375572i
$225$	10.3677			0.691177
$226$	−9.30587	+	16.1182i	−0.619017	+	1.07217i
$227$	−4.75695	−	8.23927i	−0.315730	−	0.546860i	0.663863	−	0.747854i	$-0.268916\pi$
$227$	−4.75695	−	8.23927i	−0.315730	−	0.546860i	−0.979592	+	0.200995i	$0.935583\pi$
$228$	−0.380391	−	0.658857i	−0.0251920	−	0.0436339i
$229$	−3.98104	+	6.89536i	−0.263074	+	0.455658i	−0.967057	−	0.254559i	$-0.918070\pi$
$229$	−3.98104	+	6.89536i	−0.263074	+	0.455658i	0.703983	+	0.710217i	$0.251403\pi$
$230$	−0.615877			−0.0406097
$231$	5.51238	−	2.85088i	0.362688	−	0.187574i
$232$	8.25031			0.541660
$233$	−1.38156	+	2.39293i	−0.0905091	+	0.156766i	−0.907725	−	0.419565i	$-0.862183\pi$
$233$	−1.38156	+	2.39293i	−0.0905091	+	0.156766i	0.817216	+	0.576331i	$0.195516\pi$
$234$	−3.96787	−	6.87255i	−0.259388	−	0.449273i
$235$	1.00791	+	1.74575i	0.0657486	+	0.113880i
$236$	−19.7082	+	34.1356i	−1.28290	+	2.22204i
$237$	−3.17576			−0.206288
$238$	−25.2551	−	16.1843i	−1.63705	−	1.04907i
$239$	−29.2782			−1.89385			−0.946924	−	0.321458i	$-0.895827\pi$
$239$	−29.2782			−1.89385			−0.946924	+	0.321458i	$0.895827\pi$
$240$	1.23940	−	2.14670i	0.0800030	−	0.138569i
$241$	0.718774	+	1.24495i	0.0463003	+	0.0801944i	0.888247	−	0.459367i	$-0.151924\pi$
$241$	0.718774	+	1.24495i	0.0463003	+	0.0801944i	−0.841947	+	0.539561i	$0.818590\pi$
$242$	−5.19195	−	8.99272i	−0.333751	−	0.578074i
$243$	−8.06975	+	13.9772i	−0.517675	+	0.896639i
$244$	−57.9301			−3.70860
$245$	3.65967	+	0.339883i	0.233808	+	0.0217143i
$246$	−4.11240			−0.262197
$247$	−0.146409	+	0.253588i	−0.00931580	+	0.0161354i
$248$	−4.93858	−	8.55386i	−0.313600	−	0.543171i
$249$	−7.83221	−	13.5658i	−0.496346	−	0.859697i
$250$	6.35836	−	11.0130i	0.402138	−	0.696523i
$251$	−9.26401			−0.584739			−0.292370	−	0.956305i	$-0.594444\pi$
$251$	−9.26401			−0.584739			−0.292370	+	0.956305i	$0.594444\pi$
$252$	20.5473	+	13.1674i	1.29436	+	0.829466i
$253$	−1.23087			−0.0773844
$254$	1.24531	−	2.15694i	0.0781376	−	0.135338i
$255$	−1.07253	−	1.85768i	−0.0671644	−	0.116332i
$256$	16.2746	+	28.1884i	1.01716	+	1.76177i
$257$	5.34788	−	9.26279i	0.333591	−	0.577797i	−0.649622	−	0.760257i	$-0.725073\pi$
$257$	5.34788	−	9.26279i	0.333591	−	0.577797i	0.983213	+	0.182460i	$0.0584061\pi$
$258$	14.1608			0.881610
$259$	−2.26072	+	1.16920i	−0.140474	+	0.0726503i
$260$	−3.20424			−0.198718
$261$	−1.64979	+	2.85752i	−0.102119	+	0.176876i
$262$	0.0133296	+	0.0230875i	0.000823503	+	0.00142635i
$263$	10.7959	+	18.6990i	0.665701	+	1.15303i	0.979095	+	0.203405i	$0.0652007\pi$
$263$	10.7959	+	18.6990i	0.665701	+	1.15303i	−0.313394	+	0.949623i	$0.601466\pi$
$264$	6.43552	−	11.1466i	0.396079	−	0.686029i
$265$	−1.61479			−0.0991959
$266$	0.0615140	−	1.32755i	0.00377166	−	0.0813971i
$267$	−5.08536			−0.311219
$268$	−28.1214	+	48.7076i	−1.71779	+	2.97529i
$269$	3.07589	+	5.32760i	0.187540	+	0.324830i	0.944430	−	0.328714i	$-0.106615\pi$
$269$	3.07589	+	5.32760i	0.187540	+	0.324830i	−0.756889	+	0.653543i	$0.773282\pi$
$270$	3.04829	+	5.27980i	0.185513	+	0.321318i
$271$	0.118396	−	0.205068i	0.00719205	−	0.0124570i	−0.862407	−	0.506216i	$-0.831044\pi$
$271$	0.118396	−	0.205068i	0.00719205	−	0.0124570i	0.869599	+	0.493759i	$0.164377\pi$
$272$	−23.9450			−1.45188
$273$	−0.159577	+	3.44387i	−0.00965804	+	0.208432i
$274$	6.16621			0.372515
$275$	6.17368	−	10.6931i	0.372287	−	0.644820i
$276$	0.888278	+	1.53854i	0.0534680	+	0.0926094i
$277$	−3.23884	−	5.60984i	−0.194603	−	0.337063i	0.752167	−	0.658972i	$-0.229009\pi$
$277$	−3.23884	−	5.60984i	−0.194603	−	0.337063i	−0.946770	+	0.321910i	$0.895675\pi$
$278$	−7.15052	+	12.3851i	−0.428860	+	0.742807i
$279$	3.95021			0.236493
$280$	6.77084	−	3.50173i	0.404635	−	0.209268i
$281$	8.39461			0.500781			0.250390	−	0.968145i	$-0.419441\pi$
$281$	8.39461			0.500781			0.250390	+	0.968145i	$0.419441\pi$
$282$	4.29084	−	7.43195i	0.255516	−	0.442566i
$283$	11.6391	+	20.1595i	0.691871	+	1.19836i	0.971224	+	0.238167i	$0.0765466\pi$
$283$	11.6391	+	20.1595i	0.691871	+	1.19836i	−0.279353	+	0.960188i	$0.590120\pi$
$284$	−22.0818	−	38.2468i	−1.31032	−	2.26953i
$285$	0.0475186	−	0.0823046i	0.00281476	−	0.00487530i
$286$	−9.45107			−0.558853
$287$	−4.09828	−	2.62630i	−0.241914	−	0.155026i
$288$	4.66740			0.275029
$289$	−1.86053	+	3.22253i	−0.109443	+	0.189561i
$290$	0.983111	+	1.70280i	0.0577303	+	0.0999917i
$291$	−3.06373	−	5.30654i	−0.179599	−	0.311075i
$292$	6.18506	−	10.7128i	0.361953	−	0.626922i
$293$	5.84226			0.341308			0.170654	−	0.985331i	$-0.445412\pi$
$293$	5.84226			0.341308			0.170654	+	0.985331i	$0.445412\pi$
$294$	−6.53685	−	14.2160i	−0.381237	−	0.829096i
$295$	−4.92391			−0.286681
$296$	−2.63932	+	4.57143i	−0.153407	+	0.265709i
$297$	6.09223	+	10.5520i	0.353507	+	0.612292i
$298$	7.41587	+	12.8447i	0.429590	+	0.744072i
$299$	0.341890	−	0.592171i	0.0197720	−	0.0342461i
$300$	−17.8213			−1.02891
$301$	14.1121	+	9.04349i	0.813410	+	0.521258i
$302$	−39.3270			−2.26301
$303$	−3.13687	+	5.43321i	−0.180208	+	0.312130i
$304$	−0.530442	−	0.918753i	−0.0304229	−	0.0526941i
$305$	−3.61832	−	6.26712i	−0.207185	−	0.358854i
$306$	12.4401	−	21.5469i	0.711154	−	1.23176i
$307$	6.39402			0.364926			0.182463	−	0.983213i	$-0.441593\pi$
$307$	6.39402			0.364926			0.182463	+	0.983213i	$0.441593\pi$
$308$	25.8162	−	13.3515i	1.47101	−	0.760775i
$309$	3.59721			0.204638
$310$	1.17697	−	2.03856i	0.0668472	−	0.115783i
$311$	−7.71506	−	13.3629i	−0.437481	−	0.757739i	0.560014	−	0.828483i	$-0.310796\pi$
$311$	−7.71506	−	13.3629i	−0.437481	−	0.757739i	−0.997494	+	0.0707444i	$0.977463\pi$
$312$	3.57509	+	6.19223i	0.202400	+	0.350566i
$313$	9.86775	−	17.0914i	0.557758	−	0.966065i	−0.439925	−	0.898034i	$-0.644995\pi$
$313$	9.86775	−	17.0914i	0.557758	−	0.966065i	0.997683	−	0.0680310i	$-0.0216717\pi$
$314$	16.3042			0.920101
$315$	−0.141110	+	3.04533i	−0.00795066	+	0.171585i
$316$	−14.8730			−0.836674
$317$	5.92534	−	10.2630i	0.332800	−	0.576427i	−0.650259	−	0.759712i	$-0.725340\pi$
$317$	5.92534	−	10.2630i	0.332800	−	0.576427i	0.983060	+	0.183285i	$0.0586731\pi$
$318$	3.43723	+	5.95345i	0.192750	+	0.333853i
$319$	1.96482	+	3.40316i	0.110009	+	0.190540i
$320$	−1.37130	+	2.37517i	−0.0766582	+	0.132776i
$321$	−5.48698			−0.306253
$322$	−0.143645	+	3.10004i	−0.00800505	+	0.172759i
$323$	−0.918049			−0.0510816
$324$	−5.04288	+	8.73453i	−0.280160	+	0.485251i
$325$	3.42963	+	5.94029i	0.190242	+	0.329508i
$326$	7.84575	+	13.5892i	0.434536	+	0.752639i
$327$	2.01855	−	3.49623i	0.111626	−	0.193342i
$328$	−10.0953			−0.557418
$329$	9.02237	−	4.66617i	0.497419	−	0.257254i
$330$	3.06744			0.168857
$331$	4.86647	−	8.42898i	0.267486	−	0.463299i	−0.700726	−	0.713430i	$-0.747141\pi$
$331$	4.86647	−	8.42898i	0.267486	−	0.463299i	0.968212	+	0.250132i	$0.0804739\pi$
$332$	−36.6806	−	63.5327i	−2.01311	−	3.48681i
$333$	−1.05555	−	1.82827i	−0.0578439	−	0.100189i
$334$	20.5369	−	35.5710i	1.12373	−	1.94636i
$335$	−7.02585			−0.383863
$336$	−10.5165	−	6.73927i	−0.573720	−	0.367657i
$337$	27.8574			1.51749			0.758746	−	0.651387i	$-0.225812\pi$
$337$	27.8574			1.51749			0.758746	+	0.651387i	$0.225812\pi$
$338$	−13.5639	+	23.4933i	−0.737776	+	1.27787i
$339$	3.35332	+	5.80811i	0.182127	+	0.315453i
$340$	−5.02298	−	8.70006i	−0.272410	−	0.471827i
$341$	2.35225	−	4.07421i	0.127381	−	0.220631i
$342$	1.10232			0.0596067
$343$	2.56439	−	18.3419i	0.138464	−	0.990367i
$344$	34.7624			1.87426
$345$	−0.110964	+	0.192195i	−0.00597409	+	0.0103474i
$346$	26.3955	+	45.7184i	1.41903	+	2.45784i
$347$	−7.85989	−	13.6137i	−0.421941	−	0.730823i	0.574188	−	0.818723i	$-0.305318\pi$
$347$	−7.85989	−	13.6137i	−0.421941	−	0.730823i	−0.996129	+	0.0879002i	$0.971984\pi$
$348$	2.83588	−	4.91188i	0.152019	−	0.263305i
$349$	−25.6094			−1.37084			−0.685419	−	0.728149i	$-0.740381\pi$
$349$	−25.6094			−1.37084			−0.685419	+	0.728149i	$0.740381\pi$
$350$	−26.2109	−	16.7968i	−1.40103	−	0.897825i
$351$	−6.76876			−0.361290
$352$	2.77932	−	4.81393i	0.148138	−	0.256583i
$353$	7.83459	+	13.5699i	0.416993	+	0.722254i	0.995635	−	0.0933280i	$-0.0297505\pi$
$353$	7.83459	+	13.5699i	0.416993	+	0.722254i	−0.578642	+	0.815582i	$0.696417\pi$
$354$	10.4810	+	18.1536i	0.557058	+	0.964852i
$355$	2.75847	−	4.77780i	0.146404	−	0.253579i
$356$	−23.8163			−1.26226
$357$	−9.60085	+	4.96535i	−0.508131	+	0.262794i
$358$	15.5837			0.823622
$359$	−4.98729	+	8.63823i	−0.263219	+	0.455909i	−0.967095	−	0.254414i	$-0.918117\pi$
$359$	−4.98729	+	8.63823i	−0.263219	+	0.455909i	0.703877	+	0.710322i	$0.251451\pi$
$360$	3.16137	+	5.47565i	0.166619	+	0.288592i
$361$	9.47966	+	16.4193i	0.498930	+	0.864171i
$362$	8.98580	−	15.5639i	0.472283	−	0.818019i
$363$	−3.74178			−0.196392
$364$	−0.747347	+	16.1287i	−0.0391716	+	0.845372i
$365$	1.54528			0.0808836
$366$	−15.4038	+	26.6802i	−0.805172	+	1.39460i
$367$	−3.91901	−	6.78793i	−0.204571	−	0.354327i	0.745425	−	0.666589i	$-0.232247\pi$
$367$	−3.91901	−	6.78793i	−0.204571	−	0.354327i	−0.949996	+	0.312262i	$0.898913\pi$
$368$	1.23867	+	2.14544i	0.0645702	+	0.111839i
$369$	2.01872	−	3.49652i	0.105090	−	0.182022i
$370$	−1.25801			−0.0654007
$371$	−0.376630	+	8.12813i	−0.0195536	+	0.421991i
$372$	−6.79014			−0.352052
$373$	9.61390	−	16.6518i	0.497789	−	0.862196i	−0.502208	−	0.864747i	$-0.667479\pi$
$373$	9.61390	−	16.6518i	0.497789	−	0.862196i	0.999997	+	0.00255103i	$0.000812018\pi$
$374$	−14.8156	−	25.6613i	−0.766094	−	1.32691i
$375$	−2.29120	−	3.96847i	−0.118317	−	0.204931i
$376$	10.5333	−	18.2442i	0.543214	−	0.940874i
$377$	−2.18301			−0.112431
$378$	27.2871	−	14.1123i	1.40350	−	0.725857i
$379$	34.6924			1.78203			0.891014	−	0.453976i	$-0.149995\pi$
$379$	34.6924			1.78203			0.891014	+	0.453976i	$0.149995\pi$
$380$	0.222544	−	0.385457i	0.0114163	−	0.0197735i
$381$	−0.448739	−	0.777240i	−0.0229896	−	0.0398192i
$382$	28.6563	+	49.6342i	1.46618	+	2.53950i
$383$	−5.81375	+	10.0697i	−0.297069	+	0.514538i	−0.975464	−	0.220159i	$-0.929342\pi$
$383$	−5.81375	+	10.0697i	−0.297069	+	0.514538i	0.678395	+	0.734697i	$0.262676\pi$
$384$	15.4933			0.790642
$385$	3.05691	+	1.95896i	0.155794	+	0.0998378i
$386$	−33.3995			−1.69999
$387$	−6.95132	+	12.0400i	−0.353355	+	0.612030i
$388$	−14.3484	−	24.8521i	−0.728429	−	1.26168i
$389$	−3.35763	−	5.81558i	−0.170238	−	0.294862i	0.768265	−	0.640132i	$-0.221120\pi$
$389$	−3.35763	−	5.81558i	−0.170238	−	0.294862i	−0.938503	+	0.345271i	$0.887787\pi$
$390$	−0.852018	+	1.47574i	−0.0431436	+	0.0747269i
$391$	2.14380			0.108417
$392$	−16.0469	−	34.8981i	−0.810491	−	1.76262i
$393$	0.00960646			0.000484582
$394$	5.17698	−	8.96679i	0.260812	−	0.451740i
$395$	−0.928972	−	1.60903i	−0.0467417	−	0.0809589i
$396$	12.0538	+	20.8778i	0.605726	+	1.04915i
$397$	−9.26544	+	16.0482i	−0.465019	+	0.805437i	−0.999202	−	0.0399319i	$-0.987286\pi$
$397$	−9.26544	+	16.0482i	−0.465019	+	0.805437i	0.534183	+	0.845369i	$0.320619\pi$
$398$	11.8438			0.593675
$399$	−0.403201	−	0.258383i	−0.0201853	−	0.0129354i
$400$	−24.8512			−1.24256
$401$	−1.95867	+	3.39251i	−0.0978112	+	0.169414i	−0.910778	−	0.412895i	$-0.864517\pi$
$401$	−1.95867	+	3.39251i	−0.0978112	+	0.169414i	0.812967	+	0.582310i	$0.197851\pi$
$402$	14.9551	+	25.9031i	0.745895	+	1.29193i
$403$	1.30673	+	2.26333i	0.0650930	+	0.112744i
$404$	−14.6909	+	25.4454i	−0.730899	+	1.26595i
$405$	−1.25992			−0.0626057
$406$	8.80041	−	4.55138i	0.436757	−	0.225881i
$407$	−2.51422			−0.124625
$408$	−11.2087	+	19.4140i	−0.554912	+	0.961136i
$409$	11.9849	+	20.7584i	0.592614	+	1.02644i	0.993879	+	0.110476i	$0.0352374\pi$
$409$	11.9849	+	20.7584i	0.592614	+	1.02644i	−0.401265	+	0.915962i	$0.631429\pi$
$410$	−1.20296	−	2.08358i	−0.0594098	−	0.102901i
$411$	1.11098	−	1.92427i	0.0548006	−	0.0949174i
$412$	16.8468			0.829982
$413$	−1.14844	+	24.7847i	−0.0565110	+	1.21958i
$414$	−2.57411			−0.126510
$415$	4.58215	−	7.93652i	0.224929	−	0.389589i
$416$	1.54398	+	2.67426i	0.0757000	+	0.131116i
$417$	2.57665	+	4.46289i	0.126179	+	0.218548i
$418$	0.656405	−	1.13693i	0.0321058	−	0.0556089i
$419$	16.6001			0.810970			0.405485	−	0.914102i	$-0.367103\pi$
$419$	16.6001			0.810970			0.405485	+	0.914102i	$0.367103\pi$
$420$	0.242559	−	5.23472i	0.0118357	−	0.255428i
$421$	24.9623			1.21659			0.608294	−	0.793712i	$-0.291854\pi$
$421$	24.9623			1.21659			0.608294	+	0.793712i	$0.291854\pi$
$422$	34.5233	−	59.7961i	1.68057	−	2.91083i
$423$	4.21262	+	7.29648i	0.204825	+	0.354767i
$424$	8.43784	+	14.6148i	0.409778	+	0.709756i
$425$	−10.7526	+	18.6241i	−0.521579	+	0.903401i
$426$	−23.4866			−1.13793
$427$	−32.3898	+	16.7513i	−1.56745	+	0.810651i
$428$	−25.6972			−1.24212
$429$	−1.70282	+	2.94937i	−0.0822129	+	0.142397i
$430$	4.14230	+	7.17467i	0.199759	+	0.345993i
$431$	11.8693	+	20.5582i	0.571723	+	0.990254i	0.996389	+	0.0849035i	$0.0270582\pi$
$431$	11.8693	+	20.5582i	0.571723	+	0.990254i	−0.424666	+	0.905350i	$0.639608\pi$
$432$	12.2616	−	21.2378i	0.589939	−	1.02180i
$433$	26.6967			1.28296			0.641481	−	0.767139i	$-0.278320\pi$
$433$	26.6967			1.28296			0.641481	+	0.767139i	$0.278320\pi$
$434$	−9.98670	−	6.39978i	−0.479377	−	0.307199i
$435$	0.708517			0.0339708
$436$	9.45347	−	16.3739i	0.452739	−	0.784167i
$437$	0.0474906	+	0.0822562i	0.00227178	+	0.00393485i
$438$	−3.28926	−	5.69717i	−0.157167	−	0.272221i
$439$	−0.381229	+	0.660308i	−0.0181951	+	0.0315148i	−0.874980	−	0.484160i	$-0.839125\pi$
$439$	−0.381229	+	0.660308i	−0.0181951	+	0.0315148i	0.856784	+	0.515675i	$0.172459\pi$
$440$	7.53006			0.358982
$441$	15.2959	+	1.42057i	0.728376	+	0.0676461i
$442$	16.4608			0.782961
$443$	6.04312	−	10.4670i	0.287117	−	0.497302i	−0.686003	−	0.727599i	$-0.740636\pi$
$443$	6.04312	−	10.4670i	0.287117	−	0.497302i	0.973120	+	0.230297i	$0.0739697\pi$
$444$	1.81442	+	3.14267i	0.0861087	+	0.149145i
$445$	−1.48757	−	2.57654i	−0.0705174	−	0.122140i
$446$	24.3862	−	42.2382i	1.15472	−	2.00004i
$447$	5.34453			0.252788
$448$	11.6357	+	7.45650i	0.549734	+	0.352287i
$449$	−1.21186			−0.0571911			−0.0285955	−	0.999591i	$-0.509103\pi$
$449$	−1.21186			−0.0571911			−0.0285955	+	0.999591i	$0.509103\pi$
$450$	12.9109	−	22.3624i	0.608626	−	1.05417i
$451$	−2.40419	−	4.16419i	−0.113209	−	0.196084i
$452$	15.7046	+	27.2012i	0.738682	+	1.27943i
$453$	−7.08562	+	12.2727i	−0.332912	+	0.576620i
$454$	−23.6954			−1.11208
$455$	−1.79154	+	0.926547i	−0.0839889	+	0.0434372i
$456$	−0.993203			−0.0465110
$457$	13.4544	−	23.3038i	0.629372	−	1.09011i	−0.358305	−	0.933604i	$-0.616645\pi$
$457$	13.4544	−	23.3038i	0.629372	−	1.09011i	0.987678	−	0.156501i	$-0.0500213\pi$
$458$	9.91523	+	17.1737i	0.463308	+	0.802474i
$459$	−10.6108	−	18.3784i	−0.495268	−	0.857829i
$460$	−0.519677	+	0.900108i	−0.0242301	+	0.0419677i
$461$	−5.84995			−0.272459			−0.136230	−	0.990677i	$-0.543499\pi$
$461$	−5.84995			−0.272459			−0.136230	+	0.990677i	$0.543499\pi$
$462$	0.715441	−	15.4401i	0.0332853	−	0.718338i
$463$	6.82196			0.317043			0.158522	−	0.987355i	$-0.449327\pi$
$463$	6.82196			0.317043			0.158522	+	0.987355i	$0.449327\pi$
$464$	3.95453	−	6.84944i	0.183584	−	0.317977i
$465$	−0.424113	−	0.734585i	−0.0196678	−	0.0340656i
$466$	3.44094	+	5.95988i	0.159398	+	0.276086i
$467$	−16.2687	+	28.1783i	−0.752827	+	1.30393i	0.193620	+	0.981077i	$0.437977\pi$
$467$	−16.2687	+	28.1783i	−0.752827	+	1.30393i	−0.946447	+	0.322858i	$0.895356\pi$
$468$	−13.3924			−0.619062
$469$	−1.63869	+	35.3649i	−0.0756677	+	1.63300i
$470$	5.02062			0.231584
$471$	2.93757	−	5.08802i	0.135356	−	0.234443i
$472$	25.7291	+	44.5641i	1.18428	+	2.05123i
$473$	8.27868	+	14.3391i	0.380654	+	0.659312i
$474$	−3.95480	+	6.84991i	−0.181650	+	0.314627i
$475$	−0.952793			−0.0437171
$476$	−44.9637	+	23.2542i	−2.06091	+	1.06586i
$477$	−6.74915			−0.309022
$478$	−36.4603	+	63.1512i	−1.66766	+	2.88847i
$479$	−7.64409	−	13.2400i	−0.349268	−	0.604949i	0.636852	−	0.770986i	$-0.280236\pi$
$479$	−7.64409	−	13.2400i	−0.349268	−	0.604949i	−0.986120	+	0.166037i	$0.946903\pi$
$480$	−0.501115	−	0.867956i	−0.0228727	−	0.0396166i
$481$	0.698355	−	1.20959i	0.0318422	−	0.0551524i
$482$	3.58038			0.163082
$483$	0.941542	+	0.603369i	0.0428416	+	0.0274542i
$484$	−17.5239			−0.796540
$485$	1.79240	−	3.10453i	0.0813888	−	0.140970i
$486$	20.0987	+	34.8119i	0.911693	+	1.57910i
$487$	11.6410	+	20.1628i	0.527504	+	0.913663i	0.999486	+	0.0320550i	$0.0102052\pi$
$487$	11.6410	+	20.1628i	0.527504	+	0.913663i	−0.471983	+	0.881608i	$0.656461\pi$
$488$	−37.8139	+	65.4957i	−1.71176	+	2.96485i
$489$	5.65434			0.255698
$490$	5.29053	−	7.47042i	0.239002	−	0.337479i
$491$	16.4779			0.743639			0.371820	−	0.928305i	$-0.378734\pi$
$491$	16.4779			0.743639			0.371820	+	0.928305i	$0.378734\pi$
$492$	−3.47004	+	6.01029i	−0.156442	+	0.270965i
$493$	−3.42210	−	5.92725i	−0.154124	−	0.266950i
$494$	0.364649	+	0.631591i	0.0164063	+	0.0284166i
$495$	−1.50576	+	2.60806i	−0.0676790	+	0.117223i
$496$	−9.46860			−0.425153
$497$	−23.4059	−	14.9992i	−1.04990	−	0.672807i
$498$	−39.0141			−1.74826
$499$	12.9873	−	22.4946i	0.581390	−	1.00700i	−0.413925	−	0.910311i	$-0.635843\pi$
$499$	12.9873	−	22.4946i	0.581390	−	1.00700i	0.995315	−	0.0966856i	$-0.0308241\pi$
$500$	−10.7304	−	18.5855i	−0.479877	−	0.831171i
$501$	−7.40035	−	12.8178i	−0.330623	−	0.572657i
$502$	−11.5365	+	19.9819i	−0.514901	+	0.891835i
$503$	−22.6548			−1.01013			−0.505063	−	0.863082i	$-0.668531\pi$
$503$	−22.6548			−1.01013			−0.505063	+	0.863082i	$0.668531\pi$
$504$	28.2993	−	14.6358i	1.26055	−	0.651929i
$505$	−3.67038			−0.163330
$506$	−1.53282	+	2.65492i	−0.0681420	+	0.118025i
$507$	4.88766	+	8.46567i	0.217068	+	0.375974i
$508$	−2.10158	−	3.64005i	−0.0932427	−	0.161501i
$509$	−10.5563	+	18.2841i	−0.467901	+	0.810429i	−0.999327	−	0.0366760i	$-0.988323\pi$
$509$	−10.5563	+	18.2841i	−0.467901	+	0.810429i	0.531426	+	0.847105i	$0.321656\pi$
$510$	−5.34252			−0.236571
$511$	0.360417	−	7.77823i	0.0159439	−	0.344089i
$512$	46.5410			2.05684
$513$	0.470111	−	0.814256i	0.0207559	−	0.0359503i
$514$	−13.3195	−	23.0701i	−0.587498	−	1.01758i
$515$	1.05225	+	1.82256i	0.0463678	+	0.0803114i
$516$	11.9489	−	20.6960i	0.526019	−	0.911092i
$517$	10.0341			0.441297
$518$	−0.293414	+	6.33224i	−0.0128919	+	0.278223i
$519$	19.0230			0.835015
$520$	−2.09157	+	3.62270i	−0.0917213	+	0.158866i
$521$	−5.93230	−	10.2750i	−0.259899	−	0.450158i	0.706316	−	0.707897i	$-0.250356\pi$
$521$	−5.93230	−	10.2750i	−0.259899	−	0.450158i	−0.966215	+	0.257739i	$0.917023\pi$
$522$	4.10899	+	7.11698i	0.179846	+	0.311502i
$523$	−19.7339	+	34.1801i	−0.862903	+	1.49459i	0.00621204	+	0.999981i	$0.498023\pi$
$523$	−19.7339	+	34.1801i	−0.862903	+	1.49459i	−0.869115	+	0.494611i	$0.835311\pi$
$524$	0.0449899			0.00196539
$525$	−9.96420	+	5.15326i	−0.434873	+	0.224907i
$526$	53.7766			2.34477
$527$	−4.09689	+	7.09601i	−0.178463	+	0.309107i
$528$	−6.16933	−	10.6856i	−0.268485	−	0.465031i
$529$	11.3891	+	19.7265i	0.495178	+	0.857674i
$530$	−2.01091	+	3.48300i	−0.0873485	+	0.151292i
$531$	−20.5799			−0.893090
$532$	−1.88831	−	1.21009i	−0.0818687	−	0.0524640i
$533$	2.67118			0.115702
$534$	−6.33283	+	10.9688i	−0.274048	+	0.474666i
$535$	−1.60505	−	2.78003i	−0.0693923	−	0.120191i
$536$	36.7125	+	63.5879i	1.58574	+	2.74658i
$537$	2.80774	−	4.86315i	0.121163	−	0.209860i
$538$	15.3217			0.660566
$539$	10.5735	−	14.9302i	0.455432	−	0.643088i
$540$	10.2886			0.442751
$541$	9.26318	−	16.0443i	0.398255	−	0.689798i	−0.595255	−	0.803537i	$-0.702949\pi$
$541$	9.26318	−	16.0443i	0.398255	−	0.689798i	0.993511	+	0.113738i	$0.0362825\pi$
$542$	−0.294879	−	0.510746i	−0.0126661	−	0.0219384i
$543$	−3.23798	−	5.60835i	−0.138955	−	0.240677i
$544$	−4.84072	+	8.38437i	−0.207544	+	0.359477i
$545$	2.36186			0.101171
$546$	7.22948	+	4.63287i	0.309393	+	0.198269i
$547$	19.8599			0.849148			0.424574	−	0.905393i	$-0.360424\pi$
$547$	19.8599			0.849148			0.424574	+	0.905393i	$0.360424\pi$
$548$	5.20306	−	9.01196i	0.222264	−	0.384972i
$549$	−15.1231	−	26.1939i	−0.645437	−	1.11793i
$550$	−15.3763	−	26.6325i	−0.655646	−	1.13561i
$551$	0.151616	−	0.262607i	0.00645908	−	0.0111875i
$552$	2.31930			0.0987158
$553$	−8.31578	+	4.30074i	−0.353623	+	0.182886i
$554$	−16.1334			−0.685444
$555$	−0.226658	+	0.392583i	−0.00962110	+	0.0166642i
$556$	12.0672	+	20.9010i	0.511764	+	0.886402i
$557$	8.13454	+	14.0894i	0.344672	+	0.596989i	0.985294	−	0.170867i	$-0.0546569\pi$
$557$	8.13454	+	14.0894i	0.344672	+	0.596989i	−0.640622	+	0.767856i	$0.721324\pi$
$558$	4.91922	−	8.52034i	0.208247	−	0.360695i
$559$	−9.19801			−0.389035
$560$	0.338240	−	7.29963i	0.0142932	−	0.308466i
$561$	−10.6774			−0.450800
$562$	10.4539	−	18.1066i	0.440970	−	0.763783i
$563$	−15.9603	−	27.6440i	−0.672645	−	1.16506i	−0.977151	−	0.212545i	$-0.931825\pi$
$563$	−15.9603	−	27.6440i	−0.672645	−	1.16506i	0.304506	−	0.952510i	$-0.401509\pi$
$564$	−7.24122	−	12.5422i	−0.304910	−	0.528120i
$565$	−1.96182	+	3.39797i	−0.0825344	+	0.142954i
$566$	57.9769			2.43695
$567$	−0.293859	+	6.34184i	−0.0123409	+	0.266332i
$568$	−57.6557			−2.41918
$569$	9.33702	−	16.1722i	0.391428	−	0.677974i	−0.601210	−	0.799091i	$-0.705314\pi$
$569$	9.33702	−	16.1722i	0.391428	−	0.677974i	0.992638	+	0.121117i	$0.0386477\pi$
$570$	−0.118351	−	0.204989i	−0.00495716	−	0.00858605i
$571$	−15.3214	−	26.5375i	−0.641182	−	1.11056i	−0.985169	−	0.171585i	$-0.945111\pi$
$571$	−15.3214	−	26.5375i	−0.641182	−	1.11056i	0.343988	−	0.938974i	$-0.388222\pi$
$572$	−7.97481	+	13.8128i	−0.333444	+	0.577542i
$573$	20.6523			0.862761
$574$	−10.7684	+	5.56917i	−0.449464	+	0.232453i
$575$	2.22493			0.0927860
$576$	−5.73147	+	9.92720i	−0.238811	+	0.413634i
$577$	6.86958	+	11.8985i	0.285984	+	0.495339i	0.972847	−	0.231447i	$-0.0743461\pi$
$577$	6.86958	+	11.8985i	0.285984	+	0.495339i	−0.686863	+	0.726787i	$0.741013\pi$
$578$	4.63386	+	8.02608i	0.192743	+	0.333841i
$579$	−6.01765	+	10.4229i	−0.250085	+	0.433160i
$580$	3.31820			0.137781
$581$	−38.8801	−	24.9156i	−1.61302	−	1.03367i
$582$	−15.2612			−0.632595
$583$	−4.01895	+	6.96103i	−0.166448	+	0.288296i
$584$	−8.07461	−	13.9856i	−0.334130	−	0.578729i
$585$	−0.836488	−	1.44884i	−0.0345845	−	0.0599022i
$586$	7.27541	−	12.6014i	0.300544	−	0.520558i
$587$	43.1552			1.78121			0.890603	−	0.454782i	$-0.150283\pi$
$587$	43.1552			1.78121			0.890603	+	0.454782i	$0.150283\pi$
$588$	−26.2926	−	2.44186i	−1.08429	−	0.100701i
$589$	−0.363026			−0.0149582
$590$	−6.13178	+	10.6206i	−0.252442	+	0.437242i
$591$	−1.86549	−	3.23113i	−0.0767362	−	0.132911i
$592$	2.53015	+	4.38234i	0.103988	+	0.180113i
$593$	−18.9321	+	32.7914i	−0.777450	+	1.34658i	0.155957	+	0.987764i	$0.450154\pi$
$593$	−18.9321	+	32.7914i	−0.777450	+	1.34658i	−0.933407	+	0.358819i	$0.883180\pi$
$594$	30.3468			1.24514
$595$	−5.32418	−	3.41190i	−0.218270	−	0.139874i
$596$	25.0301			1.02527
$597$	2.13392	−	3.69606i	0.0873355	−	0.151270i
$598$	−0.851517	−	1.47487i	−0.0348211	−	0.0603120i
$599$	−21.7322	−	37.6412i	−0.887952	−	1.53798i	−0.842292	−	0.539021i	$-0.818794\pi$
$599$	−21.7322	−	37.6412i	−0.887952	−	1.53798i	−0.0456595	−	0.998957i	$-0.514539\pi$
$600$	−11.6329	+	20.1487i	−0.474910	+	0.822568i
$601$	−6.30594			−0.257225			−0.128612	−	0.991695i	$-0.541052\pi$
$601$	−6.30594			−0.257225			−0.128612	+	0.991695i	$0.541052\pi$
$602$	37.0802	−	19.1770i	1.51128	−	0.781598i
$603$	−29.3651			−1.19584
$604$	−33.1841	+	57.4766i	−1.35024	+	2.33869i
$605$	−1.09454	−	1.89581i	−0.0444995	−	0.0770755i
$606$	7.81273	+	13.5320i	0.317370	+	0.549701i
$607$	−17.3272	+	30.0116i	−0.703291	+	1.21814i	0.264014	+	0.964519i	$0.414953\pi$
$607$	−17.3272	+	30.0116i	−0.703291	+	1.21814i	−0.967305	+	0.253616i	$0.918380\pi$
$608$	−0.428937			−0.0173957
$609$	0.165252	−	3.56635i	0.00669637	−	0.144516i
$610$	−18.0237			−0.729759
$611$	−2.78708	+	4.82737i	−0.112753	+	0.195294i
$612$	−20.9940	−	36.3626i	−0.848630	−	1.46987i
$613$	10.2054	+	17.6763i	0.412192	+	0.713938i	0.995129	−	0.0985793i	$-0.0314298\pi$
$613$	10.2054	+	17.6763i	0.412192	+	0.713938i	−0.582937	+	0.812517i	$0.698096\pi$
$614$	7.96252	−	13.7915i	0.321341	−	0.556579i
$615$	−0.866957			−0.0349591
$616$	1.75629	−	37.9029i	0.0707630	−	1.52715i
$617$	−7.50281			−0.302052			−0.151026	−	0.988530i	$-0.548258\pi$
$617$	−7.50281			−0.302052			−0.151026	+	0.988530i	$0.548258\pi$
$618$	4.47963	−	7.75894i	0.180197	−	0.312110i
$619$	−8.58028	−	14.8615i	−0.344871	−	0.597333i	0.640460	−	0.767992i	$-0.278744\pi$
$619$	−8.58028	−	14.8615i	−0.344871	−	0.597333i	−0.985330	+	0.170659i	$0.945411\pi$
$620$	−1.98625	−	3.44028i	−0.0797697	−	0.138165i
$621$	−1.09779	+	1.90143i	−0.0440527	+	0.0763016i
$622$	−38.4305			−1.54092
$623$	−13.3161	+	6.88679i	−0.533498	+	0.275913i
$624$	6.85442			0.274397
$625$	−10.4703	+	18.1352i	−0.418814	+	0.725406i
$626$	−24.5768	−	42.5682i	−0.982285	−	1.70137i
$627$	−0.236532	−	0.409685i	−0.00944617	−	0.0163612i
$628$	13.7575	−	23.8287i	0.548985	−	0.950870i
$629$	4.37899			0.174602
$630$	6.39286	+	4.09674i	0.254698	+	0.163218i
$631$	8.55084			0.340403			0.170202	−	0.985409i	$-0.445558\pi$
$631$	8.55084			0.340403			0.170202	+	0.985409i	$0.445558\pi$
$632$	−9.70839	+	16.8154i	−0.386179	+	0.668882i
$633$	−12.4403	−	21.5472i	−0.494456	−	0.856423i
$634$	−14.7578	−	25.5612i	−0.586105	−	1.01516i
$635$	0.262530	−	0.454716i	0.0104182	−	0.0180448i
$636$	11.6013			0.460023
$637$	4.24596	+	9.23393i	0.168231	+	0.365861i
$638$	9.78720			0.387479
$639$	11.5292	−	19.9692i	0.456089	−	0.789970i
$640$	4.53211	+	7.84984i	0.179147	+	0.310292i
$641$	−11.3506	−	19.6598i	−0.448322	−	0.776517i	0.549955	−	0.835194i	$-0.314645\pi$
$641$	−11.3506	−	19.6598i	−0.448322	−	0.776517i	−0.998277	+	0.0586777i	$0.981312\pi$
$642$	−6.83298	+	11.8351i	−0.269676	+	0.467093i
$643$	10.9385			0.431374			0.215687	−	0.976463i	$-0.430801\pi$
$643$	10.9385			0.431374			0.215687	+	0.976463i	$0.430801\pi$
$644$	4.40952	+	2.82576i	0.173760	+	0.111350i
$645$	2.98531			0.117546
$646$	−1.14325	+	1.98017i	−0.0449807	+	0.0779089i
$647$	1.37721	+	2.38539i	0.0541436	+	0.0937795i	0.891827	−	0.452377i	$-0.149424\pi$
$647$	1.37721	+	2.38539i	0.0541436	+	0.0937795i	−0.837683	+	0.546156i	$0.816090\pi$
$648$	6.58349	+	11.4029i	0.258624	+	0.447950i
$649$	−12.2548	+	21.2259i	−0.481043	+	0.833191i
$650$	17.0838			0.670081
$651$	−3.79649	+	1.96346i	−0.148796	+	0.0769540i
$652$	26.4810			1.03708
$653$	17.5243	−	30.3529i	0.685778	−	1.18780i	−0.287414	−	0.957806i	$-0.592796\pi$
$653$	17.5243	−	30.3529i	0.685778	−	1.18780i	0.973192	−	0.229996i	$-0.0738712\pi$
$654$	−5.02743	−	8.70776i	−0.196588	−	0.340500i
$655$	0.00281008	+	0.00486720i	0.000109799	+	0.000190177i
$656$	−4.83885	+	8.38114i	−0.188925	+	0.327228i
$657$	6.45861			0.251975
$658$	1.17099	−	25.2715i	0.0456501	−	0.985185i
$659$	−44.9909			−1.75260			−0.876299	−	0.481767i	$-0.839995\pi$
$659$	−44.9909			−1.75260			−0.876299	+	0.481767i	$0.839995\pi$
$660$	2.58831	−	4.48308i	0.100750	−	0.174504i
$661$	−7.40286	−	12.8221i	−0.287938	−	0.498723i	0.685380	−	0.728186i	$-0.259636\pi$
$661$	−7.40286	−	12.8221i	−0.287938	−	0.498723i	−0.973317	+	0.229463i	$0.926303\pi$
$662$	−12.1205	−	20.9933i	−0.471077	−	0.815930i
$663$	2.96578	−	5.13688i	0.115181	−	0.199500i
$664$	−95.7732			−3.71672
$665$	0.0129681	−	0.279867i	0.000502881	−	0.0108528i
$666$	−5.25795			−0.203741
$667$	−0.354050	+	0.613233i	−0.0137089	+	0.0237445i
$668$	−34.6581	−	60.0296i	−1.34096	−	2.32261i
$669$	−8.78744	−	15.2203i	−0.339742	−	0.588451i
$670$	−8.74935	+	15.1543i	−0.338017	+	0.585462i
$671$	−36.0216			−1.39060
$672$	−4.48578	+	2.31994i	−0.173043	+	0.0894938i
$673$	−30.9268			−1.19214			−0.596070	−	0.802932i	$-0.703272\pi$
$673$	−30.9268			−1.19214			−0.596070	+	0.802932i	$0.703272\pi$
$674$	34.6911	−	60.0867i	1.33625	−	2.31445i
$675$	−11.0123	−	19.0739i	−0.423865	−	0.734155i
$676$	22.8904	+	39.6473i	0.880399	+	1.52490i
$677$	−25.6794	+	44.4779i	−0.986938	+	1.70943i	−0.353950	+	0.935264i	$0.615162\pi$
$677$	−25.6794	+	44.4779i	−0.986938	+	1.70943i	−0.632988	+	0.774162i	$0.718172\pi$
$678$	16.7036			0.641499
$679$	−15.2088	−	9.74624i	−0.583658	−	0.374026i
$680$	−13.1150			−0.502938
$681$	−4.26926	+	7.39457i	−0.163598	+	0.283361i
$682$	−5.85855	−	10.1473i	−0.224335	−	0.388560i
$683$	7.38965	+	12.7993i	0.282757	+	0.489750i	0.972063	−	0.234721i	$-0.0754176\pi$
$683$	7.38965	+	12.7993i	0.282757	+	0.489750i	−0.689306	+	0.724471i	$0.742084\pi$
$684$	0.930140	−	1.61105i	0.0355648	−	0.0616000i
$685$	1.29993			0.0496679
$686$	−36.3688	−	28.3725i	−1.38857	−	1.08327i
$687$	7.14579			0.272629
$688$	16.6622	−	28.8599i	0.635242	−	1.10027i
$689$	−2.23263	−	3.86702i	−0.0850563	−	0.147322i
$690$	0.276368	+	0.478684i	0.0105212	+	0.0182232i
$691$	16.3221	−	28.2707i	0.620922	−	1.07547i	−0.368393	−	0.929670i	$-0.620092\pi$
$691$	16.3221	−	28.2707i	0.620922	−	1.07547i	0.989314	−	0.145798i	$-0.0465749\pi$
$692$	89.0903			3.38670
$693$	12.7766	+	8.18762i	0.485342	+	0.311022i
$694$	−39.1519			−1.48619
$695$	−1.50744	+	2.61096i	−0.0571805	+	0.0990395i
$696$	−3.70224	−	6.41247i	−0.140333	−	0.243064i
$697$	4.18736	+	7.25272i	0.158608	+	0.274716i
$698$	−31.8915	+	55.2377i	−1.20711	+	2.09078i
$699$	2.47984			0.0937963
$700$	−46.6654	+	24.1343i	−1.76379	+	0.912191i
$701$	−28.6064			−1.08045			−0.540224	−	0.841521i	$-0.681661\pi$
$701$	−28.6064			−1.08045			−0.540224	+	0.841521i	$0.681661\pi$
$702$	−8.42919	+	14.5998i	−0.318139	+	0.551034i
$703$	0.0970057	+	0.168019i	0.00365864	+	0.00633695i
$704$	6.82590	+	11.8228i	0.257261	+	0.445589i
$705$	0.904575	−	1.56677i	0.0340683	−	0.0590080i
$706$	39.0259			1.46876
$707$	−0.856069	+	18.4750i	−0.0321958	+	0.694825i
$708$	35.3754			1.32949
$709$	2.00977	−	3.48103i	0.0754785	−	0.130733i	−0.825816	−	0.563940i	$-0.809285\pi$
$709$	2.00977	−	3.48103i	0.0754785	−	0.130733i	0.901294	+	0.433207i	$0.142618\pi$
$710$	−6.87028	−	11.8997i	−0.257837	−	0.446587i
$711$	−3.88271	−	6.72506i	−0.145613	−	0.252209i
$712$	−15.5461	+	26.9266i	−0.582614	+	1.00912i
$713$	0.847727			0.0317476
$714$	−1.24607	+	26.8918i	−0.0466332	+	1.00640i
$715$	−1.99243			−0.0745127
$716$	13.1495	−	22.7756i	0.491420	−	0.851164i
$717$	13.1383	+	22.7562i	0.490658	+	0.849844i
$718$	12.4214	+	21.5145i	0.463563	+	0.802915i
$719$	−1.18715	+	2.05620i	−0.0442731	+	0.0766833i	−0.887313	−	0.461168i	$-0.847431\pi$
$719$	−1.18715	+	2.05620i	−0.0442731	+	0.0766833i	0.843040	+	0.537851i	$0.180764\pi$
$720$	6.06121			0.225888
$721$	9.41934	−	4.87148i	0.350795	−	0.181423i
$722$	47.2204			1.75736
$723$	0.645084	−	1.11732i	0.0239909	−	0.0415535i
$724$	−15.1645	−	26.2656i	−0.563583	−	0.976154i
$725$	−3.55161	−	6.15157i	−0.131903	−	0.228463i
$726$	−4.65967	+	8.07078i	−0.172936	+	0.299535i
$727$	24.6101			0.912737			0.456368	−	0.889791i	$-0.349150\pi$
$727$	24.6101			0.912737			0.456368	+	0.889791i	$0.349150\pi$
$728$	17.7472	+	11.3729i	0.657755	+	0.421509i
$729$	7.28618			0.269858
$730$	1.92435	−	3.33307i	0.0712233	−	0.123362i
$731$	−14.4189	−	24.9742i	−0.533301	−	0.923705i
$732$	25.9955	+	45.0256i	0.960823	+	1.66419i
$733$	−9.50215	+	16.4582i	−0.350970	+	0.607897i	−0.986420	−	0.164245i	$-0.947481\pi$
$733$	−9.50215	+	16.4582i	−0.350970	+	0.607897i	0.635450	+	0.772142i	$0.280815\pi$
$734$	−19.5215			−0.720552
$735$	−1.37807	−	2.99696i	−0.0508309	−	0.110545i
$736$	1.00164			0.0369209
$737$	−17.4862	+	30.2870i	−0.644112	+	1.11563i
$738$	−5.02785	−	8.70850i	−0.185078	−	0.320564i
$739$	−17.5504	−	30.3981i	−0.645600	−	1.11821i	−0.984163	−	0.177268i	$-0.943274\pi$
$739$	−17.5504	−	30.3981i	−0.645600	−	1.11821i	0.338562	−	0.940944i	$-0.390059\pi$
$740$	−1.06151	+	1.83859i	−0.0390218	+	0.0675878i
$741$	0.262798			0.00965414
$742$	17.0628	+	10.9344i	0.626396	+	0.401414i
$743$	21.0754			0.773180			0.386590	−	0.922252i	$-0.373653\pi$
$743$	21.0754			0.773180			0.386590	+	0.922252i	$0.373653\pi$
$744$	−4.43227	+	7.67691i	−0.162495	+	0.281449i
$745$	1.56338	+	2.70786i	0.0572778	+	0.0992081i
$746$	−23.9445	−	41.4732i	−0.876672	−	1.51844i
$747$	19.1515	−	33.1713i	0.700716	−	1.21368i
$748$	−50.0055			−1.82838
$749$	−14.3677	+	7.43068i	−0.524986	+	0.271511i
$750$	−11.4130			−0.416743
$751$	−9.01353	+	15.6119i	−0.328908	+	0.569686i	−0.982296	−	0.187338i	$-0.940014\pi$
$751$	−9.01353	+	15.6119i	−0.328908	+	0.569686i	0.653387	+	0.757024i	$0.273347\pi$
$752$	−10.0976	−	17.4896i	−0.368222	−	0.637780i
$753$	4.15713	+	7.20035i	0.151494	+	0.262396i
$754$	−2.71852	+	4.70861i	−0.0990025	+	0.171477i
$755$	−8.29074			−0.301731
$756$	2.39969	−	51.7882i	0.0872757	−	1.88352i
$757$	4.30504			0.156469			0.0782347	−	0.996935i	$-0.475072\pi$
$757$	4.30504			0.156469			0.0782347	+	0.996935i	$0.475072\pi$
$758$	43.2027	−	74.8293i	1.56919	−	2.71792i
$759$	0.552342	+	0.956684i	0.0200487	+	0.0347254i
$760$	−0.290531	−	0.503215i	−0.0105387	−	0.0182535i
$761$	−8.84721	+	15.3238i	−0.320711	+	0.555488i	−0.980635	−	0.195845i	$-0.937255\pi$
$761$	−8.84721	+	15.3238i	−0.320711	+	0.555488i	0.659924	+	0.751332i	$0.270589\pi$
$762$	−2.23528			−0.0809755
$763$	0.550874	−	11.8885i	0.0199430	−	0.430394i
$764$	96.7208			3.49924
$765$	2.62257	−	4.54242i	0.0948192	−	0.164232i
$766$	14.4798	+	25.0798i	0.523177	+	0.906169i
$767$	−6.80784	−	11.7915i	−0.245817	−	0.425767i
$768$	14.6061	−	25.2985i	0.527052	−	0.912880i
$769$	30.3350			1.09391			0.546954	−	0.837163i	$-0.315787\pi$
$769$	30.3350			1.09391			0.546954	+	0.837163i	$0.315787\pi$
$770$	8.03214	−	4.15404i	0.289458	−	0.149701i
$771$	−9.59921			−0.345707
$772$	−28.1825	+	48.8135i	−1.01431	+	1.75684i
$773$	19.0957	+	33.0748i	0.686825	+	1.18962i	0.972859	+	0.231397i	$0.0743296\pi$
$773$	19.0957	+	33.0748i	0.686825	+	1.18962i	−0.286034	+	0.958219i	$0.592337\pi$
$774$	17.3131	+	29.9871i	0.622305	+	1.07786i
$775$	−4.25193	+	7.36456i	−0.152734	+	0.264543i
$776$	−37.4637			−1.34487
$777$	1.92322	+	1.23246i	0.0689952	+	0.0442142i
$778$	−16.7251			−0.599624
$779$	−0.185521	+	0.321333i	−0.00664699	+	0.0115129i
$780$	1.43787	+	2.49046i	0.0514839	+	0.0891727i
$781$	−13.7307	−	23.7823i	−0.491324	−	0.850999i
$782$	2.66969	−	4.62404i	0.0954679	−	0.165355i
$783$	7.00950			0.250499
$784$	−36.6641	−	3.40509i	−1.30943	−	0.121610i
$785$	3.43719			0.122678
$786$	0.0119630	−	0.0207205i	0.000426706	−	0.000739076i
$787$	−11.5332	−	19.9761i	−0.411115	−	0.712072i	0.583897	−	0.811828i	$-0.301527\pi$
$787$	−11.5332	−	19.9761i	−0.411115	−	0.712072i	−0.995012	+	0.0997560i	$0.968194\pi$
$788$	−8.73668	−	15.1324i	−0.311231	−	0.539068i
$789$	9.68905	−	16.7819i	0.344939	−	0.597453i
$790$	−4.62743			−0.164636
$791$	16.6463	+	10.6675i	0.591874	+	0.379291i
$792$	31.4725			1.11833
$793$	10.0055	−	17.3300i	0.355304	−	0.615405i
$794$	23.0767	+	39.9699i	0.818960	+	1.41848i
$795$	0.724621	+	1.25508i	0.0256997	+	0.0445131i
$796$	9.99379	−	17.3098i	0.354221	−	0.613528i
$797$	−40.2087			−1.42427			−0.712133	−	0.702044i	$-0.752271\pi$
$797$	−40.2087			−1.42427			−0.712133	+	0.702044i	$0.752271\pi$
$798$	−1.05943	+	0.547912i	−0.0375033	+	0.0193959i
$799$	−17.4762			−0.618263
$800$	−5.02391	+	8.70167i	−0.177622	+	0.307651i
$801$	−6.21740	−	10.7689i	−0.219681	−	0.380499i
$802$	4.87829	+	8.44945i	0.172258	+	0.298360i
$803$	3.84594	−	6.66137i	0.135720	−	0.235075i
$804$	50.4766			1.78017
$805$	−0.0302827	+	0.653538i	−0.00106732	+	0.0230342i
$806$	6.50913			0.229274
$807$	2.76055	−	4.78141i	0.0971759	−	0.168314i
$808$	19.1790	+	33.2190i	0.674714	+	1.16864i
$809$	−5.05480	−	8.75516i	−0.177717	−	0.307815i	0.763381	−	0.645948i	$-0.223538\pi$
$809$	−5.05480	−	8.75516i	−0.177717	−	0.307815i	−0.941098	+	0.338133i	$0.890205\pi$
$810$	−1.56898	+	2.71756i	−0.0551284	+	0.0954852i
$811$	30.6004			1.07452			0.537262	−	0.843416i	$-0.319459\pi$
$811$	30.6004			1.07452			0.537262	+	0.843416i	$0.319459\pi$
$812$	0.773927	−	16.7023i	0.0271595	−	0.586136i
$813$	−0.212516			−0.00745326
$814$	−3.13098	+	5.42301i	−0.109741	+	0.190076i
$815$	1.65401	+	2.86482i	0.0579373	+	0.100350i
$816$	10.7450	+	18.6110i	0.376152	+	0.651514i
$817$	0.638830	−	1.10649i	0.0223498	−	0.0387110i
$818$	59.6994			2.08734
$819$	−7.48790	+	3.87258i	−0.261648	+	0.135319i
$820$	−4.06022			−0.141789
$821$	−3.40220	+	5.89278i	−0.118738	+	0.205660i	−0.919268	−	0.393633i	$-0.871218\pi$
$821$	−3.40220	+	5.89278i	−0.118738	+	0.205660i	0.800530	+	0.599293i	$0.204551\pi$
$822$	−2.76702	−	4.79263i	−0.0965110	−	0.167162i
$823$	−18.5702	−	32.1646i	−0.647318	−	1.12119i	−0.983761	−	0.179483i	$-0.942557\pi$
$823$	−18.5702	−	32.1646i	−0.647318	−	1.12119i	0.336444	−	0.941704i	$-0.390776\pi$
$824$	10.9968	−	19.0470i	0.383090	−	0.663532i
$825$	−11.0815			−0.385808
$826$	52.0289	+	33.3417i	1.81032	+	1.16011i
$827$	24.5185			0.852591			0.426296	−	0.904584i	$-0.359818\pi$
$827$	24.5185			0.852591			0.426296	+	0.904584i	$0.359818\pi$
$828$	−2.17203	+	3.76207i	−0.0754834	+	0.130741i
$829$	22.0323	+	38.1611i	0.765215	+	1.32539i	0.940133	+	0.340808i	$0.110701\pi$
$829$	22.0323	+	38.1611i	0.765215	+	1.32539i	−0.174918	+	0.984583i	$0.555966\pi$
$830$	−11.4124	−	19.7668i	−0.396130	−	0.686116i
$831$	−2.90679	+	5.03471i	−0.100836	+	0.174652i
$832$	−7.58391			−0.262925
$833$	−18.4157	+	26.0037i	−0.638067	+	0.900975i
$834$	12.8349			0.444436
$835$	4.32950	−	7.49891i	0.149828	−	0.259511i
$836$	−1.10775	−	1.91868i	−0.0383123	−	0.0663589i
$837$	−4.19584	−	7.26740i	−0.145029	−	0.251198i
$838$	20.6723	−	35.8054i	0.714112	−	1.23688i
$839$	4.05620			0.140036			0.0700178	−	0.997546i	$-0.477694\pi$
$839$	4.05620			0.140036			0.0700178	+	0.997546i	$0.477694\pi$
$840$	−5.76003	−	3.69120i	−0.198740	−	0.127359i
$841$	−26.7394			−0.922047
$842$	31.0857	−	53.8421i	1.07129	−	1.85552i
$843$	−3.76699	−	6.52462i	−0.129742	−	0.224720i
$844$	−58.2615	−	100.912i	−2.00544	−	3.47353i
$845$	−2.85947	+	4.95275i	−0.0983688	+	0.170380i
$846$	20.9841			0.721447
$847$	−9.79791	+	5.06726i	−0.336660	+	0.174113i
$848$	16.1776			0.555543
$849$	10.4458	−	18.0927i	0.358500	−	0.620940i
$850$	26.7807	+	46.3855i	0.918569	+	1.59101i
$851$	−0.226525	−	0.392352i	−0.00776517	−	0.0134497i
$852$	−19.8180	+	34.3257i	−0.678952	+	1.17598i
$853$	50.0794			1.71469			0.857343	−	0.514745i	$-0.172113\pi$
$853$	50.0794			1.71469			0.857343	+	0.514745i	$0.172113\pi$
$854$	−4.20380	+	90.7231i	−0.143851	+	3.10448i
$855$	0.232387			0.00794745
$856$	−16.7739	+	29.0532i	−0.573319	+	0.993017i
$857$	−6.63830	−	11.4979i	−0.226760	−	0.392760i	0.730086	−	0.683355i	$-0.239480\pi$
$857$	−6.63830	−	11.4979i	−0.226760	−	0.392760i	−0.956846	+	0.290595i	$0.906147\pi$
$858$	4.24107	+	7.34574i	0.144788	+	0.250779i
$859$	−15.0067	+	25.9923i	−0.512021	+	0.886846i	0.487882	+	0.872909i	$0.337770\pi$
$859$	−15.0067	+	25.9923i	−0.512021	+	0.886846i	−0.999903	+	0.0139364i	$0.995564\pi$
$860$	13.9811			0.476751
$861$	−0.202207	+	4.36387i	−0.00689119	+	0.148720i
$862$	59.1236			2.01376
$863$	−22.5347	+	39.0313i	−0.767091	+	1.32864i	0.172043	+	0.985090i	$0.444963\pi$
$863$	−22.5347	+	39.0313i	−0.767091	+	1.32864i	−0.939134	+	0.343552i	$0.888370\pi$
$864$	−4.95763	−	8.58687i	−0.168662	−	0.292131i
$865$	5.56459	+	9.63815i	0.189202	+	0.327707i
$866$	33.2456	−	57.5831i	1.12973	−	1.95675i
$867$	3.33957			0.113418
$868$	−17.7801	+	9.19547i	−0.603496	+	0.312115i
$869$	−9.24824			−0.313725
$870$	0.882321	−	1.52823i	0.0299135	−	0.0518117i
$871$	−9.71401	−	16.8252i	−0.329147	−	0.570099i
$872$	−12.3415	−	21.3761i	−0.417937	−	0.723887i
$873$	7.49149	−	12.9756i	0.253549	−	0.439159i
$874$	0.236562			0.00800182
$875$	−11.3738	−	7.28868i	−0.384504	−	0.246402i
$876$	−11.1019			−0.375099
$877$	14.4774	−	25.0756i	0.488867	−	0.846742i	−0.511051	−	0.859550i	$-0.670744\pi$
$877$	14.4774	−	25.0756i	0.488867	−	0.846742i	0.999918	+	0.0128081i	$0.00407704\pi$
$878$	0.949496	+	1.64457i	0.0320439	+	0.0555017i
$879$	−2.62165	−	4.54083i	−0.0884261	−	0.153159i
$880$	3.60930	−	6.25149i	0.121669	−	0.210738i
$881$	43.4223			1.46294			0.731468	−	0.681876i	$-0.238836\pi$
$881$	43.4223			1.46294			0.731468	+	0.681876i	$0.238836\pi$
$882$	22.1122	−	31.2232i	0.744556	−	1.05134i
$883$	28.5142			0.959578			0.479789	−	0.877384i	$-0.340713\pi$
$883$	28.5142			0.959578			0.479789	+	0.877384i	$0.340713\pi$
$884$	13.8896	−	24.0576i	0.467159	−	0.809144i
$885$	2.20955	+	3.82706i	0.0742733	+	0.128645i
$886$	−15.0511	−	26.0693i	−0.505652	−	0.875814i
$887$	−24.2409	+	41.9864i	−0.813929	+	1.40977i	0.0961655	+	0.995365i	$0.469342\pi$
$887$	−24.2409	+	41.9864i	−0.813929	+	1.40977i	−0.910094	+	0.414401i	$0.863991\pi$
$888$	4.73746			0.158979
$889$	−2.22760	−	1.42751i	−0.0747113	−	0.0478773i
$890$	−7.40991			−0.248381
$891$	−3.13572	+	5.43123i	−0.105051	+	0.181953i
$892$	−41.1543	−	71.2813i	−1.37795	−	2.38667i
$893$	−0.387143	−	0.670550i	−0.0129552	−	0.0224391i
$894$	6.65559	−	11.5278i	0.222596	−	0.385548i
$895$	3.28528			0.109815
$896$	40.5696	−	20.9817i	1.35533	−	0.700949i
$897$	−0.613679			−0.0204901
$898$	−1.50914	+	2.61390i	−0.0503605	+	0.0872269i
$899$	−1.35321	−	2.34382i	−0.0451320	−	0.0781709i
$900$	−21.7885	−	37.7387i	−0.726283	−	1.25796i
$901$	6.99976	−	12.1239i	0.233196	−	0.403907i
$902$	−11.9758			−0.398752
$903$	0.696285	−	15.0267i	0.0231709	−	0.500057i
$904$	41.0047			1.36380
$905$	1.89435	−	3.28111i	0.0629702	−	0.109068i
$906$	17.6476	+	30.5665i	0.586301	+	1.01550i
$907$	23.4213	+	40.5669i	0.777692	+	1.34700i	0.933269	+	0.359178i	$0.116943\pi$
$907$	23.4213	+	40.5669i	0.777692	+	1.34700i	−0.155578	+	0.987824i	$0.549724\pi$
$908$	−19.9942	+	34.6310i	−0.663532	+	1.14927i
$909$	−15.3406			−0.508817
$910$	−0.232521	+	5.01808i	−0.00770799	+	0.166348i
$911$	10.1028			0.334722			0.167361	−	0.985896i	$-0.446476\pi$
$911$	10.1028			0.334722			0.167361	+	0.985896i	$0.446476\pi$
$912$	−0.476061	+	0.824561i	−0.0157639	+	0.0273039i
$913$	−22.8084	−	39.5054i	−0.754849	−	1.30744i
$914$	−33.5099	−	58.0408i	−1.10841	−	1.91982i
$915$	−3.24737	+	5.62461i	−0.107355	+	0.185944i
$916$	33.4659			1.10575
$917$	0.0251547	−	0.0130094i	0.000830680	−	0.000429609i
$918$	−52.8547			−1.74446
$919$	8.00171	−	13.8594i	0.263952	−	0.457178i	−0.703336	−	0.710857i	$-0.748307\pi$
$919$	8.00171	−	13.8594i	0.263952	−	0.457178i	0.967289	+	0.253679i	$0.0816406\pi$
$920$	0.678440	+	1.17509i	0.0223675	+	0.0387416i
$921$	−2.86925	−	4.96968i	−0.0945449	−	0.163757i
$922$	−7.28499	+	12.6180i	−0.239918	+	0.415551i
$923$	15.2555			0.502142
$924$	−21.9621	−	14.0740i	−0.722499	−	0.463000i
$925$	4.54471			0.149429
$926$	8.49544	−	14.7145i	0.279178	−	0.483550i
$927$	4.39798	+	7.61752i	0.144448	+	0.250192i
$928$	−1.59890	−	2.76937i	−0.0524863	−	0.0909090i
$929$	−9.19778	+	15.9310i	−0.301769	+	0.522680i	−0.976537	−	0.215350i	$-0.930911\pi$
$929$	−9.19778	+	15.9310i	−0.301769	+	0.522680i	0.674767	+	0.738030i	$0.264244\pi$
$930$	−2.11260			−0.0692750
$931$	−1.40570	−	0.130551i	−0.0460700	−	0.00427864i
$932$	11.6139			0.380425
$933$	−6.92410	+	11.9929i	−0.226685	+	0.392630i
$934$	40.5191	+	70.1812i	1.32583	+	2.29640i
$935$	−3.12335	−	5.40980i	−0.102144	−	0.176919i
$936$	−8.74187	+	15.1414i	−0.285737	+	0.494911i
$937$	−24.7977			−0.810105			−0.405053	−	0.914293i	$-0.632747\pi$
$937$	−24.7977			−0.810105			−0.405053	+	0.914293i	$0.632747\pi$
$938$	74.2393	+	47.5748i	2.42400	+	1.55337i
$939$	−17.7122			−0.578016
$940$	4.23640	−	7.33766i	0.138176	−	0.239328i
$941$	−22.5274	−	39.0185i	−0.734371	−	1.27197i	−0.954999	−	0.296610i	$-0.904144\pi$
$941$	−22.5274	−	39.0185i	−0.734371	−	1.27197i	0.220628	−	0.975358i	$-0.429189\pi$
$942$	−7.31635	−	12.6723i	−0.238380	−	0.412886i
$943$	0.433224	−	0.750365i	0.0141077	−	0.0244353i
$944$	49.3298			1.60555
$945$	5.75254	−	2.97509i	0.187130	−	0.0967796i
$946$	41.2380			1.34076
$947$	−25.1436	+	43.5499i	−0.817056	+	1.41518i	0.0907864	+	0.995870i	$0.471062\pi$
$947$	−25.1436	+	43.5499i	−0.817056	+	1.41518i	−0.907842	+	0.419312i	$0.862271\pi$
$948$	6.67412	+	11.5599i	0.216765	+	0.375449i
$949$	2.13652	+	3.70055i	0.0693542	+	0.120125i
$950$	−1.18652	+	2.05511i	−0.0384958	+	0.0666767i
$951$	−10.6357			−0.344888
$952$	−3.05891	+	66.0151i	−0.0991399	+	2.13956i
$953$	22.8566			0.740398			0.370199	−	0.928952i	$-0.379289\pi$
$953$	22.8566			0.740398			0.370199	+	0.928952i	$0.379289\pi$
$954$	−8.40477	+	14.5575i	−0.272114	+	0.471316i
$955$	6.04119	+	10.4637i	0.195488	+	0.338596i
$956$	61.5305	+	106.574i	1.99004	+	3.44685i
$957$	1.76338	−	3.05427i	0.0570020	−	0.0987304i
$958$	−38.0770			−1.23021
$959$	0.303193	−	6.54328i	0.00979061	−	0.211293i
$960$	2.46143			0.0794424
$961$	13.8800	−	24.0408i	0.447741	−	0.775510i
$962$	−1.73933	−	3.01261i	−0.0560784	−	0.0971306i
$963$	−6.70843	−	11.6193i	−0.216176	−	0.374428i
$964$	3.02112	−	5.23274i	0.0973039	−	0.168535i
$965$	−7.04113			−0.226662
$966$	2.47394	−	1.27947i	0.0795976	−	0.0411661i
$967$	−32.5270			−1.04600			−0.522998	−	0.852334i	$-0.675187\pi$
$967$	−32.5270			−1.04600			−0.522998	+	0.852334i	$0.675187\pi$
$968$	−11.4387	+	19.8125i	−0.367655	+	0.636797i
$969$	0.411965	+	0.713544i	0.0132342	+	0.0229223i
$970$	−4.46419	−	7.73220i	−0.143336	−	0.248266i
$971$	27.8167	−	48.1800i	0.892682	−	1.54617i	0.0560344	−	0.998429i	$-0.482154\pi$
$971$	27.8167	−	48.1800i	0.892682	−	1.54617i	0.836648	−	0.547742i	$-0.184512\pi$
$972$	67.8370			2.17587
$973$	12.7908	+	8.19675i	0.410055	+	0.262776i
$974$	57.9865			1.85801
$975$	3.07802	−	5.33129i	0.0985755	−	0.170738i
$976$	36.2499	+	62.7866i	1.16033	+	2.00975i
$977$	23.2568	+	40.2819i	0.744051	+	1.28873i	0.950637	+	0.310305i	$0.100431\pi$
$977$	23.2568	+	40.2819i	0.744051	+	1.28873i	−0.206586	+	0.978428i	$0.566235\pi$
$978$	7.04140	−	12.1961i	0.225159	−	0.389987i
$979$	−14.8092			−0.473305
$980$	−6.45392	−	14.0357i	−0.206163	−	0.448353i
$981$	9.87158			0.315175
$982$	20.5201	−	35.5419i	0.654823	−	1.13419i
$983$	−11.3916	−	19.7308i	−0.363335	−	0.629314i	0.625173	−	0.780486i	$-0.285029\pi$
$983$	−11.3916	−	19.7308i	−0.363335	−	0.629314i	−0.988507	+	0.151172i	$0.951695\pi$
$984$	4.53015	+	7.84644i	0.144416	+	0.250136i
$985$	1.09139	−	1.89034i	0.0347745	−	0.0602312i
$986$	−17.0463			−0.542864
$987$	−7.67543	−	4.91865i	−0.244311	−	0.156562i
$988$	1.23076			0.0391558
$989$	−1.49178	+	2.58383i	−0.0474357	+	0.0821610i
$990$	3.75028	+	6.49567i	0.119192	+	0.206446i
$991$	−12.9723	−	22.4687i	−0.412079	−	0.713742i	0.583038	−	0.812445i	$-0.301864\pi$
$991$	−12.9723	−	22.4687i	−0.412079	−	0.713742i	−0.995117	+	0.0987030i	$0.968531\pi$
$992$	−1.91417	+	3.31545i	−0.0607751	+	0.105266i
$993$	−8.73512			−0.277201
$994$	−61.4999	+	31.8064i	−1.95066	+	1.00884i
$995$	2.49685			0.0791556
$996$	−32.9201	+	57.0193i	−1.04311	+	1.80672i
$997$	−20.3293	−	35.2115i	−0.643837	−	1.11516i	−0.984569	−	0.174998i	$-0.944008\pi$
$997$	−20.3293	−	35.2115i	−0.643837	−	1.11516i	0.340732	−	0.940160i	$-0.389325\pi$
$998$	−32.3463	−	56.0254i	−1.02390	−	1.77345i
$999$	−2.24237	+	3.88391i	−0.0709456	+	0.122881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.f.c.128.36	✓	76
7.2	even	3		6223.2.a.p.1.3		38
7.4	even	3	inner	889.2.f.c.382.36	yes	76
7.5	odd	6		6223.2.a.o.1.3		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.f.c.128.36	✓	76	1.1	even	1	trivial
889.2.f.c.382.36	yes	76	7.4	even	3	inner
6223.2.a.o.1.3		38	7.5	odd	6
6223.2.a.p.1.3		38	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24531 - 2.15694i) q^{2} +(-0.448739 - 0.777240i) q^{3} +(-2.10158 - 3.64005i) q^{4} +(0.262530 - 0.454716i) q^{5} -2.23528 q^{6} +(-2.22760 - 1.42751i) q^{7} -5.48724 q^{8} +(1.09727 - 1.90052i) q^{9} +(-0.653862 - 1.13252i) q^{10} +(-1.30679 - 2.26342i) q^{11} +(-1.88613 + 3.26687i) q^{12} +1.45191 q^{13} +(-5.85311 + 3.02710i) q^{14} -0.471231 q^{15} +(-2.63014 + 4.55553i) q^{16} +(2.27602 + 3.94218i) q^{17} +(-2.73287 - 4.73346i) q^{18} +(-0.100839 + 0.174659i) q^{19} -2.20692 q^{20} +(-0.109909 + 2.37196i) q^{21} -6.50942 q^{22} +(0.235477 - 0.407858i) q^{23} +(2.46234 + 4.26490i) q^{24} +(2.36216 + 4.09137i) q^{25} +(1.80807 - 3.13167i) q^{26} -4.66198 q^{27} +(-0.514735 + 11.1086i) q^{28} -1.50355 q^{29} +(-0.586827 + 1.01641i) q^{30} +(0.900011 + 1.55886i) q^{31} +(1.06342 + 1.84189i) q^{32} +(-1.17282 + 2.03138i) q^{33} +11.3374 q^{34} +(-1.23393 + 0.638159i) q^{35} -9.22398 q^{36} +(0.480992 - 0.833102i) q^{37} +(0.251152 + 0.435008i) q^{38} +(-0.651528 - 1.12848i) q^{39} +(-1.44057 + 2.49513i) q^{40} +1.83977 q^{41} +(4.97930 + 3.19089i) q^{42} -6.33513 q^{43} +(-5.49265 + 9.51355i) q^{44} +(-0.576131 - 0.997888i) q^{45} +(-0.586482 - 1.01582i) q^{46} +(-1.91960 + 3.32485i) q^{47} +4.72098 q^{48} +(2.92441 + 6.35986i) q^{49} +11.7664 q^{50} +(2.04268 - 3.53802i) q^{51} +(-3.05130 - 5.28501i) q^{52} +(-1.53772 - 2.66341i) q^{53} +(-5.80560 + 10.0556i) q^{54} -1.37229 q^{55} +(12.2234 + 7.83311i) q^{56} +0.181002 q^{57} +(-1.87238 + 3.24305i) q^{58} +(-4.68890 - 8.12141i) q^{59} +(0.990330 + 1.71530i) q^{60} +(6.89125 - 11.9360i) q^{61} +4.48316 q^{62} +(-5.15729 + 2.66724i) q^{63} -5.22342 q^{64} +(0.381169 - 0.660205i) q^{65} +(2.92103 + 5.05938i) q^{66} +(-6.69052 - 11.5883i) q^{67} +(9.56649 - 16.5696i) q^{68} -0.422671 q^{69} +(-0.160149 + 3.45620i) q^{70} +10.5072 q^{71} +(-6.02096 + 10.4286i) q^{72} +(1.47152 + 2.54876i) q^{73} +(-1.19797 - 2.07494i) q^{74} +(2.11999 - 3.67192i) q^{75} +0.847689 q^{76} +(-0.320068 + 6.90747i) q^{77} -3.24541 q^{78} +(1.76927 - 3.06446i) q^{79} +(1.38098 + 2.39193i) q^{80} +(-1.19978 - 2.07808i) q^{81} +(2.29108 - 3.96827i) q^{82} +17.4538 q^{83} +(8.86503 - 4.58480i) q^{84} +2.39010 q^{85} +(-7.88919 + 13.6645i) q^{86} +(0.674700 + 1.16861i) q^{87} +(7.17066 + 12.4200i) q^{88} +(2.83313 - 4.90713i) q^{89} -2.86984 q^{90} +(-3.23427 - 2.07262i) q^{91} -1.97950 q^{92} +(0.807741 - 1.39905i) q^{93} +(4.78099 + 8.28091i) q^{94} +(0.0529467 + 0.0917064i) q^{95} +(0.954394 - 1.65306i) q^{96} +6.82742 q^{97} +(17.3596 + 1.61223i) q^{98} -5.73558 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 2 q^{2} - 11 q^{3} - 38 q^{4} - 16 q^{5} + 22 q^{6} + 3 q^{7} - 47 q^{9} - 12 q^{10} + 2 q^{11} - 30 q^{12} + 42 q^{13} - 2 q^{14} + 14 q^{15} - 46 q^{16} - 58 q^{17} + 13 q^{18} - 17 q^{19} + 88 q^{20}+ \cdots + 32 q^{99}+O(q^{100}) \) 76 * q + 2 * q^2 - 11 * q^3 - 38 * q^4 - 16 * q^5 + 22 * q^6 + 3 * q^7 - 47 * q^9 - 12 * q^10 + 2 * q^11 - 30 * q^12 + 42 * q^13 - 2 * q^14 + 14 * q^15 - 46 * q^16 - 58 * q^17 + 13 * q^18 - 17 * q^19 + 88 * q^20 + q^21 + 42 * q^22 - 7 * q^23 - 21 * q^24 - 52 * q^25 - 49 * q^26 + 70 * q^27 - 26 * q^28 - 4 * q^29 - 6 * q^30 - 2 * q^31 + 22 * q^32 - 29 * q^33 + 74 * q^34 + 22 * q^35 + 50 * q^36 - 11 * q^37 - 40 * q^38 - 2 * q^39 + 8 * q^40 + 136 * q^41 + 14 * q^42 - 76 * q^43 - 43 * q^44 - 60 * q^45 + 28 * q^46 - 35 * q^47 + 132 * q^48 + 73 * q^49 - 50 * q^50 + 3 * q^51 - 32 * q^52 + 18 * q^53 + 68 * q^54 + 38 * q^55 + 45 * q^56 - 62 * q^57 - 55 * q^58 - 21 * q^59 + 11 * q^60 - 5 * q^61 + 76 * q^62 + 53 * q^63 + 36 * q^64 + 9 * q^65 - 20 * q^66 - 6 * q^67 - 74 * q^68 + 106 * q^69 + 193 * q^70 - 52 * q^71 - 24 * q^72 - 22 * q^73 + 2 * q^74 - 38 * q^75 + 78 * q^76 + 5 * q^77 - 228 * q^78 + 14 * q^79 - 140 * q^80 - 58 * q^81 + 8 * q^82 + 92 * q^83 + 149 * q^84 - 22 * q^85 - 51 * q^86 - 59 * q^87 + 4 * q^88 - 74 * q^89 + 2 * q^90 + 65 * q^91 - 162 * q^92 - 92 * q^93 + 36 * q^94 - 20 * q^95 + 108 * q^96 + 132 * q^97 - 11 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more