LMFDB - Embedded newform 558.2.g.a.211.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(211,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.211"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.11
Character	$\chi$	$=$	558.211
Dual form			558.2.g.a.439.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.07682 + 1.35663i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.251592 + 0.435771i) q^{5} +(0.636470 - 1.61087i) q^{6} +(1.49612 - 2.59136i) q^{7} +1.00000 q^{8} +(-0.680914 + 2.92170i) q^{9} +(0.251592 - 0.435771i) q^{10} +3.41738 q^{11} +(-1.71329 + 0.254237i) q^{12} +(0.745981 + 1.29208i) q^{13} -2.99224 q^{14} +(-0.320262 + 0.810566i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.107908 - 0.186902i) q^{17} +(2.87073 - 0.871163i) q^{18} +(-0.313601 - 0.543174i) q^{19} -0.503185 q^{20} +(5.12658 - 0.760738i) q^{21} +(-1.70869 - 2.95953i) q^{22} +(-2.34285 + 4.05794i) q^{23} +(1.07682 + 1.35663i) q^{24} +(2.37340 - 4.11085i) q^{25} +(0.745981 - 1.29208i) q^{26} +(-4.69691 + 2.22240i) q^{27} +(1.49612 + 2.59136i) q^{28} +(0.870491 + 1.50773i) q^{29} +(0.862101 - 0.127928i) q^{30} +(3.91747 - 3.95645i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.67990 + 4.63613i) q^{33} +(-0.107908 + 0.186902i) q^{34} +1.50565 q^{35} +(-2.18981 - 2.05054i) q^{36} +(3.77685 + 6.54170i) q^{37} +(-0.313601 + 0.543174i) q^{38} +(-0.949589 + 2.40336i) q^{39} +(0.251592 + 0.435771i) q^{40} +(3.90895 + 6.77051i) q^{41} +(-3.22211 - 4.05938i) q^{42} +(2.24243 - 3.88401i) q^{43} +(-1.70869 + 2.95953i) q^{44} +(-1.44451 + 0.438356i) q^{45} +4.68570 q^{46} +(2.96572 + 5.13679i) q^{47} +(0.636470 - 1.61087i) q^{48} +(-0.976756 - 1.69179i) q^{49} -4.74681 q^{50} +(0.137360 - 0.347652i) q^{51} -1.49196 q^{52} +(-0.744043 + 1.28872i) q^{53} +(4.27311 + 2.95644i) q^{54} +(0.859785 + 1.48919i) q^{55} +(1.49612 - 2.59136i) q^{56} +(0.399196 - 1.01034i) q^{57} +(0.870491 - 1.50773i) q^{58} -6.72438 q^{59} +(-0.541840 - 0.682638i) q^{60} +(-5.06352 - 8.77028i) q^{61} +(-5.38512 - 1.41440i) q^{62} +(6.55245 + 6.13572i) q^{63} +1.00000 q^{64} +(-0.375366 + 0.650154i) q^{65} +(2.17506 - 5.50495i) q^{66} +(-7.40223 - 12.8210i) q^{67} +0.215816 q^{68} +(-8.02796 + 1.19128i) q^{69} +(-0.752825 - 1.30393i) q^{70} +(-1.88140 + 3.25868i) q^{71} +(-0.680914 + 2.92170i) q^{72} +(0.325049 - 0.563001i) q^{73} +(3.77685 - 6.54170i) q^{74} +(8.13266 - 1.20681i) q^{75} +0.627203 q^{76} +(5.11281 - 8.85564i) q^{77} +(2.55617 - 0.379312i) q^{78} +(2.19974 - 3.81007i) q^{79} +(0.251592 - 0.435771i) q^{80} +(-8.07271 - 3.97886i) q^{81} +(3.90895 - 6.77051i) q^{82} +4.72515 q^{83} +(-1.90447 + 4.82012i) q^{84} +(0.0542976 - 0.0940463i) q^{85} -4.48487 q^{86} +(-1.10808 + 2.80450i) q^{87} +3.41738 q^{88} -15.8136 q^{89} +(1.10188 + 1.03180i) q^{90} +4.46431 q^{91} +(-2.34285 - 4.05794i) q^{92} +(9.58586 + 1.05419i) q^{93} +(2.96572 - 5.13679i) q^{94} +(0.157799 - 0.273317i) q^{95} +(-1.71329 + 0.254237i) q^{96} +(-5.15725 - 8.93262i) q^{97} +(-0.976756 + 1.69179i) q^{98} +(-2.32694 + 9.98456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.07682	+	1.35663i	0.621703	+	0.783253i
$3$	1.07682	+	1.35663i	0.621703	+	0.783253i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.251592	+	0.435771i	0.112515	+	0.194883i	0.916784	−	0.399384i	$-0.130776\pi$
$5$	0.251592	+	0.435771i	0.112515	+	0.194883i	−0.804268	+	0.594266i	$0.797443\pi$
$6$	0.636470	−	1.61087i	0.259838	−	0.657635i
$7$	1.49612	−	2.59136i	0.565481	−	0.979441i	−0.431524	−	0.902101i	$-0.642024\pi$
$7$	1.49612	−	2.59136i	0.565481	−	0.979441i	0.997005	−	0.0773398i	$-0.0246426\pi$
$8$	1.00000			0.353553
$9$	−0.680914	+	2.92170i	−0.226971	+	0.973901i
$10$	0.251592	−	0.435771i	0.0795605	−	0.137803i
$11$	3.41738			1.03038			0.515189	−	0.857077i	$-0.327722\pi$
$11$	3.41738			1.03038			0.515189	+	0.857077i	$0.327722\pi$
$12$	−1.71329	+	0.254237i	−0.494584	+	0.0733919i
$13$	0.745981	+	1.29208i	0.206898	+	0.358358i	0.950736	−	0.310002i	$-0.100330\pi$
$13$	0.745981	+	1.29208i	0.206898	+	0.358358i	−0.743838	+	0.668360i	$0.766997\pi$
$14$	−2.99224			−0.799710
$15$	−0.320262	+	0.810566i	−0.0826912	+	0.209287i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.107908	−	0.186902i	−0.0261715	−	0.0453304i	0.852643	−	0.522494i	$-0.174998\pi$
$17$	−0.107908	−	0.186902i	−0.0261715	−	0.0453304i	−0.878815	+	0.477164i	$0.841665\pi$
$18$	2.87073	−	0.871163i	0.676637	−	0.205335i
$19$	−0.313601	−	0.543174i	−0.0719451	−	0.124613i	0.827809	−	0.561011i	$-0.189587\pi$
$19$	−0.313601	−	0.543174i	−0.0719451	−	0.124613i	−0.899754	+	0.436398i	$0.856254\pi$
$20$	−0.503185			−0.112515
$21$	5.12658	−	0.760738i	1.11871	−	0.166007i
$22$	−1.70869	−	2.95953i	−0.364293	−	0.630975i
$23$	−2.34285	+	4.05794i	−0.488518	+	0.846138i	−0.999913	−	0.0132079i	$-0.995796\pi$
$23$	−2.34285	+	4.05794i	−0.488518	+	0.846138i	0.511395	+	0.859346i	$0.329129\pi$
$24$	1.07682	+	1.35663i	0.219805	+	0.276922i
$25$	2.37340	−	4.11085i	0.474681	−	0.822171i
$26$	0.745981	−	1.29208i	0.146299	−	0.253397i
$27$	−4.69691	+	2.22240i	−0.903920	+	0.427701i
$28$	1.49612	+	2.59136i	0.282740	+	0.489721i
$29$	0.870491	+	1.50773i	0.161646	+	0.279979i	0.935459	−	0.353435i	$-0.114986\pi$
$29$	0.870491	+	1.50773i	0.161646	+	0.279979i	−0.773813	+	0.633414i	$0.781653\pi$
$30$	0.862101	−	0.127928i	0.157397	−	0.0233564i
$31$	3.91747	−	3.95645i	0.703598	−	0.710599i
$31$	3.91747	−	3.95645i	0.703598	−	0.710599i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.67990	+	4.63613i	0.640588	+	0.807046i
$34$	−0.107908	+	0.186902i	−0.0185061	+	0.0320535i
$35$	1.50565			0.254501
$36$	−2.18981	−	2.05054i	−0.364969	−	0.341757i
$37$	3.77685	+	6.54170i	0.620910	+	1.07545i	0.989317	+	0.145783i	$0.0465703\pi$
$37$	3.77685	+	6.54170i	0.620910	+	1.07545i	−0.368406	+	0.929665i	$0.620096\pi$
$38$	−0.313601	+	0.543174i	−0.0508729	+	0.0881144i
$39$	−0.949589	+	2.40336i	−0.152056	+	0.384846i
$40$	0.251592	+	0.435771i	0.0397802	+	0.0689014i
$41$	3.90895	+	6.77051i	0.610476	+	1.05738i	0.991160	+	0.132670i	$0.0423552\pi$
$41$	3.90895	+	6.77051i	0.610476	+	1.05738i	−0.380684	+	0.924705i	$0.624312\pi$
$42$	−3.22211	−	4.05938i	−0.497182	−	0.626376i
$43$	2.24243	−	3.88401i	0.341968	−	0.592306i	−0.642830	−	0.766009i	$-0.722240\pi$
$43$	2.24243	−	3.88401i	0.341968	−	0.592306i	0.984798	+	0.173703i	$0.0555732\pi$
$44$	−1.70869	+	2.95953i	−0.257594	+	0.446166i
$45$	−1.44451	+	0.438356i	−0.215334	+	0.0653462i
$46$	4.68570			0.690869
$47$	2.96572	+	5.13679i	0.432595	+	0.749277i	0.997096	−	0.0761555i	$-0.0242645\pi$
$47$	2.96572	+	5.13679i	0.432595	+	0.749277i	−0.564501	+	0.825433i	$0.690931\pi$
$48$	0.636470	−	1.61087i	0.0918665	−	0.232509i
$49$	−0.976756	−	1.69179i	−0.139537	−	0.241685i
$50$	−4.74681			−0.671300
$51$	0.137360	−	0.347652i	0.0192343	−	0.0486810i
$52$	−1.49196			−0.206898
$53$	−0.744043	+	1.28872i	−0.102202	+	0.177019i	−0.912592	−	0.408872i	$-0.865922\pi$
$53$	−0.744043	+	1.28872i	−0.102202	+	0.177019i	0.810390	+	0.585891i	$0.199256\pi$
$54$	4.27311	+	2.95644i	0.581496	+	0.402321i
$55$	0.859785	+	1.48919i	0.115933	+	0.200803i
$56$	1.49612	−	2.59136i	0.199928	−	0.346285i
$57$	0.399196	−	1.01034i	0.0528747	−	0.133823i
$58$	0.870491	−	1.50773i	0.114301	−	0.197975i
$59$	−6.72438			−0.875440			−0.437720	−	0.899111i	$-0.644214\pi$
$59$	−6.72438			−0.875440			−0.437720	+	0.899111i	$0.644214\pi$
$60$	−0.541840	−	0.682638i	−0.0699512	−	0.0881281i
$61$	−5.06352	−	8.77028i	−0.648317	−	1.12292i	−0.983525	−	0.180774i	$-0.942140\pi$
$61$	−5.06352	−	8.77028i	−0.648317	−	1.12292i	0.335207	−	0.942144i	$-0.391194\pi$
$62$	−5.38512	−	1.41440i	−0.683910	−	0.179629i
$63$	6.55245	+	6.13572i	0.825531	+	0.773027i
$64$	1.00000			0.125000
$65$	−0.375366	+	0.650154i	−0.0465585	+	0.0806416i
$66$	2.17506	−	5.50495i	0.267731	−	0.677613i
$67$	−7.40223	−	12.8210i	−0.904326	−	1.56634i	−0.821820	−	0.569748i	$-0.807041\pi$
$67$	−7.40223	−	12.8210i	−0.904326	−	1.56634i	−0.0825063	−	0.996591i	$-0.526292\pi$
$68$	0.215816			0.0261715
$69$	−8.02796	+	1.19128i	−0.966453	+	0.143413i
$70$	−0.752825	−	1.30393i	−0.0899798	−	0.155850i
$71$	−1.88140	+	3.25868i	−0.223281	+	0.386734i	−0.955802	−	0.294010i	$-0.905010\pi$
$71$	−1.88140	+	3.25868i	−0.223281	+	0.386734i	0.732521	+	0.680744i	$0.238343\pi$
$72$	−0.680914	+	2.92170i	−0.0802465	+	0.344326i
$73$	0.325049	−	0.563001i	0.0380441	−	0.0658943i	−0.846376	−	0.532585i	$-0.821221\pi$
$73$	0.325049	−	0.563001i	0.0380441	−	0.0658943i	0.884420	+	0.466691i	$0.154554\pi$
$74$	3.77685	−	6.54170i	0.439050	−	0.760457i
$75$	8.13266	−	1.20681i	0.939078	−	0.139351i
$76$	0.627203			0.0719451
$77$	5.11281	−	8.85564i	0.582658	−	1.00919i
$78$	2.55617	−	0.379312i	0.289429	−	0.0429486i
$79$	2.19974	−	3.81007i	0.247490	−	0.428666i	−0.715338	−	0.698778i	$-0.753727\pi$
$79$	2.19974	−	3.81007i	0.247490	−	0.428666i	0.962829	+	0.270112i	$0.0870608\pi$
$80$	0.251592	−	0.435771i	0.0281289	−	0.0487206i
$81$	−8.07271	−	3.97886i	−0.896968	−	0.442096i
$82$	3.90895	−	6.77051i	0.431672	−	0.747677i
$83$	4.72515			0.518653			0.259326	−	0.965790i	$-0.416499\pi$
$83$	4.72515			0.518653			0.259326	+	0.965790i	$0.416499\pi$
$84$	−1.90447	+	4.82012i	−0.207795	+	0.525918i
$85$	0.0542976	−	0.0940463i	0.00588941	−	0.0102008i
$86$	−4.48487			−0.483616
$87$	−1.10808	+	2.80450i	−0.118799	+	0.300674i
$88$	3.41738			0.364293
$89$	−15.8136			−1.67623			−0.838117	−	0.545490i	$-0.816343\pi$
$89$	−15.8136			−1.67623			−0.838117	+	0.545490i	$0.816343\pi$
$90$	1.10188	+	1.03180i	0.116148	+	0.108761i
$91$	4.46431			0.467987
$92$	−2.34285	−	4.05794i	−0.244259	−	0.423069i
$93$	9.58586	+	1.05419i	0.994007	+	0.109314i
$94$	2.96572	−	5.13679i	0.305891	−	0.529819i
$95$	0.157799	−	0.273317i	0.0161899	−	0.0280417i
$96$	−1.71329	+	0.254237i	−0.174862	+	0.0259479i
$97$	−5.15725	−	8.93262i	−0.523639	−	0.906970i	−0.999621	−	0.0275148i	$-0.991241\pi$
$97$	−5.15725	−	8.93262i	−0.523639	−	0.906970i	0.475982	−	0.879455i	$-0.342093\pi$
$98$	−0.976756	+	1.69179i	−0.0986673	+	0.170897i
$99$	−2.32694	+	9.98456i	−0.233866	+	1.00349i
$100$	2.37340	+	4.11085i	0.237340	+	0.411085i
$101$	−6.91596	−	11.9788i	−0.688164	−	1.19193i	−0.972431	−	0.233190i	$-0.925084\pi$
$101$	−6.91596	−	11.9788i	−0.688164	−	1.19193i	0.284268	−	0.958745i	$-0.408250\pi$
$102$	−0.369755	+	0.0548684i	−0.0366112	+	0.00543278i
$103$	5.15407	+	8.92711i	0.507846	+	0.879614i	0.999959	+	0.00908319i	$0.00289131\pi$
$103$	5.15407	+	8.92711i	0.507846	+	0.879614i	−0.492113	+	0.870531i	$0.663775\pi$
$104$	0.745981	+	1.29208i	0.0731495	+	0.126699i
$105$	1.62132	+	2.04262i	0.158224	+	0.199339i
$106$	1.48809			0.144536
$107$	−1.33208	−	2.30724i	−0.128777	−	0.223049i	0.794426	−	0.607361i	$-0.207772\pi$
$107$	−1.33208	−	2.30724i	−0.128777	−	0.223049i	−0.923203	+	0.384312i	$0.874439\pi$
$108$	0.423799	−	5.17884i	0.0407801	−	0.498334i
$109$	−15.9550			−1.52821			−0.764107	−	0.645090i	$-0.776820\pi$
$109$	−15.9550			−1.52821			−0.764107	+	0.645090i	$0.776820\pi$
$110$	0.859785	−	1.48919i	0.0819773	−	0.141989i
$111$	−4.80770	+	12.1680i	−0.456327	+	1.15494i
$112$	−2.99224			−0.282740
$113$	−8.48882	−	14.7031i	−0.798561	−	1.38315i	−0.920553	−	0.390617i	$-0.872262\pi$
$113$	−8.48882	−	14.7031i	−0.798561	−	1.38315i	0.121992	−	0.992531i	$-0.461072\pi$
$114$	−1.07458	+	0.159458i	−0.100644	+	0.0149346i
$115$	−2.35777			−0.219863
$116$	−1.74098			−0.161646
$117$	−4.28302	+	1.29974i	−0.395965	+	0.120161i
$118$	3.36219	+	5.82349i	0.309515	+	0.536095i
$119$	−0.645774			−0.0591980
$120$	−0.320262	+	0.810566i	−0.0292358	+	0.0739942i
$121$	0.678453			0.0616775
$122$	−5.06352	+	8.77028i	−0.458430	+	0.794024i
$123$	−4.97586	+	12.5936i	−0.448658	+	1.13553i
$124$	1.46765	+	5.37085i	0.131799	+	0.482316i
$125$	4.90444			0.438667
$126$	2.03746	−	8.74245i	0.181511	−	0.778839i
$127$	9.66532	+	16.7408i	0.857659	+	1.48551i	0.874157	+	0.485644i	$0.161415\pi$
$127$	9.66532	+	16.7408i	0.857659	+	1.48551i	−0.0164980	+	0.999864i	$0.505252\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	7.68388	−	1.14022i	0.676528	−	0.100391i
$130$	0.750733			0.0658436
$131$	−0.108524			−0.00948176			−0.00474088	−	0.999989i	$-0.501509\pi$
$131$	−0.108524			−0.00948176			−0.00474088	+	0.999989i	$0.501509\pi$
$132$	−5.85496	+	0.868823i	−0.509608	+	0.0756213i
$133$	−1.87674			−0.162734
$134$	−7.40223	+	12.8210i	−0.639455	+	1.10757i
$135$	−2.15016	−	1.48764i	−0.185057	−	0.128035i
$136$	−0.107908	−	0.186902i	−0.00925304	−	0.0160267i
$137$	−13.4640			−1.15031			−0.575154	−	0.818045i	$-0.695058\pi$
$137$	−13.4640			−1.15031			−0.575154	+	0.818045i	$0.695058\pi$
$138$	5.04566	+	6.35678i	0.429515	+	0.541125i
$139$	3.04467	−	5.27352i	0.258245	−	0.447294i	−0.707527	−	0.706687i	$-0.750189\pi$
$139$	3.04467	−	5.27352i	0.258245	−	0.447294i	0.965772	+	0.259393i	$0.0835224\pi$
$140$	−0.752825	+	1.30393i	−0.0636253	+	0.110202i
$141$	−3.77519	+	9.55480i	−0.317928	+	0.804659i
$142$	3.76280			0.315767
$143$	2.54930	+	4.41551i	0.213183	+	0.369244i
$144$	2.87073	−	0.871163i	0.239227	−	0.0725969i
$145$	−0.438017	+	0.758668i	−0.0363754	+	0.0630040i
$146$	−0.650097			−0.0538024
$147$	1.24335	−	3.14686i	0.102550	−	0.259548i
$148$	−7.55370			−0.620910
$149$	5.50336			0.450852			0.225426	−	0.974260i	$-0.427623\pi$
$149$	5.50336			0.450852			0.225426	+	0.974260i	$0.427623\pi$
$150$	−5.11146	−	6.43968i	−0.417349	−	0.525798i
$151$	1.12514	+	1.94880i	0.0915625	+	0.158591i	0.908169	−	0.418604i	$-0.137481\pi$
$151$	1.12514	+	1.94880i	0.0915625	+	0.158591i	−0.816606	+	0.577195i	$0.804147\pi$
$152$	−0.313601	−	0.543174i	−0.0254364	−	0.0440572i
$153$	0.619549	−	0.188011i	0.0500876	−	0.0151998i
$154$	−10.2256			−0.824003
$155$	2.70971	+	0.711705i	0.217649	+	0.0571655i
$156$	−1.60658	−	2.02405i	−0.128629	−	0.162054i
$157$	−2.36692	+	4.09962i	−0.188901	+	0.327186i	−0.944884	−	0.327405i	$-0.893826\pi$
$157$	−2.36692	+	4.09962i	−0.188901	+	0.327186i	0.755983	+	0.654591i	$0.227159\pi$
$158$	−4.39949			−0.350004
$159$	−2.54952	+	0.378326i	−0.202190	+	0.0300032i
$160$	−0.503185			−0.0397802
$161$	7.01037	+	12.1423i	0.552495	+	0.956949i
$162$	0.590562	+	8.98060i	0.0463989	+	0.705583i
$163$	−8.36515			−0.655209			−0.327604	−	0.944815i	$-0.606241\pi$
$163$	−8.36515			−0.655209			−0.327604	+	0.944815i	$0.606241\pi$
$164$	−7.81791			−0.610476
$165$	−1.09445	+	2.77001i	−0.0852031	+	0.215645i
$166$	−2.36258	−	4.09210i	−0.183371	−	0.317609i
$167$	3.47128			0.268616			0.134308	−	0.990940i	$-0.457119\pi$
$167$	3.47128			0.268616			0.134308	+	0.990940i	$0.457119\pi$
$168$	5.12658	−	0.760738i	0.395524	−	0.0586922i
$169$	5.38702	−	9.33060i	0.414386	−	0.717738i
$170$	−0.108595			−0.00832888
$171$	1.80053	−	0.546396i	0.137690	−	0.0417840i
$172$	2.24243	+	3.88401i	0.170984	+	0.296153i
$173$	−8.91361			−0.677689			−0.338845	−	0.940842i	$-0.610036\pi$
$173$	−8.91361			−0.677689			−0.338845	+	0.940842i	$0.610036\pi$
$174$	2.98281	−	0.442622i	0.226126	−	0.0335551i
$175$	−7.10180	−	12.3007i	−0.536845	−	0.929843i
$176$	−1.70869	−	2.95953i	−0.128797	−	0.223083i
$177$	−7.24095	−	9.12253i	−0.544263	−	0.685691i
$178$	7.90678	+	13.6949i	0.592638	+	1.02648i
$179$	−9.76971	−	16.9216i	−0.730222	−	1.26478i	−0.956788	−	0.290786i	$-0.906083\pi$
$179$	−9.76971	−	16.9216i	−0.730222	−	1.26478i	0.226566	−	0.973996i	$-0.427250\pi$
$180$	0.342626	−	1.47016i	0.0255378	−	0.109579i
$181$	−5.75215	+	9.96302i	−0.427554	+	0.740546i	−0.996655	−	0.0817221i	$-0.973958\pi$
$181$	−5.75215	+	9.96302i	−0.427554	+	0.740546i	0.569101	+	0.822268i	$0.307291\pi$
$182$	−2.23216	−	3.86621i	−0.165458	−	0.286583i
$183$	6.44555	−	16.3134i	0.476469	−	1.20592i
$184$	−2.34285	+	4.05794i	−0.172717	+	0.299155i
$185$	−1.90045	+	3.29168i	−0.139724	+	0.242009i
$186$	−3.87998	−	8.82869i	−0.284494	−	0.647351i
$187$	−0.368762	−	0.638715i	−0.0269666	−	0.0467074i
$188$	−5.93145			−0.432595
$189$	−1.26811	+	15.4963i	−0.0922413	+	1.12719i
$190$	−0.315599			−0.0228959
$191$	4.16012			0.301016			0.150508	−	0.988609i	$-0.451909\pi$
$191$	4.16012			0.301016			0.150508	+	0.988609i	$0.451909\pi$
$192$	1.07682	+	1.35663i	0.0777128	+	0.0979067i
$193$	−12.8309			−0.923591			−0.461795	−	0.886986i	$-0.652795\pi$
$193$	−12.8309			−0.923591			−0.461795	+	0.886986i	$0.652795\pi$
$194$	−5.15725	+	8.93262i	−0.370269	+	0.641324i
$195$	−1.28622	+	0.190864i	−0.0921083	+	0.0136681i
$196$	1.95351			0.139537
$197$	1.20027	−	2.07893i	0.0855157	−	0.148117i	−0.820095	−	0.572227i	$-0.806080\pi$
$197$	1.20027	−	2.07893i	0.0855157	−	0.148117i	0.905611	+	0.424110i	$0.139413\pi$
$198$	9.81035	−	2.97709i	0.697191	−	0.211573i
$199$	4.96174	−	8.59399i	0.351729	−	0.609212i	−0.634824	−	0.772657i	$-0.718927\pi$
$199$	4.96174	−	8.59399i	0.351729	−	0.609212i	0.986552	+	0.163445i	$0.0522607\pi$
$200$	2.37340	−	4.11085i	0.167825	−	0.290681i
$201$	9.42258	−	23.8481i	0.664618	−	1.68211i
$202$	−6.91596	+	11.9788i	−0.486605	+	0.842825i
$203$	5.20944			0.365631
$204$	0.232395	+	0.292783i	0.0162709	+	0.0204989i
$205$	−1.96693	+	3.40681i	−0.137376	+	0.237942i
$206$	5.15407	−	8.92711i	0.359101	−	0.621981i
$207$	−10.2608	−	9.60822i	−0.713175	−	0.667817i
$208$	0.745981	−	1.29208i	0.0517245	−	0.0895895i
$209$	−1.07169	−	1.85623i	−0.0741306	−	0.128398i
$210$	0.958300	−	2.42541i	0.0661290	−	0.167369i
$211$	1.44788			0.0996762			0.0498381	−	0.998757i	$-0.484129\pi$
$211$	1.44788			0.0996762			0.0498381	+	0.998757i	$0.484129\pi$
$212$	−0.744043	−	1.28872i	−0.0511011	−	0.0885096i
$213$	−6.44677	+	0.956643i	−0.441725	+	0.0655481i
$214$	−1.33208	+	2.30724i	−0.0910594	+	0.157720i
$215$	2.25672			0.153907
$216$	−4.69691	+	2.22240i	−0.319584	+	0.151215i
$217$	−4.39156	−	16.0709i	−0.298119	−	1.09096i
$218$	7.97751	+	13.8175i	0.540305	+	0.935836i
$219$	1.11381	−	0.165279i	0.0752640	−	0.0111685i
$220$	−1.71957			−0.115933
$221$	0.160995	−	0.278851i	0.0108297	−	0.0187576i
$222$	12.9417	−	1.92043i	0.868589	−	0.128891i
$223$	−1.56823	+	2.71626i	−0.105017	+	0.181894i	−0.913745	−	0.406288i	$-0.866823\pi$
$223$	−1.56823	+	2.71626i	−0.105017	+	0.181894i	0.808728	+	0.588182i	$0.200156\pi$
$224$	1.49612	+	2.59136i	0.0999638	+	0.173142i
$225$	10.3946	+	9.73352i	0.692974	+	0.648901i
$226$	−8.48882	+	14.7031i	−0.564668	+	0.978033i
$227$	8.57661			0.569249			0.284625	−	0.958639i	$-0.408131\pi$
$227$	8.57661			0.569249			0.284625	+	0.958639i	$0.408131\pi$
$228$	0.675385	+	0.850885i	0.0447285	+	0.0563512i
$229$	−6.08136			−0.401868			−0.200934	−	0.979605i	$-0.564398\pi$
$229$	−6.08136			−0.401868			−0.200934	+	0.979605i	$0.564398\pi$
$230$	1.17889	+	2.04189i	0.0777334	+	0.134638i
$231$	17.5194	−	2.59973i	1.15269	−	0.171050i
$232$	0.870491	+	1.50773i	0.0571505	+	0.0989876i
$233$	27.2939			1.78808			0.894042	−	0.447982i	$-0.147857\pi$
$233$	27.2939			1.78808			0.894042	+	0.447982i	$0.147857\pi$
$234$	3.26712	+	3.05933i	0.213578	+	0.199995i
$235$	−1.49231	+	2.58475i	−0.0973474	+	0.168611i
$236$	3.36219	−	5.82349i	0.218860	−	0.379077i
$237$	7.53760	−	1.11851i	0.489620	−	0.0726552i
$238$	0.322887	+	0.559256i	0.0209296	+	0.0362512i
$239$	9.32939	+	16.1590i	0.603468	+	1.04524i	0.992292	+	0.123925i	$0.0395483\pi$
$239$	9.32939	+	16.1590i	0.603468	+	1.04524i	−0.388823	+	0.921312i	$0.627118\pi$
$240$	0.862101	−	0.127928i	0.0556484	−	0.00825772i
$241$	−5.24358	+	9.08214i	−0.337769	+	0.585032i	−0.984013	−	0.178098i	$-0.943005\pi$
$241$	−5.24358	+	9.08214i	−0.337769	+	0.585032i	0.646244	+	0.763131i	$0.276339\pi$
$242$	−0.339226	−	0.587557i	−0.0218063	−	0.0377696i
$243$	−3.29500	−	15.2362i	−0.211375	−	0.977405i
$244$	10.1270			0.648317
$245$	0.491489	−	0.851283i	0.0314001	−	0.0543865i
$246$	13.3943	−	1.98760i	0.853992	−	0.126725i
$247$	0.467882	−	0.810395i	0.0297706	−	0.0515642i
$248$	3.91747	−	3.95645i	0.248759	−	0.251235i
$249$	5.08814	+	6.41030i	0.322448	+	0.406236i
$250$	−2.45222	−	4.24737i	−0.155092	−	0.268627i
$251$	−1.44756	−	2.50725i	−0.0913694	−	0.158256i	0.816718	−	0.577037i	$-0.195791\pi$
$251$	−1.44756	−	2.50725i	−0.0913694	−	0.158256i	−0.908088	+	0.418780i	$0.862458\pi$
$252$	−8.58991	+	2.60673i	−0.541114	+	0.164209i
$253$	−8.00640	+	13.8675i	−0.503358	+	0.871841i
$254$	9.66532	−	16.7408i	0.606456	−	1.05041i
$255$	0.186055	−	0.0276089i	0.0116512	−	0.00172894i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.52702	+	4.37693i	0.157631	+	0.273025i	0.934014	−	0.357236i	$-0.116281\pi$
$257$	2.52702	+	4.37693i	0.157631	+	0.273025i	−0.776383	+	0.630262i	$0.782948\pi$
$258$	−4.82940	−	6.08433i	−0.300665	−	0.378794i
$259$	22.6025			1.40445
$260$	−0.375366	−	0.650154i	−0.0232792	−	0.0403208i
$261$	−4.99788	+	1.51668i	−0.309361	+	0.0938800i
$262$	0.0542619	+	0.0939843i	0.00335231	+	0.00580637i
$263$	12.2997	+	21.3038i	0.758434	+	1.31365i	0.943649	+	0.330948i	$0.107369\pi$
$263$	12.2997	+	21.3038i	0.758434	+	1.31365i	−0.185215	+	0.982698i	$0.559298\pi$
$264$	3.67990	+	4.63613i	0.226482	+	0.285334i
$265$	−0.748782			−0.0459973
$266$	0.938371	+	1.62531i	0.0575352	+	0.0996540i
$267$	−17.0284	−	21.4532i	−1.04212	−	1.31292i
$268$	14.8045			0.904326
$269$	9.30033	−	16.1086i	0.567051	−	0.982161i	−0.429805	−	0.902922i	$-0.641418\pi$
$269$	9.30033	−	16.1086i	0.567051	−	0.982161i	0.996856	−	0.0792393i	$-0.0252491\pi$
$270$	−0.213249	+	2.60591i	−0.0129779	+	0.158591i
$271$	5.43100			0.329910			0.164955	−	0.986301i	$-0.447252\pi$
$271$	5.43100			0.329910			0.164955	+	0.986301i	$0.447252\pi$
$272$	−0.107908	+	0.186902i	−0.00654288	+	0.0113326i
$273$	4.80727	+	6.05644i	0.290949	+	0.366553i
$274$	6.73200	+	11.6602i	0.406695	+	0.704417i
$275$	8.11081	−	14.0483i	0.489100	−	0.847146i
$276$	2.98231	−	7.54806i	0.179514	−	0.454340i
$277$	−4.29110	−	7.43240i	−0.257827	−	0.446570i	0.707833	−	0.706380i	$-0.249673\pi$
$277$	−4.29110	−	7.43240i	−0.257827	−	0.446570i	−0.965660	+	0.259811i	$0.916340\pi$
$278$	−6.08933			−0.365214
$279$	8.89211	+	14.1397i	0.532357	+	0.846520i
$280$	1.50565			0.0899798
$281$	−5.87824	−	10.1814i	−0.350666	−	0.607372i	0.635700	−	0.771936i	$-0.280712\pi$
$281$	−5.87824	−	10.1814i	−0.350666	−	0.607372i	−0.986366	+	0.164564i	$0.947378\pi$
$282$	10.1623	−	1.50799i	0.605156	−	0.0897997i
$283$	−13.5289	+	23.4327i	−0.804208	+	1.39293i	0.112616	+	0.993639i	$0.464077\pi$
$283$	−13.5289	+	23.4327i	−0.804208	+	1.39293i	−0.916824	+	0.399291i	$0.869256\pi$
$284$	−1.88140	−	3.25868i	−0.111641	−	0.193367i
$285$	0.540712	−	0.0802369i	0.0320290	−	0.00475282i
$286$	2.54930	−	4.41551i	0.150743	−	0.261095i
$287$	23.3931			1.38085
$288$	−2.18981	−	2.05054i	−0.129036	−	0.120829i
$289$	8.47671	−	14.6821i	0.498630	−	0.863653i
$290$	0.876035			0.0514425
$291$	6.56486	−	16.6153i	0.384839	−	0.974008i
$292$	0.325049	+	0.563001i	0.0190220	+	0.0329471i
$293$	0.768533			0.0448982			0.0224491	−	0.999748i	$-0.492854\pi$
$293$	0.768533			0.0448982			0.0224491	+	0.999748i	$0.492854\pi$
$294$	−3.34693	+	0.496655i	−0.195197	+	0.0289655i
$295$	−1.69180	−	2.93029i	−0.0985006	−	0.170608i
$296$	3.77685	+	6.54170i	0.219525	+	0.380228i
$297$	−16.0511	+	7.59477i	−0.931379	+	0.440694i
$298$	−2.75168	−	4.76605i	−0.159400	−	0.276090i
$299$	−6.99089			−0.404294
$300$	−3.02120	+	7.64649i	−0.174429	+	0.441470i
$301$	−6.70991	−	11.6219i	−0.386753	−	0.669875i
$302$	1.12514	−	1.94880i	0.0647445	−	0.112141i
$303$	8.80360	−	22.2814i	0.505753	−	1.28004i
$304$	−0.313601	+	0.543174i	−0.0179863	+	0.0311531i
$305$	2.54789	−	4.41307i	0.145892	−	0.252692i
$306$	−0.472597	−	0.442540i	−0.0270166	−	0.0252983i
$307$	−5.72092	−	9.90893i	−0.326510	−	0.565533i	0.655306	−	0.755363i	$-0.272539\pi$
$307$	−5.72092	−	9.90893i	−0.326510	−	0.565533i	−0.981817	+	0.189830i	$0.939206\pi$
$308$	5.11281	+	8.85564i	0.291329	+	0.504597i
$309$	−6.56082	+	16.6051i	−0.373232	+	0.944630i
$310$	−0.738499	−	2.70253i	−0.0419439	−	0.153493i
$311$	5.12987	−	8.88520i	0.290888	−	0.503834i	−0.683132	−	0.730295i	$-0.739382\pi$
$311$	5.12987	−	8.88520i	0.290888	−	0.503834i	0.974020	+	0.226462i	$0.0727158\pi$
$312$	−0.949589	+	2.40336i	−0.0537599	+	0.136063i
$313$	1.26067	−	2.18355i	0.0712574	−	0.123422i	−0.828195	−	0.560440i	$-0.810632\pi$
$313$	1.26067	−	2.18355i	0.0712574	−	0.123422i	0.899453	+	0.437018i	$0.143965\pi$
$314$	4.73384			0.267146
$315$	−1.02522	+	4.39906i	−0.0577645	+	0.247859i
$316$	2.19974	+	3.81007i	0.123745	+	0.214333i
$317$	−2.61051	+	4.52153i	−0.146621	+	0.253955i	−0.929976	−	0.367619i	$-0.880173\pi$
$317$	−2.61051	+	4.52153i	−0.146621	+	0.253955i	0.783356	+	0.621574i	$0.213506\pi$
$318$	1.60240	+	2.01879i	0.0898582	+	0.113208i
$319$	2.97479	+	5.15249i	0.166556	+	0.288484i
$320$	0.251592	+	0.435771i	0.0140644	+	0.0243603i
$321$	1.69566	−	4.29163i	0.0946426	−	0.239536i
$322$	7.01037	−	12.1423i	0.390673	−	0.676665i
$323$	−0.0676802	+	0.117226i	−0.00376583	+	0.00652261i
$324$	7.48215	−	5.00174i	0.415675	−	0.277875i
$325$	7.08206			0.392842
$326$	4.18257	+	7.24443i	0.231651	+	0.401232i
$327$	−17.1807	−	21.6451i	−0.950095	−	1.19698i
$328$	3.90895	+	6.77051i	0.215836	+	0.373839i
$329$	17.7483			0.978497
$330$	2.94612	−	0.437178i	0.162179	−	0.0240659i
$331$	31.4910			1.73090			0.865452	−	0.500992i	$-0.167031\pi$
$331$	31.4910			1.73090			0.865452	+	0.500992i	$0.167031\pi$
$332$	−2.36258	+	4.09210i	−0.129663	+	0.224583i
$333$	−21.6846	+	6.58051i	−1.18831	+	0.360609i
$334$	−1.73564	−	3.00622i	−0.0949701	−	0.164493i
$335$	3.72469	−	6.45135i	0.203501	−	0.352475i
$336$	−3.22211	−	4.05938i	−0.175780	−	0.221457i
$337$	−11.3810	+	19.7124i	−0.619960	+	1.07380i	0.369532	+	0.929218i	$0.379518\pi$
$337$	−11.3810	+	19.7124i	−0.619960	+	1.07380i	−0.989492	+	0.144585i	$0.953815\pi$
$338$	−10.7740			−0.586031
$339$	10.8057	−	27.3488i	0.586888	−	1.48538i
$340$	0.0542976	+	0.0940463i	0.00294470	+	0.00510038i
$341$	13.3874	−	13.5207i	0.724971	−	0.732185i
$342$	−1.37346	−	1.28611i	−0.0742681	−	0.0695446i
$343$	15.1003			0.815340
$344$	2.24243	−	3.88401i	0.120904	−	0.209412i
$345$	−2.53890	−	3.19863i	−0.136690	−	0.172209i
$346$	4.45681	+	7.71942i	0.239599	+	0.414998i
$347$	−6.96915			−0.374124			−0.187062	−	0.982348i	$-0.559896\pi$
$347$	−6.96915			−0.374124			−0.187062	+	0.982348i	$0.559896\pi$
$348$	−1.87472	−	2.36187i	−0.100496	−	0.126610i
$349$	−6.12136	−	10.6025i	−0.327669	−	0.567539i	0.654380	−	0.756166i	$-0.272930\pi$
$349$	−6.12136	−	10.6025i	−0.327669	−	0.567539i	−0.982049	+	0.188627i	$0.939596\pi$
$350$	−7.10180	+	12.3007i	−0.379607	+	0.657498i
$351$	−6.37532	−	4.41090i	−0.340289	−	0.235436i
$352$	−1.70869	+	2.95953i	−0.0910734	+	0.157744i
$353$	−12.3151	+	21.3304i	−0.655467	+	1.13530i	0.326309	+	0.945263i	$0.394195\pi$
$353$	−12.3151	+	21.3304i	−0.655467	+	1.13530i	−0.981776	+	0.190040i	$0.939138\pi$
$354$	−4.27986	+	10.8321i	−0.227472	+	0.575720i
$355$	−1.89338			−0.100490
$356$	7.90678	−	13.6949i	0.419059	−	0.725831i
$357$	−0.695383	−	0.876079i	−0.0368035	−	0.0463670i
$358$	−9.76971	+	16.9216i	−0.516345	+	0.894336i
$359$	−11.0485	+	19.1366i	−0.583120	+	1.00999i	0.411987	+	0.911190i	$0.364835\pi$
$359$	−11.0485	+	19.1366i	−0.583120	+	1.00999i	−0.995107	+	0.0988035i	$0.968498\pi$
$360$	−1.44451	+	0.438356i	−0.0761321	+	0.0231034i
$361$	9.30331	−	16.1138i	0.489648	−	0.848095i
$362$	11.5043			0.604653
$363$	0.730572	+	0.920413i	0.0383451	+	0.0483091i
$364$	−2.23216	+	3.86621i	−0.116997	+	0.202644i
$365$	0.327119			0.0171222
$366$	−17.3506	+	2.57467i	−0.906929	+	0.134580i
$367$	6.60738			0.344903			0.172451	−	0.985018i	$-0.444831\pi$
$367$	6.60738			0.344903			0.172451	+	0.985018i	$0.444831\pi$
$368$	4.68570			0.244259
$369$	−22.4431	+	6.81067i	−1.16834	+	0.354549i
$370$	3.80091			0.197600
$371$	2.22636	+	3.85616i	0.115587	+	0.200202i
$372$	−5.70588	+	7.77450i	−0.295836	+	0.403089i
$373$	−6.13389	+	10.6242i	−0.317601	+	0.550100i	−0.979987	−	0.199062i	$-0.936210\pi$
$373$	−6.13389	+	10.6242i	−0.317601	+	0.550100i	0.662386	+	0.749162i	$0.269544\pi$
$374$	−0.368762	+	0.638715i	−0.0190682	+	0.0330272i
$375$	5.28120	+	6.65354i	0.272720	+	0.343587i
$376$	2.96572	+	5.13679i	0.152946	+	0.264909i
$377$	−1.29874	+	2.24948i	−0.0668885	+	0.115854i
$378$	14.0543	−	6.64996i	0.722874	−	0.342037i
$379$	8.31995	+	14.4106i	0.427367	+	0.740221i	0.996638	−	0.0819284i	$-0.0261079\pi$
$379$	8.31995	+	14.4106i	0.427367	+	0.740221i	−0.569271	+	0.822150i	$0.692775\pi$
$380$	0.157799	+	0.273317i	0.00809494	+	0.0140208i
$381$	−12.3034	+	31.1392i	−0.630320	+	1.59531i
$382$	−2.08006	−	3.60277i	−0.106425	−	0.184334i
$383$	−14.1137	−	24.4457i	−0.721177	−	1.24912i	−0.960528	−	0.278183i	$-0.910268\pi$
$383$	−14.1137	−	24.4457i	−0.721177	−	1.24912i	0.239351	−	0.970933i	$-0.423065\pi$
$384$	0.636470	−	1.61087i	0.0324797	−	0.0822044i
$385$	5.14537			0.262232
$386$	6.41547	+	11.1119i	0.326539	+	0.565582i
$387$	9.82102	+	9.19641i	0.499231	+	0.467480i
$388$	10.3145			0.523639
$389$	−2.57513	+	4.46025i	−0.130564	+	0.226144i	−0.923894	−	0.382648i	$-0.875012\pi$
$389$	−2.57513	+	4.46025i	−0.130564	+	0.226144i	0.793330	+	0.608792i	$0.208346\pi$
$390$	0.808405	+	1.01847i	0.0409352	+	0.0515722i
$391$	1.01125			0.0511411
$392$	−0.976756	−	1.69179i	−0.0493336	−	0.0854484i
$393$	−0.116861	−	0.147227i	−0.00589484	−	0.00742662i
$394$	−2.40054			−0.120937
$395$	2.21375			0.111386
$396$	−7.48341	−	7.00747i	−0.376056	−	0.352139i
$397$	14.9268	+	25.8540i	0.749156	+	1.29758i	0.948228	+	0.317591i	$0.102874\pi$
$397$	14.9268	+	25.8540i	0.749156	+	1.29758i	−0.199072	+	0.979985i	$0.563793\pi$
$398$	−9.92348			−0.497419
$399$	−2.02092	−	2.54605i	−0.101172	−	0.127462i
$400$	−4.74681			−0.237340
$401$	10.1117	−	17.5140i	0.504956	−	0.874609i	−0.495028	−	0.868877i	$-0.664842\pi$
$401$	10.1117	−	17.5140i	0.504956	−	0.874609i	0.999984	−	0.00573174i	$-0.00182448\pi$
$402$	−25.3643	+	3.76384i	−1.26506	+	0.187723i
$403$	8.03439	+	2.11023i	0.400222	+	0.105118i
$404$	13.8319			0.688164
$405$	−0.297162	−	4.51890i	−0.0147661	−	0.224546i
$406$	−2.60472	−	4.51150i	−0.129270	−	0.223902i
$407$	12.9069	+	22.3554i	0.639772	+	1.10812i
$408$	0.137360	−	0.347652i	0.00680035	−	0.0172113i
$409$	7.62920			0.377240			0.188620	−	0.982050i	$-0.439599\pi$
$409$	7.62920			0.377240			0.188620	+	0.982050i	$0.439599\pi$
$410$	3.93385			0.194279
$411$	−14.4983	−	18.2657i	−0.715149	−	0.900982i
$412$	−10.3081			−0.507846
$413$	−10.0605	+	17.4253i	−0.495044	+	0.857442i
$414$	−3.19056	+	13.6902i	−0.156807	+	0.672838i
$415$	1.18881	+	2.05908i	0.0583565	+	0.101076i
$416$	−1.49196			−0.0731495
$417$	10.4328	−	1.54813i	0.510896	−	0.0758124i
$418$	−1.07169	+	1.85623i	−0.0524183	+	0.0907911i
$419$	−12.6772	+	21.9576i	−0.619323	+	1.07270i	0.370287	+	0.928917i	$0.379259\pi$
$419$	−12.6772	+	21.9576i	−0.619323	+	1.07270i	−0.989610	+	0.143781i	$0.954074\pi$
$420$	−2.57962	+	0.382792i	−0.125872	+	0.0186783i
$421$	−37.9032			−1.84729			−0.923645	−	0.383248i	$-0.874805\pi$
$421$	−37.9032			−1.84729			−0.923645	+	0.383248i	$0.874805\pi$
$422$	−0.723940	−	1.25390i	−0.0352409	−	0.0610390i
$423$	−17.0276	+	5.16726i	−0.827909	+	0.251241i
$424$	−0.744043	+	1.28872i	−0.0361339	+	0.0625858i
$425$	−1.02444			−0.0496925
$426$	4.05186	+	5.10475i	0.196313	+	0.247326i
$427$	−30.3026			−1.46644
$428$	2.66417			0.128777
$429$	−3.24510	+	8.21318i	−0.156675	+	0.396536i
$430$	−1.12836	−	1.95437i	−0.0544143	−	0.0942483i
$431$	−18.0237	−	31.2180i	−0.868171	−	1.50372i	−0.863864	−	0.503725i	$-0.831962\pi$
$431$	−18.0237	−	31.2180i	−0.868171	−	1.50372i	−0.00430706	−	0.999991i	$-0.501371\pi$
$432$	4.27311	+	2.95644i	0.205590	+	0.142242i
$433$	−36.1852			−1.73895			−0.869475	−	0.493977i	$-0.835543\pi$
$433$	−36.1852			−1.73895			−0.869475	+	0.493977i	$0.835543\pi$
$434$	−11.7220	+	11.8386i	−0.562674	+	0.568273i
$435$	−1.50090	+	0.222720i	−0.0719627	+	0.0106786i
$436$	7.97751	−	13.8175i	0.382053	−	0.661736i
$437$	2.93888			0.140586
$438$	−0.700038	−	0.881945i	−0.0334491	−	0.0421409i
$439$	−17.8814			−0.853431			−0.426715	−	0.904386i	$-0.640329\pi$
$439$	−17.8814			−0.853431			−0.426715	+	0.904386i	$0.640329\pi$
$440$	0.859785	+	1.48919i	0.0409887	+	0.0709944i
$441$	5.60800	−	1.70183i	0.267048	−	0.0810394i
$442$	−0.321989			−0.0153155
$443$	−10.6424			−0.505637			−0.252818	−	0.967514i	$-0.581358\pi$
$443$	−10.6424			−0.505637			−0.252818	+	0.967514i	$0.581358\pi$
$444$	−8.13398	−	10.2476i	−0.386022	−	0.486330i
$445$	−3.97857	−	6.89109i	−0.188602	−	0.326669i
$446$	3.13647			0.148516
$447$	5.92613	+	7.46604i	0.280296	+	0.353132i
$448$	1.49612	−	2.59136i	0.0706851	−	0.122430i
$449$	31.6508			1.49370			0.746848	−	0.664995i	$-0.231566\pi$
$449$	31.6508			1.49370			0.746848	+	0.664995i	$0.231566\pi$
$450$	3.23217	−	13.8688i	0.152366	−	0.653780i
$451$	13.3584	+	23.1374i	0.629021	+	1.08950i
$452$	16.9776			0.798561
$453$	−1.43223	+	3.62491i	−0.0672922	+	0.170313i
$454$	−4.28830	−	7.42756i	−0.201260	−	0.348593i
$455$	1.12319	+	1.94542i	0.0526558	+	0.0912026i
$456$	0.399196	−	1.01034i	0.0186940	−	0.0473137i
$457$	15.8234	+	27.4070i	0.740189	+	1.28205i	0.952409	+	0.304824i	$0.0985976\pi$
$457$	15.8234	+	27.4070i	0.740189	+	1.28205i	−0.212219	+	0.977222i	$0.568069\pi$
$458$	3.04068	+	5.26662i	0.142082	+	0.246093i
$459$	0.922205	+	0.638047i	0.0430449	+	0.0297815i
$460$	1.17889	−	2.04189i	0.0549658	−	0.0952036i
$461$	−15.0787	−	26.1171i	−0.702285	−	1.21639i	−0.967662	−	0.252249i	$-0.918830\pi$
$461$	−15.0787	−	26.1171i	−0.702285	−	1.21639i	0.265377	−	0.964145i	$-0.414504\pi$
$462$	−11.0112	−	13.8724i	−0.512285	−	0.645403i
$463$	15.3266	−	26.5465i	0.712289	−	1.23372i	−0.251708	−	0.967803i	$-0.580992\pi$
$463$	15.3266	−	26.5465i	0.712289	−	1.23372i	0.963996	−	0.265917i	$-0.0856746\pi$
$464$	0.870491	−	1.50773i	0.0404115	−	0.0699948i
$465$	1.95234	+	4.44246i	0.0905378	+	0.206014i
$466$	−13.6470	−	23.6372i	−0.632183	−	1.09497i
$467$	−12.0165			−0.556056			−0.278028	−	0.960573i	$-0.589681\pi$
$467$	−12.0165			−0.556056			−0.278028	+	0.960573i	$0.589681\pi$
$468$	1.01590	−	4.35907i	0.0469599	−	0.201498i
$469$	−44.2985			−2.04551
$470$	2.98461			0.137670
$471$	−8.11044	+	1.20352i	−0.373709	+	0.0554551i
$472$	−6.72438			−0.309515
$473$	7.66324	−	13.2731i	0.352356	−	0.610299i
$474$	−4.73746	−	5.96850i	−0.217599	−	0.274142i
$475$	−2.97721			−0.136604
$476$	0.322887	−	0.559256i	0.0147995	−	0.0256335i
$477$	−3.25863	−	3.05138i	−0.149202	−	0.139713i
$478$	9.32939	−	16.1590i	0.426717	−	0.739095i
$479$	−10.0399	+	17.3896i	−0.458735	+	0.794553i	−0.998894	−	0.0470100i	$-0.985031\pi$
$479$	−10.0399	+	17.3896i	−0.458735	+	0.794553i	0.540159	+	0.841563i	$0.318364\pi$
$480$	−0.541840	−	0.682638i	−0.0247315	−	0.0311580i
$481$	−5.63492	+	9.75997i	−0.256930	+	0.445016i
$482$	10.4872			0.477677
$483$	−8.92378	+	22.5856i	−0.406046	+	1.02768i
$484$	−0.339226	+	0.587557i	−0.0154194	+	0.0267072i
$485$	2.59505	−	4.49475i	0.117835	−	0.204096i
$486$	−11.5475	+	10.4717i	−0.523804	+	0.475005i
$487$	−8.54869	+	14.8068i	−0.387378	+	0.670958i	−0.992096	−	0.125481i	$-0.959952\pi$
$487$	−8.54869	+	14.8068i	−0.387378	+	0.670958i	0.604718	+	0.796440i	$0.293286\pi$
$488$	−5.06352	−	8.77028i	−0.229215	−	0.397012i
$489$	−9.00776	−	11.3484i	−0.407345	−	0.513194i
$490$	−0.982978			−0.0444064
$491$	14.0523	+	24.3393i	0.634172	+	1.09842i	0.986690	+	0.162613i	$0.0519921\pi$
$491$	14.0523	+	24.3393i	0.634172	+	1.09842i	−0.352518	+	0.935805i	$0.614675\pi$
$492$	−8.41848	−	10.6060i	−0.379535	−	0.478157i
$493$	0.187866	−	0.325393i	0.00846105	−	0.0146550i
$494$	−0.935763			−0.0421020
$495$	−4.93642	+	1.49803i	−0.221875	+	0.0673313i
$496$	−5.38512	−	1.41440i	−0.241799	−	0.0635085i
$497$	5.62961	+	9.75076i	0.252522	+	0.437381i
$498$	3.00741	−	7.61161i	0.134765	−	0.341084i
$499$	18.7866			0.841002			0.420501	−	0.907292i	$-0.361854\pi$
$499$	18.7866			0.841002			0.420501	+	0.907292i	$0.361854\pi$
$500$	−2.45222	+	4.24737i	−0.109667	+	0.189948i
$501$	3.73795	+	4.70926i	0.166999	+	0.210394i
$502$	−1.44756	+	2.50725i	−0.0646079	+	0.111904i
$503$	7.87967	+	13.6480i	0.351337	+	0.608533i	0.986484	−	0.163858i	$-0.0523938\pi$
$503$	7.87967	+	13.6480i	0.351337	+	0.608533i	−0.635147	+	0.772391i	$0.719060\pi$
$504$	6.55245	+	6.13572i	0.291869	+	0.273306i
$505$	3.48000	−	6.02754i	0.154858	−	0.268222i
$506$	16.0128			0.711856
$507$	18.4591	−	2.73916i	0.819796	−	0.121650i
$508$	−19.3306			−0.857659
$509$	10.9607	+	18.9845i	0.485826	+	0.841475i	0.999867	−	0.0162901i	$-0.00518552\pi$
$509$	10.9607	+	18.9845i	0.485826	+	0.841475i	−0.514041	+	0.857765i	$0.671852\pi$
$510$	−0.116938	−	0.147324i	−0.00517809	−	0.00652362i
$511$	−0.972624	−	1.68463i	−0.0430264	−	0.0745239i
$512$	1.00000			0.0441942
$513$	2.68011	+	1.85429i	0.118330	+	0.0818688i
$514$	2.52702	−	4.37693i	0.111462	−	0.193058i
$515$	−2.59345	+	4.49199i	−0.114281	+	0.197941i
$516$	−2.85448	+	7.22455i	−0.125662	+	0.318043i
$517$	10.1350	+	17.5543i	0.445737	+	0.772038i
$518$	−11.3013	−	19.5743i	−0.496548	−	0.860047i
$519$	−9.59836	−	12.0925i	−0.421321	−	0.530802i
$520$	−0.375366	+	0.650154i	−0.0164609	+	0.0285111i
$521$	−21.8435	−	37.8340i	−0.956979	−	1.65754i	−0.729772	−	0.683691i	$-0.760374\pi$
$521$	−21.8435	−	37.8340i	−0.956979	−	1.65754i	−0.227207	−	0.973846i	$-0.572960\pi$
$522$	3.81242	+	3.56995i	0.166865	+	0.156253i
$523$	12.2033			0.533613			0.266807	−	0.963750i	$-0.414031\pi$
$523$	12.2033			0.533613			0.266807	+	0.963750i	$0.414031\pi$
$524$	0.0542619	−	0.0939843i	0.00237044	−	0.00410572i
$525$	9.04015	−	22.8802i	0.394545	−	0.998572i
$526$	12.2997	−	21.3038i	0.536294	−	0.928888i
$527$	−1.16219	−	0.305251i	−0.0506260	−	0.0132969i
$528$	2.17506	−	5.50495i	0.0946571	−	0.239572i
$529$	0.522108	+	0.904317i	0.0227003	+	0.0393181i
$530$	0.374391	+	0.648464i	0.0162625	+	0.0281675i
$531$	4.57873	−	19.6467i	0.198700	−	0.852592i
$532$	0.938371	−	1.62531i	0.0406836	−	0.0704660i
$533$	−5.83201	+	10.1013i	−0.252613	+	0.437538i
$534$	−10.0649	+	25.4736i	−0.435549	+	1.10235i
$535$	0.670284	−	1.16097i	0.0289789	−	0.0501930i
$536$	−7.40223	−	12.8210i	−0.319727	−	0.553784i
$537$	12.4362	−	31.4755i	0.536663	−	1.35827i
$538$	−18.6007			−0.801931
$539$	−3.33794	−	5.78149i	−0.143775	−	0.249026i
$540$	2.36341	−	1.11828i	0.101705	−	0.0481230i
$541$	10.8833	+	18.8504i	0.467909	+	0.810442i	0.999328	−	0.0366671i	$-0.0116741\pi$
$541$	10.8833	+	18.8504i	0.467909	+	0.810442i	−0.531418	+	0.847109i	$0.678341\pi$
$542$	−2.71550	−	4.70338i	−0.116641	−	0.202028i
$543$	−19.7102	+	2.92482i	−0.845846	+	0.125516i
$544$	0.215816			0.00925304
$545$	−4.01416	−	6.95273i	−0.171948	−	0.297822i
$546$	2.84140	−	7.19144i	0.121601	−	0.307765i
$547$	25.7658			1.10167			0.550834	−	0.834615i	$-0.314310\pi$
$547$	25.7658			1.10167			0.550834	+	0.834615i	$0.314310\pi$
$548$	6.73200	−	11.6602i	0.287577	−	0.498098i
$549$	29.0720	−	8.82231i	1.24076	−	0.376527i
$550$	−16.2216			−0.691692
$551$	0.545974	−	0.945655i	0.0232593	−	0.0402863i
$552$	−8.02796	+	1.19128i	−0.341693	+	0.0507041i
$553$	−6.58217	−	11.4006i	−0.279902	−	0.484805i
$554$	−4.29110	+	7.43240i	−0.182311	+	0.315772i
$555$	−6.51206	+	0.966330i	−0.276421	+	0.0410184i
$556$	3.04467	+	5.27352i	0.129123	+	0.223647i
$557$	−21.8646			−0.926432			−0.463216	−	0.886245i	$-0.653305\pi$
$557$	−21.8646			−0.926432			−0.463216	+	0.886245i	$0.653305\pi$
$558$	7.79927	−	14.7706i	0.330169	−	0.625291i
$559$	6.69126			0.283010
$560$	−0.752825	−	1.30393i	−0.0318127	−	0.0551012i
$561$	0.469412	−	1.18806i	0.0198186	−	0.0501598i
$562$	−5.87824	+	10.1814i	−0.247958	+	0.429477i
$563$	11.1206	+	19.2615i	0.468678	+	0.811774i	0.999359	−	0.0357973i	$-0.0113971\pi$
$563$	11.1206	+	19.2615i	0.468678	+	0.811774i	−0.530681	+	0.847572i	$0.678064\pi$
$564$	−6.38711	−	8.04681i	−0.268946	−	0.338832i
$565$	4.27144	−	7.39836i	0.179701	−	0.311251i
$566$	27.0577			1.13732
$567$	−22.3884	+	14.9664i	−0.940225	+	0.628531i
$568$	−1.88140	+	3.25868i	−0.0789418	+	0.136731i
$569$	26.4288			1.10795			0.553977	−	0.832532i	$-0.313109\pi$
$569$	26.4288			1.10795			0.553977	+	0.832532i	$0.313109\pi$
$570$	−0.339843	−	0.428152i	−0.0142345	−	0.0179333i
$571$	5.36835	+	9.29825i	0.224658	+	0.389120i	0.956217	−	0.292659i	$-0.0945400\pi$
$571$	5.36835	+	9.29825i	0.224658	+	0.389120i	−0.731558	+	0.681779i	$0.761207\pi$
$572$	−5.09860			−0.213183
$573$	4.47971	+	5.64377i	0.187142	+	0.235772i
$574$	−11.6965	−	20.2590i	−0.488204	−	0.845594i
$575$	11.1211	+	19.2622i	0.463780	+	0.803290i
$576$	−0.680914	+	2.92170i	−0.0283714	+	0.121738i
$577$	19.1846	+	33.2287i	0.798666	+	1.38333i	0.920485	+	0.390778i	$0.127794\pi$
$577$	19.1846	+	33.2287i	0.798666	+	1.38333i	−0.121818	+	0.992552i	$0.538873\pi$
$578$	−16.9534			−0.705169
$579$	−13.8166	−	17.4069i	−0.574199	−	0.723406i
$580$	−0.438017	−	0.758668i	−0.0181877	−	0.0315020i
$581$	7.06940	−	12.2446i	0.293288	−	0.507990i
$582$	−17.6717	+	2.62233i	−0.732517	+	0.108699i
$583$	−2.54267	+	4.40404i	−0.105307	+	0.182397i
$584$	0.325049	−	0.563001i	0.0134506	−	0.0232971i
$585$	−1.64396	−	1.53941i	−0.0679696	−	0.0636467i
$586$	−0.384266	−	0.665569i	−0.0158739	−	0.0274944i
$587$	−8.66777	−	15.0130i	−0.357757	−	0.619653i	0.629829	−	0.776734i	$-0.283125\pi$
$587$	−8.66777	−	15.0130i	−0.357757	−	0.619653i	−0.987586	+	0.157081i	$0.949792\pi$
$588$	2.10358	+	2.65020i	0.0867503	+	0.109293i
$589$	−3.37756	−	0.887117i	−0.139170	−	0.0365530i
$590$	−1.69180	+	2.93029i	−0.0696504	+	0.120638i
$591$	4.11282	−	0.610306i	0.169179	−	0.0251046i
$592$	3.77685	−	6.54170i	0.155228	−	0.268862i
$593$	−23.2682			−0.955511			−0.477755	−	0.878493i	$-0.658549\pi$
$593$	−23.2682			−0.955511			−0.477755	+	0.878493i	$0.658549\pi$
$594$	14.6028	+	10.1033i	0.599161	+	0.414542i
$595$	−0.162472	−	0.281409i	−0.00666069	−	0.0115367i
$596$	−2.75168	+	4.76605i	−0.112713	+	0.195225i
$597$	17.0018	−	2.52292i	0.695838	−	0.103256i
$598$	3.49545	+	6.05429i	0.142939	+	0.247578i
$599$	9.37723	+	16.2418i	0.383143	+	0.663623i	0.991510	−	0.130033i	$-0.0415083\pi$
$599$	9.37723	+	16.2418i	0.383143	+	0.663623i	−0.608367	+	0.793656i	$0.708175\pi$
$600$	8.13266	−	1.20681i	0.332014	−	0.0492679i
$601$	2.40297	−	4.16206i	0.0980192	−	0.169774i	−0.812846	−	0.582479i	$-0.802083\pi$
$601$	2.40297	−	4.16206i	0.0980192	−	0.169774i	0.910865	+	0.412705i	$0.135416\pi$
$602$	−6.70991	+	11.6219i	−0.273475	+	0.473673i
$603$	42.4995	−	12.8971i	1.73072	−	0.525210i
$604$	−2.25028			−0.0915625
$605$	0.170694	+	0.295650i	0.00693968	+	0.0120199i
$606$	−23.6981	+	3.51658i	−0.962669	+	0.142851i
$607$	6.51125	+	11.2778i	0.264283	+	0.457752i	0.967376	−	0.253346i	$-0.0815313\pi$
$607$	6.51125	+	11.2778i	0.264283	+	0.457752i	−0.703092	+	0.711099i	$0.748198\pi$
$608$	0.627203			0.0254364
$609$	5.60963	+	7.06730i	0.227314	+	0.286382i
$610$	−5.09577			−0.206322
$611$	−4.42475	+	7.66389i	−0.179006	+	0.310048i
$612$	−0.146952	+	0.630551i	−0.00594019	+	0.0254885i
$613$	−22.5833	−	39.1155i	−0.912133	−	1.57986i	−0.811046	−	0.584983i	$-0.801101\pi$
$613$	−22.5833	−	39.1155i	−0.912133	−	1.57986i	−0.101087	−	0.994878i	$-0.532232\pi$
$614$	−5.72092	+	9.90893i	−0.230878	+	0.399892i
$615$	−6.73983	+	1.00013i	−0.271776	+	0.0403291i
$616$	5.11281	−	8.85564i	0.206001	−	0.356804i
$617$	40.8474			1.64446			0.822228	−	0.569158i	$-0.192731\pi$
$617$	40.8474			1.64446			0.822228	+	0.569158i	$0.192731\pi$
$618$	17.6608	−	2.62071i	0.710423	−	0.105420i
$619$	−3.78254	−	6.55155i	−0.152033	−	0.263329i	0.779942	−	0.625852i	$-0.215249\pi$
$619$	−3.78254	−	6.55155i	−0.152033	−	0.263329i	−0.931975	+	0.362523i	$0.881915\pi$
$620$	−1.97121	+	1.99082i	−0.0791656	+	0.0799534i
$621$	1.98579	−	24.2665i	0.0796872	−	0.973781i
$622$	−10.2597			−0.411378
$623$	−23.6590	+	40.9786i	−0.947878	+	1.64177i
$624$	2.55617	−	0.379312i	0.102329	−	0.0151846i
$625$	−10.6331	−	18.4171i	−0.425324	−	0.736682i
$626$	−2.52135			−0.100773
$627$	1.36420	−	3.45272i	0.0544809	−	0.137888i
$628$	−2.36692	−	4.09962i	−0.0944504	−	0.163593i
$629$	0.815105	−	1.41180i	0.0325004	−	0.0562923i
$630$	4.32231	−	1.31167i	0.172205	−	0.0522581i
$631$	10.0926	−	17.4809i	0.401781	−	0.695905i	−0.592160	−	0.805820i	$-0.701725\pi$
$631$	10.0926	−	17.4809i	0.401781	−	0.695905i	0.993941	+	0.109915i	$0.0350580\pi$
$632$	2.19974	−	3.81007i	0.0875011	−	0.151556i
$633$	1.55911	+	1.96424i	0.0619690	+	0.0780717i
$634$	5.22102			0.207353
$635$	−4.86344	+	8.42373i	−0.193000	+	0.334285i
$636$	0.947121	−	2.39711i	0.0375558	−	0.0950517i
$637$	1.45728	−	2.52409i	0.0577397	−	0.100008i
$638$	2.97479	−	5.15249i	0.117773	−	0.203989i
$639$	−8.23983	−	7.71578i	−0.325963	−	0.305231i
$640$	0.251592	−	0.435771i	0.00994506	−	0.0172253i
$641$	−7.86394			−0.310607			−0.155304	−	0.987867i	$-0.549636\pi$
$641$	−7.86394			−0.310607			−0.155304	+	0.987867i	$0.549636\pi$
$642$	−4.56449	+	0.677330i	−0.180146	+	0.0267321i
$643$	9.84791	−	17.0571i	0.388364	−	0.672666i	−0.603866	−	0.797086i	$-0.706374\pi$
$643$	9.84791	−	17.0571i	0.388364	−	0.672666i	0.992230	+	0.124420i	$0.0397071\pi$
$644$	−14.0207			−0.552495
$645$	2.43008	+	3.06154i	0.0956843	+	0.120548i
$646$	0.135360			0.00532568
$647$	−18.5409			−0.728918			−0.364459	−	0.931219i	$-0.618746\pi$
$647$	−18.5409			−0.728918			−0.364459	+	0.931219i	$0.618746\pi$
$648$	−8.07271	−	3.97886i	−0.317126	−	0.156304i
$649$	−22.9797			−0.902034
$650$	−3.54103	−	6.13324i	−0.138891	−	0.240566i
$651$	17.0734	−	23.2632i	0.669158	−	0.911757i
$652$	4.18257	−	7.24443i	0.163802	−	0.283714i
$653$	−3.53181	+	6.11727i	−0.138210	+	0.239387i	−0.926819	−	0.375508i	$-0.877468\pi$
$653$	−3.53181	+	6.11727i	−0.138210	+	0.239387i	0.788609	+	0.614895i	$0.210802\pi$
$654$	−10.1549	+	25.7015i	−0.397087	+	1.00501i
$655$	−0.0273037	−	0.0472914i	−0.00106684	−	0.00184783i
$656$	3.90895	−	6.77051i	0.152619	−	0.264344i
$657$	1.42359	+	1.33305i	0.0555396	+	0.0520073i
$658$	−8.87417	−	15.3705i	−0.345951	−	0.599205i
$659$	−22.5386	−	39.0380i	−0.877979	−	1.52070i	−0.853556	−	0.521002i	$-0.825558\pi$
$659$	−22.5386	−	39.0380i	−0.877979	−	1.52070i	−0.0244230	−	0.999702i	$-0.507775\pi$
$660$	−1.85167	−	2.33283i	−0.0720761	−	0.0908052i
$661$	5.45170	+	9.44263i	0.212047	+	0.367276i	0.952355	−	0.304992i	$-0.0986538\pi$
$661$	5.45170	+	9.44263i	0.212047	+	0.367276i	−0.740308	+	0.672268i	$0.765320\pi$
$662$	−15.7455	−	27.2720i	−0.611967	−	1.05996i
$663$	0.551661	−	0.0818616i	0.0214248	−	0.00317924i
$664$	4.72515			0.183371
$665$	−0.472174	−	0.817829i	−0.0183101	−	0.0317141i
$666$	16.5412	+	15.4892i	0.640958	+	0.600193i
$667$	−8.15772			−0.315868
$668$	−1.73564	+	3.00622i	−0.0671540	+	0.116314i
$669$	−5.37368	+	0.797406i	−0.207759	+	0.0308295i
$670$	−7.44937			−0.287794
$671$	−17.3040	−	29.9713i	−0.668012	−	1.15703i
$672$	−1.90447	+	4.82012i	−0.0734666	+	0.185940i
$673$	28.3360			1.09227			0.546137	−	0.837696i	$-0.316098\pi$
$673$	28.3360			1.09227			0.546137	+	0.837696i	$0.316098\pi$
$674$	22.7619			0.876756
$675$	−2.01169	+	24.5830i	−0.0774300	+	0.946198i
$676$	5.38702	+	9.33060i	0.207193	+	0.358869i
$677$	29.4500			1.13185			0.565927	−	0.824455i	$-0.308518\pi$
$677$	29.4500			1.13185			0.565927	+	0.824455i	$0.308518\pi$
$678$	−29.0876	+	4.31634i	−1.11710	+	0.165768i
$679$	−30.8635			−1.18443
$680$	0.0542976	−	0.0940463i	0.00208222	−	0.00360651i
$681$	9.23547	+	11.6353i	0.353904	+	0.445866i
$682$	−18.4030	−	4.83354i	−0.704686	−	0.185086i
$683$	13.5928			0.520113			0.260057	−	0.965593i	$-0.416259\pi$
$683$	13.5928			0.520113			0.260057	+	0.965593i	$0.416259\pi$
$684$	−0.427071	+	1.83250i	−0.0163295	+	0.0700674i
$685$	−3.38744	−	5.86722i	−0.129427	−	0.224175i
$686$	−7.55016	−	13.0773i	−0.288266	−	0.499292i
$687$	−6.54854	−	8.25019i	−0.249842	−	0.314764i
$688$	−4.48487			−0.170984
$689$	−2.22017			−0.0845817
$690$	−1.50065	+	3.79807i	−0.0571288	+	0.144590i
$691$	−15.3335			−0.583314			−0.291657	−	0.956523i	$-0.594207\pi$
$691$	−15.3335			−0.583314			−0.291657	+	0.956523i	$0.594207\pi$
$692$	4.45681	−	7.71942i	0.169422	−	0.293448i
$693$	22.3922	+	20.9680i	0.850609	+	0.796510i
$694$	3.48458	+	6.03546i	0.132273	+	0.229103i
$695$	3.06406			0.116226
$696$	−1.10808	+	2.80450i	−0.0420017	+	0.106304i
$697$	0.843615	−	1.46118i	0.0319542	−	0.0553463i
$698$	−6.12136	+	10.6025i	−0.231697	+	0.401311i
$699$	29.3907	+	37.0279i	1.11166	+	1.40052i
$700$	14.2036			0.536845
$701$	5.41705	+	9.38260i	0.204599	+	0.354376i	0.950005	−	0.312235i	$-0.101078\pi$
$701$	5.41705	+	9.38260i	0.204599	+	0.354376i	−0.745406	+	0.666611i	$0.767744\pi$
$702$	−0.632292	+	7.72664i	−0.0238643	+	0.291623i
$703$	2.36885	−	4.10297i	0.0893429	−	0.154746i
$704$	3.41738			0.128797
$705$	−5.11351	+	0.758799i	−0.192586	+	0.0285780i
$706$	24.6302			0.926971
$707$	−41.3885			−1.55657
$708$	11.5208	−	1.70959i	0.432979	−	0.0642502i
$709$	24.5137	+	42.4590i	0.920631	+	1.59458i	0.798441	+	0.602073i	$0.205658\pi$
$709$	24.5137	+	42.4590i	0.920631	+	1.59458i	0.122190	+	0.992507i	$0.461008\pi$
$710$	0.946692	+	1.63972i	0.0355287	+	0.0615375i
$711$	9.63405	+	9.02133i	0.361305	+	0.338326i
$712$	−15.8136			−0.592638
$713$	6.87697	+	25.1662i	0.257544	+	0.942481i
$714$	−0.411015	+	1.04026i	−0.0153819	+	0.0389307i
$715$	−1.28277	+	2.22182i	−0.0479728	+	0.0830913i
$716$	19.5394			0.730222
$717$	−11.8757	+	30.0569i	−0.443508	+	1.12250i
$718$	22.0971			0.824656
$719$	−13.9628	−	24.1842i	−0.520723	−	0.901919i	−0.999710	−	0.0240967i	$-0.992329\pi$
$719$	−13.9628	−	24.1842i	−0.520723	−	0.901919i	0.478987	−	0.877822i	$-0.341004\pi$
$720$	1.10188	+	1.03180i	0.0410646	+	0.0384529i
$721$	30.8445			1.14871
$722$	−18.6066			−0.692467
$723$	−17.9675	+	2.66622i	−0.668220	+	0.0991579i
$724$	−5.75215	−	9.96302i	−0.213777	−	0.370273i
$725$	8.26410			0.306921
$726$	0.431815	−	1.09290i	0.0160261	−	0.0405613i
$727$	−24.4221	+	42.3003i	−0.905765	+	1.56883i	−0.0858774	+	0.996306i	$0.527369\pi$
$727$	−24.4221	+	42.3003i	−0.905765	+	1.56883i	−0.819887	+	0.572525i	$0.805964\pi$
$728$	4.46431			0.165458
$729$	17.1219	−	20.8768i	0.634144	−	0.773215i
$730$	−0.163559	−	0.283293i	−0.00605361	−	0.0104852i
$731$	−0.967906			−0.0357993
$732$	10.9050	+	13.7387i	0.403061	+	0.507797i
$733$	9.86372	+	17.0845i	0.364325	+	0.631029i	0.988668	−	0.150122i	$-0.0479665\pi$
$733$	9.86372	+	17.0845i	0.364325	+	0.631029i	−0.624343	+	0.781150i	$0.714633\pi$
$734$	−3.30369	−	5.72216i	−0.121942	−	0.211209i
$735$	1.68413	−	0.249909i	0.0621199	−	0.00921804i
$736$	−2.34285	−	4.05794i	−0.0863586	−	0.149577i
$737$	−25.2962	−	43.8143i	−0.931797	−	1.61392i
$738$	17.1198	+	16.0309i	0.630187	+	0.590107i
$739$	23.1467	−	40.0913i	0.851465	−	1.47478i	−0.0284204	−	0.999596i	$-0.509048\pi$
$739$	23.1467	−	40.0913i	0.851465	−	1.47478i	0.879886	−	0.475185i	$-0.157619\pi$
$740$	−1.90045	−	3.29168i	−0.0698620	−	0.121005i
$741$	1.60323	−	0.237906i	0.0588963	−	0.00873968i
$742$	2.22636	−	3.85616i	0.0817321	−	0.141564i
$743$	−25.8397	+	44.7556i	−0.947966	+	1.64193i	−0.198265	+	0.980148i	$0.563531\pi$
$743$	−25.8397	+	44.7556i	−0.947966	+	1.64193i	−0.749701	+	0.661777i	$0.769803\pi$
$744$	9.58586	+	1.05419i	0.351435	+	0.0386483i
$745$	1.38460	+	2.39820i	0.0507279	+	0.0878633i
$746$	12.2678			0.449155
$747$	−3.21742	+	13.8055i	−0.117719	+	0.505117i
$748$	0.737524			0.0269666
$749$	−7.97184			−0.291285
$750$	3.12153	−	7.90043i	0.113982	−	0.288483i
$751$	44.9222			1.63923			0.819617	−	0.572912i	$-0.194187\pi$
$751$	44.9222			1.63923			0.819617	+	0.572912i	$0.194187\pi$
$752$	2.96572	−	5.13679i	0.108149	−	0.187319i
$753$	1.84266	−	4.66368i	0.0671503	−	0.169954i
$754$	2.59748			0.0945946
$755$	−0.566153	+	0.980605i	−0.0206044	+	0.0356879i
$756$	−12.7862	−	8.84639i	−0.465029	−	0.321740i
$757$	7.25508	−	12.5662i	0.263690	−	0.456725i	−0.703529	−	0.710666i	$-0.748394\pi$
$757$	7.25508	−	12.5662i	0.263690	−	0.456725i	0.967220	+	0.253941i	$0.0817270\pi$
$758$	8.31995	−	14.4106i	0.302194	−	0.523416i
$759$	−27.4346	+	4.07104i	−0.995812	+	0.147769i
$760$	0.157799	−	0.273317i	0.00572399	−	0.00991424i
$761$	54.1047			1.96129			0.980647	−	0.195783i	$-0.0627249\pi$
$761$	54.1047			1.96129			0.980647	+	0.195783i	$0.0627249\pi$
$762$	33.1190	−	4.91456i	1.19977	−	0.178036i
$763$	−23.8706	+	41.3452i	−0.864175	+	1.49680i
$764$	−2.08006	+	3.60277i	−0.0752540	+	0.130344i
$765$	0.237803	+	0.222679i	0.00859780	+	0.00805098i
$766$	−14.1137	+	24.4457i	−0.509949	+	0.883258i
$767$	−5.01626	−	8.68842i	−0.181127	−	0.313721i
$768$	−1.71329	+	0.254237i	−0.0618230	+	0.00917398i
$769$	−11.1636			−0.402569			−0.201285	−	0.979533i	$-0.564512\pi$
$769$	−11.1636			−0.402569			−0.201285	+	0.979533i	$0.564512\pi$
$770$	−2.57269	−	4.45602i	−0.0927132	−	0.160584i
$771$	−3.21675	+	8.14141i	−0.115848	+	0.293206i
$772$	6.41547	−	11.1119i	0.230898	−	0.399927i
$773$	−51.7015			−1.85957			−0.929787	−	0.368098i	$-0.880009\pi$
$773$	−51.7015			−1.85957			−0.929787	+	0.368098i	$0.880009\pi$
$774$	3.05381	−	13.1035i	0.109767	−	0.470994i
$775$	−6.96665	−	25.4944i	−0.250249	−	0.915785i
$776$	−5.15725	−	8.93262i	−0.185134	−	0.320662i
$777$	24.3388	+	30.6633i	0.873151	+	1.10004i
$778$	5.15025			0.184646
$779$	2.45171	−	4.24648i	0.0878415	−	0.152146i
$780$	0.477819	−	1.20933i	0.0171086	−	0.0433011i
$781$	−6.42945	+	11.1361i	−0.230064	+	0.398482i
$782$	−0.505625	−	0.875767i	−0.0180811	−	0.0313174i
$783$	−7.43940	−	5.14711i	−0.265863	−	0.183943i
$784$	−0.976756	+	1.69179i	−0.0348842	+	0.0604211i
$785$	−2.38199			−0.0850170
$786$	−0.0690720	+	0.174818i	−0.00246372	+	0.00623554i
$787$	6.09813			0.217375			0.108687	−	0.994076i	$-0.465335\pi$
$787$	6.09813			0.217375			0.108687	+	0.994076i	$0.465335\pi$
$788$	1.20027	+	2.07893i	0.0427578	+	0.0740587i
$789$	−15.6568	+	39.6266i	−0.557397	+	1.41074i
$790$	−1.10688	−	1.91717i	−0.0393809	−	0.0682098i
$791$	−50.8012			−1.80628
$792$	−2.32694	+	9.98456i	−0.0826842	+	0.354786i
$793$	7.55459	−	13.0849i	0.268271	−	0.464659i
$794$	14.9268	−	25.8540i	0.529733	−	0.917525i
$795$	−0.806303	−	1.01582i	−0.0285966	−	0.0360275i
$796$	4.96174	+	8.59399i	0.175864	+	0.304606i
$797$	26.2865	+	45.5296i	0.931117	+	1.61274i	0.781416	+	0.624011i	$0.214498\pi$
$797$	26.2865	+	45.5296i	0.931117	+	1.61274i	0.149701	+	0.988731i	$0.452169\pi$
$798$	−1.19449	+	3.02319i	−0.0422845	+	0.107020i
$799$	0.640051	−	1.10860i	0.0226434	−	0.0392195i
$800$	2.37340	+	4.11085i	0.0839125	+	0.145341i
$801$	10.7677	−	46.2025i	0.380457	−	1.63249i
$802$	−20.2235			−0.714115
$803$	1.11081	−	1.92399i	0.0391998	−	0.0678960i
$804$	15.9417	+	20.0842i	0.562222	+	0.708316i
$805$	−3.52751	+	6.10983i	−0.124328	+	0.215343i
$806$	−2.18968	−	8.01311i	−0.0771282	−	0.282250i
$807$	31.8683	−	4.72897i	1.12182	−	0.166468i
$808$	−6.91596	−	11.9788i	−0.243303	−	0.421412i
$809$	−23.1168	−	40.0395i	−0.812744	−	1.40771i	−0.910937	−	0.412546i	$-0.864640\pi$
$809$	−23.1168	−	40.0395i	−0.812744	−	1.40771i	0.0981929	−	0.995167i	$-0.468694\pi$
$810$	−3.76490	+	2.51680i	−0.132285	+	0.0884313i
$811$	−24.3552	+	42.1845i	−0.855227	+	1.48130i	0.0212072	+	0.999775i	$0.493249\pi$
$811$	−24.3552	+	42.1845i	−0.855227	+	1.48130i	−0.876434	+	0.481522i	$0.840084\pi$
$812$	−2.60472	+	4.51150i	−0.0914077	+	0.158323i
$813$	5.84821	+	7.36788i	0.205106	+	0.258403i
$814$	12.9069	−	22.3554i	0.452387	−	0.783558i
$815$	−2.10461	−	3.64529i	−0.0737211	−	0.127689i
$816$	−0.369755	+	0.0548684i	−0.0129440	+	0.00192078i
$817$	−2.81292			−0.0984117
$818$	−3.81460	−	6.60708i	−0.133374	−	0.231011i
$819$	−3.03981	+	13.0434i	−0.106220	+	0.455773i
$820$	−1.96693	−	3.40681i	−0.0686880	−	0.118971i
$821$	−12.0392	−	20.8525i	−0.420171	−	0.727758i	0.575785	−	0.817601i	$-0.304697\pi$
$821$	−12.0392	−	20.8525i	−0.420171	−	0.727758i	−0.995956	+	0.0898436i	$0.971363\pi$
$822$	−8.56943	+	21.6888i	−0.298893	+	0.756483i
$823$	32.4403			1.13080			0.565398	−	0.824818i	$-0.308722\pi$
$823$	32.4403			1.13080			0.565398	+	0.824818i	$0.308722\pi$
$824$	5.15407	+	8.92711i	0.179551	+	0.310991i
$825$	27.7923	−	4.12413i	0.967605	−	0.143584i
$826$	20.1210			0.700098
$827$	−13.1241	+	22.7317i	−0.456371	+	0.790458i	−0.998766	−	0.0496657i	$-0.984184\pi$
$827$	−13.1241	+	22.7317i	−0.456371	+	0.790458i	0.542395	+	0.840124i	$0.317518\pi$
$828$	13.4514	−	4.08201i	0.467467	−	0.141860i
$829$	−6.77611			−0.235344			−0.117672	−	0.993053i	$-0.537543\pi$
$829$	−6.77611			−0.235344			−0.117672	+	0.993053i	$0.537543\pi$
$830$	1.18881	−	2.05908i	0.0412642	−	0.0714718i
$831$	5.46231	−	13.8248i	0.189485	−	0.479577i
$832$	0.745981	+	1.29208i	0.0258623	+	0.0447947i
$833$	−0.210800	+	0.365116i	−0.00730378	+	0.0126505i
$834$	−6.55712	−	8.26100i	−0.227054	−	0.286055i
$835$	0.873348	+	1.51268i	0.0302235	+	0.0523486i
$836$	2.14339			0.0741306
$837$	−9.60717	+	27.2892i	−0.332072	+	0.943254i
$838$	25.3544			0.875854
$839$	20.2110	+	35.0065i	0.697762	+	1.20856i	0.969241	+	0.246115i	$0.0791541\pi$
$839$	20.2110	+	35.0065i	0.697762	+	1.20856i	−0.271479	+	0.962444i	$0.587513\pi$
$840$	1.62132	+	2.04262i	0.0559407	+	0.0704770i
$841$	12.9845	−	22.4898i	0.447741	−	0.775510i
$842$	18.9516	+	32.8252i	0.653116	+	1.13123i
$843$	7.48264	−	18.9382i	0.257716	−	0.652265i
$844$	−0.723940	+	1.25390i	−0.0249191	+	0.0431611i
$845$	5.42133			0.186500
$846$	12.9888	+	12.1627i	0.446563	+	0.418162i
$847$	1.01505	−	1.75811i	0.0348775	−	0.0604095i
$848$	1.48809			0.0511011
$849$	−46.3578	+	6.87908i	−1.59099	+	0.236089i
$850$	0.512218	+	0.887188i	0.0175689	+	0.0304303i
$851$	−35.3944			−1.21330
$852$	2.39491	−	6.06139i	0.0820482	−	0.207660i
$853$	−24.0086	−	41.5841i	−0.822038	−	1.42381i	−0.904162	−	0.427189i	$-0.859504\pi$
$853$	−24.0086	−	41.5841i	−0.822038	−	1.42381i	0.0821244	−	0.996622i	$-0.473830\pi$
$854$	15.1513	+	26.2428i	0.518466	+	0.898010i
$855$	0.691102	+	0.647148i	0.0236352	+	0.0221320i
$856$	−1.33208	−	2.30724i	−0.0455297	−	0.0788598i
$857$	−14.4996			−0.495297			−0.247649	−	0.968850i	$-0.579658\pi$
$857$	−14.4996			−0.495297			−0.247649	+	0.968850i	$0.579658\pi$
$858$	8.73538	−	1.29625i	0.298221	−	0.0442533i
$859$	−13.8382	−	23.9685i	−0.472154	−	0.817794i	0.527339	−	0.849655i	$-0.323190\pi$
$859$	−13.8382	−	23.9685i	−0.472154	−	0.817794i	−0.999492	+	0.0318611i	$0.989857\pi$
$860$	−1.12836	+	1.95437i	−0.0384767	+	0.0666436i
$861$	25.1901	+	31.7358i	0.858478	+	1.08155i
$862$	−18.0237	+	31.2180i	−0.613890	+	1.06329i
$863$	−0.000852621		0.00147678i	−2.90236e−5		5.02703e-5i	−0.866040	−	0.499975i	$-0.833343\pi$
$863$	−0.000852621		0.00147678i	−2.90236e−5		5.02703e-5i	0.866011	+	0.500025i	$0.166676\pi$
$864$	0.423799	−	5.17884i	0.0144179	−	0.176188i
$865$	−2.24260	−	3.88429i	−0.0762506	−	0.132070i
$866$	18.0926	+	31.3373i	0.614812	+	1.06489i
$867$	29.0461	−	4.31019i	0.986458	−	0.146382i
$868$	16.1136	+	4.23223i	0.546930	+	0.143651i
$869$	7.51735	−	13.0204i	0.255009	−	0.441688i
$870$	0.943332	+	1.18846i	0.0319820	+	0.0402925i
$871$	11.0438	−	19.1285i	0.374206	−	0.648145i
$872$	−15.9550			−0.540305
$873$	29.6101	−	8.98561i	1.00215	−	0.304117i
$874$	−1.46944	−	2.54515i	−0.0497046	−	0.0860909i
$875$	7.33764	−	12.7092i	0.248057	−	0.429648i
$876$	−0.413767	+	1.04722i	−0.0139799	+	0.0353824i
$877$	17.6037	+	30.4906i	0.594436	+	1.02959i	0.993626	+	0.112725i	$0.0359580\pi$
$877$	17.6037	+	30.4906i	0.594436	+	1.02959i	−0.399190	+	0.916868i	$0.630709\pi$
$878$	8.94068	+	15.4857i	0.301733	+	0.522617i
$879$	0.827572	+	1.04262i	0.0279133	+	0.0351666i
$880$	0.859785	−	1.48919i	0.0289834	−	0.0502006i
$881$	2.99880	−	5.19407i	0.101032	−	0.174993i	−0.811078	−	0.584938i	$-0.801119\pi$
$881$	2.99880	−	5.19407i	0.101032	−	0.174993i	0.912110	+	0.409945i	$0.134452\pi$
$882$	−4.27783	−	4.00576i	−0.144042	−	0.134881i
$883$	11.2673			0.379174			0.189587	−	0.981864i	$-0.439285\pi$
$883$	11.2673			0.379174			0.189587	+	0.981864i	$0.439285\pi$
$884$	0.160995	+	0.278851i	0.00541484	+	0.00937878i
$885$	2.15356	−	5.45055i	0.0723912	−	0.183218i
$886$	5.32121	+	9.21661i	0.178770	+	0.309638i
$887$	0.0152303			0.000511383			0.000255692	−	1.00000i	$-0.499919\pi$
$887$	0.0152303			0.000511383			0.000255692		1.00000i	$0.499919\pi$
$888$	−4.80770	+	12.1680i	−0.161336	+	0.408333i
$889$	57.8420			1.93996
$890$	−3.97857	+	6.89109i	−0.133362	+	0.230990i
$891$	−27.5875	−	13.5973i	−0.924216	−	0.455525i
$892$	−1.56823	−	2.71626i	−0.0525084	−	0.0909472i
$893$	1.86011	−	3.22181i	0.0622462	−	0.107814i
$894$	3.50272	−	8.86520i	0.117148	−	0.296497i
$895$	4.91597	−	8.51470i	0.164323	−	0.284615i
$896$	−2.99224			−0.0999638
$897$	−7.52794	−	9.48408i	−0.251350	−	0.316664i
$898$	−15.8254	−	27.4104i	−0.528101	−	0.914698i
$899$	9.37538	+	2.46245i	0.312687	+	0.0821272i
$900$	−13.6268	+	4.13524i	−0.454226	+	0.137841i
$901$	0.321153			0.0106991
$902$	13.3584	−	23.1374i	0.444785	−	0.770390i
$903$	8.54130	−	21.6176i	0.284237	−	0.719388i
$904$	−8.48882	−	14.7031i	−0.282334	−	0.489017i
$905$	−5.78879			−0.192426
$906$	3.85538	−	0.572104i	0.128086	−	0.0190069i
$907$	2.69738	+	4.67199i	0.0895649	+	0.155131i	0.907327	−	0.420425i	$-0.138119\pi$
$907$	2.69738	+	4.67199i	0.0895649	+	0.155131i	−0.817762	+	0.575556i	$0.804786\pi$
$908$	−4.28830	+	7.42756i	−0.142312	+	0.246492i
$909$	39.7077	−	12.0499i	1.31702	−	0.399669i
$910$	1.12319	−	1.94542i	0.0372333	−	0.0644899i
$911$	19.0797	−	33.0470i	0.632138	−	1.09490i	−0.354976	−	0.934876i	$-0.615511\pi$
$911$	19.0797	−	33.0470i	0.632138	−	1.09490i	0.987114	−	0.160020i	$-0.0511558\pi$
$912$	−1.07458	+	0.159458i	−0.0355829	+	0.00528019i
$913$	16.1476			0.534408
$914$	15.8234	−	27.4070i	0.523393	−	0.906543i
$915$	8.73054	−	1.29553i	0.288623	−	0.0428290i
$916$	3.04068	−	5.26662i	0.100467	−	0.174014i
$917$	−0.162365	+	0.281224i	−0.00536175	+	0.00928683i
$918$	0.0914626	−	1.11768i	0.00301871	−	0.0368888i
$919$	19.7752	−	34.2517i	0.652325	−	1.12986i	−0.330233	−	0.943900i	$-0.607127\pi$
$919$	19.7752	−	34.2517i	0.652325	−	1.12986i	0.982557	−	0.185960i	$-0.0595394\pi$
$920$	−2.35777			−0.0777334
$921$	7.28239	−	18.4313i	0.239963	−	0.607334i
$922$	−15.0787	+	26.1171i	−0.496591	+	0.860120i
$923$	−5.61396			−0.184786
$924$	−6.50829	+	16.4721i	−0.214107	+	0.541894i
$925$	35.8559			1.17894
$926$	−30.6532			−1.00733
$927$	−29.5919	+	8.98007i	−0.971924	+	0.294944i
$928$	−1.74098			−0.0571505
$929$	−17.8691	−	30.9502i	−0.586266	−	1.01544i	−0.994716	−	0.102662i	$-0.967264\pi$
$929$	−17.8691	−	30.9502i	−0.586266	−	1.01544i	0.408450	−	0.912781i	$-0.366069\pi$
$930$	2.87111	−	3.91201i	0.0941475	−	0.128280i
$931$	−0.612624	+	1.06110i	−0.0200780	+	0.0347760i
$932$	−13.6470	+	23.6372i	−0.447021	+	0.774263i
$933$	17.5779	−	2.60841i	0.575475	−	0.0853954i
$934$	6.00824	+	10.4066i	0.196596	+	0.340514i
$935$	0.185555	−	0.321391i	0.00606831	−	0.0105106i
$936$	−4.28302	+	1.29974i	−0.139995	+	0.0424834i
$937$	25.8978	+	44.8564i	0.846046	+	1.46539i	0.884710	+	0.466142i	$0.154356\pi$
$937$	25.8978	+	44.8564i	0.846046	+	1.46539i	−0.0386644	+	0.999252i	$0.512310\pi$
$938$	22.1493	+	38.3636i	0.723199	+	1.25262i
$939$	4.31980	−	0.641019i	0.140971	−	0.0209189i
$940$	−1.49231	−	2.58475i	−0.0486737	−	0.0843053i
$941$	−25.7265	−	44.5596i	−0.838660	−	1.45260i	−0.891016	−	0.453973i	$-0.850006\pi$
$941$	−25.7265	−	44.5596i	−0.838660	−	1.45260i	0.0523560	−	0.998628i	$-0.483327\pi$
$942$	5.09750	+	6.42209i	0.166085	+	0.209243i
$943$	−36.6324			−1.19291
$944$	3.36219	+	5.82349i	0.109430	+	0.189538i
$945$	−7.07190	+	3.34616i	−0.230049	+	0.108850i
$946$	−15.3265			−0.498307
$947$	5.21043	−	9.02473i	0.169316	−	0.293264i	−0.768863	−	0.639413i	$-0.779177\pi$
$947$	5.21043	−	9.02473i	0.169316	−	0.293264i	0.938180	+	0.346149i	$0.112511\pi$
$948$	−2.80014	+	7.08701i	−0.0909443	+	0.230175i
$949$	0.969921			0.0314850
$950$	1.48861	+	2.57834i	0.0482967	+	0.0836524i
$951$	−8.94512	+	1.32738i	−0.290065	+	0.0430431i
$952$	−0.645774			−0.0209296
$953$	−41.8851			−1.35679			−0.678396	−	0.734697i	$-0.737324\pi$
$953$	−41.8851			−1.35679			−0.678396	+	0.734697i	$0.737324\pi$
$954$	−1.01326	+	4.34774i	−0.0328055	+	0.140763i
$955$	1.04666	+	1.81286i	0.0338690	+	0.0586628i
$956$	−18.6588			−0.603468
$957$	−3.78673	+	9.58402i	−0.122408	+	0.309807i
$958$	20.0798			0.648750
$959$	−20.1438	+	34.8900i	−0.650477	+	1.12666i
$960$	−0.320262	+	0.810566i	−0.0103364	+	0.0261609i
$961$	−0.306928	−	30.9985i	−0.00990089	−	0.999951i
$962$	11.2698			0.363354
$963$	7.64810	−	2.32093i	0.246457	−	0.0747908i
$964$	−5.24358	−	9.08214i	−0.168884	−	0.292516i
$965$	−3.22816	−	5.59134i	−0.103918	−	0.179992i
$966$	24.0216	−	3.56459i	0.772883	−	0.114689i
$967$	21.7366			0.699002			0.349501	−	0.936936i	$-0.386351\pi$
$967$	21.7366			0.699002			0.349501	+	0.936936i	$0.386351\pi$
$968$	0.678453			0.0218063
$969$	−0.231912	+	0.0344136i	−0.00745008	+	0.00110552i
$970$	−5.19010			−0.166644
$971$	−9.13196	+	15.8170i	−0.293059	+	0.507592i	−0.974531	−	0.224251i	$-0.928006\pi$
$971$	−9.13196	+	15.8170i	−0.293059	+	0.507592i	0.681473	+	0.731843i	$0.261340\pi$
$972$	14.8425	+	4.76456i	0.476072	+	0.152823i
$973$	−9.11038	−	15.7796i	−0.292065	−	0.505872i
$974$	17.0974			0.547835
$975$	7.62611	+	9.60776i	0.244231	+	0.307695i
$976$	−5.06352	+	8.77028i	−0.162079	+	0.280730i
$977$	−14.8937	+	25.7967i	−0.476492	+	0.825308i	−0.999637	−	0.0269352i	$-0.991425\pi$
$977$	−14.8937	+	25.7967i	−0.476492	+	0.825308i	0.523145	+	0.852244i	$0.324759\pi$
$978$	−5.32416	+	13.4752i	−0.170248	+	0.430889i
$979$	−54.0409			−1.72715
$980$	0.491489	+	0.851283i	0.0157000	+	0.0271933i
$981$	10.8640	−	46.6158i	0.346861	−	1.48833i
$982$	14.0523	−	24.3393i	0.448427	−	0.776699i
$983$	18.9908			0.605712			0.302856	−	0.953036i	$-0.402060\pi$
$983$	18.9908			0.605712			0.302856	+	0.953036i	$0.402060\pi$
$984$	−4.97586	+	12.5936i	−0.158625	+	0.401471i
$985$	1.20791			0.0384873
$986$	−0.375732			−0.0119657
$987$	19.1118	+	24.0780i	0.608334	+	0.766411i
$988$	0.467882	+	0.810395i	0.0148853	+	0.0257821i
$989$	10.5074	+	18.1993i	0.334115	+	0.578704i
$990$	3.76554	+	3.52605i	0.119677	+	0.112065i
$991$	35.9569			1.14221			0.571105	−	0.820877i	$-0.306515\pi$
$991$	35.9569			1.14221			0.571105	+	0.820877i	$0.306515\pi$
$992$	1.46765	+	5.37085i	0.0465979	+	0.170525i
$993$	33.9102	+	42.7218i	1.07611	+	1.35574i
$994$	5.62961	−	9.75076i	0.178560	−	0.309275i
$995$	4.99334			0.158300
$996$	−8.09555	+	1.20131i	−0.256517	+	0.0380649i
$997$	−23.1461			−0.733045			−0.366523	−	0.930409i	$-0.619452\pi$
$997$	−23.1461			−0.733045			−0.366523	+	0.930409i	$0.619452\pi$
$998$	−9.39328	−	16.2696i	−0.297339	−	0.515007i
$999$	−32.2778	−	22.3321i	−1.02122	−	0.706555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.g.a.211.11	✓	32
3.2	odd	2		1674.2.g.b.955.8		32
9.2	odd	6		1674.2.h.b.397.9		32
9.7	even	3		558.2.h.a.25.12	yes	32
31.5	even	3		558.2.h.a.67.12	yes	32
93.5	odd	6		1674.2.h.b.253.9		32
279.160	even	3	inner	558.2.g.a.439.11	yes	32
279.191	odd	6		1674.2.g.b.1369.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.11	✓	32	1.1	even	1	trivial
558.2.g.a.439.11	yes	32	279.160	even	3	inner
558.2.h.a.25.12	yes	32	9.7	even	3
558.2.h.a.67.12	yes	32	31.5	even	3
1674.2.g.b.955.8		32	3.2	odd	2
1674.2.g.b.1369.8		32	279.191	odd	6
1674.2.h.b.253.9		32	93.5	odd	6
1674.2.h.b.397.9		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.07682 + 1.35663i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.251592 + 0.435771i) q^{5} +(0.636470 - 1.61087i) q^{6} +(1.49612 - 2.59136i) q^{7} +1.00000 q^{8} +(-0.680914 + 2.92170i) q^{9} +(0.251592 - 0.435771i) q^{10} +3.41738 q^{11} +(-1.71329 + 0.254237i) q^{12} +(0.745981 + 1.29208i) q^{13} -2.99224 q^{14} +(-0.320262 + 0.810566i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.107908 - 0.186902i) q^{17} +(2.87073 - 0.871163i) q^{18} +(-0.313601 - 0.543174i) q^{19} -0.503185 q^{20} +(5.12658 - 0.760738i) q^{21} +(-1.70869 - 2.95953i) q^{22} +(-2.34285 + 4.05794i) q^{23} +(1.07682 + 1.35663i) q^{24} +(2.37340 - 4.11085i) q^{25} +(0.745981 - 1.29208i) q^{26} +(-4.69691 + 2.22240i) q^{27} +(1.49612 + 2.59136i) q^{28} +(0.870491 + 1.50773i) q^{29} +(0.862101 - 0.127928i) q^{30} +(3.91747 - 3.95645i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.67990 + 4.63613i) q^{33} +(-0.107908 + 0.186902i) q^{34} +1.50565 q^{35} +(-2.18981 - 2.05054i) q^{36} +(3.77685 + 6.54170i) q^{37} +(-0.313601 + 0.543174i) q^{38} +(-0.949589 + 2.40336i) q^{39} +(0.251592 + 0.435771i) q^{40} +(3.90895 + 6.77051i) q^{41} +(-3.22211 - 4.05938i) q^{42} +(2.24243 - 3.88401i) q^{43} +(-1.70869 + 2.95953i) q^{44} +(-1.44451 + 0.438356i) q^{45} +4.68570 q^{46} +(2.96572 + 5.13679i) q^{47} +(0.636470 - 1.61087i) q^{48} +(-0.976756 - 1.69179i) q^{49} -4.74681 q^{50} +(0.137360 - 0.347652i) q^{51} -1.49196 q^{52} +(-0.744043 + 1.28872i) q^{53} +(4.27311 + 2.95644i) q^{54} +(0.859785 + 1.48919i) q^{55} +(1.49612 - 2.59136i) q^{56} +(0.399196 - 1.01034i) q^{57} +(0.870491 - 1.50773i) q^{58} -6.72438 q^{59} +(-0.541840 - 0.682638i) q^{60} +(-5.06352 - 8.77028i) q^{61} +(-5.38512 - 1.41440i) q^{62} +(6.55245 + 6.13572i) q^{63} +1.00000 q^{64} +(-0.375366 + 0.650154i) q^{65} +(2.17506 - 5.50495i) q^{66} +(-7.40223 - 12.8210i) q^{67} +0.215816 q^{68} +(-8.02796 + 1.19128i) q^{69} +(-0.752825 - 1.30393i) q^{70} +(-1.88140 + 3.25868i) q^{71} +(-0.680914 + 2.92170i) q^{72} +(0.325049 - 0.563001i) q^{73} +(3.77685 - 6.54170i) q^{74} +(8.13266 - 1.20681i) q^{75} +0.627203 q^{76} +(5.11281 - 8.85564i) q^{77} +(2.55617 - 0.379312i) q^{78} +(2.19974 - 3.81007i) q^{79} +(0.251592 - 0.435771i) q^{80} +(-8.07271 - 3.97886i) q^{81} +(3.90895 - 6.77051i) q^{82} +4.72515 q^{83} +(-1.90447 + 4.82012i) q^{84} +(0.0542976 - 0.0940463i) q^{85} -4.48487 q^{86} +(-1.10808 + 2.80450i) q^{87} +3.41738 q^{88} -15.8136 q^{89} +(1.10188 + 1.03180i) q^{90} +4.46431 q^{91} +(-2.34285 - 4.05794i) q^{92} +(9.58586 + 1.05419i) q^{93} +(2.96572 - 5.13679i) q^{94} +(0.157799 - 0.273317i) q^{95} +(-1.71329 + 0.254237i) q^{96} +(-5.15725 - 8.93262i) q^{97} +(-0.976756 + 1.69179i) q^{98} +(-2.32694 + 9.98456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

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