LMFDB - Embedded newform 57.2.i.a.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [57,2,Mod(4,57)] 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("57.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(57, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] 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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	57.25
Dual form			57.2.i.a.16.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.266044 + 0.223238i) q^{2} +(0.939693 + 0.342020i) q^{3} +(-0.326352 + 1.85083i) q^{4} +(-0.233956 - 1.32683i) q^{5} +(-0.326352 + 0.118782i) q^{6} +(0.326352 - 0.565258i) q^{7} +(-0.673648 - 1.16679i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.358441 + 0.300767i) q^{10} +(-1.97178 - 3.41523i) q^{11} +(-0.939693 + 1.62760i) q^{12} +(-1.59240 + 0.579585i) q^{13} +(0.0393628 + 0.223238i) q^{14} +(0.233956 - 1.32683i) q^{15} +(-3.09240 - 1.12554i) q^{16} +(-2.93969 + 2.46669i) q^{17} -0.347296 q^{18} +(2.82635 - 3.31839i) q^{19} +2.53209 q^{20} +(0.500000 - 0.419550i) q^{21} +(1.28699 + 0.468426i) q^{22} +(-0.631759 + 3.58288i) q^{23} +(-0.233956 - 1.32683i) q^{24} +(2.99273 - 1.08926i) q^{25} +(0.294263 - 0.509678i) q^{26} +(0.500000 + 0.866025i) q^{27} +(0.939693 + 0.788496i) q^{28} +(8.05690 + 6.76055i) q^{29} +(0.233956 + 0.405223i) q^{30} +(-3.23396 + 5.60138i) q^{31} +(3.60607 - 1.31250i) q^{32} +(-0.684793 - 3.88365i) q^{33} +(0.231429 - 1.31250i) q^{34} +(-0.826352 - 0.300767i) q^{35} +(-1.43969 + 1.20805i) q^{36} -2.94356 q^{37} +(-0.0111444 + 1.51379i) q^{38} -1.69459 q^{39} +(-1.39053 + 1.16679i) q^{40} +(1.41875 + 0.516382i) q^{41} +(-0.0393628 + 0.223238i) q^{42} +(-1.62701 - 9.22724i) q^{43} +(6.96451 - 2.53487i) q^{44} +(0.673648 - 1.16679i) q^{45} +(-0.631759 - 1.09424i) q^{46} +(-9.77972 - 8.20616i) q^{47} +(-2.52094 - 2.11532i) q^{48} +(3.28699 + 5.69323i) q^{49} +(-0.553033 + 0.957882i) q^{50} +(-3.60607 + 1.31250i) q^{51} +(-0.553033 - 3.13641i) q^{52} +(-1.87551 + 10.6366i) q^{53} +(-0.326352 - 0.118782i) q^{54} +(-4.07011 + 3.41523i) q^{55} -0.879385 q^{56} +(3.79086 - 2.15160i) q^{57} -3.65270 q^{58} +(-2.12449 + 1.78265i) q^{59} +(2.37939 + 0.866025i) q^{60} +(0.748970 - 4.24762i) q^{61} +(-0.390063 - 2.21216i) q^{62} +(0.613341 - 0.223238i) q^{63} +(2.62449 - 4.54574i) q^{64} +(1.14156 + 1.97724i) q^{65} +(1.04916 + 0.880352i) q^{66} +(6.04189 + 5.06975i) q^{67} +(-3.60607 - 6.24589i) q^{68} +(-1.81908 + 3.15074i) q^{69} +(0.286989 - 0.104455i) q^{70} +(-0.932419 - 5.28801i) q^{71} +(0.233956 - 1.32683i) q^{72} +(-5.51114 - 2.00589i) q^{73} +(0.783119 - 0.657115i) q^{74} +3.18479 q^{75} +(5.21941 + 6.31407i) q^{76} -2.57398 q^{77} +(0.450837 - 0.378297i) q^{78} +(2.93969 + 1.06996i) q^{79} +(-0.769915 + 4.36640i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.492726 + 0.179338i) q^{82} +(2.25490 - 3.90560i) q^{83} +(0.613341 + 1.06234i) q^{84} +(3.96064 + 3.32337i) q^{85} +(2.49273 + 2.09165i) q^{86} +(5.25877 + 9.10846i) q^{87} +(-2.65657 + 4.60132i) q^{88} +(10.4620 - 3.80785i) q^{89} +(0.0812519 + 0.460802i) q^{90} +(-0.192066 + 1.08926i) q^{91} +(-6.42514 - 2.33856i) q^{92} +(-4.95471 + 4.15749i) q^{93} +4.43376 q^{94} +(-5.06418 - 2.97373i) q^{95} +3.83750 q^{96} +(5.13429 - 4.30818i) q^{97} +(-2.14543 - 0.780873i) q^{98} +(0.684793 - 3.88365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^11 - 6 * q^13 + 9 * q^14 + 6 * q^15 - 15 * q^16 - 12 * q^17 + 18 * q^19 + 6 * q^20 + 3 * q^21 - 9 * q^23 - 6 * q^24 + 12 * q^26 + 3 * q^27 + 12 * q^29 + 6 * q^30 - 24 * q^31 - 3 * q^32 + 3 * q^33 + 21 * q^34 - 6 * q^35 - 3 * q^36 + 12 * q^37 + 6 * q^38 - 6 * q^39 + 9 * q^40 + 6 * q^41 - 9 * q^42 + 18 * q^43 + 9 * q^44 + 3 * q^45 - 9 * q^46 - 33 * q^47 - 12 * q^48 + 12 * q^49 + 9 * q^50 + 3 * q^51 + 9 * q^52 - 24 * q^53 - 3 * q^54 - 33 * q^55 + 6 * q^56 - 9 * q^57 - 24 * q^58 + 3 * q^60 - 21 * q^61 - 51 * q^62 - 3 * q^63 + 3 * q^64 + 15 * q^65 + 18 * q^66 + 30 * q^67 + 3 * q^68 + 6 * q^69 - 6 * q^70 + 18 * q^71 + 6 * q^72 - 27 * q^73 + 21 * q^74 + 12 * q^75 - 9 * q^78 + 12 * q^79 + 24 * q^80 + 15 * q^82 + 15 * q^83 - 3 * q^84 + 15 * q^85 - 3 * q^86 + 9 * q^87 + 6 * q^88 + 45 * q^89 + 3 * q^90 - 12 * q^91 + 3 * q^92 + 6 * q^93 - 6 * q^94 - 12 * q^95 + 18 * q^96 + 21 * q^97 + 3 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.266044	+	0.223238i	−0.188122	+	0.157853i	−0.731985	−	0.681321i	$-0.761406\pi$
$2$	−0.266044	+	0.223238i	−0.188122	+	0.157853i	0.543863	+	0.839174i	$0.316961\pi$
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$	−0.326352	+	1.85083i	−0.163176	+	0.925417i
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	−0.991368	−	0.131107i	$-0.958147\pi$
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	0.886740	−	0.462268i	$-0.152964\pi$
$6$	−0.326352	+	0.118782i	−0.133233	+	0.0484927i
$7$	0.326352	−	0.565258i	0.123349	−	0.213647i	−0.797737	−	0.603005i	$-0.793970\pi$
$7$	0.326352	−	0.565258i	0.123349	−	0.213647i	0.921087	+	0.389358i	$0.127303\pi$
$8$	−0.673648	−	1.16679i	−0.238171	−	0.412524i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	0.358441	+	0.300767i	0.113349	+	0.0951110i
$11$	−1.97178	−	3.41523i	−0.594514	−	1.02973i	−0.993615	−	0.112822i	$-0.964011\pi$
$11$	−1.97178	−	3.41523i	−0.594514	−	1.02973i	0.399101	−	0.916907i	$-0.369322\pi$
$12$	−0.939693	+	1.62760i	−0.271266	+	0.469846i
$13$	−1.59240	+	0.579585i	−0.441651	+	0.160748i	−0.553268	−	0.833003i	$-0.686619\pi$
$13$	−1.59240	+	0.579585i	−0.441651	+	0.160748i	0.111617	+	0.993751i	$0.464397\pi$
$14$	0.0393628	+	0.223238i	0.0105202	+	0.0596628i
$15$	0.233956	−	1.32683i	0.0604071	−	0.342585i
$16$	−3.09240	−	1.12554i	−0.773099	−	0.281385i
$17$	−2.93969	+	2.46669i	−0.712980	+	0.598261i	−0.925434	−	0.378910i	$-0.876299\pi$
$17$	−2.93969	+	2.46669i	−0.712980	+	0.598261i	0.212453	+	0.977171i	$0.431855\pi$
$18$	−0.347296			−0.0818585
$19$	2.82635	−	3.31839i	0.648410	−	0.761292i
$19$	2.82635	−	3.31839i	0.648410	−	0.761292i
$20$	2.53209			0.566192
$21$	0.500000	−	0.419550i	0.109109	−	0.0915533i
$22$	1.28699	+	0.468426i	0.274387	+	0.0998687i
$23$	−0.631759	+	3.58288i	−0.131731	+	0.747083i	0.845350	+	0.534213i	$0.179392\pi$
$23$	−0.631759	+	3.58288i	−0.131731	+	0.747083i	−0.977081	+	0.212870i	$0.931719\pi$
$24$	−0.233956	−	1.32683i	−0.0477560	−	0.270838i
$25$	2.99273	−	1.08926i	0.598545	−	0.217853i
$26$	0.294263	−	0.509678i	0.0577097	−	0.0999561i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	0.939693	+	0.788496i	0.177585	+	0.149012i
$29$	8.05690	+	6.76055i	1.49613	+	1.25540i	0.886512	+	0.462706i	$0.153122\pi$
$29$	8.05690	+	6.76055i	1.49613	+	1.25540i	0.609618	+	0.792695i	$0.291323\pi$
$30$	0.233956	+	0.405223i	0.0427142	+	0.0739832i
$31$	−3.23396	+	5.60138i	−0.580836	+	1.00604i	0.414545	+	0.910029i	$0.363941\pi$
$31$	−3.23396	+	5.60138i	−0.580836	+	1.00604i	−0.995381	+	0.0960079i	$0.969393\pi$
$32$	3.60607	−	1.31250i	0.637469	−	0.232020i
$33$	−0.684793	−	3.88365i	−0.119207	−	0.676057i
$34$	0.231429	−	1.31250i	0.0396898	−	0.225092i
$35$	−0.826352	−	0.300767i	−0.139679	−	0.0508390i
$36$	−1.43969	+	1.20805i	−0.239949	+	0.201341i
$37$	−2.94356			−0.483919			−0.241959	−	0.970286i	$-0.577790\pi$
$37$	−2.94356			−0.483919			−0.241959	+	0.970286i	$0.577790\pi$
$38$	−0.0111444	+	1.51379i	−0.00180785	+	0.245569i
$39$	−1.69459			−0.271352
$40$	−1.39053	+	1.16679i	−0.219862	+	0.184486i
$41$	1.41875	+	0.516382i	0.221571	+	0.0806453i	0.450421	−	0.892817i	$-0.351274\pi$
$41$	1.41875	+	0.516382i	0.221571	+	0.0806453i	−0.228849	+	0.973462i	$0.573496\pi$
$42$	−0.0393628	+	0.223238i	−0.00607382	+	0.0344463i
$43$	−1.62701	−	9.22724i	−0.248117	−	1.40714i	−0.813141	−	0.582067i	$-0.802244\pi$
$43$	−1.62701	−	9.22724i	−0.248117	−	1.40714i	0.565024	−	0.825074i	$-0.308867\pi$
$44$	6.96451	−	2.53487i	1.04994	−	0.382147i
$45$	0.673648	−	1.16679i	0.100422	−	0.173935i
$46$	−0.631759	−	1.09424i	−0.0931478	−	0.161337i
$47$	−9.77972	−	8.20616i	−1.42652	−	1.19699i	−0.947735	−	0.319057i	$-0.896634\pi$
$47$	−9.77972	−	8.20616i	−1.42652	−	1.19699i	−0.478783	−	0.877933i	$-0.658922\pi$
$48$	−2.52094	−	2.11532i	−0.363867	−	0.305321i
$49$	3.28699	+	5.69323i	0.469570	+	0.813319i
$50$	−0.553033	+	0.957882i	−0.0782107	+	0.135465i
$51$	−3.60607	+	1.31250i	−0.504950	+	0.183787i
$52$	−0.553033	−	3.13641i	−0.0766919	−	0.434942i
$53$	−1.87551	+	10.6366i	−0.257622	+	1.46105i	0.531630	+	0.846976i	$0.321580\pi$
$53$	−1.87551	+	10.6366i	−0.257622	+	1.46105i	−0.789252	+	0.614069i	$0.789532\pi$
$54$	−0.326352	−	0.118782i	−0.0444109	−	0.0161642i
$55$	−4.07011	+	3.41523i	−0.548813	+	0.460509i
$56$	−0.879385			−0.117513
$57$	3.79086	−	2.15160i	0.502112	−	0.284986i
$58$	−3.65270			−0.479623
$59$	−2.12449	+	1.78265i	−0.276584	+	0.232082i	−0.770519	−	0.637417i	$-0.780003\pi$
$59$	−2.12449	+	1.78265i	−0.276584	+	0.232082i	0.493934	+	0.869499i	$0.335558\pi$
$60$	2.37939	+	0.866025i	0.307177	+	0.111803i
$61$	0.748970	−	4.24762i	0.0958958	−	0.543852i	−0.898573	−	0.438823i	$-0.855395\pi$
$61$	0.748970	−	4.24762i	0.0958958	−	0.543852i	0.994469	−	0.105029i	$-0.0334935\pi$
$62$	−0.390063	−	2.21216i	−0.0495380	−	0.280944i
$63$	0.613341	−	0.223238i	0.0772737	−	0.0281253i
$64$	2.62449	−	4.54574i	0.328061	−	0.568218i
$65$	1.14156	+	1.97724i	0.141593	+	0.245246i
$66$	1.04916	+	0.880352i	0.129143	+	0.108364i
$67$	6.04189	+	5.06975i	0.738134	+	0.619368i	0.932336	−	0.361593i	$-0.117767\pi$
$67$	6.04189	+	5.06975i	0.738134	+	0.619368i	−0.194202	+	0.980962i	$0.562212\pi$
$68$	−3.60607	−	6.24589i	−0.437300	−	0.757426i
$69$	−1.81908	+	3.15074i	−0.218991	+	0.379304i
$70$	0.286989	−	0.104455i	0.0343017	−	0.0124848i
$71$	−0.932419	−	5.28801i	−0.110658	−	0.627571i	−0.988809	−	0.149188i	$-0.952334\pi$
$71$	−0.932419	−	5.28801i	−0.110658	−	0.627571i	0.878151	−	0.478383i	$-0.158777\pi$
$72$	0.233956	−	1.32683i	0.0275719	−	0.156368i
$73$	−5.51114	−	2.00589i	−0.645031	−	0.234772i	−0.00127039	−	0.999999i	$-0.500404\pi$
$73$	−5.51114	−	2.00589i	−0.645031	−	0.234772i	−0.643760	+	0.765227i	$0.722627\pi$
$74$	0.783119	−	0.657115i	0.0910357	−	0.0763880i
$75$	3.18479			0.367748
$76$	5.21941	+	6.31407i	0.598707	+	0.724273i
$77$	−2.57398			−0.293332
$78$	0.450837	−	0.378297i	0.0510472	−	0.0428337i
$79$	2.93969	+	1.06996i	0.330741	+	0.120380i	0.502053	−	0.864837i	$-0.332578\pi$
$79$	2.93969	+	1.06996i	0.330741	+	0.120380i	−0.171312	+	0.985217i	$0.554800\pi$
$80$	−0.769915	+	4.36640i	−0.0860791	+	0.488179i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−0.492726	+	0.179338i	−0.0544125	+	0.0198045i
$83$	2.25490	−	3.90560i	0.247507	−	0.428695i	−0.715326	−	0.698791i	$-0.753722\pi$
$83$	2.25490	−	3.90560i	0.247507	−	0.428695i	0.962834	+	0.270095i	$0.0870552\pi$
$84$	0.613341	+	1.06234i	0.0669210	+	0.115911i
$85$	3.96064	+	3.32337i	0.429591	+	0.360470i
$86$	2.49273	+	2.09165i	0.268798	+	0.225548i
$87$	5.25877	+	9.10846i	0.563799	+	0.976529i
$88$	−2.65657	+	4.60132i	−0.283192	+	0.490502i
$89$	10.4620	−	3.80785i	1.10897	−	0.403631i	0.278353	−	0.960479i	$-0.410211\pi$
$89$	10.4620	−	3.80785i	1.10897	−	0.403631i	0.830615	+	0.556848i	$0.187989\pi$
$90$	0.0812519	+	0.460802i	0.00856470	+	0.0485728i
$91$	−0.192066	+	1.08926i	−0.0201340	+	0.114186i
$92$	−6.42514	−	2.33856i	−0.669868	−	0.243812i
$93$	−4.95471	+	4.15749i	−0.513779	+	0.431112i
$94$	4.43376			0.457308
$95$	−5.06418	−	2.97373i	−0.519574	−	0.305098i
$96$	3.83750			0.391663
$97$	5.13429	−	4.30818i	0.521308	−	0.437429i	−0.343780	−	0.939050i	$-0.611707\pi$
$97$	5.13429	−	4.30818i	0.521308	−	0.437429i	0.865087	+	0.501621i	$0.167263\pi$
$98$	−2.14543	−	0.780873i	−0.216721	−	0.0788800i
$99$	0.684793	−	3.88365i	0.0688242	−	0.390322i
$100$	1.03936	+	5.89452i	0.103936	+	0.589452i
$101$	1.81908	−	0.662090i	0.181005	−	0.0658804i	−0.249928	−	0.968265i	$-0.580407\pi$
$101$	1.81908	−	0.662090i	0.181005	−	0.0658804i	0.430933	+	0.902384i	$0.358185\pi$
$102$	0.666374	−	1.15419i	0.0659809	−	0.114282i
$103$	−0.518418	−	0.897927i	−0.0510813	−	0.0884754i	0.839354	−	0.543585i	$-0.182933\pi$
$103$	−0.518418	−	0.897927i	−0.0510813	−	0.0884754i	−0.890435	+	0.455110i	$0.849600\pi$
$104$	1.74897	+	1.46756i	0.171501	+	0.143906i
$105$	−0.673648	−	0.565258i	−0.0657413	−	0.0551635i
$106$	−1.87551	−	3.24849i	−0.182166	−	0.315521i
$107$	6.10607	−	10.5760i	0.590296	−	1.02242i	−0.403897	−	0.914805i	$-0.632344\pi$
$107$	6.10607	−	10.5760i	0.590296	−	1.02242i	0.994192	−	0.107618i	$-0.0343222\pi$
$108$	−1.76604	+	0.642788i	−0.169938	+	0.0618523i
$109$	−0.699340	−	3.96616i	−0.0669847	−	0.379889i	−0.999809	−	0.0195568i	$-0.993774\pi$
$109$	−0.699340	−	3.96616i	−0.0669847	−	0.379889i	0.932824	−	0.360332i	$-0.117337\pi$
$110$	0.320422	−	1.81720i	0.0305510	−	0.173264i
$111$	−2.76604	−	1.00676i	−0.262541	−	0.0955572i
$112$	−1.64543	+	1.38068i	−0.155478	+	0.130462i
$113$	−13.1925			−1.24105			−0.620525	−	0.784187i	$-0.713080\pi$
$113$	−13.1925			−1.24105			−0.620525	+	0.784187i	$0.713080\pi$
$114$	−0.528218	+	1.41868i	−0.0494722	+	0.132872i
$115$	4.90167			0.457083
$116$	−15.1420	+	12.7057i	−1.40590	+	1.17969i
$117$	−1.59240	−	0.579585i	−0.147217	−	0.0535826i
$118$	0.167252	−	0.948531i	0.0153968	−	0.0873193i
$119$	0.434945	+	2.46669i	0.0398713	+	0.226122i
$120$	−1.70574	+	0.620838i	−0.155712	+	0.0566745i
$121$	−2.27584	+	3.94188i	−0.206895	+	0.358353i
$122$	0.748970	+	1.29725i	0.0678086	+	0.117448i
$123$	1.15657	+	0.970481i	0.104285	+	0.0875053i
$124$	−9.31180	−	7.81353i	−0.836225	−	0.701676i
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$	−0.113341	+	0.196312i	−0.0100972	+	0.0174889i
$127$	−12.4500	+	4.53141i	−1.10476	+	0.402098i	−0.829067	−	0.559149i	$-0.811128\pi$
$127$	−12.4500	+	4.53141i	−1.10476	+	0.402098i	−0.275688	+	0.961247i	$0.588906\pi$
$128$	1.64930	+	9.35365i	0.145779	+	0.826753i
$129$	1.62701	−	9.22724i	0.143250	−	0.812413i
$130$	−0.745100	−	0.271194i	−0.0653496	−	0.0237853i
$131$	13.1591	−	11.0418i	1.14972	−	0.964726i	0.150003	−	0.988686i	$-0.452072\pi$
$131$	13.1591	−	11.0418i	1.14972	−	0.964726i	0.999713	+	0.0239593i	$0.00762722\pi$
$132$	7.41147			0.645086
$133$	−0.953363	−	2.68058i	−0.0826671	−	0.232436i
$134$	−2.73917			−0.236628
$135$	1.03209	−	0.866025i	0.0888281	−	0.0745356i
$136$	4.85844	+	1.76833i	0.416608	+	0.151633i
$137$	−1.83140	+	10.3864i	−0.156467	+	0.887371i	0.800965	+	0.598712i	$0.204321\pi$
$137$	−1.83140	+	10.3864i	−0.156467	+	0.887371i	−0.957432	+	0.288659i	$0.906791\pi$
$138$	−0.219408	−	1.24432i	−0.0186772	−	0.105924i
$139$	−10.1309	+	3.68734i	−0.859290	+	0.312756i	−0.733822	−	0.679342i	$-0.762265\pi$
$139$	−10.1309	+	3.68734i	−0.859290	+	0.312756i	−0.125468	+	0.992098i	$0.540043\pi$
$140$	0.826352	−	1.43128i	0.0698395	−	0.120966i
$141$	−6.38326	−	11.0561i	−0.537567	−	0.931094i
$142$	1.42855	+	1.19869i	0.119881	+	0.100592i
$143$	5.11927	+	4.29558i	0.428095	+	0.359214i
$144$	−1.64543	−	2.84997i	−0.137119	−	0.237497i
$145$	7.08512	−	12.2718i	0.588387	−	1.01912i
$146$	1.91400	−	0.696639i	0.158404	−	0.0576543i
$147$	1.14156	+	6.47410i	0.0941542	+	0.533975i
$148$	0.960637	−	5.44804i	0.0789639	−	0.447826i
$149$	18.5608	+	6.75557i	1.52056	+	0.553438i	0.961287	−	0.275547i	$-0.0888591\pi$
$149$	18.5608	+	6.75557i	1.52056	+	0.553438i	0.559270	+	0.828985i	$0.311081\pi$
$150$	−0.847296	+	0.710966i	−0.0691815	+	0.0580501i
$151$	3.10607			0.252768			0.126384	−	0.991981i	$-0.459663\pi$
$151$	3.10607			0.252768			0.126384	+	0.991981i	$0.459663\pi$
$152$	−5.77584	−	1.06234i	−0.468483	−	0.0861669i
$153$	−3.83750			−0.310243
$154$	0.684793	−	0.574609i	0.0551822	−	0.0463033i
$155$	8.18866	+	2.98043i	0.657729	+	0.239394i
$156$	0.553033	−	3.13641i	0.0442781	−	0.251114i
$157$	0.127889	+	0.725293i	0.0102066	+	0.0578847i	0.989486	−	0.144631i	$-0.0461995\pi$
$157$	0.127889	+	0.725293i	0.0102066	+	0.0578847i	−0.979279	+	0.202516i	$0.935088\pi$
$158$	−1.02094	+	0.371593i	−0.0812220	+	0.0295624i
$159$	−5.40033	+	9.35365i	−0.428274	+	0.741792i
$160$	−2.58512	−	4.47756i	−0.204372	−	0.353982i
$161$	1.81908	+	1.52639i	0.143363	+	0.120296i
$162$	−0.266044	−	0.223238i	−0.0209024	−	0.0175392i
$163$	6.31180	+	10.9324i	0.494379	+	0.856289i	0.999979	−	0.00647887i	$-0.00206230\pi$
$163$	6.31180	+	10.9324i	0.494379	+	0.856289i	−0.505600	+	0.862768i	$0.668729\pi$
$164$	−1.41875	+	2.45734i	−0.110786	+	0.191886i
$165$	−4.99273	+	1.81720i	−0.388683	+	0.141469i
$166$	0.271974	+	1.54244i	0.0211093	+	0.119717i
$167$	−0.958111	+	5.43372i	−0.0741409	+	0.420474i	0.925035	+	0.379882i	$0.124035\pi$
$167$	−0.958111	+	5.43372i	−0.0741409	+	0.420474i	−0.999176	+	0.0405917i	$0.987076\pi$
$168$	−0.826352	−	0.300767i	−0.0637544	−	0.0232047i
$169$	−7.75877	+	6.51038i	−0.596828	+	0.500799i
$170$	−1.79561			−0.137717
$171$	4.29813	−	0.725293i	0.328686	−	0.0554645i
$172$	17.6091			1.34268
$173$	9.90420	−	8.31061i	0.753002	−	0.631844i	−0.183293	−	0.983058i	$-0.558676\pi$
$173$	9.90420	−	8.31061i	0.753002	−	0.631844i	0.936295	+	0.351214i	$0.114231\pi$
$174$	−3.43242	−	1.24930i	−0.260211	−	0.0947091i
$175$	0.360967	−	2.04715i	0.0272865	−	0.154750i
$176$	2.25356	+	12.7806i	0.169868	+	0.963370i
$177$	−2.60607	+	0.948531i	−0.195884	+	0.0712959i
$178$	−1.93330	+	3.34857i	−0.144907	+	0.250986i
$179$	7.54323	+	13.0653i	0.563808	+	0.976544i	0.997160	+	0.0753188i	$0.0239974\pi$
$179$	7.54323	+	13.0653i	0.563808	+	0.976544i	−0.433352	+	0.901225i	$0.642669\pi$
$180$	1.93969	+	1.62760i	0.144576	+	0.121314i
$181$	−14.3118	−	12.0090i	−1.06379	−	0.892624i	−0.0693127	−	0.997595i	$-0.522081\pi$
$181$	−14.3118	−	12.0090i	−1.06379	−	0.892624i	−0.994475	+	0.104971i	$0.966525\pi$
$182$	−0.192066	−	0.332669i	−0.0142369	−	0.0246591i
$183$	2.15657	−	3.73530i	0.159419	−	0.276121i
$184$	4.60607	−	1.67647i	0.339564	−	0.123591i
$185$	0.688663	+	3.90560i	0.0506315	+	0.287146i
$186$	0.390063	−	2.21216i	0.0286008	−	0.162203i
$187$	14.2208	+	5.17593i	1.03992	+	0.378502i
$188$	18.3799	−	15.4225i	1.34049	−	1.12480i
$189$	0.652704			0.0474772
$190$	2.01114	−	0.339373i	0.145904	−	0.0246207i
$191$	−8.55169			−0.618779			−0.309389	−	0.950935i	$-0.600125\pi$
$191$	−8.55169			−0.618779			−0.309389	+	0.950935i	$0.600125\pi$
$192$	4.02094	−	3.37397i	0.290187	−	0.243496i
$193$	−15.9363	−	5.80033i	−1.14712	−	0.417517i	−0.302640	−	0.953105i	$-0.597868\pi$
$193$	−15.9363	−	5.80033i	−1.14712	−	0.417517i	−0.844480	+	0.535588i	$0.820090\pi$
$194$	−0.404200	+	2.29233i	−0.0290199	+	0.164580i
$195$	0.396459	+	2.24843i	0.0283910	+	0.161014i
$196$	−11.6099	+	4.22567i	−0.829281	+	0.301834i
$197$	−2.25877	+	3.91231i	−0.160931	+	0.278740i	−0.935203	−	0.354113i	$-0.884783\pi$
$197$	−2.25877	+	3.91231i	−0.160931	+	0.278740i	0.774272	+	0.632853i	$0.218116\pi$
$198$	0.684793	+	1.18610i	0.0486661	+	0.0842921i
$199$	−6.16431	−	5.17247i	−0.436977	−	0.366667i	0.397600	−	0.917559i	$-0.369843\pi$
$199$	−6.16431	−	5.17247i	−0.436977	−	0.366667i	−0.834577	+	0.550892i	$0.814288\pi$
$200$	−3.28699	−	2.75811i	−0.232425	−	0.195028i
$201$	3.94356	+	6.83045i	0.278157	+	0.481783i
$202$	−0.336152	+	0.582232i	−0.0236516	+	0.0409657i
$203$	6.45084	−	2.34791i	0.452760	−	0.164791i
$204$	−1.25237	−	7.10257i	−0.0876837	−	0.497279i
$205$	0.353226	−	2.00324i	0.0246704	−	0.139913i
$206$	0.338374	+	0.123158i	0.0235756	+	0.00858082i
$207$	−2.78699	+	2.33856i	−0.193709	+	0.162541i
$208$	5.57667			0.386672
$209$	−16.9060	−	3.10948i	−1.16941	−	0.215087i
$210$	0.305407			0.0210751
$211$	15.3851	−	12.9096i	1.05915	−	0.888734i	0.0651256	−	0.997877i	$-0.479255\pi$
$211$	15.3851	−	12.9096i	1.05915	−	0.888734i	0.994026	+	0.109143i	$0.0348107\pi$
$212$	−19.0744	−	6.94253i	−1.31004	−	0.476815i
$213$	0.932419	−	5.28801i	0.0638883	−	0.362328i
$214$	0.736482	+	4.17680i	0.0503449	+	0.285520i
$215$	−11.8623	+	4.31753i	−0.809003	+	0.294453i
$216$	0.673648	−	1.16679i	0.0458360	−	0.0793902i
$217$	2.11081	+	3.65604i	0.143291	+	0.248188i
$218$	1.07145	+	0.899055i	0.0725679	+	0.0608917i
$219$	−4.49273	−	3.76984i	−0.303590	−	0.254743i
$220$	−4.99273	−	8.64766i	−0.336610	−	0.583025i
$221$	3.25150	−	5.63176i	0.218719	−	0.378833i
$222$	0.960637	−	0.349643i	0.0644737	−	0.0234665i
$223$	3.40167	+	19.2919i	0.227793	+	1.29188i	0.857273	+	0.514862i	$0.172157\pi$
$223$	3.40167	+	19.2919i	0.227793	+	1.29188i	−0.629480	+	0.777016i	$0.716732\pi$
$224$	0.434945	−	2.46669i	0.0290610	−	0.164813i
$225$	2.99273	+	1.08926i	0.199515	+	0.0726175i
$226$	3.50980	−	2.94507i	0.233468	−	0.195903i
$227$	−18.4979			−1.22775			−0.613876	−	0.789403i	$-0.710390\pi$
$227$	−18.4979			−1.22775			−0.613876	+	0.789403i	$0.710390\pi$
$228$	2.74510	+	7.71843i	0.181799	+	0.511165i
$229$	−28.1634			−1.86109			−0.930546	−	0.366175i	$-0.880667\pi$
$229$	−28.1634			−1.86109			−0.930546	+	0.366175i	$0.880667\pi$
$230$	−1.30406	+	1.09424i	−0.0859874	+	0.0721520i
$231$	−2.41875	−	0.880352i	−0.159142	−	0.0579229i
$232$	2.46064	−	13.9550i	0.161549	−	0.916188i
$233$	0.0270364	+	0.153331i	0.00177122	+	0.0100451i	0.985681	−	0.168623i	$-0.0539322\pi$
$233$	0.0270364	+	0.153331i	0.00177122	+	0.0100451i	−0.983909	+	0.178668i	$0.942821\pi$
$234$	0.553033	−	0.201288i	0.0361529	−	0.0131586i
$235$	−8.60014	+	14.8959i	−0.561011	+	0.971700i
$236$	−2.60607	−	4.51384i	−0.169641	−	0.293826i
$237$	2.39646	+	2.01087i	0.155667	+	0.130620i
$238$	−0.666374	−	0.559154i	−0.0431946	−	0.0362446i
$239$	−3.31521	−	5.74211i	−0.214443	−	0.371426i	0.738657	−	0.674081i	$-0.235460\pi$
$239$	−3.31521	−	5.74211i	−0.214443	−	0.371426i	−0.953100	+	0.302655i	$0.902127\pi$
$240$	−2.21688	+	3.83975i	−0.143099	+	0.247855i
$241$	4.94356	−	1.79931i	0.318443	−	0.115904i	−0.177853	−	0.984057i	$-0.556915\pi$
$241$	4.94356	−	1.79931i	0.318443	−	0.115904i	0.496296	+	0.868153i	$0.334693\pi$
$242$	−0.274500	−	1.55677i	−0.0176456	−	0.100073i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	7.61721	+	2.77244i	0.487642	+	0.177487i
$245$	6.78493	−	5.69323i	0.433473	−	0.363727i
$246$	−0.524348			−0.0334312
$247$	−2.57738	+	6.92231i	−0.163995	+	0.440456i
$248$	8.71419			0.553352
$249$	3.45471	−	2.89884i	0.218933	−	0.183707i
$250$	3.59879	+	1.30985i	0.227608	+	0.0828424i
$251$	2.57263	−	14.5901i	0.162383	−	0.920921i	−0.789338	−	0.613958i	$-0.789576\pi$
$251$	2.57263	−	14.5901i	0.162383	−	0.920921i	0.951722	−	0.306963i	$-0.0993126\pi$
$252$	0.213011	+	1.20805i	0.0134184	+	0.0760997i
$253$	13.4820	−	4.90706i	0.847609	−	0.308504i
$254$	2.30066	−	3.98486i	0.144356	−	0.250032i
$255$	2.58512	+	4.47756i	0.161887	+	0.280396i
$256$	5.51501	+	4.62765i	0.344688	+	0.289228i
$257$	−14.6800	−	12.3180i	−0.915716	−	0.768377i	0.0574818	−	0.998347i	$-0.481693\pi$
$257$	−14.6800	−	12.3180i	−0.915716	−	0.768377i	−0.973198	+	0.229970i	$0.926137\pi$
$258$	1.62701	+	2.81807i	0.101293	+	0.175445i
$259$	−0.960637	+	1.66387i	−0.0596911	+	0.103388i
$260$	−4.03209	+	1.46756i	−0.250060	+	0.0910142i
$261$	1.82635	+	10.3578i	0.113048	+	0.641129i
$262$	−1.03596	+	5.87522i	−0.0640018	+	0.362972i
$263$	15.5030	+	5.64263i	0.955956	+	0.347939i	0.772447	−	0.635079i	$-0.219032\pi$
$263$	15.5030	+	5.64263i	0.955956	+	0.347939i	0.183508	+	0.983018i	$0.441255\pi$
$264$	−4.07011	+	3.41523i	−0.250498	+	0.210193i
$265$	14.5517			0.893903
$266$	0.852044	+	0.500327i	0.0522422	+	0.0306770i
$267$	11.1334			0.681354
$268$	−11.3550	+	9.52801i	−0.693619	+	0.582016i
$269$	−3.95811	−	1.44063i	−0.241330	−	0.0878370i	0.218524	−	0.975832i	$-0.429876\pi$
$269$	−3.95811	−	1.44063i	−0.241330	−	0.0878370i	−0.459854	+	0.887995i	$0.652098\pi$
$270$	−0.0812519	+	0.460802i	−0.00494483	+	0.0280435i
$271$	1.59105	+	9.02330i	0.0966495	+	0.548127i	0.994229	+	0.107275i	$0.0342125\pi$
$271$	1.59105	+	9.02330i	0.0966495	+	0.548127i	−0.897580	+	0.440852i	$0.854676\pi$
$272$	11.8671	−	4.31926i	0.719546	−	0.261893i
$273$	−0.553033	+	0.957882i	−0.0334711	+	0.0579737i
$274$	−1.83140	−	3.17209i	−0.110639	−	0.191633i
$275$	−9.62108	−	8.07305i	−0.580173	−	0.486823i
$276$	−5.23783	−	4.39506i	−0.315280	−	0.264551i
$277$	11.2476	+	19.4815i	0.675804	+	1.17053i	0.976233	+	0.216723i	$0.0695369\pi$
$277$	11.2476	+	19.4815i	0.675804	+	1.17053i	−0.300429	+	0.953804i	$0.597130\pi$
$278$	1.87211	−	3.24259i	0.112282	−	0.194478i
$279$	−6.07785	+	2.21216i	−0.363871	+	0.132438i
$280$	0.205737	+	1.16679i	0.0122951	+	0.0697292i
$281$	−4.08559	+	23.1705i	−0.243726	+	1.38224i	0.579707	+	0.814825i	$0.303167\pi$
$281$	−4.08559	+	23.1705i	−0.243726	+	1.38224i	−0.823433	+	0.567413i	$0.807944\pi$
$282$	4.16637	+	1.51644i	0.248104	+	0.0903025i
$283$	20.4893	−	17.1926i	1.21796	−	1.02199i	0.219035	−	0.975717i	$-0.429709\pi$
$283$	20.4893	−	17.1926i	1.21796	−	1.02199i	0.998929	−	0.0462760i	$-0.0147354\pi$
$284$	10.0915			0.598821
$285$	−3.74170	−	4.52644i	−0.221639	−	0.268123i
$286$	−2.32089			−0.137237
$287$	0.754900	−	0.633436i	0.0445603	−	0.0373906i
$288$	3.60607	+	1.31250i	0.212490	+	0.0773399i
$289$	−0.394811	+	2.23908i	−0.0232241	+	0.131711i
$290$	0.854570	+	4.84651i	0.0501821	+	0.284597i
$291$	6.29813	−	2.29233i	0.369203	−	0.134379i
$292$	5.51114	−	9.54558i	0.322515	−	0.558613i
$293$	0.103541	+	0.179338i	0.00604891	+	0.0104770i	0.869034	−	0.494752i	$-0.164741\pi$
$293$	0.103541	+	0.179338i	0.00604891	+	0.0104770i	−0.862985	+	0.505229i	$0.831408\pi$
$294$	−1.74897	−	1.46756i	−0.102002	−	0.0855899i
$295$	2.86231	+	2.40176i	0.166650	+	0.139836i
$296$	1.98293	+	3.43453i	0.115255	+	0.199628i
$297$	1.97178	−	3.41523i	0.114414	−	0.198171i
$298$	−6.44609	+	2.34618i	−0.373412	+	0.135911i
$299$	−1.07057	−	6.07153i	−0.0619129	−	0.351126i
$300$	−1.03936	+	5.89452i	−0.0600076	+	0.340320i
$301$	−5.74675	−	2.09165i	−0.331237	−	0.120560i
$302$	−0.826352	+	0.693392i	−0.0475512	+	0.0399002i
$303$	1.93582			0.111210
$304$	−12.4752	+	7.08062i	−0.715501	+	0.406101i
$305$	−5.81109			−0.332742
$306$	1.02094	−	0.856674i	0.0583635	−	0.0489728i
$307$	−14.3944	−	5.23913i	−0.821532	−	0.299013i	−0.103153	−	0.994665i	$-0.532893\pi$
$307$	−14.3944	−	5.23913i	−0.821532	−	0.299013i	−0.718379	+	0.695652i	$0.755115\pi$
$308$	0.840022	−	4.76400i	0.0478647	−	0.271454i
$309$	−0.180045	−	1.02108i	−0.0102424	−	0.0580875i
$310$	−2.84389	+	1.03509i	−0.161522	+	0.0587893i
$311$	−7.82160	+	13.5474i	−0.443522	+	0.768203i	−0.997948	−	0.0640299i	$-0.979605\pi$
$311$	−7.82160	+	13.5474i	−0.443522	+	0.768203i	0.554426	+	0.832233i	$0.312938\pi$
$312$	1.14156	+	1.97724i	0.0646281	+	0.111939i
$313$	7.78493	+	6.53233i	0.440030	+	0.369229i	0.835721	−	0.549155i	$-0.185050\pi$
$313$	7.78493	+	6.53233i	0.440030	+	0.369229i	−0.395690	+	0.918384i	$0.629495\pi$
$314$	−0.195937	−	0.164411i	−0.0110574	−	0.00927823i
$315$	−0.439693	−	0.761570i	−0.0247739	−	0.0429096i
$316$	−2.93969	+	5.09170i	−0.165371	+	0.286430i
$317$	7.18644	−	2.61565i	0.403631	−	0.146910i	−0.132224	−	0.991220i	$-0.542212\pi$
$317$	7.18644	−	2.61565i	0.403631	−	0.146910i	0.535855	+	0.844310i	$0.319990\pi$
$318$	−0.651359	−	3.69404i	−0.0365264	−	0.207152i
$319$	7.20233	−	40.8465i	0.403253	−	2.28696i
$320$	−6.64543	−	2.41874i	−0.371491	−	0.135212i
$321$	9.35504	−	7.84981i	0.522147	−	0.438134i
$322$	−0.824703			−0.0459589
$323$	−0.123141	+	16.7268i	−0.00685175	+	0.930704i
$324$	−1.87939			−0.104410
$325$	−4.13429	+	3.46908i	−0.229329	+	0.192430i
$326$	−4.11974	−	1.49946i	−0.228171	−	0.0830475i
$327$	0.699340	−	3.96616i	0.0386736	−	0.219329i
$328$	−0.353226	−	2.00324i	−0.0195037	−	0.110611i
$329$	−7.83022	+	2.84997i	−0.431694	+	0.157124i
$330$	0.922618	−	1.59802i	0.0507885	−	0.0879682i
$331$	2.05303	+	3.55596i	0.112845	+	0.195453i	0.916916	−	0.399080i	$-0.130670\pi$
$331$	2.05303	+	3.55596i	0.112845	+	0.195453i	−0.804071	+	0.594533i	$0.797337\pi$
$332$	6.49273	+	5.44804i	0.356335	+	0.299000i
$333$	−2.25490	−	1.89209i	−0.123568	−	0.103686i
$334$	−0.958111	−	1.65950i	−0.0524255	−	0.0908036i
$335$	5.31315	−	9.20264i	0.290288	−	0.502794i
$336$	−2.01842	+	0.734644i	−0.110114	+	0.0400781i
$337$	−2.09967	−	11.9078i	−0.114376	−	0.648660i	−0.987057	−	0.160369i	$-0.948732\pi$
$337$	−2.09967	−	11.9078i	−0.114376	−	0.648660i	0.872681	−	0.488291i	$-0.162380\pi$
$338$	0.610815	−	3.46410i	0.0332239	−	0.188422i
$339$	−12.3969	−	4.51211i	−0.673309	−	0.245064i
$340$	−7.44356	+	6.24589i	−0.403684	+	0.338731i
$341$	25.5066			1.38126
$342$	−0.981582	+	1.15247i	−0.0530779	+	0.0623182i
$343$	8.85978			0.478383
$344$	−9.67024	+	8.11430i	−0.521385	+	0.437494i
$345$	4.60607	+	1.67647i	0.247982	+	0.0902582i
$346$	−0.779715	+	4.42198i	−0.0419177	+	0.237727i
$347$	−0.719408	−	4.07996i	−0.0386198	−	0.219024i	0.959390	−	0.282083i	$-0.0910254\pi$
$347$	−0.719408	−	4.07996i	−0.0386198	−	0.219024i	−0.998010	+	0.0630592i	$0.979914\pi$
$348$	−18.5744	+	6.76055i	−0.995695	+	0.362403i
$349$	0.0196004	−	0.0339488i	0.00104918	−	0.00181724i	−0.865500	−	0.500908i	$-0.832999\pi$
$349$	0.0196004	−	0.0339488i	0.00104918	−	0.00181724i	0.866550	+	0.499091i	$0.166333\pi$
$350$	0.360967	+	0.625213i	0.0192945	+	0.0334190i
$351$	−1.29813	−	1.08926i	−0.0692892	−	0.0581406i
$352$	−11.5929	−	9.72757i	−0.617902	−	0.518481i
$353$	−3.58125	−	6.20291i	−0.190611	−	0.330148i	0.754842	−	0.655907i	$-0.227714\pi$
$353$	−3.58125	−	6.20291i	−0.190611	−	0.330148i	−0.945453	+	0.325759i	$0.894380\pi$
$354$	0.481582	−	0.834124i	0.0255958	−	0.0443332i
$355$	−6.79813	+	2.47432i	−0.360807	+	0.131323i
$356$	3.63341	+	20.6061i	0.192570	+	1.09212i
$357$	−0.434945	+	2.46669i	−0.0230197	+	0.130551i
$358$	−4.92350	−	1.79201i	−0.260215	−	0.0947105i
$359$	−15.6591	+	13.1395i	−0.826456	+	0.693479i	−0.954474	−	0.298293i	$-0.903583\pi$
$359$	−15.6591	+	13.1395i	−0.826456	+	0.693479i	0.128019	+	0.991772i	$0.459138\pi$
$360$	−1.81521			−0.0956698
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$	6.48845			0.341025
$363$	−3.48680	+	2.92577i	−0.183009	+	0.153563i
$364$	−1.95336	−	0.710966i	−0.102384	−	0.0372647i
$365$	−1.37211	+	7.78163i	−0.0718196	+	0.407309i
$366$	0.260115	+	1.47518i	0.0135964	+	0.0771091i
$367$	1.49912	−	0.545636i	0.0782536	−	0.0284820i	−0.302597	−	0.953119i	$-0.597854\pi$
$367$	1.49912	−	0.545636i	0.0782536	−	0.0284820i	0.380850	+	0.924637i	$0.375631\pi$
$368$	5.98633	−	10.3686i	0.312059	−	0.540502i
$369$	0.754900	+	1.30753i	0.0392985	+	0.0680670i
$370$	−1.05509	−	0.885328i	−0.0548517	−	0.0460260i
$371$	5.40033	+	4.53141i	0.280371	+	0.235259i
$372$	−6.07785	−	10.5271i	−0.315122	−	0.545807i
$373$	6.42602	−	11.1302i	0.332727	−	0.576300i	−0.650319	−	0.759661i	$-0.725365\pi$
$373$	6.42602	−	11.1302i	0.332727	−	0.576300i	0.983046	+	0.183362i	$0.0586980\pi$
$374$	−4.93882	+	1.79758i	−0.255380	+	0.0929507i
$375$	−1.91488	−	10.8598i	−0.0988839	−	0.560798i
$376$	−2.98680	+	16.9390i	−0.154032	+	0.873560i
$377$	−16.7481	−	6.09581i	−0.862571	−	0.313950i
$378$	−0.173648	+	0.145708i	−0.00893150	+	0.00749442i
$379$	−15.7023			−0.806575			−0.403287	−	0.915073i	$-0.632132\pi$
$379$	−15.7023			−0.806575			−0.403287	+	0.915073i	$0.632132\pi$
$380$	7.15657	−	8.40247i	0.367125	−	0.431037i
$381$	−13.2490			−0.678765
$382$	2.27513	−	1.90906i	0.116406	−	0.0976760i
$383$	15.4564	+	5.62565i	0.789783	+	0.287457i	0.705246	−	0.708963i	$-0.250837\pi$
$383$	15.4564	+	5.62565i	0.789783	+	0.287457i	0.0845371	+	0.996420i	$0.473059\pi$
$384$	−1.64930	+	9.35365i	−0.0841655	+	0.477326i
$385$	0.602196	+	3.41523i	0.0306908	+	0.174056i
$386$	5.53462	−	2.01444i	0.281704	−	0.102532i
$387$	4.68479	−	8.11430i	0.238141	−	0.412473i
$388$	6.29813	+	10.9087i	0.319739	+	0.553805i
$389$	5.77063	+	4.84213i	0.292583	+	0.245506i	0.777249	−	0.629193i	$-0.216615\pi$
$389$	5.77063	+	4.84213i	0.292583	+	0.245506i	−0.484666	+	0.874699i	$0.661059\pi$
$390$	−0.607411	−	0.509678i	−0.0307575	−	0.0258086i
$391$	−6.98070	−	12.0909i	−0.353029	−	0.611465i
$392$	4.42855	−	7.67047i	0.223675	−	0.387417i
$393$	16.1420	−	5.87522i	0.814258	−	0.296365i
$394$	−0.272441	−	1.54509i	−0.0137254	−	0.0778405i
$395$	0.731896	−	4.15079i	0.0368257	−	0.208849i
$396$	6.96451	+	2.53487i	0.349980	+	0.127382i
$397$	−8.59421	+	7.21140i	−0.431331	+	0.361930i	−0.832454	−	0.554095i	$-0.813065\pi$
$397$	−8.59421	+	7.21140i	−0.431331	+	0.361930i	0.401123	+	0.916024i	$0.368620\pi$
$398$	2.79467			0.140084
$399$	0.0209445	−	2.84499i	0.00104854	−	0.142428i
$400$	−10.4807			−0.524035
$401$	18.5804	−	15.5908i	0.927860	−	0.778567i	−0.0475723	−	0.998868i	$-0.515148\pi$
$401$	18.5804	−	15.5908i	0.927860	−	0.778567i	0.975432	+	0.220301i	$0.0707040\pi$
$402$	−2.57398	−	0.936851i	−0.128378	−	0.0467259i
$403$	1.90327	−	10.7940i	0.0948085	−	0.537685i
$404$	0.631759	+	3.58288i	0.0314312	+	0.178255i
$405$	1.26604	−	0.460802i	0.0629103	−	0.0228975i
$406$	−1.19207	+	2.06472i	−0.0591613	+	0.102470i
$407$	5.80406	+	10.0529i	0.287697	+	0.498305i
$408$	3.96064	+	3.32337i	0.196081	+	0.164531i
$409$	20.1348	+	16.8951i	0.995599	+	0.835407i	0.986369	−	0.164550i	$-0.0526173\pi$
$409$	20.1348	+	16.8951i	0.995599	+	0.835407i	0.00923072	+	0.999957i	$0.497062\pi$
$410$	0.353226	+	0.611806i	0.0174446	+	0.0302149i
$411$	−5.27332	+	9.13366i	−0.260114	+	0.450530i
$412$	1.83110	−	0.666466i	0.0902118	−	0.0328344i
$413$	0.314330	+	1.78265i	0.0154672	+	0.0877187i
$414$	0.219408	−	1.24432i	0.0107833	−	0.0611551i
$415$	−5.70961	−	2.07813i	−0.280274	−	0.102011i
$416$	−4.98158	+	4.18004i	−0.244242	+	0.204943i
$417$	−10.7811			−0.527951
$418$	5.19190	−	2.94680i	0.253944	−	0.144133i
$419$	13.2226			0.645964			0.322982	−	0.946405i	$-0.395315\pi$
$419$	13.2226			0.645964			0.322982	+	0.946405i	$0.395315\pi$
$420$	1.26604	−	1.06234i	0.0617766	−	0.0518368i
$421$	34.8025	+	12.6671i	1.69617	+	0.617355i	0.995380	−	0.0960141i	$-0.0306094\pi$
$421$	34.8025	+	12.6671i	1.69617	+	0.617355i	0.700789	+	0.713369i	$0.252832\pi$
$422$	−1.21120	+	6.86906i	−0.0589603	+	0.334380i
$423$	−2.21688	−	12.5726i	−0.107788	−	0.611299i
$424$	13.6741	−	4.97697i	0.664074	−	0.241703i
$425$	−6.11081	+	10.5842i	−0.296418	+	0.513411i
$426$	0.932419	+	1.61500i	0.0451758	+	0.0782468i
$427$	−2.15657	−	1.80958i	−0.104364	−	0.0875717i
$428$	17.5817	+	14.7528i	0.849844	+	0.713104i
$429$	3.34137	+	5.78742i	0.161323	+	0.279419i
$430$	2.19207	−	3.79677i	0.105711	−	0.183097i
$431$	−8.90167	+	3.23994i	−0.428779	+	0.156063i	−0.547389	−	0.836878i	$-0.684378\pi$
$431$	−8.90167	+	3.23994i	−0.428779	+	0.156063i	0.118611	+	0.992941i	$0.462156\pi$
$432$	−0.571452	−	3.24086i	−0.0274940	−	0.155926i
$433$	−3.91101	+	22.1804i	−0.187951	+	1.06592i	0.734154	+	0.678983i	$0.237579\pi$
$433$	−3.91101	+	22.1804i	−0.187951	+	1.06592i	−0.922105	+	0.386940i	$0.873532\pi$
$434$	−1.37774	−	0.501455i	−0.0661335	−	0.0240706i
$435$	10.8550	−	9.10846i	0.520459	−	0.436717i
$436$	7.56893			0.362486
$437$	10.1038	+	12.2229i	0.483332	+	0.584701i
$438$	2.03684			0.0973238
$439$	−25.4577	+	21.3615i	−1.21503	+	1.01953i	−0.215960	+	0.976402i	$0.569288\pi$
$439$	−25.4577	+	21.3615i	−1.21503	+	1.01953i	−0.999070	+	0.0431289i	$0.986267\pi$
$440$	6.72668	+	2.44831i	0.320682	+	0.116719i
$441$	−1.14156	+	6.47410i	−0.0543600	+	0.308291i
$442$	0.392178	+	2.22415i	0.0186540	+	0.105792i
$443$	−28.7818	+	10.4757i	−1.36747	+	0.497717i	−0.918355	−	0.395759i	$-0.870482\pi$
$443$	−28.7818	+	10.4757i	−1.36747	+	0.497717i	−0.449112	+	0.893476i	$0.648259\pi$
$444$	2.76604	−	4.79093i	0.131271	−	0.227367i
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	−5.21167	−	4.37311i	−0.246780	−	0.207073i
$447$	15.1309	+	12.6963i	0.715666	+	0.600515i
$448$	−1.71301	−	2.96702i	−0.0809322	−	0.140179i
$449$	−7.54623	+	13.0704i	−0.356128	+	0.616833i	−0.987310	−	0.158802i	$-0.949237\pi$
$449$	−7.54623	+	13.0704i	−0.356128	+	0.616833i	0.631182	+	0.775635i	$0.282570\pi$
$450$	−1.03936	+	0.378297i	−0.0489960	+	0.0178331i
$451$	−1.03390	−	5.86354i	−0.0486844	−	0.276103i
$452$	4.30541	−	24.4172i	0.202509	−	1.14849i
$453$	2.91875	+	1.06234i	0.137135	+	0.0499130i
$454$	4.92127	−	4.12944i	0.230967	−	0.193804i
$455$	1.49020			0.0698616
$456$	−5.06418	−	2.97373i	−0.237152	−	0.139257i
$457$	19.8462			0.928365			0.464182	−	0.885740i	$-0.346348\pi$
$457$	19.8462			0.928365			0.464182	+	0.885740i	$0.346348\pi$
$458$	7.49273	−	6.28714i	0.350112	−	0.293779i
$459$	−3.60607	−	1.31250i	−0.168317	−	0.0612623i
$460$	−1.59967	+	9.07218i	−0.0745850	+	0.422993i
$461$	−6.03684	−	34.2366i	−0.281164	−	1.59456i	−0.718676	−	0.695345i	$-0.755252\pi$
$461$	−6.03684	−	34.2366i	−0.281164	−	1.59456i	0.437512	−	0.899212i	$-0.355860\pi$
$462$	0.840022	−	0.305743i	0.0390814	−	0.0142245i
$463$	1.71301	−	2.96702i	0.0796104	−	0.137889i	−0.823472	−	0.567358i	$-0.807966\pi$
$463$	1.71301	−	2.96702i	0.0796104	−	0.137889i	0.903082	+	0.429468i	$0.141299\pi$
$464$	−17.3059	−	29.9747i	−0.803405	−	1.39154i
$465$	6.67546	+	5.60138i	0.309567	+	0.259758i
$466$	−0.0414222	−	0.0347574i	−0.00191885	−	0.00161010i
$467$	5.66250	+	9.80774i	0.262029	+	0.453848i	0.966781	−	0.255606i	$-0.0822749\pi$
$467$	5.66250	+	9.80774i	0.262029	+	0.453848i	−0.704752	+	0.709454i	$0.748942\pi$
$468$	1.59240	−	2.75811i	0.0736085	−	0.127494i
$469$	4.83750	−	1.76070i	0.223375	−	0.0813018i
$470$	−1.03730	−	5.88284i	−0.0478472	−	0.271355i
$471$	−0.127889	+	0.725293i	−0.00589280	+	0.0334197i
$472$	3.51114	+	1.27795i	0.161614	+	0.0588225i
$473$	−28.3050	+	23.7507i	−1.30147	+	1.09206i
$474$	−1.08647			−0.0499031
$475$	4.84389	−	13.0097i	0.222253	−	0.596925i
$476$	−4.70739			−0.215763
$477$	−8.27379	+	6.94253i	−0.378831	+	0.317877i
$478$	2.16385	+	0.787576i	0.0989721	+	0.0360229i
$479$	2.00862	−	11.3914i	0.0917761	−	0.520488i	−0.903912	−	0.427719i	$-0.859317\pi$
$479$	2.00862	−	11.3914i	0.0917761	−	0.520488i	0.995688	−	0.0927688i	$-0.0295717\pi$
$480$	−0.897804	−	5.09170i	−0.0409789	−	0.232403i
$481$	4.68732	−	1.70604i	0.213723	−	0.0777889i
$482$	−0.913534	+	1.58229i	−0.0416103	+	0.0720712i
$483$	1.18732	+	2.05650i	0.0540249	+	0.0935738i
$484$	−6.55303	−	5.49865i	−0.297865	−	0.249939i
$485$	−6.91740	−	5.80439i	−0.314103	−	0.263564i
$486$	−0.173648	−	0.300767i	−0.00787684	−	0.0136431i
$487$	−5.87346	+	10.1731i	−0.266152	+	0.460988i	−0.967865	−	0.251471i	$-0.919086\pi$
$487$	−5.87346	+	10.1731i	−0.266152	+	0.460988i	0.701713	+	0.712460i	$0.252419\pi$
$488$	−5.46064	+	1.98751i	−0.247191	+	0.0899703i
$489$	2.19207	+	12.4318i	0.0991287	+	0.562187i
$490$	−0.534148	+	3.02931i	−0.0241304	+	0.136850i
$491$	−9.63563	−	3.50708i	−0.434850	−	0.158272i	0.115314	−	0.993329i	$-0.463213\pi$
$491$	−9.63563	−	3.50708i	−0.434850	−	0.158272i	−0.550164	+	0.835057i	$0.685435\pi$
$492$	−2.17365	+	1.82391i	−0.0979956	+	0.0822281i
$493$	−40.3610			−1.81777
$494$	−0.859623	−	2.41701i	−0.0386763	−	0.108746i
$495$	−5.31315			−0.238808
$496$	16.3052	−	13.6817i	0.732127	−	0.614328i
$497$	−3.29339	−	1.19869i	−0.147729	−	0.0537688i
$498$	−0.271974	+	1.54244i	−0.0121875	+	0.0691185i
$499$	−1.12149	−	6.36030i	−0.0502049	−	0.284726i	0.949361	−	0.314187i	$-0.101732\pi$
$499$	−1.12149	−	6.36030i	−0.0502049	−	0.284726i	−0.999566	+	0.0294612i	$0.990621\pi$
$500$	19.4748	−	7.08824i	0.870938	−	0.316996i
$501$	−2.75877	+	4.77833i	−0.123253	+	0.213480i
$502$	2.57263	+	4.45593i	0.114822	+	0.198878i
$503$	−14.0248	−	11.7682i	−0.625336	−	0.524719i	0.274140	−	0.961690i	$-0.411607\pi$
$503$	−14.0248	−	11.7682i	−0.625336	−	0.524719i	−0.899476	+	0.436971i	$0.856051\pi$
$504$	−0.673648	−	0.565258i	−0.0300067	−	0.0251786i
$505$	−1.30406	−	2.25870i	−0.0580300	−	0.100511i
$506$	−2.49138	+	4.31520i	−0.110755	+	0.191834i
$507$	−9.51754	+	3.46410i	−0.422689	+	0.153846i
$508$	−4.32383	−	24.5216i	−0.191839	−	1.08797i
$509$	2.09580	−	11.8859i	0.0928947	−	0.526832i	−0.902477	−	0.430737i	$-0.858254\pi$
$509$	2.09580	−	11.8859i	0.0928947	−	0.526832i	0.995372	−	0.0960949i	$-0.0306352\pi$
$510$	−1.68732	−	0.614134i	−0.0747157	−	0.0271943i
$511$	−2.93242	+	2.46059i	−0.129723	+	0.108850i
$512$	−21.4962			−0.950006
$513$	4.28699	+	0.788496i	0.189275	+	0.0348129i
$514$	6.65539			0.293557
$515$	−1.07011	+	0.897927i	−0.0471546	+	0.0395674i
$516$	16.5471	+	6.02265i	0.728446	+	0.265133i
$517$	−8.74241	+	49.5807i	−0.384491	+	2.18056i
$518$	−0.115867	−	0.657115i	−0.00509090	−	0.0288720i
$519$	12.1493	−	4.42198i	0.533295	−	0.194104i
$520$	1.53802	−	2.66393i	0.0674466	−	0.116821i
$521$	−14.2849	−	24.7422i	−0.625834	−	1.08398i	−0.988379	−	0.152010i	$-0.951425\pi$
$521$	−14.2849	−	24.7422i	−0.625834	−	1.08398i	0.362545	−	0.931966i	$-0.381908\pi$
$522$	−2.79813	−	2.34791i	−0.122471	−	0.102765i
$523$	14.2836	+	11.9854i	0.624578	+	0.524083i	0.899239	−	0.437458i	$-0.144121\pi$
$523$	14.2836	+	11.9854i	0.624578	+	0.524083i	−0.274661	+	0.961541i	$0.588566\pi$
$524$	16.1420	+	27.9588i	0.705168	+	1.22139i
$525$	1.03936	−	1.80023i	0.0453615	−	0.0785684i
$526$	−5.38413	+	1.95966i	−0.234759	+	0.0854454i
$527$	−4.31005	−	24.4435i	−0.187749	−	1.06478i
$528$	−2.25356	+	12.7806i	−0.0980734	+	0.556202i
$529$	9.17499	+	3.33942i	0.398913	+	0.145192i
$530$	−3.87140	+	3.24849i	−0.168163	+	0.141105i
$531$	−2.77332			−0.120352
$532$	5.27244	−	0.889704i	0.228589	−	0.0385735i
$533$	−2.55850			−0.110821
$534$	−2.96198	+	2.48540i	−0.128177	+	0.107554i
$535$	−15.4611	−	5.62738i	−0.668442	−	0.243293i
$536$	1.84524	−	10.4649i	0.0797021	−	0.452013i
$537$	2.61974	+	14.8573i	0.113050	+	0.641138i
$538$	1.37464	−	0.500327i	0.0592648	−	0.0215706i
$539$	12.9624	−	22.4516i	0.558332	−	0.967060i
$540$	1.26604	+	2.19285i	0.0544819	+	0.0943654i
$541$	−13.3007	−	11.1606i	−0.571840	−	0.479831i	0.310416	−	0.950601i	$-0.399532\pi$
$541$	−13.3007	−	11.1606i	−0.571840	−	0.479831i	−0.882256	+	0.470770i	$0.843976\pi$
$542$	−2.43763	−	2.04542i	−0.104705	−	0.0878582i
$543$	−9.34137	−	16.1797i	−0.400876	−	0.694338i
$544$	−7.36319	+	12.7534i	−0.315694	+	0.546798i
$545$	−5.09879	+	1.85581i	−0.218408	+	0.0794941i
$546$	−0.0667040	−	0.378297i	−0.00285467	−	0.0161896i
$547$	0.877326	−	4.97556i	0.0375117	−	0.212740i	−0.960290	−	0.279002i	$-0.909996\pi$
$547$	0.877326	−	4.97556i	0.0375117	−	0.212740i	0.997802	+	0.0662625i	$0.0211075\pi$
$548$	−18.6258	−	6.77925i	−0.795656	−	0.289595i
$549$	3.30406	−	2.77244i	0.141014	−	0.118325i
$550$	4.36184			0.185990
$551$	45.2058	−	7.62830i	1.92583	−	0.324976i
$552$	4.90167			0.208629
$553$	1.56418	−	1.31250i	0.0665156	−	0.0558132i
$554$	−7.34137	−	2.67204i	−0.311905	−	0.113524i
$555$	−0.688663	+	3.90560i	−0.0292321	+	0.165784i
$556$	−3.51842	−	19.9539i	−0.149214	−	0.846236i
$557$	22.5303	−	8.20037i	0.954641	−	0.347461i	0.182710	−	0.983167i	$-0.441513\pi$
$557$	22.5303	−	8.20037i	0.954641	−	0.347461i	0.771931	+	0.635706i	$0.219291\pi$
$558$	1.12314	−	1.94534i	0.0475463	−	0.0823527i
$559$	7.93882	+	13.7504i	0.335776	+	0.581581i
$560$	2.21688	+	1.86018i	0.0936803	+	0.0786071i
$561$	11.5929	+	9.72757i	0.489451	+	0.410698i
$562$	−4.08559	−	7.07645i	−0.172340	−	0.298502i
$563$	−21.3418	+	36.9651i	−0.899451	+	1.55789i	−0.0712538	+	0.997458i	$0.522700\pi$
$563$	−21.3418	+	36.9651i	−0.899451	+	1.55789i	−0.828197	+	0.560437i	$0.810633\pi$
$564$	22.5462	−	8.20616i	0.949367	−	0.345541i
$565$	3.08647	+	17.5042i	0.129849	+	0.736408i
$566$	−1.61304	+	9.14798i	−0.0678010	+	0.384518i
$567$	0.613341	+	0.223238i	0.0257579	+	0.00937511i
$568$	−5.54189	+	4.65020i	−0.232532	+	0.195118i
$569$	21.9358			0.919598			0.459799	−	0.888023i	$-0.347922\pi$
$569$	21.9358			0.919598			0.459799	+	0.888023i	$0.347922\pi$
$570$	2.00593	+	0.368946i	0.0840192	+	0.0154534i
$571$	−32.3063			−1.35198			−0.675989	−	0.736912i	$-0.736283\pi$
$571$	−32.3063			−1.35198			−0.675989	+	0.736912i	$0.736283\pi$
$572$	−9.62108	+	8.07305i	−0.402278	+	0.337551i
$573$	−8.03596	−	2.92485i	−0.335707	−	0.122187i
$574$	−0.0594300	+	0.337044i	−0.00248056	+	0.0140680i
$575$	2.01202	+	11.4107i	0.0839071	+	0.475861i
$576$	4.93242	−	1.79525i	0.205517	−	0.0748022i
$577$	23.4060	−	40.5404i	0.974405	−	1.68772i	0.292520	−	0.956259i	$-0.405506\pi$
$577$	23.4060	−	40.5404i	0.974405	−	1.68772i	0.681885	−	0.731460i	$-0.261161\pi$
$578$	−0.394811	−	0.683832i	−0.0164220	−	0.0284437i
$579$	−12.9914	−	10.9011i	−0.539903	−	0.453033i
$580$	20.4008	+	17.1183i	0.847097	+	0.710799i
$581$	−1.47178	−	2.54920i	−0.0610598	−	0.105759i
$582$	−1.16385	+	2.01584i	−0.0482431	+	0.0835594i
$583$	40.0244	−	14.5677i	1.65764	−	0.603332i
$584$	1.37211	+	7.78163i	0.0567784	+	0.322006i
$585$	−0.396459	+	2.24843i	−0.0163916	+	0.0929613i
$586$	−0.0675813	−	0.0245976i	−0.00279176	−	0.00101612i
$587$	−18.9841	+	15.9296i	−0.783558	+	0.657483i	−0.944142	−	0.329539i	$-0.893107\pi$
$587$	−18.9841	+	15.9296i	−0.783558	+	0.657483i	0.160584	+	0.987022i	$0.448662\pi$
$588$	−12.3550			−0.509513
$589$	9.44727	+	26.5630i	0.389268	+	1.09451i
$590$	−1.29767			−0.0534241
$591$	−3.46064	+	2.90382i	−0.142352	+	0.119447i
$592$	9.10266	+	3.31310i	0.374117	+	0.136168i
$593$	−0.634447	+	3.59813i	−0.0260536	+	0.147758i	−0.995060	−	0.0992801i	$-0.968346\pi$
$593$	−0.634447	+	3.59813i	−0.0260536	+	0.147758i	0.969006	+	0.247038i	$0.0794571\pi$
$594$	0.237826	+	1.34878i	0.00975812	+	0.0553410i
$595$	3.17112	−	1.15419i	0.130003	−	0.0473173i
$596$	−18.5608	+	32.1482i	−0.760279	+	1.31684i
$597$	−4.02347	−	6.96886i	−0.164670	−	0.285216i
$598$	1.64022	+	1.37630i	0.0670734	+	0.0562813i
$599$	1.14677	+	0.962258i	0.0468559	+	0.0393168i	0.665915	−	0.746028i	$-0.268041\pi$
$599$	1.14677	+	0.962258i	0.0468559	+	0.0393168i	−0.619059	+	0.785344i	$0.712486\pi$
$600$	−2.14543	−	3.71599i	−0.0875868	−	0.151705i
$601$	−11.9119	+	20.6321i	−0.485898	+	0.841600i	−0.999869	−	0.0162075i	$-0.994841\pi$
$601$	−11.9119	+	20.6321i	−0.485898	+	0.841600i	0.513970	+	0.857808i	$0.328174\pi$
$602$	1.99582	−	0.726421i	0.0813438	−	0.0296067i
$603$	1.36959	+	7.76730i	0.0557738	+	0.316309i
$604$	−1.01367	+	5.74881i	−0.0412457	+	0.233916i
$605$	5.76264	+	2.09743i	0.234285	+	0.0852726i
$606$	−0.515015	+	0.432149i	−0.0209210	+	0.0175548i
$607$	16.4757			0.668726			0.334363	−	0.942444i	$-0.391479\pi$
$607$	16.4757			0.668726			0.334363	+	0.942444i	$0.391479\pi$
$608$	5.83662	−	15.6759i	0.236706	−	0.635743i
$609$	6.86484			0.278177
$610$	1.54601	−	1.29725i	0.0625960	−	0.0525243i
$611$	20.3293	+	7.39928i	0.822437	+	0.299343i
$612$	1.25237	−	7.10257i	0.0506242	−	0.287104i
$613$	0.231591	+	1.31342i	0.00935389	+	0.0530486i	0.989127	−	0.147061i	$-0.0469813\pi$
$613$	0.231591	+	1.31342i	0.00935389	+	0.0530486i	−0.979774	+	0.200109i	$0.935870\pi$
$614$	4.99912	−	1.81953i	0.201748	−	0.0734303i
$615$	1.01707	−	1.76162i	0.0410124	−	0.0710355i
$616$	1.73396	+	3.00330i	0.0698631	+	0.121006i
$617$	27.6864	+	23.2317i	1.11461	+	0.935272i	0.998320	−	0.0579425i	$-0.0184540\pi$
$617$	27.6864	+	23.2317i	1.11461	+	0.935272i	0.116294	+	0.993215i	$0.462898\pi$
$618$	0.275845	+	0.231461i	0.0110961	+	0.00931073i
$619$	−9.65792	−	16.7280i	−0.388185	−	0.672355i	0.604021	−	0.796968i	$-0.293564\pi$
$619$	−9.65792	−	16.7280i	−0.388185	−	0.672355i	−0.992205	+	0.124613i	$0.960231\pi$
$620$	−8.18866	+	14.1832i	−0.328865	+	0.569610i
$621$	−3.41875	+	1.24432i	−0.137190	+	0.0499329i
$622$	−0.943401	−	5.35029i	−0.0378269	−	0.214527i
$623$	1.26187	−	7.15642i	0.0505557	−	0.286716i
$624$	5.24035	+	1.90733i	0.209782	+	0.0763544i
$625$	0.817267	−	0.685768i	0.0326907	−	0.0274307i
$626$	−3.52940			−0.141063
$627$	−14.8229	−	8.70415i	−0.591972	−	0.347610i
$628$	−1.38413			−0.0552329
$629$	8.65317	−	7.26087i	0.345025	−	0.289510i
$630$	0.286989	+	0.104455i	0.0114339	+	0.00416160i
$631$	4.95290	−	28.0893i	0.197172	−	1.11822i	−0.712120	−	0.702057i	$-0.752265\pi$
$631$	4.95290	−	28.0893i	0.197172	−	1.11822i	0.909292	−	0.416159i	$-0.136624\pi$
$632$	−0.731896	−	4.15079i	−0.0291133	−	0.165110i
$633$	18.8726	−	6.86906i	0.750118	−	0.273020i
$634$	−1.32800	+	2.30016i	−0.0527416	+	0.0913512i
$635$	8.92514	+	15.4588i	0.354184	+	0.613464i
$636$	−15.5496	−	13.0477i	−0.616583	−	0.517375i
$637$	−8.53390	−	7.16079i	−0.338125	−	0.283721i
$638$	7.20233	+	12.4748i	0.285143	+	0.493882i
$639$	2.68479	−	4.65020i	0.106209	−	0.183959i
$640$	12.0248	−	4.37667i	0.475323	−	0.173003i
$641$	−5.38342	−	30.5309i	−0.212632	−	1.20590i	−0.884968	−	0.465651i	$-0.845820\pi$
$641$	−5.38342	−	30.5309i	−0.212632	−	1.20590i	0.672336	−	0.740246i	$-0.265291\pi$
$642$	−0.736482	+	4.17680i	−0.0290666	+	0.164845i
$643$	−22.2358	−	8.09316i	−0.876893	−	0.319163i	−0.135938	−	0.990717i	$-0.543405\pi$
$643$	−22.2358	−	8.09316i	−0.876893	−	0.319163i	−0.740955	+	0.671554i	$0.765627\pi$
$644$	−3.41875	+	2.86867i	−0.134718	+	0.113041i
$645$	−12.6236			−0.497054
$646$	−3.70129	−	4.47756i	−0.145625	−	0.176167i
$647$	36.0865			1.41871			0.709353	−	0.704854i	$-0.248987\pi$
$647$	36.0865			1.41871			0.709353	+	0.704854i	$0.248987\pi$
$648$	1.03209	−	0.866025i	0.0405443	−	0.0340207i
$649$	10.2772	+	3.74059i	0.403415	+	0.146831i
$650$	0.325474	−	1.84586i	0.0127662	−	0.0724005i
$651$	0.733078	+	4.15749i	0.0287316	+	0.162945i
$652$	−22.2939	+	8.11430i	−0.873095	+	0.317780i
$653$	18.7245	−	32.4317i	0.732745	−	1.26915i	−0.222961	−	0.974827i	$-0.571572\pi$
$653$	18.7245	−	32.4317i	0.732745	−	1.26915i	0.955706	−	0.294324i	$-0.0950944\pi$
$654$	0.699340	+	1.21129i	0.0273464	+	0.0473653i
$655$	−17.7292	−	14.8766i	−0.692737	−	0.581276i
$656$	−3.80612	−	3.19372i	−0.148604	−	0.124694i
$657$	−2.93242	−	5.07910i	−0.114405	−	0.198154i
$658$	1.44697	−	2.50622i	0.0564086	−	0.0977026i
$659$	−18.1652	+	6.61159i	−0.707615	+	0.257551i	−0.670659	−	0.741766i	$-0.733989\pi$
$659$	−18.1652	+	6.61159i	−0.707615	+	0.257551i	−0.0369566	+	0.999317i	$0.511766\pi$
$660$	−1.73396	−	9.83375i	−0.0674941	−	0.382778i
$661$	−4.27584	+	24.2495i	−0.166311	+	0.943197i	0.781391	+	0.624041i	$0.214510\pi$
$661$	−4.27584	+	24.2495i	−0.166311	+	0.943197i	−0.947702	+	0.319156i	$0.896601\pi$
$662$	−1.34002	−	0.487728i	−0.0520814	−	0.0189561i
$663$	4.98158	−	4.18004i	0.193469	−	0.162339i
$664$	−6.07604			−0.235796
$665$	−3.33363	+	1.89209i	−0.129272	+	0.0733719i
$666$	1.02229			0.0396129
$667$	−29.3123	+	24.5959i	−1.13498	+	0.952358i
$668$	−9.74422	−	3.54661i	−0.377015	−	0.137222i
$669$	−3.40167	+	19.2919i	−0.131516	+	0.745866i
$670$	0.640844	+	3.63441i	0.0247580	+	0.140409i
$671$	−15.9834	+	5.81748i	−0.617032	+	0.224581i
$672$	1.25237	−	2.16918i	0.0483114	−	0.0836777i
$673$	−21.2173	−	36.7495i	−0.817869	−	1.41659i	−0.907250	−	0.420593i	$-0.861822\pi$
$673$	−21.2173	−	36.7495i	−0.817869	−	1.41659i	0.0893810	−	0.995998i	$-0.471511\pi$
$674$	3.21688	+	2.69928i	0.123910	+	0.103973i
$675$	2.43969	+	2.04715i	0.0939038	+	0.0787947i
$676$	−9.51754	−	16.4849i	−0.366059	−	0.634033i
$677$	−7.29813	+	12.6407i	−0.280490	+	0.485823i	−0.971506	−	0.237017i	$-0.923830\pi$
$677$	−7.29813	+	12.6407i	−0.280490	+	0.485823i	0.691015	+	0.722840i	$0.257164\pi$
$678$	4.30541	−	1.56704i	0.165348	−	0.0601818i
$679$	−0.759648	−	4.30818i	−0.0291526	−	0.165333i
$680$	1.20961	−	6.86002i	0.0463863	−	0.263070i
$681$	−17.3824	−	6.32667i	−0.666094	−	0.242438i
$682$	−6.78589	+	5.69404i	−0.259845	+	0.218036i
$683$	17.8043			0.681262			0.340631	−	0.940197i	$-0.389359\pi$
$683$	17.8043			0.681262			0.340631	+	0.940197i	$0.389359\pi$
$684$	−0.0603074	+	8.19183i	−0.00230591	+	0.313222i
$685$	14.2094			0.542915
$686$	−2.35710	+	1.97784i	−0.0899944	+	0.0755142i
$687$	−26.4650	−	9.63246i	−1.00970	−	0.367501i
$688$	−5.35427	+	30.3655i	−0.204129	+	1.15768i
$689$	−3.17823	−	18.0247i	−0.121081	−	0.686685i
$690$	−1.59967	+	0.582232i	−0.0608984	+	0.0221652i
$691$	−6.23648	+	10.8019i	−0.237247	+	0.410924i	−0.959923	−	0.280263i	$-0.909578\pi$
$691$	−6.23648	+	10.8019i	−0.237247	+	0.410924i	0.722676	+	0.691187i	$0.242912\pi$
$692$	12.1493	+	21.0432i	0.461847	+	0.799943i
$693$	−1.97178	−	1.65452i	−0.0749018	−	0.0628501i
$694$	1.10220	+	0.924853i	0.0418388	+	0.0351069i
$695$	7.26264	+	12.5793i	0.275488	+	0.477159i
$696$	7.08512	−	12.2718i	0.268561	−	0.465161i
$697$	−5.44444	+	1.98161i	−0.206223	+	0.0750590i
$698$	0.00236409	+	0.0134074i	8.94822e−5	+	0.000507479i
$699$	−0.0270364	+	0.153331i	−0.00102261	+	0.00579952i
$700$	3.67112	+	1.33618i	0.138755	+	0.0505028i
$701$	−2.47700	+	2.07845i	−0.0935549	+	0.0785018i	−0.688366	−	0.725364i	$-0.741671\pi$
$701$	−2.47700	+	2.07845i	−0.0935549	+	0.0785018i	0.594811	+	0.803866i	$0.297227\pi$
$702$	0.588526			0.0222125
$703$	−8.31954	+	9.76790i	−0.313778	+	0.368403i
$704$	−20.6996			−0.780147
$705$	−13.1762	+	11.0561i	−0.496243	+	0.416398i
$706$	2.33750	+	0.850779i	0.0879728	+	0.0320195i
$707$	0.219408	−	1.24432i	0.00825167	−	0.0467976i
$708$	−0.905078	−	5.13295i	−0.0340149	−	0.192908i
$709$	19.7576	−	7.19117i	0.742012	−	0.270070i	0.0567714	−	0.998387i	$-0.481919\pi$
$709$	19.7576	−	7.19117i	0.742012	−	0.270070i	0.685240	+	0.728317i	$0.259697\pi$
$710$	1.25624	−	2.17588i	0.0471460	−	0.0816593i
$711$	1.56418	+	2.70924i	0.0586612	+	0.101604i
$712$	−11.4907	−	9.64181i	−0.430631	−	0.361342i
$713$	−18.0260	−	15.1256i	−0.675079	−	0.566458i
$714$	−0.434945	−	0.753347i	−0.0162774	−	0.0281933i
$715$	4.50181	−	7.79737i	0.168358	−	0.291605i
$716$	−26.6434	+	9.69739i	−0.995709	+	0.362409i
$717$	−1.15136	−	6.52968i	−0.0429983	−	0.243856i
$718$	1.23277	−	6.99141i	0.0460067	−	0.260917i
$719$	3.80793	+	1.38597i	0.142012	+	0.0516881i	0.412048	−	0.911162i	$-0.364813\pi$
$719$	3.80793	+	1.38597i	0.142012	+	0.0516881i	−0.270036	+	0.962850i	$0.587036\pi$
$720$	−3.39646	+	2.84997i	−0.126579	+	0.106212i
$721$	−0.676747			−0.0252034
$722$	4.99185	+	4.31548i	0.185777	+	0.160606i
$723$	5.26083			0.195652
$724$	26.8974	−	22.5696i	0.999634	−	0.838792i
$725$	31.4761	+	11.4564i	1.16899	+	0.425479i
$726$	0.274500	−	1.55677i	0.0101877	−	0.0577771i
$727$	−7.10623	−	40.3014i	−0.263555	−	1.49470i	−0.773117	−	0.634263i	$-0.781304\pi$
$727$	−7.10623	−	40.3014i	−0.263555	−	1.49470i	0.509562	−	0.860434i	$-0.329808\pi$
$728$	1.40033	−	0.509678i	0.0518997	−	0.0188899i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−1.37211	−	2.37657i	−0.0507841	−	0.0879607i
$731$	27.5437	+	23.1119i	1.01874	+	0.854825i
$732$	6.20961	+	5.21048i	0.229514	+	0.192585i
$733$	−3.63429	−	6.29477i	−0.134235	−	0.232503i	0.791070	−	0.611726i	$-0.209524\pi$
$733$	−3.63429	−	6.29477i	−0.134235	−	0.232503i	−0.925305	+	0.379223i	$0.876191\pi$
$734$	−0.277027	+	0.479824i	−0.0102252	+	0.0177106i
$735$	8.32295	−	3.02931i	0.306997	−	0.111738i
$736$	2.42437	+	13.7493i	0.0893636	+	0.506806i
$737$	5.40104	−	30.6308i	0.198950	−	1.12830i
$738$	−0.492726	−	0.179338i	−0.0181375	−	0.00660151i
$739$	3.56212	−	2.98897i	0.131035	−	0.109951i	−0.574915	−	0.818213i	$-0.694965\pi$
$739$	3.56212	−	2.98897i	0.131035	−	0.109951i	0.705950	+	0.708262i	$0.250520\pi$
$740$	−7.45336			−0.273991
$741$	−4.78952	+	5.62333i	−0.175947	+	0.206578i
$742$	−2.44831			−0.0898803
$743$	−2.05484	+	1.72422i	−0.0753849	+	0.0632555i	−0.679701	−	0.733489i	$-0.737891\pi$
$743$	−2.05484	+	1.72422i	−0.0753849	+	0.0632555i	0.604317	+	0.796744i	$0.293446\pi$
$744$	8.18866	+	2.98043i	0.300211	+	0.109268i
$745$	4.62108	−	26.2075i	0.169303	−	0.960167i
$746$	0.775073	+	4.39566i	0.0283774	+	0.160936i
$747$	4.23783	−	1.54244i	0.155054	−	0.0564350i
$748$	−14.2208	+	24.6311i	−0.519962	+	0.900601i
$749$	−3.98545	−	6.90301i	−0.145625	−	0.252230i
$750$	2.93376	+	2.46172i	0.107126	+	0.0898893i
$751$	24.8444	+	20.8469i	0.906584	+	0.760714i	0.971466	−	0.237179i	$-0.0762228\pi$
$751$	24.8444	+	20.8469i	0.906584	+	0.760714i	−0.0648824	+	0.997893i	$0.520667\pi$
$752$	21.0064	+	36.3841i	0.766024	+	1.32679i
$753$	7.40760	−	12.8303i	0.269948	−	0.467564i
$754$	5.81655	−	2.11705i	0.211826	−	0.0770985i
$755$	−0.726682	−	4.12122i	−0.0264467	−	0.149986i
$756$	−0.213011	+	1.20805i	−0.00774714	+	0.0439362i
$757$	−4.47266	−	1.62791i	−0.162562	−	0.0591676i	0.259458	−	0.965755i	$-0.416456\pi$
$757$	−4.47266	−	1.62791i	−0.162562	−	0.0591676i	−0.422019	+	0.906587i	$0.638678\pi$
$758$	4.17752	−	3.50535i	0.151734	−	0.127320i
$759$	14.3473			0.520774
$760$	−0.0582480	+	7.91209i	−0.00211288	+	0.287002i
$761$	−30.2481			−1.09649			−0.548247	−	0.836316i	$-0.684705\pi$
$761$	−30.2481			−1.09649			−0.548247	+	0.836316i	$0.684705\pi$
$762$	3.52481	−	2.95767i	0.127691	−	0.107145i
$763$	−2.47013	−	0.899055i	−0.0894248	−	0.0325480i
$764$	2.79086	−	15.8278i	0.100970	−	0.572628i
$765$	0.897804	+	5.09170i	0.0324602	+	0.184091i
$766$	−5.36794	+	1.95377i	−0.193951	+	0.0705925i
$767$	2.34982	−	4.07001i	0.0848472	−	0.146960i
$768$	3.59967	+	6.23481i	0.129892	+	0.224979i
$769$	24.2108	+	20.3153i	0.873063	+	0.732587i	0.964741	−	0.263202i	$-0.0847784\pi$
$769$	24.2108	+	20.3153i	0.873063	+	0.732587i	−0.0916775	+	0.995789i	$0.529223\pi$
$770$	−0.922618	−	0.774169i	−0.0332489	−	0.0278991i
$771$	−9.58172	−	16.5960i	−0.345077	−	0.597691i
$772$	15.9363	−	27.6025i	0.573560	−	0.993434i
$773$	−43.6014	+	15.8696i	−1.56823	+	0.570790i	−0.972604	−	0.232470i	$-0.925319\pi$
$773$	−43.6014	+	15.8696i	−1.56823	+	0.570790i	−0.595629	+	0.803260i	$0.703097\pi$
$774$	0.565055	+	3.20459i	0.0203105	+	0.115186i
$775$	−3.57697	+	20.2860i	−0.128489	+	0.728695i
$776$	−8.48545	−	3.08845i	−0.304610	−	0.110869i
$777$	−1.47178	+	1.23497i	−0.0527999	+	0.0443043i
$778$	−2.61619			−0.0937950
$779$	5.72344	−	3.24849i	0.205064	−	0.116389i
$780$	−4.29086			−0.153637
$781$	−16.2212	+	13.6112i	−0.580441	+	0.487048i
$782$	4.55633	+	1.65837i	0.162934	+	0.0593032i
$783$	−1.82635	+	10.3578i	−0.0652685	+	0.370156i
$784$	−3.75671	−	21.3054i	−0.134168	−	0.760906i
$785$	0.932419	−	0.339373i	0.0332794	−	0.0121127i
$786$	−2.98293	+	5.16658i	−0.106397	+	0.184286i
$787$	18.4244	+	31.9120i	0.656760	+	1.13754i	0.981449	+	0.191721i	$0.0614069\pi$
$787$	18.4244	+	31.9120i	0.656760	+	1.13754i	−0.324689	+	0.945821i	$0.605260\pi$
$788$	−6.50387	−	5.45740i	−0.231691	−	0.194412i
$789$	12.6382	+	10.6047i	0.449930	+	0.377536i
$790$	0.731896	+	1.26768i	0.0260397	+	0.0451021i
$791$	−4.30541	+	7.45718i	−0.153083	+	0.265147i
$792$	−4.99273	+	1.81720i	−0.177409	+	0.0645715i
$793$	1.26920	+	7.19799i	0.0450706	+	0.255608i
$794$	0.676585	−	3.83710i	0.0240111	−	0.136174i
$795$	13.6741	+	4.97697i	0.484971	+	0.176515i
$796$	11.5851	−	9.72107i	0.410624	−	0.344554i
$797$	18.7939			0.665712			0.332856	−	0.942978i	$-0.391988\pi$
$797$	18.7939			0.665712			0.332856	+	0.942978i	$0.391988\pi$
$798$	0.629538	+	0.761570i	0.0222854	+	0.0269593i
$799$	48.9914			1.73319
$800$	9.36231	−	7.85591i	0.331008	−	0.277748i
$801$	10.4620	+	3.80785i	0.369656	+	0.134544i
$802$	−1.46275	+	8.29568i	−0.0516516	+	0.292931i
$803$	4.01620	+	22.7770i	0.141729	+	0.803782i
$804$	−13.9290	+	5.06975i	−0.491238	+	0.178796i
$805$	1.59967	−	2.77071i	0.0563810	−	0.0976547i
$806$	1.90327	+	3.29655i	0.0670397	+	0.116116i
$807$	−3.22668	−	2.70751i	−0.113585	−	0.0953088i
$808$	−1.99794	−	1.67647i	−0.0702873	−	0.0589781i
$809$	−3.02276	−	5.23557i	−0.106274	−	0.184073i	0.807984	−	0.589205i	$-0.200559\pi$
$809$	−3.02276	−	5.23557i	−0.106274	−	0.184073i	−0.914258	+	0.405132i	$0.867226\pi$
$810$	−0.233956	+	0.405223i	−0.00822036	+	0.0142381i
$811$	−8.41370	+	3.06233i	−0.295445	+	0.107533i	−0.485490	−	0.874242i	$-0.661359\pi$
$811$	−8.41370	+	3.06233i	−0.295445	+	0.107533i	0.190045	+	0.981775i	$0.439137\pi$
$812$	2.24035	+	12.7057i	0.0786209	+	0.445882i
$813$	−1.59105	+	9.02330i	−0.0558006	+	0.316461i
$814$	−3.78833	−	1.37884i	−0.132781	−	0.0483283i
$815$	13.0287	−	10.9324i	0.456375	−	0.382944i
$816$	12.6287			0.442092
$817$	−35.2181	−	20.6804i	−1.23213	−	0.723514i
$818$	−9.12836			−0.319165
$819$	−0.847296	+	0.710966i	−0.0296069	+	0.0248432i
$820$	3.59240	+	1.30753i	0.125452	+	0.0456608i
$821$	1.41416	−	8.02011i	0.0493546	−	0.279904i	−0.950135	−	0.311838i	$-0.899055\pi$
$821$	1.41416	−	8.02011i	0.0493546	−	0.279904i	0.999490	+	0.0319338i	$0.0101666\pi$
$822$	−0.636040	−	3.60716i	−0.0221844	−	0.125814i
$823$	2.48380	−	0.904030i	0.0865799	−	0.0315125i	−0.298367	−	0.954451i	$-0.596442\pi$
$823$	2.48380	−	0.904030i	0.0865799	−	0.0315125i	0.384947	+	0.922939i	$0.374220\pi$
$824$	−0.698463	+	1.20977i	−0.0243321	+	0.0421445i
$825$	−6.27972	−	10.8768i	−0.218632	−	0.378681i
$826$	−0.481582	−	0.404095i	−0.0167564	−	0.0140603i
$827$	−28.1464	−	23.6176i	−0.978745	−	0.821265i	0.00515463	−	0.999987i	$-0.498359\pi$
$827$	−28.1464	−	23.6176i	−0.978745	−	0.821265i	−0.983900	+	0.178722i	$0.942804\pi$
$828$	−3.41875	−	5.92145i	−0.118810	−	0.205784i
$829$	21.8717	−	37.8829i	0.759636	−	1.31573i	−0.183401	−	0.983038i	$-0.558711\pi$
$829$	21.8717	−	37.8829i	0.759636	−	1.31573i	0.943037	−	0.332689i	$-0.107956\pi$
$830$	1.98293	−	0.721726i	0.0688284	−	0.0250515i
$831$	3.90626	+	22.1535i	0.135507	+	0.768496i
$832$	−1.54458	+	8.75973i	−0.0535486	+	0.303689i
$833$	−23.7062	−	8.62835i	−0.821371	−	0.298955i
$834$	2.86824	−	2.40674i	0.0993191	−	0.0833386i
$835$	7.43376			0.257256
$836$	11.2724	−	30.2754i	0.389866	−	1.04710i
$837$	−6.46791			−0.223564
$838$	−3.51779	+	2.95178i	−0.121520	+	0.101967i
$839$	−12.9508	−	4.71372i	−0.447113	−	0.162736i	0.108644	−	0.994081i	$-0.465349\pi$
$839$	−12.9508	−	4.71372i	−0.447113	−	0.162736i	−0.555757	+	0.831345i	$0.687571\pi$
$840$	−0.205737	+	1.16679i	−0.00709860	+	0.0402582i
$841$	14.1729	+	80.3787i	0.488722	+	2.77168i
$842$	−12.0868	+	4.39922i	−0.416538	+	0.151607i
$843$	−11.7640	+	20.3758i	−0.405173	+	0.701781i
$844$	18.8726	+	32.6883i	0.649621	+	1.12518i
$845$	10.4534	+	8.77141i	0.359607	+	0.301746i
$846$	3.39646	+	2.84997i	0.116773	+	0.0979839i
$847$	1.48545	+	2.57288i	0.0510407	+	0.0884052i
$848$	17.7717	−	30.7815i	0.610284	−	1.05704i
$849$	25.1339	−	9.14798i	0.862592	−	0.313958i
$850$	−0.737054	−	4.18004i	−0.0252808	−	0.143374i
$851$	1.85962	−	10.5464i	0.0637470	−	0.361527i
$852$	9.48293	+	3.45150i	0.324880	+	0.118247i
$853$	8.09673	−	6.79397i	0.277227	−	0.232621i	−0.493564	−	0.869710i	$-0.664306\pi$
$853$	8.09673	−	6.79397i	0.277227	−	0.232621i	0.770790	+	0.637089i	$0.219862\pi$
$854$	0.977711			0.0334566
$855$	−1.96791	−	5.53320i	−0.0673011	−	0.189231i
$856$	−16.4534			−0.562364
$857$	28.2342	−	23.6913i	0.964461	−	0.809279i	−0.0172120	−	0.999852i	$-0.505479\pi$
$857$	28.2342	−	23.6913i	0.964461	−	0.809279i	0.981673	+	0.190573i	$0.0610346\pi$
$858$	−2.18092	−	0.793791i	−0.0744555	−	0.0270996i
$859$	−6.09745	+	34.5803i	−0.208042	+	1.17987i	0.684538	+	0.728977i	$0.260004\pi$
$859$	−6.09745	+	34.5803i	−0.208042	+	1.17987i	−0.892580	+	0.450889i	$0.851107\pi$
$860$	−4.11974	−	23.3642i	−0.140482	−	0.796712i
$861$	0.926022	−	0.337044i	0.0315587	−	0.0114864i
$862$	1.64496	−	2.84916i	0.0560277	−	0.0970427i
$863$	−1.50846	−	2.61272i	−0.0513484	−	0.0889381i	0.839209	−	0.543809i	$-0.183019\pi$
$863$	−1.50846	−	2.61272i	−0.0513484	−	0.0889381i	−0.890557	+	0.454871i	$0.849685\pi$
$864$	2.93969	+	2.46669i	0.100010	+	0.0839187i
$865$	−13.3439	−	11.1969i	−0.453706	−	0.380705i
$866$	−3.91101	−	6.77406i	−0.132901	−	0.230192i
$867$	−1.13681	+	1.96902i	−0.0386081	+	0.0668713i
$868$	−7.45558	+	2.71361i	−0.253059	+	0.0921060i
$869$	−2.14227	−	12.1494i	−0.0726717	−	0.412142i
$870$	−0.854570	+	4.84651i	−0.0289726	+	0.164312i
$871$	−12.5594	−	4.57126i	−0.425560	−	0.154891i
$872$	−4.15657	+	3.48778i	−0.140759	+	0.118111i
$873$	6.70233			0.226840
$874$	−5.41669	−	0.996279i	−0.183222	−	0.0336996i
$875$	−7.19759			−0.243323
$876$	8.44356	−	7.08499i	0.285282	−	0.239380i
$877$	−54.6878	−	19.9047i	−1.84668	−	0.672136i	−0.986870	−	0.161517i	$-0.948361\pi$
$877$	−54.6878	−	19.9047i	−1.84668	−	0.672136i	−0.859807	−	0.510619i	$-0.829416\pi$
$878$	2.00418	−	11.3662i	0.0676376	−	0.383592i
$879$	0.0359593	+	0.203935i	0.00121288	+	0.00687856i
$880$	16.4304	−	5.98016i	0.553867	−	0.201591i
$881$	−12.8191	+	22.2033i	−0.431886	+	0.748048i	−0.997036	−	0.0769402i	$-0.975485\pi$
$881$	−12.8191	+	22.2033i	−0.431886	+	0.748048i	0.565150	+	0.824988i	$0.308818\pi$
$882$	−1.14156	−	1.97724i	−0.0384383	−	0.0665771i
$883$	15.4886	+	12.9965i	0.521233	+	0.437367i	0.865061	−	0.501666i	$-0.167279\pi$
$883$	15.4886	+	12.9965i	0.521233	+	0.437367i	−0.343828	+	0.939033i	$0.611724\pi$
$884$	9.36231	+	7.85591i	0.314889	+	0.264223i
$885$	1.86824	+	3.23589i	0.0628002	+	0.108773i
$886$	5.31867	−	9.21220i	0.178684	−	0.309490i
$887$	19.8332	−	7.21870i	0.665934	−	0.242380i	0.0131379	−	0.999914i	$-0.495818\pi$
$887$	19.8332	−	7.21870i	0.665934	−	0.242380i	0.652796	+	0.757533i	$0.273596\pi$
$888$	0.688663	+	3.90560i	0.0231100	+	0.131063i
$889$	−1.50165	+	8.51627i	−0.0503637	+	0.285627i
$890$	4.89528	+	1.78174i	0.164090	+	0.0597239i
$891$	3.02094	−	2.53487i	0.101205	−	0.0849215i
$892$	−36.8161			−1.23270
$893$	−54.8722	+	9.25946i	−1.83623	+	0.309856i
$894$	−6.85978			−0.229426
$895$	15.5706	−	13.0653i	0.520467	−	0.436724i
$896$	5.82547	+	2.12030i	0.194615	+	0.0708342i
$897$	1.07057	−	6.07153i	0.0357454	−	0.202722i
$898$	−0.910186	−	5.16192i	−0.0303733	−	0.172256i
$899$	−63.9240	+	23.2664i	−2.13199	+	0.775979i
$900$	−2.99273	+	5.18355i	−0.0997575	+	0.172785i
$901$	−20.7237	−	35.8946i	−0.690408	−	1.19582i
$902$	1.58403	+	1.32916i	0.0527423	+	0.0442561i
$903$	−4.68479	−	3.93101i	−0.155900	−	0.130816i
$904$	8.88713	+	15.3930i	0.295581	+	0.511962i
$905$	−12.5856	+	21.7989i	−0.418359	+	0.724619i
$906$	−1.01367	+	0.368946i	−0.0336769	+	0.0122574i
$907$	4.48515	+	25.4365i	0.148927	+	0.844606i	0.964130	+	0.265431i	$0.0855142\pi$
$907$	4.48515	+	25.4365i	0.148927	+	0.844606i	−0.815203	+	0.579175i	$0.803375\pi$
$908$	6.03684	−	34.2366i	0.200339	−	1.13618i
$909$	1.81908	+	0.662090i	0.0603350	+	0.0219601i
$910$	−0.396459	+	0.332669i	−0.0131425	+	0.0110279i
$911$	15.4415			0.511600			0.255800	−	0.966730i	$-0.417661\pi$
$911$	15.4415			0.511600			0.255800	+	0.966730i	$0.417661\pi$
$912$	−14.1446	+	2.38684i	−0.468373	+	0.0790361i
$913$	−17.7847			−0.588587
$914$	−5.27996	+	4.43042i	−0.174646	+	0.146545i
$915$	−5.46064	−	1.98751i	−0.180523	−	0.0657050i
$916$	9.19119	−	52.1258i	0.303685	−	1.72229i
$917$	−1.94697	−	11.0418i	−0.0642945	−	0.364632i
$918$	1.25237	−	0.455827i	0.0413345	−	0.0150445i
$919$	−4.63223	+	8.02325i	−0.152803	+	0.264663i	−0.932257	−	0.361797i	$-0.882163\pi$
$919$	−4.63223	+	8.02325i	−0.152803	+	0.264663i	0.779454	+	0.626460i	$0.215497\pi$
$920$	−3.30200	−	5.71924i	−0.108864	−	0.188558i
$921$	−11.7344	−	9.84635i	−0.386662	−	0.324448i
$922$	9.24897	+	7.76081i	0.304599	+	0.255589i
$923$	4.54963	+	7.88019i	0.149753	+	0.259380i
$924$	2.41875	−	4.18939i	0.0795710	−	0.137821i
$925$	−8.80928	+	3.20631i	−0.289647	+	0.105423i
$926$	0.206614	+	1.17177i	0.00678977	+	0.0385067i
$927$	0.180045	−	1.02108i	0.00591345	−	0.0335368i
$928$	37.9270	+	13.8043i	1.24501	+	0.453148i
$929$	−14.0974	+	11.8292i	−0.462522	+	0.388102i	−0.844058	−	0.536252i	$-0.819840\pi$
$929$	−14.0974	+	11.8292i	−0.462522	+	0.388102i	0.381536	+	0.924354i	$0.375395\pi$
$930$	−3.02641			−0.0992398
$931$	28.1826	+	5.18355i	0.923646	+	0.169884i
$932$	−0.292614			−0.00958489
$933$	−11.9834	+	10.0553i	−0.392319	+	0.329194i
$934$	−3.69594	−	1.34521i	−0.120935	−	0.0440166i
$935$	3.54054	−	20.0794i	0.115788	−	0.656668i
$936$	0.396459	+	2.24843i	0.0129587	+	0.0734923i
$937$	−7.37851	+	2.68556i	−0.241045	+	0.0877333i	−0.459718	−	0.888065i	$-0.652050\pi$
$937$	−7.37851	+	2.68556i	−0.241045	+	0.0877333i	0.218673	+	0.975798i	$0.429827\pi$
$938$	−0.893933	+	1.54834i	−0.0291880	+	0.0505550i
$939$	5.08125	+	8.80099i	0.165820	+	0.287209i
$940$	−24.7631	−	20.7787i	−0.807684	−	0.677727i
$941$	−44.7656	−	37.5628i	−1.45932	−	1.22451i	−0.925408	−	0.378972i	$-0.876278\pi$
$941$	−44.7656	−	37.5628i	−1.45932	−	1.22451i	−0.533910	−	0.845542i	$-0.679278\pi$
$942$	−0.127889	−	0.221510i	−0.00416684	−	0.00721718i
$943$	−2.74644	+	4.75698i	−0.0894365	+	0.154909i
$944$	8.57620	−	3.12148i	0.279132	−	0.101596i
$945$	−0.152704	−	0.866025i	−0.00496745	−	0.0281718i
$946$	2.22833	−	12.6375i	0.0724493	−	0.410880i
$947$	33.8558	+	12.3225i	1.10017	+	0.400428i	0.827377	−	0.561646i	$-0.189832\pi$
$947$	33.8558	+	12.3225i	1.10017	+	0.400428i	0.272789	+	0.962074i	$0.412054\pi$
$948$	−4.50387	+	3.77920i	−0.146279	+	0.122743i
$949$	9.93851			0.322618
$950$	1.61556	+	4.54249i	0.0524158	+	0.147378i
$951$	7.64765			0.247992
$952$	2.58512	−	2.16918i	0.0837843	−	0.0703034i
$953$	−12.2138	−	4.44545i	−0.395643	−	0.144002i	0.136534	−	0.990635i	$-0.456404\pi$
$953$	−12.2138	−	4.44545i	−0.395643	−	0.144002i	−0.532177	+	0.846633i	$0.678626\pi$
$954$	0.651359	−	3.69404i	0.0210885	−	0.119599i
$955$	2.00072	+	11.3466i	0.0647416	+	0.367168i
$956$	11.7096	−	4.26195i	0.378716	−	0.137841i
$957$	20.7383	−	35.9198i	0.670374	−	1.16112i
$958$	2.00862	+	3.47903i	0.0648955	+	0.112402i
$959$	5.27332	+	4.42484i	0.170284	+	0.142886i
$960$	−5.41740	−	4.54574i	−0.174846	−	0.146713i
$961$	−5.41694	−	9.38241i	−0.174740	−	0.302658i
$962$	−0.866181	+	1.50027i	−0.0279268	+	0.0483707i
$963$	11.4757	−	4.17680i	0.369798	−	0.134595i
$964$	1.71688	+	9.73692i	0.0552970	+	0.313605i
$965$	−3.96766	+	22.5017i	−0.127724	+	0.724356i
$966$	−0.774967	−	0.282065i	−0.0249342	−	0.00907529i
$967$	38.5428	−	32.3413i	1.23945	−	1.04003i	0.241887	−	0.970304i	$-0.422234\pi$
$967$	38.5428	−	32.3413i	1.23945	−	1.04003i	0.997567	−	0.0697207i	$-0.0222108\pi$
$968$	6.13247			0.197105
$969$	−5.83662	+	15.6759i	−0.187499	+	0.503584i
$970$	3.13610			0.100694
$971$	−23.5155	+	19.7318i	−0.754648	+	0.633225i	−0.936728	−	0.350059i	$-0.886161\pi$
$971$	−23.5155	+	19.7318i	−0.754648	+	0.633225i	0.182080	+	0.983284i	$0.441717\pi$
$972$	−1.76604	−	0.642788i	−0.0566459	−	0.0206174i
$973$	−1.22193	+	6.92993i	−0.0391734	+	0.222163i
$974$	−0.708425	−	4.01768i	−0.0226994	−	0.128735i
$975$	−5.07145	+	1.84586i	−0.162416	+	0.0591147i
$976$	−7.09698	+	12.2923i	−0.227169	+	0.393468i
$977$	17.5403	+	30.3807i	0.561164	+	0.971964i	0.997395	+	0.0721297i	$0.0229796\pi$
$977$	17.5403	+	30.3807i	0.561164	+	0.971964i	−0.436231	+	0.899834i	$0.643687\pi$
$978$	−3.35844	−	2.81807i	−0.107391	−	0.0901118i
$979$	−33.6334	−	28.2218i	−1.07493	−	0.901972i
$980$	8.32295	+	14.4158i	0.265867	+	0.460495i
$981$	2.01367	−	3.48778i	0.0642916	−	0.111356i
$982$	3.34642	−	1.21800i	0.106789	−	0.0388678i
$983$	3.26130	+	18.4957i	0.104019	+	0.589922i	0.991608	+	0.129285i	$0.0412681\pi$
$983$	3.26130	+	18.4957i	0.104019	+	0.589922i	−0.887588	+	0.460638i	$0.847621\pi$
$984$	0.353226	−	2.00324i	0.0112604	−	0.0638611i
$985$	5.71941	+	2.08169i	0.182235	+	0.0663283i
$986$	10.7378	−	9.01011i	0.341962	−	0.286940i
$987$	−8.33275			−0.265234
$988$	−11.9709	−	7.02941i	−0.380845	−	0.223635i
$989$	34.0880			1.08394
$990$	1.41353	−	1.18610i	0.0449250	−	0.0376966i
$991$	12.7208	+	4.62998i	0.404088	+	0.147076i	0.536065	−	0.844177i	$-0.319910\pi$
$991$	12.7208	+	4.62998i	0.404088	+	0.147076i	−0.131977	+	0.991253i	$0.542132\pi$
$992$	−4.31005	+	24.4435i	−0.136844	+	0.776082i
$993$	0.713011	+	4.04369i	0.0226267	+	0.128323i
$994$	1.14378	−	0.416302i	0.0362785	−	0.0132043i
$995$	−5.42081	+	9.38911i	−0.171851	+	0.297655i
$996$	4.23783	+	7.34013i	0.134281	+	0.232581i
$997$	5.29086	+	4.43956i	0.167563	+	0.140602i	0.722713	−	0.691148i	$-0.242895\pi$
$997$	5.29086	+	4.43956i	0.167563	+	0.140602i	−0.555150	+	0.831750i	$0.687339\pi$
$998$	1.71823	+	1.44176i	0.0543895	+	0.0456382i
$999$	−1.47178	−	2.54920i	−0.0465651	−	0.0806531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.a.25.1	yes	6
3.2	odd	2		171.2.u.a.82.1		6
4.3	odd	2		912.2.bo.b.481.1		6
19.4	even	9		1083.2.a.m.1.2		3
19.15	odd	18		1083.2.a.n.1.2		3
19.16	even	9	inner	57.2.i.a.16.1	✓	6
57.23	odd	18		3249.2.a.w.1.2		3
57.35	odd	18		171.2.u.a.73.1		6
57.53	even	18		3249.2.a.x.1.2		3
76.35	odd	18		912.2.bo.b.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.16.1	✓	6	19.16	even	9	inner
57.2.i.a.25.1	yes	6	1.1	even	1	trivial
171.2.u.a.73.1		6	57.35	odd	18
171.2.u.a.82.1		6	3.2	odd	2
912.2.bo.b.481.1		6	4.3	odd	2
912.2.bo.b.529.1		6	76.35	odd	18
1083.2.a.m.1.2		3	19.4	even	9
1083.2.a.n.1.2		3	19.15	odd	18
3249.2.a.w.1.2		3	57.23	odd	18
3249.2.a.x.1.2		3	57.53	even	18

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.266044 + 0.223238i) q^{2} +(0.939693 + 0.342020i) q^{3} +(-0.326352 + 1.85083i) q^{4} +(-0.233956 - 1.32683i) q^{5} +(-0.326352 + 0.118782i) q^{6} +(0.326352 - 0.565258i) q^{7} +(-0.673648 - 1.16679i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.358441 + 0.300767i) q^{10} +(-1.97178 - 3.41523i) q^{11} +(-0.939693 + 1.62760i) q^{12} +(-1.59240 + 0.579585i) q^{13} +(0.0393628 + 0.223238i) q^{14} +(0.233956 - 1.32683i) q^{15} +(-3.09240 - 1.12554i) q^{16} +(-2.93969 + 2.46669i) q^{17} -0.347296 q^{18} +(2.82635 - 3.31839i) q^{19} +2.53209 q^{20} +(0.500000 - 0.419550i) q^{21} +(1.28699 + 0.468426i) q^{22} +(-0.631759 + 3.58288i) q^{23} +(-0.233956 - 1.32683i) q^{24} +(2.99273 - 1.08926i) q^{25} +(0.294263 - 0.509678i) q^{26} +(0.500000 + 0.866025i) q^{27} +(0.939693 + 0.788496i) q^{28} +(8.05690 + 6.76055i) q^{29} +(0.233956 + 0.405223i) q^{30} +(-3.23396 + 5.60138i) q^{31} +(3.60607 - 1.31250i) q^{32} +(-0.684793 - 3.88365i) q^{33} +(0.231429 - 1.31250i) q^{34} +(-0.826352 - 0.300767i) q^{35} +(-1.43969 + 1.20805i) q^{36} -2.94356 q^{37} +(-0.0111444 + 1.51379i) q^{38} -1.69459 q^{39} +(-1.39053 + 1.16679i) q^{40} +(1.41875 + 0.516382i) q^{41} +(-0.0393628 + 0.223238i) q^{42} +(-1.62701 - 9.22724i) q^{43} +(6.96451 - 2.53487i) q^{44} +(0.673648 - 1.16679i) q^{45} +(-0.631759 - 1.09424i) q^{46} +(-9.77972 - 8.20616i) q^{47} +(-2.52094 - 2.11532i) q^{48} +(3.28699 + 5.69323i) q^{49} +(-0.553033 + 0.957882i) q^{50} +(-3.60607 + 1.31250i) q^{51} +(-0.553033 - 3.13641i) q^{52} +(-1.87551 + 10.6366i) q^{53} +(-0.326352 - 0.118782i) q^{54} +(-4.07011 + 3.41523i) q^{55} -0.879385 q^{56} +(3.79086 - 2.15160i) q^{57} -3.65270 q^{58} +(-2.12449 + 1.78265i) q^{59} +(2.37939 + 0.866025i) q^{60} +(0.748970 - 4.24762i) q^{61} +(-0.390063 - 2.21216i) q^{62} +(0.613341 - 0.223238i) q^{63} +(2.62449 - 4.54574i) q^{64} +(1.14156 + 1.97724i) q^{65} +(1.04916 + 0.880352i) q^{66} +(6.04189 + 5.06975i) q^{67} +(-3.60607 - 6.24589i) q^{68} +(-1.81908 + 3.15074i) q^{69} +(0.286989 - 0.104455i) q^{70} +(-0.932419 - 5.28801i) q^{71} +(0.233956 - 1.32683i) q^{72} +(-5.51114 - 2.00589i) q^{73} +(0.783119 - 0.657115i) q^{74} +3.18479 q^{75} +(5.21941 + 6.31407i) q^{76} -2.57398 q^{77} +(0.450837 - 0.378297i) q^{78} +(2.93969 + 1.06996i) q^{79} +(-0.769915 + 4.36640i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.492726 + 0.179338i) q^{82} +(2.25490 - 3.90560i) q^{83} +(0.613341 + 1.06234i) q^{84} +(3.96064 + 3.32337i) q^{85} +(2.49273 + 2.09165i) q^{86} +(5.25877 + 9.10846i) q^{87} +(-2.65657 + 4.60132i) q^{88} +(10.4620 - 3.80785i) q^{89} +(0.0812519 + 0.460802i) q^{90} +(-0.192066 + 1.08926i) q^{91} +(-6.42514 - 2.33856i) q^{92} +(-4.95471 + 4.15749i) q^{93} +4.43376 q^{94} +(-5.06418 - 2.97373i) q^{95} +3.83750 q^{96} +(5.13429 - 4.30818i) q^{97} +(-2.14543 - 0.780873i) q^{98} +(0.684793 - 3.88365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^11 - 6 * q^13 + 9 * q^14 + 6 * q^15 - 15 * q^16 - 12 * q^17 + 18 * q^19 + 6 * q^20 + 3 * q^21 - 9 * q^23 - 6 * q^24 + 12 * q^26 + 3 * q^27 + 12 * q^29 + 6 * q^30 - 24 * q^31 - 3 * q^32 + 3 * q^33 + 21 * q^34 - 6 * q^35 - 3 * q^36 + 12 * q^37 + 6 * q^38 - 6 * q^39 + 9 * q^40 + 6 * q^41 - 9 * q^42 + 18 * q^43 + 9 * q^44 + 3 * q^45 - 9 * q^46 - 33 * q^47 - 12 * q^48 + 12 * q^49 + 9 * q^50 + 3 * q^51 + 9 * q^52 - 24 * q^53 - 3 * q^54 - 33 * q^55 + 6 * q^56 - 9 * q^57 - 24 * q^58 + 3 * q^60 - 21 * q^61 - 51 * q^62 - 3 * q^63 + 3 * q^64 + 15 * q^65 + 18 * q^66 + 30 * q^67 + 3 * q^68 + 6 * q^69 - 6 * q^70 + 18 * q^71 + 6 * q^72 - 27 * q^73 + 21 * q^74 + 12 * q^75 - 9 * q^78 + 12 * q^79 + 24 * q^80 + 15 * q^82 + 15 * q^83 - 3 * q^84 + 15 * q^85 - 3 * q^86 + 9 * q^87 + 6 * q^88 + 45 * q^89 + 3 * q^90 - 12 * q^91 + 3 * q^92 + 6 * q^93 - 6 * q^94 - 12 * q^95 + 18 * q^96 + 21 * q^97 + 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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