LMFDB - Embedded newform 798.2.cj.b.409.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			409.7
Character	$\chi$	$=$	798.409
Dual form			798.2.cj.b.439.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(3.79976 - 0.669999i) q^{5} +(-0.642788 + 0.766044i) q^{6} +(1.88576 - 1.85578i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-2.95569 - 2.48011i) q^{10} -5.68047 q^{11} +1.00000 q^{12} +(-1.43528 - 1.20434i) q^{13} +(-2.63375 - 0.251706i) q^{14} +(-1.31964 - 3.62568i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.80128 - 4.94897i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-4.08457 - 1.52194i) q^{19} +3.85837i q^{20} +(-2.15504 - 1.53486i) q^{21} +(3.65134 + 4.35149i) q^{22} +(3.10828 + 2.60816i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(9.29078 - 3.38157i) q^{25} +1.87362i q^{26} +(0.500000 + 0.866025i) q^{27} +(1.50012 + 2.17936i) q^{28} +(7.41287 + 1.30709i) q^{29} +(-1.92919 + 3.34145i) q^{30} +(-3.47053 - 6.01113i) q^{31} +(0.342020 + 0.939693i) q^{32} +(0.986403 + 5.59417i) q^{33} +(-4.94897 + 1.80128i) q^{34} +(5.92206 - 8.31496i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(0.224299 - 0.129499i) q^{37} +(1.45964 + 4.10724i) q^{38} +(-0.936810 + 1.62260i) q^{39} +(2.95569 - 2.48011i) q^{40} +(-5.27276 + 4.42437i) q^{41} +(0.209464 + 2.63745i) q^{42} +(5.01968 + 1.82701i) q^{43} +(0.986403 - 5.59417i) q^{44} +(-3.34145 + 1.92919i) q^{45} -4.05758i q^{46} +(1.49696 + 4.11286i) q^{47} +(-0.173648 + 0.984808i) q^{48} +(0.112184 - 6.99910i) q^{49} +(-8.56243 - 4.94352i) q^{50} +(-5.18657 - 0.914532i) q^{51} +(1.43528 - 1.20434i) q^{52} +(-2.44972 - 0.431952i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-21.5844 + 3.80591i) q^{55} +(0.705228 - 2.55003i) q^{56} +(-0.789536 + 4.28680i) q^{57} +(-3.76361 - 6.51877i) q^{58} +(-4.79045 - 1.74358i) q^{59} +(3.79976 - 0.669999i) q^{60} +(8.19879 - 9.77094i) q^{61} +(-2.37398 + 6.52246i) q^{62} +(-1.13732 + 2.38883i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.26060 - 3.61456i) q^{65} +(3.65134 - 4.35149i) q^{66} +(7.77442 - 9.26520i) q^{67} +(4.56099 + 2.63329i) q^{68} +(2.02879 - 3.51396i) q^{69} +(-10.1763 + 0.808191i) q^{70} +(-1.21270 + 3.33188i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(0.843521 - 0.148736i) q^{73} +(-0.243378 - 0.0885825i) q^{74} +(-4.94352 - 8.56243i) q^{75} +(2.20809 - 3.75823i) q^{76} +(-10.7120 + 10.5417i) q^{77} +(1.84516 - 0.325351i) q^{78} +(-4.72798 + 12.9900i) q^{79} +(-3.79976 - 0.669999i) q^{80} +(0.766044 - 0.642788i) q^{81} +(6.77853 + 1.19524i) q^{82} +(4.64855 + 2.68384i) q^{83} +(1.88576 - 1.85578i) q^{84} +(3.52861 - 20.0117i) q^{85} +(-1.82701 - 5.01968i) q^{86} -7.52723i q^{87} +(-4.91943 + 2.84024i) q^{88} +(-0.836416 + 4.74355i) q^{89} +(3.62568 + 1.31964i) q^{90} +(-4.94157 + 0.392456i) q^{91} +(-3.10828 + 2.60816i) q^{92} +(-5.31716 + 4.46162i) q^{93} +(2.18841 - 3.79043i) q^{94} +(-16.5401 - 3.04632i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-3.01422 - 17.0945i) q^{97} +(-5.43373 + 4.41300i) q^{98} +(5.33790 - 1.94284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	3.79976	−	0.669999i	1.69930	−	0.299633i	0.761852	−	0.647751i	$-0.224290\pi$
$5$	3.79976	−	0.669999i	1.69930	−	0.299633i	0.937451	+	0.348119i	$0.113179\pi$
$6$	−0.642788	+	0.766044i	−0.262417	+	0.312736i
$7$	1.88576	−	1.85578i	0.712750	−	0.701418i
$7$	1.88576	−	1.85578i	0.712750	−	0.701418i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−2.95569	−	2.48011i	−0.934670	−	0.784281i
$11$	−5.68047			−1.71273			−0.856363	−	0.516374i	$-0.827282\pi$
$11$	−5.68047			−1.71273			−0.856363	+	0.516374i	$0.827282\pi$
$12$	1.00000			0.288675
$13$	−1.43528	−	1.20434i	−0.398074	−	0.334024i	0.421675	−	0.906747i	$-0.361442\pi$
$13$	−1.43528	−	1.20434i	−0.398074	−	0.334024i	−0.819749	+	0.572723i	$0.805887\pi$
$14$	−2.63375	−	0.251706i	−0.703900	−	0.0672712i
$15$	−1.31964	−	3.62568i	−0.340730	−	0.936148i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.80128	−	4.94897i	0.436874	−	1.20030i	−0.504641	−	0.863329i	$-0.668375\pi$
$17$	1.80128	−	4.94897i	0.436874	−	1.20030i	0.941515	−	0.336972i	$-0.109403\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−4.08457	−	1.52194i	−0.937065	−	0.349156i
$19$	−4.08457	−	1.52194i	−0.937065	−	0.349156i
$20$			3.85837i			0.862758i
$21$	−2.15504	−	1.53486i	−0.470269	−	0.334934i
$22$	3.65134	+	4.35149i	0.778468	+	0.927742i
$23$	3.10828	+	2.60816i	0.648122	+	0.543839i	0.906500	−	0.422205i	$-0.138744\pi$
$23$	3.10828	+	2.60816i	0.648122	+	0.543839i	−0.258379	+	0.966044i	$0.583188\pi$
$24$	−0.642788	−	0.766044i	−0.131208	−	0.156368i
$25$	9.29078	−	3.38157i	1.85816	−	0.676313i
$26$			1.87362i			0.367447i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	1.50012	+	2.17936i	0.283497	+	0.411861i
$29$	7.41287	+	1.30709i	1.37654	+	0.242720i	0.812467	−	0.583007i	$-0.198124\pi$
$29$	7.41287	+	1.30709i	1.37654	+	0.242720i	0.564069	+	0.825728i	$0.309235\pi$
$30$	−1.92919	+	3.34145i	−0.352220	+	0.610062i
$31$	−3.47053	−	6.01113i	−0.623325	−	1.07963i	−0.988862	−	0.148834i	$-0.952448\pi$
$31$	−3.47053	−	6.01113i	−0.623325	−	1.07963i	0.365537	−	0.930797i	$-0.380885\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	0.986403	+	5.59417i	0.171711	+	0.973820i
$34$	−4.94897	+	1.80128i	−0.848741	+	0.308917i
$35$	5.92206	−	8.31496i	1.00101	−	1.40548i
$36$	−0.173648	−	0.984808i	−0.0289414	−	0.164135i
$37$	0.224299	−	0.129499i	0.0368745	−	0.0212895i	−0.481449	−	0.876474i	$-0.659890\pi$
$37$	0.224299	−	0.129499i	0.0368745	−	0.0212895i	0.518324	+	0.855184i	$0.326556\pi$
$38$	1.45964	+	4.10724i	0.236785	+	0.666283i
$39$	−0.936810	+	1.62260i	−0.150010	+	0.259824i
$40$	2.95569	−	2.48011i	0.467335	−	0.392140i
$41$	−5.27276	+	4.42437i	−0.823467	+	0.690971i	−0.953781	−	0.300502i	$-0.902846\pi$
$41$	−5.27276	+	4.42437i	−0.823467	+	0.690971i	0.130314	+	0.991473i	$0.458401\pi$
$42$	0.209464	+	2.63745i	0.0323210	+	0.406967i
$43$	5.01968	+	1.82701i	0.765494	+	0.278617i	0.695110	−	0.718903i	$-0.255355\pi$
$43$	5.01968	+	1.82701i	0.765494	+	0.278617i	0.0703836	+	0.997520i	$0.477578\pi$
$44$	0.986403	−	5.59417i	0.148706	−	0.843353i
$45$	−3.34145	+	1.92919i	−0.498114	+	0.287586i
$46$		−	4.05758i		−	0.598257i
$47$	1.49696	+	4.11286i	0.218354	+	0.599922i	0.999708	−	0.0241656i	$-0.00769291\pi$
$47$	1.49696	+	4.11286i	0.218354	+	0.599922i	−0.781354	+	0.624088i	$0.785471\pi$
$48$	−0.173648	+	0.984808i	−0.0250640	+	0.142145i
$49$	0.112184	−	6.99910i	0.0160263	−	0.999872i
$50$	−8.56243	−	4.94352i	−1.21091	−	0.699119i
$51$	−5.18657	−	0.914532i	−0.726265	−	0.128060i
$52$	1.43528	−	1.20434i	0.199037	−	0.167012i
$53$	−2.44972	−	0.431952i	−0.336495	−	0.0593331i	0.00284778	−	0.999996i	$-0.499094\pi$
$53$	−2.44972	−	0.431952i	−0.336495	−	0.0593331i	−0.339343	+	0.940663i	$0.610205\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	−21.5844	+	3.80591i	−2.91044	+	0.513189i
$56$	0.705228	−	2.55003i	0.0942400	−	0.340762i
$57$	−0.789536	+	4.28680i	−0.104577	+	0.567800i
$58$	−3.76361	−	6.51877i	−0.494187	−	0.855957i
$59$	−4.79045	−	1.74358i	−0.623663	−	0.226995i	0.0108076	−	0.999942i	$-0.496560\pi$
$59$	−4.79045	−	1.74358i	−0.623663	−	0.226995i	−0.634471	+	0.772947i	$0.718782\pi$
$60$	3.79976	−	0.669999i	0.490546	−	0.0864966i
$61$	8.19879	−	9.77094i	1.04975	−	1.25104i	0.0826648	−	0.996577i	$-0.473657\pi$
$61$	8.19879	−	9.77094i	1.04975	−	1.25104i	0.967083	−	0.254463i	$-0.0818986\pi$
$62$	−2.37398	+	6.52246i	−0.301496	+	0.828353i
$63$	−1.13732	+	2.38883i	−0.143289	+	0.300964i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−6.26060	−	3.61456i	−0.776532	−	0.448331i
$66$	3.65134	−	4.35149i	0.449448	−	0.535632i
$67$	7.77442	−	9.26520i	0.949797	−	1.13192i	−0.0413486	−	0.999145i	$-0.513165\pi$
$67$	7.77442	−	9.26520i	0.949797	−	1.13192i	0.991146	−	0.132779i	$-0.0423901\pi$
$68$	4.56099	+	2.63329i	0.553102	+	0.319333i
$69$	2.02879	−	3.51396i	0.244237	−	0.423032i
$70$	−10.1763	+	0.808191i	−1.21629	+	0.0965973i
$71$	−1.21270	+	3.33188i	−0.143921	+	0.395421i	−0.990619	−	0.136654i	$-0.956365\pi$
$71$	−1.21270	+	3.33188i	−0.143921	+	0.395421i	0.846697	+	0.532075i	$0.178587\pi$
$72$	−0.642788	+	0.766044i	−0.0757532	+	0.0902792i
$73$	0.843521	−	0.148736i	0.0987267	−	0.0174082i	−0.124067	−	0.992274i	$-0.539594\pi$
$73$	0.843521	−	0.148736i	0.0987267	−	0.0174082i	0.222793	+	0.974866i	$0.428483\pi$
$74$	−0.243378	−	0.0885825i	−0.0282922	−	0.0102975i
$75$	−4.94352	−	8.56243i	−0.570829	−	0.988704i
$76$	2.20809	−	3.75823i	0.253286	−	0.431099i
$77$	−10.7120	+	10.5417i	−1.22075	+	1.20134i
$78$	1.84516	−	0.325351i	0.208923	−	0.0368387i
$79$	−4.72798	+	12.9900i	−0.531939	+	1.46149i	0.324820	+	0.945776i	$0.394696\pi$
$79$	−4.72798	+	12.9900i	−0.531939	+	1.46149i	−0.856760	+	0.515716i	$0.827526\pi$
$80$	−3.79976	−	0.669999i	−0.424826	−	0.0749082i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	6.77853	+	1.19524i	0.748564	+	0.131992i
$83$	4.64855	+	2.68384i	0.510244	+	0.294590i	0.732934	−	0.680300i	$-0.238150\pi$
$83$	4.64855	+	2.68384i	0.510244	+	0.294590i	−0.222690	+	0.974889i	$0.571484\pi$
$84$	1.88576	−	1.85578i	0.205753	−	0.202482i
$85$	3.52861	−	20.0117i	0.382731	−	2.17058i
$86$	−1.82701	−	5.01968i	−0.197012	−	0.541286i
$87$		−	7.52723i		−	0.807004i
$88$	−4.91943	+	2.84024i	−0.524413	+	0.302770i
$89$	−0.836416	+	4.74355i	−0.0886600	+	0.502816i	0.907847	+	0.419302i	$0.137725\pi$
$89$	−0.836416	+	4.74355i	−0.0886600	+	0.502816i	−0.996507	+	0.0835134i	$0.973386\pi$
$90$	3.62568	+	1.31964i	0.382181	+	0.139102i
$91$	−4.94157	+	0.392456i	−0.518018	+	0.0411406i
$92$	−3.10828	+	2.60816i	−0.324061	+	0.271919i
$93$	−5.31716	+	4.46162i	−0.551363	+	0.462649i
$94$	2.18841	−	3.79043i	0.225717	−	0.390953i
$95$	−16.5401	−	3.04632i	−1.69697	−	0.312546i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−3.01422	−	17.0945i	−0.306048	−	1.73568i	−0.618530	−	0.785761i	$-0.712272\pi$
$97$	−3.01422	−	17.0945i	−0.306048	−	1.73568i	0.312482	−	0.949924i	$-0.398840\pi$
$98$	−5.43373	+	4.41300i	−0.548890	+	0.445780i
$99$	5.33790	−	1.94284i	0.536479	−	0.195262i
$100$	1.71687	+	9.73683i	0.171687	+	0.973683i
$101$	2.10795	+	5.79155i	0.209749	+	0.576281i	0.999300	−	0.0374041i	$-0.0119089\pi$
$101$	2.10795	+	5.79155i	0.209749	+	0.576281i	−0.789551	+	0.613685i	$0.789687\pi$
$102$	2.63329	+	4.56099i	0.260735	+	0.451606i
$103$	−6.02830	+	10.4413i	−0.593986	+	1.02881i	0.399703	+	0.916645i	$0.369113\pi$
$103$	−6.02830	+	10.4413i	−0.593986	+	1.02881i	−0.993689	+	0.112170i	$0.964220\pi$
$104$	−1.84516	−	0.325351i	−0.180932	−	0.0319033i
$105$	−9.21699	−	4.38821i	−0.899486	−	0.428246i
$106$	1.24376	+	2.15425i	0.120804	+	0.209239i
$107$			8.74582i			0.845490i	0.906249	+	0.422745i	$0.138933\pi$
$107$			8.74582i			0.845490i	−0.906249	+	0.422745i	$0.861067\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	10.8151	+	12.8890i	1.03590	+	1.23454i	0.971605	+	0.236610i	$0.0760364\pi$
$109$	10.8151	+	12.8890i	1.03590	+	1.23454i	0.0642981	+	0.997931i	$0.479519\pi$
$110$	16.7897	+	14.0882i	1.60083	+	1.34326i
$111$	−0.166481	−	0.198404i	−0.0158016	−	0.0188317i
$112$	−2.40675	+	1.09889i	−0.227416	+	0.103836i
$113$			8.49892i			0.799511i	0.916622	+	0.399756i	$0.130905\pi$
$113$			8.49892i			0.799511i	−0.916622	+	0.399756i	$0.869095\pi$
$114$	3.79138	−	2.15068i	0.355095	−	0.201430i
$115$	13.5582	+	7.82782i	1.26431	+	0.729948i
$116$	−2.57446	+	7.07328i	−0.239033	+	0.656738i
$117$	1.76063	+	0.640816i	0.162770	+	0.0592434i
$118$	1.74358	+	4.79045i	0.160510	+	0.440997i
$119$	−5.78740	−	12.6753i	−0.530530	−	1.16195i
$120$	−2.95569	−	2.48011i	−0.269816	−	0.226402i
$121$	21.2678			1.93343
$122$	−12.7551			−1.15479
$123$	5.27276	+	4.42437i	0.475429	+	0.398932i
$124$	6.52246	−	2.37398i	0.585734	−	0.213190i
$125$	16.3298	−	9.42801i	1.46058	−	0.843267i
$126$	2.56100	−	0.664270i	0.228152	−	0.0591779i
$127$	−2.93470	+	3.49744i	−0.260412	+	0.310348i	−0.880370	−	0.474288i	$-0.842706\pi$
$127$	−2.93470	+	3.49744i	−0.260412	+	0.310348i	0.619957	+	0.784636i	$0.287150\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	0.927599	−	5.26068i	0.0816706	−	0.463177i
$130$	1.25532	+	7.11930i	0.110099	+	0.624404i
$131$	−0.359849	−	0.428851i	−0.0314401	−	0.0374689i	0.750095	−	0.661330i	$-0.230008\pi$
$131$	−0.359849	−	0.428851i	−0.0314401	−	0.0374689i	−0.781535	+	0.623861i	$0.785563\pi$
$132$	−5.68047			−0.494422
$133$	−10.5269	+	4.71004i	−0.912797	+	0.408413i
$134$	−12.0949			−1.04484
$135$	2.48011	+	2.95569i	0.213454	+	0.254385i
$136$	−0.914532	−	5.18657i	−0.0784205	−	0.444745i
$137$	−2.52586	+	14.3249i	−0.215799	+	1.22386i	0.663716	+	0.747984i	$0.268978\pi$
$137$	−2.52586	+	14.3249i	−0.215799	+	1.22386i	−0.879515	+	0.475871i	$0.842133\pi$
$138$	−3.99593	+	0.704591i	−0.340156	+	0.0599787i
$139$	14.4399	−	17.2087i	1.22477	−	1.45963i	0.379584	−	0.925157i	$-0.376067\pi$
$139$	14.4399	−	17.2087i	1.22477	−	1.45963i	0.845188	−	0.534469i	$-0.179489\pi$
$140$	7.16028	+	7.27597i	0.605154	+	0.614931i
$141$	3.79043	−	2.18841i	0.319212	−	0.184297i
$142$	3.33188	−	1.21270i	0.279605	−	0.101768i
$143$	8.15304	+	6.84122i	0.681792	+	0.572091i
$144$	1.00000			0.0833333
$145$	29.0429			2.41188
$146$	−0.656143	−	0.550569i	−0.0543028	−	0.0455654i
$147$	−6.91225	+	1.10490i	−0.570113	+	0.0911307i
$148$	0.0885825	+	0.243378i	0.00728143	+	0.0200056i
$149$	−0.854775	−	0.311113i	−0.0700259	−	0.0254873i	0.306770	−	0.951784i	$-0.400752\pi$
$149$	−0.854775	−	0.311113i	−0.0700259	−	0.0254873i	−0.376796	+	0.926296i	$0.622974\pi$
$150$	−3.38157	+	9.29078i	−0.276104	+	0.758589i
$151$	−7.40572	−	4.27570i	−0.602669	−	0.347951i	0.167422	−	0.985885i	$-0.446456\pi$
$151$	−7.40572	−	4.27570i	−0.602669	−	0.347951i	−0.770091	+	0.637934i	$0.779789\pi$
$152$	−4.29831	+	0.724250i	−0.348639	+	0.0587444i
$153$			5.26658i			0.425778i
$154$	14.9609	+	1.42981i	1.20559	+	0.115217i
$155$	−17.2146	−	20.5156i	−1.38271	−	1.64785i
$156$	−1.43528	−	1.20434i	−0.114914	−	0.0964243i
$157$	−0.485581	−	0.578693i	−0.0387536	−	0.0461848i	0.746319	−	0.665588i	$-0.231819\pi$
$157$	−0.485581	−	0.578693i	−0.0387536	−	0.0461848i	−0.785073	+	0.619403i	$0.787375\pi$
$158$	12.9900	−	4.72798i	1.03343	−	0.376138i
$159$			2.48751i			0.197272i
$160$	1.92919	+	3.34145i	0.152516	+	0.264165i
$161$	10.7016	−	0.849917i	0.843407	−	0.0669828i
$162$	−0.984808	−	0.173648i	−0.0773738	−	0.0136431i
$163$	6.36277	−	11.0206i	0.498371	−	0.863204i	−0.501627	−	0.865084i	$-0.667265\pi$
$163$	6.36277	−	11.0206i	0.498371	−	0.863204i	0.999998	+	0.00188014i	$0.000598469\pi$
$164$	−3.44155	−	5.96094i	−0.268740	−	0.465471i
$165$	7.49618	+	20.5956i	0.583577	+	1.60337i
$166$	−0.932087	−	5.28613i	−0.0723440	−	0.410283i
$167$	15.4592	−	5.62670i	1.19627	−	0.435407i	0.334350	−	0.942449i	$-0.391483\pi$
$167$	15.4592	−	5.62670i	1.19627	−	0.435407i	0.861922	+	0.507041i	$0.169261\pi$
$168$	−2.63375	−	0.251706i	−0.203198	−	0.0194195i
$169$	−1.64784	−	9.34538i	−0.126757	−	0.718875i
$170$	−17.5980	+	10.1602i	−1.34971	+	0.779253i
$171$	4.35877	+	0.0331466i	0.333324	+	0.00253478i
$172$	−2.67092	+	4.62616i	−0.203655	+	0.352742i
$173$	0.313021	−	0.262656i	0.0237986	−	0.0199694i	−0.630811	−	0.775937i	$-0.717278\pi$
$173$	0.313021	−	0.262656i	0.0237986	−	0.0199694i	0.654609	+	0.755967i	$0.272833\pi$
$174$	−5.76619	+	4.83841i	−0.437134	+	0.366799i
$175$	11.2447	−	23.6184i	0.850023	−	1.78539i
$176$	5.33790	+	1.94284i	0.402359	+	0.146447i
$177$	−0.885239	+	5.02044i	−0.0665387	+	0.377359i
$178$	4.17141	−	2.40837i	0.312660	−	0.180515i
$179$		−	19.9397i		−	1.49037i	−0.666860	−	0.745183i	$-0.732362\pi$
$179$		−	19.9397i		−	1.49037i	0.666860	−	0.745183i	$-0.267638\pi$
$180$	−1.31964	−	3.62568i	−0.0983602	−	0.270243i
$181$	−3.02490	+	17.1551i	−0.224839	+	1.27513i	0.638153	+	0.769910i	$0.279699\pi$
$181$	−3.02490	+	17.1551i	−0.224839	+	1.27513i	−0.862992	+	0.505218i	$0.831412\pi$
$182$	3.47702	+	3.53320i	0.257734	+	0.261898i
$183$	−11.0462	−	6.37753i	−0.816558	−	0.471440i
$184$	3.99593	+	0.704591i	0.294584	+	0.0519431i
$185$	0.765516	−	0.642344i	0.0562818	−	0.0472261i
$186$	6.83560	+	1.20530i	0.501211	+	0.0883770i
$187$	−10.2321	+	28.1125i	−0.748246	+	2.05579i
$188$	−4.31032	+	0.760026i	−0.314362	+	0.0554306i
$189$	2.55003	+	0.705228i	0.185487	+	0.0512978i
$190$	8.29813	+	14.6286i	0.602009	+	1.06127i
$191$	12.8273	+	22.2175i	0.928147	+	1.60760i	0.786420	+	0.617693i	$0.211932\pi$
$191$	12.8273	+	22.2175i	0.928147	+	1.60760i	0.141728	+	0.989906i	$0.454734\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	7.01433	−	1.23682i	0.504903	−	0.0890279i	0.0846055	−	0.996415i	$-0.473037\pi$
$193$	7.01433	−	1.23682i	0.504903	−	0.0890279i	0.420297	+	0.907387i	$0.361926\pi$
$194$	−11.1577	+	13.2972i	−0.801073	+	0.954681i
$195$	−2.47251	+	6.79315i	−0.177060	+	0.486468i
$196$	6.87329	+	1.32586i	0.490949	+	0.0947044i
$197$	3.53837	−	6.12863i	0.252098	−	0.436647i	−0.712005	−	0.702174i	$-0.752213\pi$
$197$	3.53837	−	6.12863i	0.252098	−	0.436647i	0.964103	+	0.265527i	$0.0855461\pi$
$198$	−4.91943	−	2.84024i	−0.349609	−	0.201847i
$199$	−16.2953	+	19.4200i	−1.15514	+	1.37664i	−0.241361	+	0.970435i	$0.577594\pi$
$199$	−16.2953	+	19.4200i	−1.15514	+	1.37664i	−0.913780	+	0.406209i	$0.866851\pi$
$200$	6.35527	−	7.57391i	0.449385	−	0.535557i
$201$	−10.4745	−	6.04743i	−0.738811	−	0.426553i
$202$	3.08162	−	5.33752i	0.216822	−	0.375547i
$203$	16.4046	−	11.2918i	1.15138	−	0.792528i
$204$	1.80128	−	4.94897i	0.126115	−	0.346497i
$205$	−17.0709	+	20.3443i	−1.19228	+	1.42091i
$206$	11.8734	−	2.09361i	0.827262	−	0.145869i
$207$	−3.81287	−	1.38777i	−0.265013	−	0.0964569i
$208$	0.936810	+	1.62260i	0.0649561	+	0.112507i
$209$	23.2023	+	8.64531i	1.60494	+	0.598009i
$210$	2.56300	+	9.88131i	0.176864	+	0.681875i
$211$	−13.8382	+	2.44005i	−0.952662	+	0.167980i	−0.628316	−	0.777959i	$-0.716255\pi$
$211$	−13.8382	+	2.44005i	−0.952662	+	0.167980i	−0.324346	+	0.945939i	$0.605144\pi$
$212$	0.850779	−	2.33750i	0.0584317	−	0.160540i
$213$	3.49184	+	0.615706i	0.239257	+	0.0421875i
$214$	6.69968	−	5.62170i	0.457981	−	0.384292i
$215$	20.2977	+	3.57902i	1.38429	+	0.244087i
$216$	0.866025	+	0.500000i	0.0589256	+	0.0340207i
$217$	−17.6999	−	4.89502i	−1.20155	−	0.332296i
$218$	2.92170	−	16.5698i	0.197882	−	1.12225i
$219$	−0.292952	−	0.804879i	−0.0197959	−	0.0543887i
$220$		−	21.9174i		−	1.47767i
$221$	−8.54557	+	4.93379i	−0.574837	+	0.331882i
$222$	−0.0449745	+	0.255063i	−0.00301849	+	0.0171187i
$223$	−11.0552	−	4.02378i	−0.740314	−	0.269452i	−0.0557898	−	0.998443i	$-0.517768\pi$
$223$	−11.0552	−	4.02378i	−0.740314	−	0.269452i	−0.684524	+	0.728990i	$0.739990\pi$
$224$	2.38883	+	1.13732i	0.159610	+	0.0759905i
$225$	−7.57391	+	6.35527i	−0.504928	+	0.423684i
$226$	6.51055	−	5.46300i	0.433076	−	0.363394i
$227$	6.19709	−	10.7337i	0.411315	−	0.712419i	−0.583719	−	0.811956i	$-0.698403\pi$
$227$	6.19709	−	10.7337i	0.411315	−	0.712419i	0.995034	+	0.0995370i	$0.0317362\pi$
$228$	−4.08457	−	1.52194i	−0.270507	−	0.100793i
$229$	−9.97072	+	5.75660i	−0.658884	+	0.380407i	−0.791852	−	0.610714i	$-0.790883\pi$
$229$	−9.97072	+	5.75660i	−0.658884	+	0.380407i	0.132968	+	0.991120i	$0.457549\pi$
$230$	−2.71857	−	15.4178i	−0.179257	−	1.01662i
$231$	12.2417	+	8.71872i	0.805442	+	0.573650i
$232$	7.07328	−	2.57446i	0.464384	−	0.169022i
$233$	2.53521	+	14.3779i	0.166087	+	0.941929i	0.947936	+	0.318460i	$0.103166\pi$
$233$	2.53521	+	14.3779i	0.166087	+	0.941929i	−0.781849	+	0.623468i	$0.785723\pi$
$234$	−0.640816	−	1.76063i	−0.0418914	−	0.115096i
$235$	8.44369	+	14.6249i	0.550806	+	0.954023i
$236$	2.54894	−	4.41490i	0.165922	−	0.287386i
$237$	13.6137	+	2.40046i	0.884304	+	0.155927i
$238$	−5.98980	+	12.5810i	−0.388261	+	0.815502i
$239$	4.76668	+	8.25614i	0.308331	+	0.534045i	0.977997	−	0.208617i	$-0.0668962\pi$
$239$	4.76668	+	8.25614i	0.308331	+	0.534045i	−0.669666	+	0.742662i	$0.733563\pi$
$240$			3.85837i			0.249057i
$241$	15.1270	−	5.50580i	0.974419	−	0.354659i	0.194751	−	0.980853i	$-0.437610\pi$
$241$	15.1270	−	5.50580i	0.974419	−	0.354659i	0.779668	+	0.626193i	$0.215388\pi$
$242$	−13.6706	−	16.2920i	−0.878783	−	1.04729i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	8.19879	+	9.77094i	0.524874	+	0.625520i
$245$	−4.26312	−	26.6700i	−0.272361	−	1.70389i
$246$		−	6.88310i		−	0.438851i
$247$	4.02956	+	7.10361i	0.256395	+	0.451992i
$248$	−6.01113	−	3.47053i	−0.381707	−	0.220379i
$249$	1.83585	−	5.04397i	0.116343	−	0.319648i
$250$	−17.7189	−	6.44914i	−1.12064	−	0.407879i
$251$	3.29977	+	9.06604i	0.208280	+	0.572244i	0.999213	−	0.0396583i	$-0.0126269\pi$
$251$	3.29977	+	9.06604i	0.208280	+	0.572244i	−0.790934	+	0.611902i	$0.790405\pi$
$252$	−2.15504	−	1.53486i	−0.135755	−	0.0966870i
$253$	−17.6565	−	14.8156i	−1.11006	−	0.931447i
$254$	4.56558			0.286470
$255$	−20.3204			−1.27252
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	12.7436	−	4.63828i	0.794922	−	0.289328i	0.0875417	−	0.996161i	$-0.472099\pi$
$257$	12.7436	−	4.63828i	0.794922	−	0.289328i	0.707381	+	0.706833i	$0.249877\pi$
$258$	−4.62616	+	2.67092i	−0.288012	+	0.166284i
$259$	0.182652	−	0.660452i	0.0113495	−	0.0410385i
$260$	4.64679	−	5.53783i	0.288182	−	0.343442i
$261$	−7.41287	+	1.30709i	−0.458845	+	0.0809068i
$262$	−0.0972127	+	0.551321i	−0.00600582	+	0.0340607i
$263$	1.85380	+	10.5134i	0.114310	+	0.648287i	0.987089	+	0.160171i	$0.0512045\pi$
$263$	1.85380	+	10.5134i	0.114310	+	0.648287i	−0.872779	+	0.488116i	$0.837684\pi$
$264$	3.65134	+	4.35149i	0.224724	+	0.267816i
$265$	−9.59774			−0.589585
$266$	10.3747	+	5.03651i	0.636111	+	0.308808i
$267$	4.81673			0.294779
$268$	7.77442	+	9.26520i	0.474899	+	0.565962i
$269$	1.39108	+	7.88919i	0.0848155	+	0.481013i	0.997396	+	0.0721161i	$0.0229752\pi$
$269$	1.39108	+	7.88919i	0.0848155	+	0.481013i	−0.912581	+	0.408897i	$0.865914\pi$
$270$	0.669999	−	3.79976i	0.0407749	−	0.231246i
$271$	25.2952	−	4.46022i	1.53657	−	0.270939i	0.659651	−	0.751572i	$-0.270704\pi$
$271$	25.2952	−	4.46022i	1.53657	−	0.270939i	0.876922	+	0.480633i	$0.159593\pi$
$272$	−3.38529	+	4.03444i	−0.205264	+	0.244624i
$273$	1.24459	+	4.79835i	0.0753260	+	0.290409i
$274$	12.5971	−	7.27292i	0.761017	−	0.439373i
$275$	−52.7760	+	19.2089i	−3.18251	+	1.15834i
$276$	3.10828	+	2.60816i	0.187097	+	0.156993i
$277$	−9.65840			−0.580317			−0.290159	−	0.956979i	$-0.593708\pi$
$277$	−9.65840			−0.580317			−0.290159	+	0.956979i	$0.593708\pi$
$278$	−22.4644			−1.34733
$279$	5.31716	+	4.46162i	0.318330	+	0.267110i
$280$	0.971175	−	10.1620i	0.0580388	−	0.607295i
$281$	4.36671	+	11.9974i	0.260496	+	0.715708i	0.999134	+	0.0416053i	$0.0132472\pi$
$281$	4.36671	+	11.9974i	0.260496	+	0.715708i	−0.738638	+	0.674103i	$0.764531\pi$
$282$	−4.11286	−	1.49696i	−0.244917	−	0.0891426i
$283$	−0.206612	+	0.567661i	−0.0122818	+	0.0337439i	−0.945682	−	0.325093i	$-0.894604\pi$
$283$	−0.206612	+	0.567661i	−0.0122818	+	0.0337439i	0.933400	+	0.358837i	$0.116827\pi$
$284$	−3.07067	−	1.77285i	−0.182211	−	0.105200i
$285$	−0.127892	+	16.8178i	−0.00757565	+	0.996199i
$286$		−	10.6430i		−	0.629336i
$287$	−1.73252	+	18.1284i	−0.102267	+	1.07008i
$288$	−0.642788	−	0.766044i	−0.0378766	−	0.0451396i
$289$	−8.22494	−	6.90154i	−0.483820	−	0.405973i
$290$	−18.6684	−	22.2481i	−1.09625	−	1.30645i
$291$	−16.3114	+	5.93686i	−0.956191	+	0.348025i
$292$			0.856534i			0.0501249i
$293$	−5.45219	−	9.44347i	−0.318520	−	0.551693i	0.661659	−	0.749805i	$-0.269853\pi$
$293$	−5.45219	−	9.44347i	−0.318520	−	0.551693i	−0.980179	+	0.198111i	$0.936519\pi$
$294$	5.28951	+	4.58487i	0.308491	+	0.267395i
$295$	−19.3707	−	3.41558i	−1.12781	−	0.198863i
$296$	0.129499	−	0.224299i	0.00752697	−	0.0130371i
$297$	−2.84024	−	4.91943i	−0.164807	−	0.285454i
$298$	0.311113	+	0.854775i	0.0180223	+	0.0495158i
$299$	−1.32013	−	7.48686i	−0.0763454	−	0.432976i
$300$	9.29078	−	3.38157i	0.536403	−	0.195235i
$301$	12.8564	−	5.87010i	0.741033	−	0.338347i
$302$	1.48493	+	8.42148i	0.0854483	+	0.484602i
$303$	5.33752	−	3.08162i	0.306632	−	0.177034i
$304$	3.31771	+	2.82716i	0.190284	+	0.162149i
$305$	24.6069	−	42.6204i	1.40899	−	2.44043i
$306$	4.03444	−	3.38529i	0.230633	−	0.193524i
$307$	6.15809	−	5.16725i	0.351461	−	0.294910i	−0.449916	−	0.893071i	$-0.648546\pi$
$307$	6.15809	−	5.16725i	0.351461	−	0.294910i	0.801376	+	0.598161i	$0.204102\pi$
$308$	−8.52141	−	12.3798i	−0.485553	−	0.705405i
$309$	11.3295	+	4.12360i	0.644513	+	0.234584i
$310$	−4.65050	+	26.3743i	−0.264131	+	1.49796i
$311$	0.323938	−	0.187026i	0.0183688	−	0.0106052i	−0.490787	−	0.871279i	$-0.663291\pi$
$311$	0.323938	−	0.187026i	0.0183688	−	0.0106052i	0.509156	+	0.860674i	$0.329958\pi$
$312$			1.87362i			0.106073i
$313$	7.08564	+	19.4676i	0.400504	+	1.10038i	0.962036	+	0.272921i	$0.0879899\pi$
$313$	7.08564	+	19.4676i	0.400504	+	1.10038i	−0.561532	+	0.827455i	$0.689788\pi$
$314$	−0.131179	+	0.743954i	−0.00740287	+	0.0419837i
$315$	−2.72103	+	9.83897i	−0.153313	+	0.554363i
$316$	−11.9717	−	6.91185i	−0.673459	−	0.388822i
$317$	−2.52980	−	0.446071i	−0.142087	−	0.0250539i	0.102152	−	0.994769i	$-0.467427\pi$
$317$	−2.52980	−	0.446071i	−0.142087	−	0.0250539i	−0.244239	+	0.969715i	$0.578538\pi$
$318$	1.90554	−	1.59894i	0.106858	−	0.0896642i
$319$	−42.1086	−	7.42489i	−2.35763	−	0.415714i
$320$	1.31964	−	3.62568i	0.0737702	−	0.202682i
$321$	8.61295	−	1.51870i	0.480728	−	0.0847653i
$322$	−7.52996	−	7.65162i	−0.419628	−	0.426408i
$323$	−14.8895	+	17.4730i	−0.828471	+	0.972223i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−17.4074	−	6.33577i	−0.965588	−	0.351445i
$326$	−12.5322	+	2.20977i	−0.694095	+	0.122388i
$327$	10.8151	−	12.8890i	0.598079	−	0.712762i
$328$	−2.35416	+	6.46800i	−0.129987	+	0.357136i
$329$	10.4555	+	4.97785i	0.576428	+	0.274438i
$330$	10.9587	−	18.9810i	0.603256	−	1.04487i
$331$	−4.69971	−	2.71338i	−0.258320	−	0.149141i	0.365248	−	0.930910i	$-0.380984\pi$
$331$	−4.69971	−	2.71338i	−0.258320	−	0.149141i	−0.623568	+	0.781769i	$0.714317\pi$
$332$	−3.45028	+	4.11188i	−0.189359	+	0.225669i
$333$	−0.166481	+	0.198404i	−0.00912308	+	0.0108725i
$334$	−14.2473	−	8.22569i	−0.779578	−	0.450090i
$335$	23.3332	−	40.4143i	1.27483	−	2.20807i
$336$	1.50012	+	2.17936i	0.0818385	+	0.118894i
$337$	−8.18357	+	22.4842i	−0.445787	+	1.22479i	0.489843	+	0.871810i	$0.337054\pi$
$337$	−8.18357	+	22.4842i	−0.445787	+	1.22479i	−0.935631	+	0.352980i	$0.885168\pi$
$338$	−6.09976	+	7.26942i	−0.331783	+	0.395404i
$339$	8.36981	−	1.47582i	0.454585	−	0.0801557i
$340$	19.0950	+	6.95000i	1.03557	+	0.376917i
$341$	19.7142	+	34.1460i	1.06759	+	1.84911i
$342$	−2.77637	−	3.36032i	−0.150129	−	0.181705i
$343$	−12.7772	−	13.4068i	−0.689905	−	0.723900i
$344$	5.26068	−	0.927599i	0.283637	−	0.0500128i
$345$	5.35454	−	14.7115i	0.288279	−	0.792040i
$346$	−0.402412	−	0.0709561i	−0.0216338	−	0.00381463i
$347$	7.30471	−	6.12938i	0.392137	−	0.329042i	−0.425308	−	0.905049i	$-0.639834\pi$
$347$	7.30471	−	6.12938i	0.392137	−	0.329042i	0.817445	+	0.576007i	$0.195390\pi$
$348$	7.41287	+	1.30709i	0.397372	+	0.0700674i
$349$	0.495855	+	0.286282i	0.0265425	+	0.0153243i	0.513213	−	0.858262i	$-0.328455\pi$
$349$	0.495855	+	0.286282i	0.0265425	+	0.0153243i	−0.486670	+	0.873586i	$0.661789\pi$
$350$	−25.3208	+	6.56766i	−1.35345	+	0.351056i
$351$	0.325351	−	1.84516i	0.0173659	−	0.0984871i
$352$	−1.94284	−	5.33790i	−0.103553	−	0.284511i
$353$		−	0.333567i		−	0.0177540i	−0.999961	−	0.00887698i	$-0.997174\pi$
$353$		−	0.333567i		−	0.0177540i	0.999961	−	0.00887698i	$-0.00282567\pi$
$354$	4.41490	−	2.54894i	0.234649	−	0.135475i
$355$	−2.37562	+	13.4728i	−0.126085	+	0.715063i
$356$	−4.52625	−	1.64742i	−0.239891	−	0.0873130i
$357$	−11.4778	+	7.90053i	−0.607470	+	0.418140i
$358$	−15.2747	+	12.8170i	−0.807294	+	0.677400i
$359$	4.86123	−	4.07906i	0.256566	−	0.215284i	−0.505428	−	0.862869i	$-0.668665\pi$
$359$	4.86123	−	4.07906i	0.256566	−	0.215284i	0.761994	+	0.647585i	$0.224221\pi$
$360$	−1.92919	+	3.34145i	−0.101677	+	0.176110i
$361$	14.3674	+	12.4329i	0.756180	+	0.654363i
$362$	15.0859	−	8.70987i	0.792899	−	0.457780i
$363$	−3.69311	−	20.9446i	−0.193838	−	1.09931i
$364$	0.471601	−	4.93465i	0.0247186	−	0.258646i
$365$	3.10552	−	1.13032i	0.162550	−	0.0591635i
$366$	2.21489	+	12.5613i	0.115774	+	0.656588i
$367$	−0.534909	−	1.46965i	−0.0279220	−	0.0767152i	0.924948	−	0.380093i	$-0.124108\pi$
$367$	−0.534909	−	1.46965i	−0.0279220	−	0.0767152i	−0.952870	+	0.303377i	$0.901886\pi$
$368$	−2.02879	−	3.51396i	−0.105758	−	0.183178i
$369$	3.44155	−	5.96094i	0.179160	−	0.310314i
$370$	−0.984128	−	0.173528i	−0.0511624	−	0.00902131i
$371$	−5.42119	+	3.73158i	−0.281454	+	0.193734i
$372$	−3.47053	−	6.01113i	−0.179938	−	0.311662i
$373$			0.0921985i			0.00477386i	0.999997	+	0.00238693i	$0.000759784\pi$
$373$			0.0921985i			0.00477386i	−0.999997	+	0.00238693i	$0.999240\pi$
$374$	28.1125	−	10.2321i	1.45366	−	0.529089i
$375$	−12.1204	−	14.4446i	−0.625896	−	0.745914i
$376$	3.35283	+	2.81336i	0.172909	+	0.145088i
$377$	−9.06534	−	10.8037i	−0.466889	−	0.556416i
$378$	−1.09889	−	2.40675i	−0.0565209	−	0.123790i
$379$			9.97846i			0.512559i	0.966603	+	0.256280i	$0.0824968\pi$
$379$			9.97846i			0.512559i	−0.966603	+	0.256280i	$0.917503\pi$
$380$	5.87220	−	15.7598i	0.301237	−	0.808460i
$381$	3.95391	+	2.28279i	0.202565	+	0.116951i
$382$	8.77436	−	24.1073i	0.448935	−	1.23344i
$383$	−14.5985	−	5.31344i	−0.745951	−	0.271504i	−0.0590499	−	0.998255i	$-0.518807\pi$
$383$	−14.5985	−	5.31344i	−0.745951	−	0.271504i	−0.686901	+	0.726751i	$0.741029\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	−33.6401	+	47.2329i	−1.71446	+	2.40721i
$386$	−5.45618	−	4.57828i	−0.277712	−	0.233028i
$387$	−5.34183			−0.271541
$388$	17.3582			0.881230
$389$	−25.8656	−	21.7039i	−1.31144	−	1.10043i	−0.988045	−	0.154165i	$-0.950731\pi$
$389$	−25.8656	−	21.7039i	−1.31144	−	1.10043i	−0.323395	−	0.946264i	$-0.604824\pi$
$390$	6.79315	−	2.47251i	0.343985	−	0.125200i
$391$	18.5066	−	10.6848i	0.935918	−	0.540352i
$392$	−3.40240	−	6.11749i	−0.171847	−	0.308980i
$393$	−0.359849	+	0.428851i	−0.0181520	+	0.0216327i
$394$	−6.96922	+	1.22886i	−0.351104	+	0.0619092i
$395$	−9.26187	+	52.5267i	−0.466015	+	2.64290i
$396$	0.986403	+	5.59417i	0.0495686	+	0.281118i
$397$	21.7136	+	25.8772i	1.08977	+	1.29874i	0.951264	+	0.308378i	$0.0997863\pi$
$397$	21.7136	+	25.8772i	1.08977	+	1.29874i	0.138508	+	0.990361i	$0.455769\pi$
$398$	25.3509			1.27073
$399$	6.46646	+	9.54908i	0.323728	+	0.478052i
$400$	−9.88704			−0.494352
$401$	5.35503	+	6.38188i	0.267417	+	0.318696i	0.882997	−	0.469379i	$-0.155522\pi$
$401$	5.35503	+	6.38188i	0.267417	+	0.318696i	−0.615579	+	0.788075i	$0.711078\pi$
$402$	2.10025	+	11.9111i	0.104751	+	0.594072i
$403$	−2.25828	+	12.8073i	−0.112493	+	0.637978i
$404$	−6.06960	+	1.07023i	−0.301974	+	0.0532462i
$405$	2.48011	−	2.95569i	0.123238	−	0.146869i
$406$	−19.1947	−	5.30841i	−0.952615	−	0.263452i
$407$	−1.27412	+	0.735615i	−0.0631559	+	0.0364631i
$408$	−4.94897	+	1.80128i	−0.245010	+	0.0891765i
$409$	−7.89096	−	6.62130i	−0.390183	−	0.327402i	0.426502	−	0.904487i	$-0.359746\pi$
$409$	−7.89096	−	6.62130i	−0.390183	−	0.327402i	−0.816684	+	0.577084i	$0.804190\pi$
$410$	26.5576			1.31158
$411$	14.5458			0.717494
$412$	−9.23590	−	7.74984i	−0.455020	−	0.381807i
$413$	−12.2693	+	5.60203i	−0.603735	+	0.275658i
$414$	1.38777	+	3.81287i	0.0682053	+	0.187393i
$415$	19.4615	+	7.08341i	0.955328	+	0.347711i
$416$	0.640816	−	1.76063i	0.0314186	−	0.0863218i
$417$	−19.4548	−	11.2322i	−0.952704	−	0.550044i
$418$	−8.29145	−	23.3311i	−0.405548	−	1.14116i
$419$		−	4.85425i		−	0.237145i	−0.992945	−	0.118573i	$-0.962168\pi$
$419$		−	4.85425i		−	0.237145i	0.992945	−	0.118573i	$-0.0378319\pi$
$420$	5.92206	−	8.31496i	0.288967	−	0.405728i
$421$	8.94725	+	10.6629i	0.436062	+	0.519679i	0.938661	−	0.344841i	$-0.112067\pi$
$421$	8.94725	+	10.6629i	0.436062	+	0.519679i	−0.502599	+	0.864520i	$0.667623\pi$
$422$	10.7642	+	9.03225i	0.523994	+	0.439683i
$423$	−2.81336	−	3.35283i	−0.136790	−	0.163020i
$424$	−2.33750	+	0.850779i	−0.113519	+	0.0413175i
$425$		−	52.0709i		−	2.52581i
$426$	−1.77285	−	3.07067i	−0.0858951	−	0.148775i
$427$	−2.67173	−	33.6408i	−0.129294	−	1.62799i
$428$	−8.61295	−	1.51870i	−0.416323	−	0.0734089i
$429$	5.32152	−	9.21715i	0.256925	−	0.445008i
$430$	−10.3054	−	17.8495i	−0.496970	−	0.860777i
$431$	10.4418	+	28.6886i	0.502965	+	1.38188i	0.888367	+	0.459135i	$0.151841\pi$
$431$	10.4418	+	28.6886i	0.502965	+	1.38188i	−0.385402	+	0.922749i	$0.625937\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	−12.5103	+	4.55339i	−0.601209	+	0.218822i	−0.624652	−	0.780903i	$-0.714759\pi$
$433$	−12.5103	+	4.55339i	−0.601209	+	0.218822i	0.0234434	+	0.999725i	$0.492537\pi$
$434$	7.62747	+	16.7054i	0.366130	+	0.801883i
$435$	−5.04324	−	28.6016i	−0.241805	−	1.37134i
$436$	−14.5712	+	8.41269i	−0.697834	+	0.402895i
$437$	−8.72655	−	15.3838i	−0.417447	−	0.735908i
$438$	−0.428267	+	0.741780i	−0.0204634	+	0.0354436i
$439$	6.18767	−	5.19207i	0.295321	−	0.247804i	−0.483072	−	0.875580i	$-0.660479\pi$
$439$	6.18767	−	5.19207i	0.295321	−	0.247804i	0.778394	+	0.627776i	$0.216035\pi$
$440$	−16.7897	+	14.0882i	−0.800417	+	0.671629i
$441$	2.28841	+	6.61537i	0.108972	+	0.315018i
$442$	9.27249	+	3.37491i	0.441047	+	0.160528i
$443$	2.01370	−	11.4202i	0.0956736	−	0.542592i	−0.898865	−	0.438225i	$-0.855607\pi$
$443$	2.01370	−	11.4202i	0.0956736	−	0.542592i	0.994539	−	0.104367i	$-0.0332816\pi$
$444$	0.224299	−	0.129499i	0.0106447	−	0.00614575i
$445$			18.5847i			0.881001i
$446$	4.02378	+	11.0552i	0.190531	+	0.523481i
$447$	−0.157956	+	0.895813i	−0.00747107	+	0.0423705i
$448$	−0.664270	−	2.56100i	−0.0313838	−	0.120996i
$449$	−16.0910	−	9.29014i	−0.759381	−	0.438429i	0.0696927	−	0.997569i	$-0.477798\pi$
$449$	−16.0910	−	9.29014i	−0.759381	−	0.438429i	−0.829073	+	0.559140i	$0.811131\pi$
$450$	9.73683	+	1.71687i	0.458999	+	0.0809339i
$451$	29.9518	−	25.1325i	1.41037	−	1.18344i
$452$	−8.36981	−	1.47582i	−0.393683	−	0.0694169i
$453$	−2.92475	+	8.03568i	−0.137417	+	0.377549i
$454$	−12.2059	+	2.15223i	−0.572851	+	0.101009i
$455$	−18.5138	+	4.80209i	−0.867941	+	0.225125i
$456$	1.45964	+	4.10724i	0.0683539	+	0.192339i
$457$	−0.163729	−	0.283587i	−0.00765892	−	0.0132656i	0.862171	−	0.506618i	$-0.169105\pi$
$457$	−0.163729	−	0.283587i	−0.00765892	−	0.0132656i	−0.869829	+	0.493353i	$0.835771\pi$
$458$	10.8189	+	3.93775i	0.505532	+	0.183999i
$459$	5.18657	−	0.914532i	0.242088	−	0.0426867i
$460$	−10.0633	+	11.9929i	−0.469202	+	0.559173i
$461$	−7.40444	+	20.3435i	−0.344859	+	0.947492i	0.639104	+	0.769120i	$0.279305\pi$
$461$	−7.40444	+	20.3435i	−0.344859	+	0.947492i	−0.983963	+	0.178372i	$0.942917\pi$
$462$	−1.18986	−	14.9819i	−0.0553571	−	0.697023i
$463$	12.5593	−	21.7534i	0.583681	−	1.01097i	−0.411358	−	0.911474i	$-0.634945\pi$
$463$	12.5593	−	21.7534i	0.583681	−	1.01097i	0.995038	−	0.0994910i	$-0.0317214\pi$
$464$	−6.51877	−	3.76361i	−0.302626	−	0.174721i
$465$	−17.2146	+	20.5156i	−0.798308	+	0.951387i
$466$	9.38452	−	11.1840i	0.434729	−	0.518090i
$467$	−10.9614	−	6.32856i	−0.507232	−	0.292851i	0.224463	−	0.974483i	$-0.427937\pi$
$467$	−10.9614	−	6.32856i	−0.507232	−	0.292851i	−0.731695	+	0.681632i	$0.761271\pi$
$468$	−0.936810	+	1.62260i	−0.0433041	+	0.0750048i
$469$	−2.53344	−	31.8995i	−0.116983	−	1.47298i
$470$	5.77582	−	15.8689i	0.266419	−	0.731980i
$471$	−0.485581	+	0.578693i	−0.0223744	+	0.0266648i
$472$	−5.02044	+	0.885239i	−0.231085	+	0.0407464i
$473$	−28.5141	−	10.3783i	−1.31108	−	0.477195i
$474$	−6.91185	−	11.9717i	−0.317472	−	0.549877i
$475$	−43.0954	−	0.327721i	−1.97735	−	0.0150369i
$476$	13.4877	−	3.49843i	0.618210	−	0.160350i
$477$	2.44972	−	0.431952i	0.112165	−	0.0197777i
$478$	3.26060	−	8.95844i	0.149137	−	0.409749i
$479$	16.2516	+	2.86560i	0.742555	+	0.130932i	0.532112	−	0.846674i	$-0.321398\pi$
$479$	16.2516	+	2.86560i	0.742555	+	0.130932i	0.210442	+	0.977606i	$0.432510\pi$
$480$	2.95569	−	2.48011i	0.134908	−	0.113201i
$481$	−0.477891	−	0.0842651i	−0.0217900	−	0.00384216i
$482$	−13.9412	−	8.04893i	−0.635003	−	0.366619i
$483$	−2.69532	−	10.3915i	−0.122642	−	0.472828i
$484$	−3.69311	+	20.9446i	−0.167868	+	0.952030i
$485$	−22.9066	−	62.9354i	−1.04014	−	2.85775i
$486$			1.00000i			0.0453609i
$487$	−3.83713	+	2.21537i	−0.173877	+	0.100388i	−0.584413	−	0.811457i	$-0.698675\pi$
$487$	−3.83713	+	2.21537i	−0.173877	+	0.100388i	0.410536	+	0.911845i	$0.365342\pi$
$488$	2.21489	−	12.5613i	0.100263	−	0.568622i
$489$	−11.9581	−	4.35239i	−0.540764	−	0.196822i
$490$	−17.6902	+	20.4089i	−0.799160	+	0.921981i
$491$	15.0432	−	12.6228i	0.678891	−	0.569657i	−0.236791	−	0.971561i	$-0.576096\pi$
$491$	15.0432	−	12.6228i	0.678891	−	0.569657i	0.915682	+	0.401903i	$0.131651\pi$
$492$	−5.27276	+	4.42437i	−0.237714	+	0.199466i
$493$	19.8214	−	34.3316i	0.892710	−	1.54622i
$494$	2.85153	−	7.65293i	0.128296	−	0.344322i
$495$	18.9810	−	10.9587i	0.853133	−	0.492556i
$496$	1.20530	+	6.83560i	0.0541196	+	0.306928i
$497$	3.89635	+	8.53363i	0.174775	+	0.382786i
$498$	−5.04397	+	1.83585i	−0.226026	+	0.0822666i
$499$	−6.36420	−	36.0932i	−0.284901	−	1.61575i	−0.705640	−	0.708570i	$-0.749341\pi$
$499$	−6.36420	−	36.0932i	−0.284901	−	1.61575i	0.420740	−	0.907181i	$-0.361770\pi$
$500$	6.44914	+	17.7189i	0.288414	+	0.792412i
$501$	−8.22569	−	14.2473i	−0.367497	−	0.636523i
$502$	4.82394	−	8.35531i	0.215303	−	0.372916i
$503$	7.72064	+	1.36136i	0.344246	+	0.0606999i	0.343099	−	0.939299i	$-0.388524\pi$
$503$	7.72064	+	1.36136i	0.344246	+	0.0606999i	0.00114782	+	0.999999i	$0.499635\pi$
$504$	0.209464	+	2.63745i	0.00933028	+	0.117481i
$505$	11.8900	+	20.5941i	0.529099	+	0.916427i
$506$			23.0489i			1.02465i
$507$	−8.91726	+	3.24562i	−0.396029	+	0.144143i
$508$	−2.93470	−	3.49744i	−0.130206	−	0.155174i
$509$	−15.7071	−	13.1798i	−0.696204	−	0.584184i	0.224487	−	0.974477i	$-0.427929\pi$
$509$	−15.7071	−	13.1798i	−0.696204	−	0.584184i	−0.920691	+	0.390293i	$0.872374\pi$
$510$	13.0617	+	15.5664i	0.578383	+	0.689290i
$511$	1.31466	−	1.84587i	0.0581571	−	0.0816563i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.724250	−	4.29831i	−0.0319764	−	0.189775i
$514$	−11.7445	−	6.78072i	−0.518030	−	0.299085i
$515$	−15.9104	+	43.7135i	−0.701096	+	1.92625i
$516$	5.01968	+	1.82701i	0.220979	+	0.0804298i
$517$	−8.50343	−	23.3630i	−0.373980	−	1.02750i
$518$	−0.623342	+	0.284611i	−0.0273881	+	0.0125051i
$519$	−0.313021	−	0.262656i	−0.0137401	−	0.0115293i
$520$	−7.22912			−0.317018
$521$	14.4927			0.634937			0.317468	−	0.948269i	$-0.397167\pi$
$521$	14.4927			0.634937			0.317468	+	0.948269i	$0.397167\pi$
$522$	5.76619	+	4.83841i	0.252379	+	0.211771i
$523$	−0.775182	+	0.282143i	−0.0338964	+	0.0123373i	−0.358913	−	0.933371i	$-0.616852\pi$
$523$	−0.775182	+	0.282143i	−0.0338964	+	0.0123373i	0.325016	+	0.945708i	$0.394630\pi$
$524$	0.484823	−	0.279913i	0.0211796	−	0.0122280i
$525$	−25.2123	−	6.97262i	−1.10035	−	0.304310i
$526$	6.86216	−	8.17801i	0.299205	−	0.356578i
$527$	−36.0003	+	6.34782i	−1.56820	+	0.276515i
$528$	0.986403	−	5.59417i	0.0429277	−	0.243455i
$529$	−1.13498	−	6.43678i	−0.0493469	−	0.279860i
$530$	6.16931	+	7.35230i	0.267978	+	0.319363i
$531$	5.09789			0.221230
$532$	−2.81051	−	11.1849i	−0.121851	−	0.484925i
$533$	12.8963			0.558601
$534$	−3.09613	−	3.68983i	−0.133983	−	0.159675i
$535$	5.85969	+	33.2320i	0.253337	+	1.43674i
$536$	2.10025	−	11.9111i	0.0907170	−	0.514482i
$537$	−19.6368	+	3.46250i	−0.847391	+	0.149418i
$538$	5.14931	−	6.13670i	0.222002	−	0.264572i
$539$	−0.637259	+	39.7582i	−0.0274487	+	1.71251i
$540$	−3.34145	+	1.92919i	−0.143793	+	0.0830190i
$541$	27.3662	−	9.96047i	1.17656	−	0.428234i	0.321576	−	0.946884i	$-0.395787\pi$
$541$	27.3662	−	9.96047i	1.17656	−	0.428234i	0.854987	+	0.518650i	$0.173565\pi$
$542$	−19.6762	−	16.5103i	−0.845163	−	0.709176i
$543$	17.4197			0.747552
$544$	5.26658			0.225803
$545$	49.7305	+	41.7289i	2.13022	+	1.78747i
$546$	2.87574	−	4.03773i	0.123070	−	0.172799i
$547$	−3.16328	−	8.69104i	−0.135252	−	0.371602i	0.853515	−	0.521069i	$-0.174467\pi$
$547$	−3.16328	−	8.69104i	−0.135252	−	0.371602i	−0.988767	+	0.149467i	$0.952244\pi$
$548$	−13.6686	−	4.97497i	−0.583895	−	0.212520i
$549$	−4.36248	+	11.9858i	−0.186186	+	0.511543i
$550$	48.6386	+	28.0815i	2.07396	+	1.19740i
$551$	−28.2891	−	16.6208i	−1.20516	−	0.708071i
$552$		−	4.05758i		−	0.172702i
$553$	15.1907	+	33.2701i	0.645976	+	1.41479i
$554$	6.20830	+	7.39877i	0.263765	+	0.314343i
$555$	−0.765516	−	0.642344i	−0.0324943	−	0.0272660i
$556$	14.4399	+	17.2087i	0.612386	+	0.729813i
$557$	28.8028	−	10.4834i	1.22042	−	0.444195i	0.350111	−	0.936708i	$-0.386144\pi$
$557$	28.8028	−	10.4834i	1.22042	−	0.444195i	0.870305	+	0.492513i	$0.163922\pi$
$558$		−	6.94105i		−	0.293838i
$559$	−5.00428	−	8.66767i	−0.211659	−	0.366603i
$560$	−8.40880	+	5.78804i	−0.355337	+	0.244589i
$561$	29.4622	+	5.19498i	1.24389	+	0.219332i
$562$	6.38371	−	11.0569i	0.269281	−	0.466408i
$563$	−17.2335	−	29.8492i	−0.726304	−	1.25800i	−0.958435	−	0.285311i	$-0.907903\pi$
$563$	−17.2335	−	29.8492i	−0.726304	−	1.25800i	0.232131	−	0.972684i	$-0.425430\pi$
$564$	1.49696	+	4.11286i	0.0630333	+	0.173183i
$565$	5.69427	+	32.2938i	0.239560	+	1.35861i
$566$	0.567661	−	0.206612i	0.0238606	−	0.00868453i
$567$	0.251706	−	2.63375i	0.0105707	−	0.110607i
$568$	0.615706	+	3.49184i	0.0258344	+	0.146514i
$569$	−7.57909	+	4.37579i	−0.317732	+	0.183443i	−0.650381	−	0.759608i	$-0.725391\pi$
$569$	−7.57909	+	4.37579i	−0.317732	+	0.183443i	0.332649	+	0.943051i	$0.392057\pi$
$570$	12.9654	−	10.7123i	0.543059	−	0.448688i
$571$	−9.11435	+	15.7865i	−0.381424	+	0.660645i	−0.991266	−	0.131878i	$-0.957899\pi$
$571$	−9.11435	+	15.7865i	−0.381424	+	0.660645i	0.609842	+	0.792523i	$0.291233\pi$
$572$	−8.15304	+	6.84122i	−0.340896	+	0.286046i
$573$	19.6525	−	16.4904i	0.820995	−	0.688896i
$574$	15.0008	−	10.3255i	0.626120	−	0.430978i
$575$	37.6980	+	13.7210i	1.57212	+	0.572204i
$576$	−0.173648	+	0.984808i	−0.00723534	+	0.0410337i
$577$	−38.3126	+	22.1198i	−1.59497	+	0.920859i	−0.602540	+	0.798089i	$0.705844\pi$
$577$	−38.3126	+	22.1198i	−1.59497	+	0.920859i	−0.992435	+	0.122770i	$0.960822\pi$
$578$			10.7369i			0.446596i
$579$	−2.43605	−	6.69300i	−0.101239	−	0.278151i
$580$	−5.04324	+	28.6016i	−0.209409	+	1.18762i
$581$	13.7466	−	3.56559i	0.570307	−	0.147925i
$582$	15.0327	+	8.67911i	0.623124	+	0.359761i
$583$	13.9156	+	2.45369i	0.576324	+	0.101621i
$584$	0.656143	−	0.550569i	0.0271514	−	0.0227827i
$585$	7.11930	+	1.25532i	0.294347	+	0.0519013i
$586$	−3.72952	+	10.2468i	−0.154065	+	0.423290i
$587$	−19.6523	+	3.46523i	−0.811137	+	0.143025i	−0.563808	−	0.825906i	$-0.690664\pi$
$587$	−19.6523	+	3.46523i	−0.811137	+	0.143025i	−0.247329	+	0.968931i	$0.579553\pi$
$588$	0.112184	−	6.99910i	0.00462640	−	0.288638i
$589$	5.02706	+	29.8348i	0.207136	+	1.22932i
$590$	9.83478	+	17.0343i	0.404891	+	0.701293i
$591$	−6.64996	−	2.42039i	−0.273543	−	0.0995614i
$592$	−0.255063	+	0.0449745i	−0.0104830	+	0.00184844i
$593$	−8.82745	+	10.5201i	−0.362500	+	0.432011i	−0.916210	−	0.400699i	$-0.868767\pi$
$593$	−8.82745	+	10.5201i	−0.362500	+	0.432011i	0.553710	+	0.832710i	$0.313212\pi$
$594$	−1.94284	+	5.33790i	−0.0797155	+	0.219017i
$595$	−30.4832	−	44.2856i	−1.24969	−	1.81553i
$596$	0.454816	−	0.787765i	0.0186300	−	0.0322681i
$597$	21.9546	+	12.6755i	0.898541	+	0.518773i
$598$	−4.88670	+	5.82374i	−0.199832	+	0.238150i
$599$	1.70146	−	2.02772i	0.0695197	−	0.0828504i	−0.730164	−	0.683272i	$-0.760556\pi$
$599$	1.70146	−	2.02772i	0.0695197	−	0.0828504i	0.799683	+	0.600422i	$0.205001\pi$
$600$	−8.56243	−	4.94352i	−0.349560	−	0.201818i
$601$	6.50673	−	11.2700i	0.265415	−	0.459712i	−0.702257	−	0.711923i	$-0.747824\pi$
$601$	6.50673	−	11.2700i	0.265415	−	0.459712i	0.967672	+	0.252211i	$0.0811577\pi$
$602$	−12.7607	−	6.07538i	−0.520088	−	0.247614i
$603$	−4.13668	+	11.3654i	−0.168459	+	0.462837i
$604$	5.49673	−	6.55075i	0.223659	−	0.266546i
$605$	80.8123	−	14.2494i	3.28549	−	0.579320i
$606$	−5.79155	−	2.10795i	−0.235266	−	0.0856297i
$607$	3.55664	+	6.16028i	0.144359	+	0.250038i	0.929134	−	0.369744i	$-0.120555\pi$
$607$	3.55664	+	6.16028i	0.144359	+	0.250038i	−0.784774	+	0.619782i	$0.787221\pi$
$608$	0.0331466	−	4.35877i	0.00134427	−	0.176772i
$609$	−13.9689	−	14.1946i	−0.566047	−	0.575192i
$610$	−48.4661	+	8.54588i	−1.96233	+	0.346012i
$611$	2.80473	−	7.70594i	0.113467	−	0.311749i
$612$	−5.18657	−	0.914532i	−0.209655	−	0.0369678i
$613$	−15.5088	+	13.0134i	−0.626394	+	0.525607i	−0.899806	−	0.436290i	$-0.856292\pi$
$613$	−15.5088	+	13.0134i	−0.626394	+	0.525607i	0.273412	+	0.961897i	$0.411848\pi$
$614$	−7.91668	−	1.39592i	−0.319491	−	0.0563349i
$615$	22.9995	+	13.2788i	0.927431	+	0.535452i
$616$	−4.00603	+	14.4854i	−0.161407	+	0.583632i
$617$	1.17412	−	6.65874i	0.0472681	−	0.268071i	−0.952010	−	0.306068i	$-0.900987\pi$
$617$	1.17412	−	6.65874i	0.0472681	−	0.268071i	0.999278	+	0.0379969i	$0.0120977\pi$
$618$	−4.12360	−	11.3295i	−0.165876	−	0.455740i
$619$			41.9576i			1.68642i	0.537584	+	0.843210i	$0.319337\pi$
$619$			41.9576i			1.68642i	−0.537584	+	0.843210i	$0.680663\pi$
$620$	23.1932	−	13.3906i	0.931460	−	0.537779i
$621$	−0.704591	+	3.99593i	−0.0282742	+	0.160351i
$622$	−0.351493	−	0.127933i	−0.0140936	−	0.00512965i
$623$	7.22570	+	10.4974i	0.289491	+	0.420570i
$624$	1.43528	−	1.20434i	0.0574570	−	0.0482122i
$625$	17.8629	−	14.9888i	0.714516	−	0.599550i
$626$	10.3585	−	17.9415i	0.414010	−	0.717086i
$627$	4.48494	−	24.3510i	0.179111	−	0.972486i
$628$	0.654222	−	0.377715i	0.0261063	−	0.0150725i
$629$	−0.236862	−	1.34331i	−0.00944430	−	0.0535613i
$630$	9.28613	−	4.23993i	0.369968	−	0.168923i
$631$	3.57809	−	1.30232i	0.142442	−	0.0518445i	−0.269816	−	0.962912i	$-0.586963\pi$
$631$	3.57809	−	1.30232i	0.142442	−	0.0518445i	0.412257	+	0.911067i	$0.364741\pi$
$632$	2.40046	+	13.6137i	0.0954851	+	0.541523i
$633$	4.80596	+	13.2043i	0.191020	+	0.524822i
$634$	1.28441	+	2.22466i	0.0510105	+	0.0883527i
$635$	−8.80786	+	15.2557i	−0.349529	+	0.605402i
$636$	−2.44972	−	0.431952i	−0.0971377	−	0.0171280i
$637$	−8.59031	+	9.91053i	−0.340360	+	0.392670i
$638$	21.3791	+	37.0297i	0.846407	+	1.46602i
$639$		−	3.54571i		−	0.140266i
$640$	−3.62568	+	1.31964i	−0.143318	+	0.0521634i
$641$	−14.6441	−	17.4521i	−0.578406	−	0.689318i	0.394927	−	0.918712i	$-0.370770\pi$
$641$	−14.6441	−	17.4521i	−0.578406	−	0.689318i	−0.973333	+	0.229395i	$0.926325\pi$
$642$	−6.69968	−	5.62170i	−0.264415	−	0.221871i
$643$	22.1722	+	26.4237i	0.874384	+	1.04205i	0.998758	+	0.0498154i	$0.0158633\pi$
$643$	22.1722	+	26.4237i	0.874384	+	1.04205i	−0.124374	+	0.992235i	$0.539692\pi$
$644$	−1.02132	+	10.6866i	−0.0402455	+	0.421113i
$645$		−	20.6108i		−	0.811549i
$646$	22.9558	+	0.174569i	0.903185	+	0.00686833i
$647$	−22.3372	−	12.8964i	−0.878167	−	0.507010i	−0.00811328	−	0.999967i	$-0.502583\pi$
$647$	−22.3372	−	12.8964i	−0.878167	−	0.507010i	−0.870054	+	0.492957i	$0.835916\pi$
$648$	0.342020	−	0.939693i	0.0134358	−	0.0369146i
$649$	27.2120	+	9.90436i	1.06816	+	0.388780i
$650$	6.33577	+	17.4074i	0.248509	+	0.682774i
$651$	−1.74710	+	18.2810i	−0.0684744	+	0.716489i
$652$	9.74833	+	8.17982i	0.381774	+	0.320347i
$653$	−28.6304			−1.12039			−0.560197	−	0.828359i	$-0.689275\pi$
$653$	−28.6304			−1.12039			−0.560197	+	0.828359i	$0.689275\pi$
$654$	−16.8254			−0.657924
$655$	−1.65467	−	1.38843i	−0.0646532	−	0.0542505i
$656$	6.46800	−	2.35416i	0.252533	−	0.0919145i
$657$	−0.741780	+	0.428267i	−0.0289396	+	0.0167083i
$658$	−2.90739	−	11.2090i	−0.113342	−	0.436974i
$659$	−11.3425	+	13.5175i	−0.441842	+	0.526567i	−0.940300	−	0.340347i	$-0.889455\pi$
$659$	−11.3425	+	13.5175i	−0.441842	+	0.526567i	0.498458	+	0.866914i	$0.333900\pi$
$660$	−21.5844	+	3.80591i	−0.840172	+	0.148145i
$661$	3.29275	−	18.6741i	0.128073	−	0.726338i	−0.851362	−	0.524579i	$-0.824223\pi$
$661$	3.29275	−	18.6741i	0.128073	−	0.726338i	0.979435	−	0.201760i	$-0.0646660\pi$
$662$	0.942347	+	5.34432i	0.0366254	+	0.207713i
$663$	6.34275	+	7.55900i	0.246332	+	0.293567i
$664$	5.36768			0.208306
$665$	−36.8439	+	24.9500i	−1.42874	+	0.967521i
$666$	0.258998			0.0100360
$667$	19.6322	+	23.3968i	0.760162	+	0.905926i
$668$	2.85675	+	16.2014i	0.110531	+	0.626853i
$669$	−2.04293	+	11.5860i	−0.0789841	+	0.447941i
$670$	−45.9575	+	8.10355i	−1.77549	+	0.313067i
$671$	−46.5730	+	55.5035i	−1.79793	+	2.14269i
$672$	0.705228	−	2.55003i	0.0272048	−	0.0983695i
$673$	−38.8234	+	22.4147i	−1.49653	+	0.864024i	−0.999992	−	0.00398975i	$-0.998730\pi$
$673$	−38.8234	+	22.4147i	−1.49653	+	0.864024i	−0.496541	+	0.868013i	$0.665397\pi$
$674$	22.4842	−	8.18357i	0.866058	−	0.315219i
$675$	7.57391	+	6.35527i	0.291520	+	0.244614i
$676$	9.48955			0.364983
$677$	45.6771			1.75551			0.877757	−	0.479105i	$-0.159039\pi$
$677$	45.6771			1.75551			0.877757	+	0.479105i	$0.159039\pi$
$678$	−6.51055	−	5.46300i	−0.250036	−	0.209805i
$679$	−37.4077	−	26.6424i	−1.43558	−	1.02244i
$680$	−6.95000	−	19.0950i	−0.266520	−	0.732259i
$681$	−11.6467	−	4.23906i	−0.446303	−	0.162441i
$682$	13.4853	−	37.0506i	0.516380	−	1.41874i
$683$	6.08186	+	3.51136i	0.232716	+	0.134359i	0.611824	−	0.790994i	$-0.290436\pi$
$683$	6.08186	+	3.51136i	0.232716	+	0.134359i	−0.379108	+	0.925352i	$0.623769\pi$
$684$	−0.789536	+	4.28680i	−0.0301887	+	0.163910i
$685$			56.1233i			2.14436i
$686$	−2.05718	+	18.4057i	−0.0785435	+	0.702731i
$687$	7.40054	+	8.81962i	0.282348	+	0.336489i
$688$	−4.09208	−	3.43366i	−0.156009	−	0.130907i
$689$	2.99581	+	3.57026i	0.114131	+	0.136016i
$690$	−14.7115	+	5.35454i	−0.560057	+	0.203844i
$691$		−	50.3084i		−	1.91382i	−0.290381	−	0.956911i	$-0.593782\pi$
$691$		−	50.3084i		−	1.91382i	0.290381	−	0.956911i	$-0.406218\pi$
$692$	0.204310	+	0.353875i	0.00776670	+	0.0134523i
$693$	6.46052	−	13.5697i	0.245415	−	0.515469i
$694$	−9.39075	−	1.65584i	−0.356468	−	0.0628549i
$695$	43.3381	−	75.0637i	1.64391	−	2.84733i
$696$	−3.76361	−	6.51877i	−0.142659	−	0.247093i
$697$	12.3984	+	34.0643i	0.469622	+	1.29028i
$698$	−0.0994246	−	0.563865i	−0.00376328	−	0.0213426i
$699$	13.7192	−	4.99340i	0.518910	−	0.188868i
$700$	21.3070	+	15.1752i	0.805329	+	0.573569i
$701$	7.38646	+	41.8907i	0.278983	+	1.58219i	0.726019	+	0.687675i	$0.241368\pi$
$701$	7.38646	+	41.8907i	0.278983	+	1.58219i	−0.447036	+	0.894516i	$0.647520\pi$
$702$	−1.62260	+	0.936810i	−0.0612412	+	0.0353576i
$703$	−1.11325	+	0.187579i	−0.0419871	+	0.00707468i
$704$	−2.84024	+	4.91943i	−0.107045	+	0.185408i
$705$	12.9365	−	10.8550i	0.487216	−	0.408823i
$706$	−0.255527	+	0.214413i	−0.00961688	+	0.00806952i
$707$	14.7229	+	7.00958i	0.553712	+	0.263623i
$708$	−4.79045	−	1.74358i	−0.180036	−	0.0655278i
$709$	7.13289	−	40.4527i	0.267881	−	1.51923i	−0.492821	−	0.870131i	$-0.664034\pi$
$709$	7.13289	−	40.4527i	0.267881	−	1.51923i	0.760703	−	0.649101i	$-0.224855\pi$
$710$	11.8478	−	6.84033i	0.444640	−	0.256713i
$711$		−	13.8237i		−	0.518429i
$712$	1.64742	+	4.52625i	0.0617396	+	0.169628i
$713$	4.89060	−	27.7360i	0.183154	−	1.03872i
$714$	13.4299	+	3.71414i	0.502603	+	0.138998i
$715$	35.5632	+	20.5324i	1.32999	+	0.767869i
$716$	19.6368	+	3.46250i	0.733862	+	0.129400i
$717$	7.30298	−	6.12793i	0.272735	−	0.228852i
$718$	−6.24948	−	1.10195i	−0.233228	−	0.0411245i
$719$	2.77896	−	7.63514i	0.103638	−	0.284743i	−0.877026	−	0.480443i	$-0.840476\pi$
$719$	2.77896	−	7.63514i	0.103638	−	0.284743i	0.980664	+	0.195701i	$0.0626981\pi$
$720$	3.79976	−	0.669999i	0.141609	−	0.0249694i
$721$	8.00884	+	30.8770i	0.298265	+	1.14992i
$722$	0.288957	−	18.9978i	0.0107539	−	0.707025i
$723$	−8.04893	−	13.9412i	−0.299343	−	0.518477i
$724$	−16.3692	−	5.95790i	−0.608356	−	0.221424i
$725$	73.2914	−	12.9232i	2.72197	−	0.479957i
$726$	−13.6706	+	16.2920i	−0.507365	+	0.604655i
$727$	5.07450	−	13.9421i	0.188203	−	0.517082i	−0.809325	−	0.587361i	$-0.800167\pi$
$727$	5.07450	−	13.9421i	0.188203	−	0.517082i	0.997527	+	0.0702790i	$0.0223889\pi$
$728$	−4.08330	+	2.81066i	−0.151337	+	0.104170i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−2.86206	−	1.65241i	−0.105930	−	0.0611586i
$731$	18.0837	−	21.5513i	0.668849	−	0.797103i
$732$	8.19879	−	9.77094i	0.303036	−	0.361144i
$733$	−19.0946	−	11.0243i	−0.705274	−	0.407190i	0.104035	−	0.994574i	$-0.466825\pi$
$733$	−19.0946	−	11.0243i	−0.705274	−	0.407190i	−0.809309	+	0.587384i	$0.800158\pi$
$734$	−0.781985	+	1.35444i	−0.0288636	+	0.0499932i
$735$	−25.5246	+	8.82956i	−0.941488	+	0.325683i
$736$	−1.38777	+	3.81287i	−0.0511540	+	0.140544i
$737$	−44.1624	+	52.6307i	−1.62674	+	1.93868i
$738$	−6.77853	+	1.19524i	−0.249521	+	0.0439973i
$739$	−33.4900	−	12.1894i	−1.23195	−	0.448393i	−0.357685	−	0.933842i	$-0.616434\pi$
$739$	−33.4900	−	12.1894i	−1.23195	−	0.448393i	−0.874265	+	0.485449i	$0.838656\pi$
$740$	0.499655	+	0.865428i	0.0183677	+	0.0318138i
$741$	6.29596	−	5.20187i	0.231288	−	0.191095i
$742$	6.34323	+	1.75426i	0.232867	+	0.0644010i
$743$	28.9785	−	5.10970i	1.06312	−	0.187457i	0.385379	−	0.922758i	$-0.374071\pi$
$743$	28.9785	−	5.10970i	1.06312	−	0.187457i	0.677740	+	0.735302i	$0.262959\pi$
$744$	−2.37398	+	6.52246i	−0.0870343	+	0.239125i
$745$	−3.45638	−	0.609453i	−0.126632	−	0.0223286i
$746$	0.0706281	−	0.0592640i	0.00258588	−	0.00216981i
$747$	−5.28613	−	0.932087i	−0.193409	−	0.0341033i
$748$	−25.9086	−	14.9583i	−0.947312	−	0.546931i
$749$	16.2303	+	16.4925i	0.593042	+	0.602623i
$750$	−3.27431	+	18.5696i	−0.119561	+	0.678064i
$751$	11.8846	+	32.6528i	0.433676	+	1.19152i	0.943539	+	0.331261i	$0.107474\pi$
$751$	11.8846	+	32.6528i	0.433676	+	1.19152i	−0.509863	+	0.860256i	$0.670304\pi$
$752$		−	4.37681i		−	0.159606i
$753$	8.35531	−	4.82394i	0.304484	−	0.175794i
$754$	−2.44899	+	13.8889i	−0.0891869	+	0.505804i
$755$	−31.0046	−	11.2848i	−1.12837	−	0.410695i
$756$	−1.13732	+	2.38883i	−0.0413640	+	0.0868808i
$757$	−24.2785	+	20.3721i	−0.882419	+	0.740437i	−0.966675	−	0.256007i	$-0.917593\pi$
$757$	−24.2785	+	20.3721i	−0.882419	+	0.740437i	0.0842564	+	0.996444i	$0.473149\pi$
$758$	7.64395	−	6.41403i	0.277641	−	0.232968i
$759$	−11.5245	+	19.9610i	−0.418312	+	0.724537i
$760$	−15.8473	+	5.63184i	−0.574841	+	0.204288i
$761$	30.5586	−	17.6430i	1.10775	−	0.639560i	0.169504	−	0.985529i	$-0.445783\pi$
$761$	30.5586	−	17.6430i	1.10775	−	0.639560i	0.938246	+	0.345970i	$0.112450\pi$
$762$	−0.792805	−	4.49622i	−0.0287203	−	0.162881i
$763$	44.3138	+	4.23504i	1.60427	+	0.153319i
$764$	−24.1073	+	8.77436i	−0.872173	+	0.317445i
$765$	3.52861	+	20.0117i	0.127577	+	0.723525i
$766$	5.31344	+	14.5985i	0.191982	+	0.527467i
$767$	4.77575	+	8.27185i	0.172442	+	0.298679i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−20.4209	−	3.60076i	−0.736396	−	0.129847i	−0.207143	−	0.978311i	$-0.566417\pi$
$769$	−20.4209	−	3.60076i	−0.736396	−	0.129847i	−0.529253	+	0.848464i	$0.677528\pi$
$770$	57.8059	−	4.59091i	2.08318	−	0.165445i
$771$	−6.78072	−	11.7445i	−0.244201	−	0.422969i
$772$			7.12254i			0.256346i
$773$	−17.5974	+	6.40492i	−0.632934	+	0.230369i	−0.638508	−	0.769615i	$-0.720448\pi$
$773$	−17.5974	+	6.40492i	−0.632934	+	0.230369i	0.00557392	+	0.999984i	$0.498226\pi$
$774$	3.43366	+	4.09208i	0.123420	+	0.147087i
$775$	−52.5709	−	44.1122i	−1.88840	−	1.58456i
$776$	−11.1577	−	13.2972i	−0.400536	−	0.477341i
$777$	−0.682136	−	0.0651913i	−0.0244715	−	0.00233872i
$778$			33.7652i			1.21054i
$779$	28.2706	−	10.0469i	1.01290	−	0.359966i
$780$	−6.26060	−	3.61456i	−0.224166	−	0.129422i
$781$	6.88873	−	18.9266i	0.246498	−	0.677248i
$782$	−20.0808	−	7.30882i	−0.718088	−	0.261363i
$783$	2.57446	+	7.07328i	0.0920038	+	0.252778i
$784$	−2.49925	+	6.53863i	−0.0892590	+	0.233523i
$785$	−2.23281	−	1.87355i	−0.0796926	−	0.0668700i
$786$	0.559826			0.0199683
$787$	−46.9662			−1.67416			−0.837082	−	0.547078i	$-0.815740\pi$
$787$	−46.9662			−1.67416			−0.837082	+	0.547078i	$0.815740\pi$
$788$	5.42109	+	4.54884i	0.193118	+	0.162046i
$789$	10.0318	−	3.65128i	0.357142	−	0.129989i
$790$	46.1912	−	26.6685i	1.64341	−	0.948822i
$791$	15.7721	+	16.0269i	0.560792	+	0.569852i
$792$	3.65134	−	4.35149i	0.129745	−	0.154624i
$793$	−23.5351	+	4.14986i	−0.835754	+	0.147366i
$794$	5.86589	−	33.2671i	0.208173	−	1.18060i
$795$	1.66663	+	9.45193i	0.0591093	+	0.335226i
$796$	−16.2953	−	19.4200i	−0.577571	−	0.688322i
$797$	39.8428			1.41131			0.705653	−	0.708558i	$-0.250654\pi$
$797$	39.8428			1.41131			0.705653	+	0.708558i	$0.250654\pi$
$798$	3.15845	−	11.0916i	0.111808	−	0.392639i
$799$	23.0509			0.815481
$800$	6.35527	+	7.57391i	0.224693	+	0.267778i
$801$	−0.836416	−	4.74355i	−0.0295533	−	0.167605i
$802$	1.44665	−	8.20438i	0.0510831	−	0.289707i
$803$	−4.79160	+	0.844888i	−0.169092	+	0.0298154i
$804$	7.77442	−	9.26520i	0.274183	−	0.326758i
$805$	40.0942	−	10.3996i	1.41313	−	0.366537i
$806$	11.2626	−	6.50245i	0.396707	−	0.229039i
$807$	7.52778	−	2.73989i	0.264990	−	0.0964486i
$808$	4.72131	+	3.96165i	0.166095	+	0.139370i
$809$	−48.1977			−1.69454			−0.847271	−	0.531161i	$-0.821756\pi$
$809$	−48.1977			−1.69454			−0.847271	+	0.531161i	$0.821756\pi$
$810$	−3.85837			−0.135569
$811$	16.1773	+	13.5744i	0.568062	+	0.476660i	0.881002	−	0.473112i	$-0.156870\pi$
$811$	16.1773	+	13.5744i	0.568062	+	0.476660i	−0.312940	+	0.949773i	$0.601314\pi$
$812$	8.27161	+	18.1161i	0.290277	+	0.635752i
$813$	−8.78492	−	24.1364i	−0.308101	−	0.846500i
$814$	1.38250	+	0.503190i	0.0484567	+	0.0176368i
$815$	16.7932	−	46.1388i	0.588239	−	1.61617i
$816$	4.56099	+	2.63329i	0.159667	+	0.0921836i
$817$	−17.7226	−	15.1022i	−0.620037	−	0.528359i
$818$			10.3009i			0.360163i
$819$	4.50933	−	2.05891i	0.157569	−	0.0719440i
$820$	−17.0709	−	20.3443i	−0.596141	−	0.710453i
$821$	−1.62268	−	1.36159i	−0.0566321	−	0.0475200i	0.614032	−	0.789281i	$-0.289546\pi$
$821$	−1.62268	−	1.36159i	−0.0566321	−	0.0475200i	−0.670664	+	0.741761i	$0.733991\pi$
$822$	−9.34989	−	11.1428i	−0.326115	−	0.388648i
$823$	−12.1430	+	4.41969i	−0.423278	+	0.154061i	−0.544872	−	0.838519i	$-0.683422\pi$
$823$	−12.1430	+	4.41969i	−0.423278	+	0.154061i	0.121594	+	0.992580i	$0.461199\pi$
$824$			12.0566i			0.420012i
$825$	28.0815	+	48.6386i	0.977673	+	1.69338i
$826$	12.1780	+	5.79794i	0.423726	+	0.201736i
$827$	−49.4781	−	8.72433i	−1.72052	−	0.303375i	−0.775736	−	0.631058i	$-0.782621\pi$
$827$	−49.4781	−	8.72433i	−1.72052	−	0.303375i	−0.944788	+	0.327684i	$0.893732\pi$
$828$	2.02879	−	3.51396i	0.0705053	−	0.122119i
$829$	−11.3740	−	19.7003i	−0.395035	−	0.684221i	0.598070	−	0.801444i	$-0.295934\pi$
$829$	−11.3740	−	19.7003i	−0.395035	−	0.684221i	−0.993106	+	0.117222i	$0.962601\pi$
$830$	−7.08341	−	19.4615i	−0.245869	−	0.675519i
$831$	1.67716	+	9.51167i	0.0581802	+	0.329956i
$832$	−1.76063	+	0.640816i	−0.0610387	+	0.0222163i
$833$	−34.4363	−	13.1625i	−1.19315	−	0.456054i
$834$	3.90091	+	22.1231i	0.135077	+	0.766061i
$835$	54.9715	−	31.7378i	1.90237	−	1.09833i
$836$	−12.5430	+	21.3485i	−0.433809	+	0.738355i
$837$	3.47053	−	6.01113i	0.119959	−	0.207775i
$838$	−3.71857	+	3.12025i	−0.128456	+	0.107787i
$839$	−6.75599	+	5.66895i	−0.233243	+	0.195714i	−0.751916	−	0.659258i	$-0.770870\pi$
$839$	−6.75599	+	5.66895i	−0.233243	+	0.195714i	0.518674	+	0.854972i	$0.326426\pi$
$840$	−10.1763	+	0.808191i	−0.351114	+	0.0278852i
$841$	25.9911	+	9.46000i	0.896246	+	0.326207i
$842$	2.41709	−	13.7080i	0.0832983	−	0.472408i
$843$	11.0569	−	6.38371i	0.380820	−	0.219867i
$844$		−	14.0517i		−	0.483679i
$845$	−12.5228	−	34.4061i	−0.430797	−	1.18361i
$846$	−0.760026	+	4.31032i	−0.0261302	+	0.148192i
$847$	40.1059	−	39.4682i	1.37805	−	1.35614i
$848$	2.15425	+	1.24376i	0.0739772	+	0.0427107i
$849$	0.594914	+	0.104899i	0.0204174	+	0.00360014i
$850$	−39.8886	+	33.4705i	−1.36817	+	1.14803i
$851$	1.03494	+	0.182487i	0.0354772	+	0.00625559i
$852$	−1.21270	+	3.33188i	−0.0415466	+	0.114148i
$853$	4.09529	−	0.722110i	0.140220	−	0.0247246i	−0.103098	−	0.994671i	$-0.532875\pi$
$853$	4.09529	−	0.722110i	0.140220	−	0.0247246i	0.243318	+	0.969947i	$0.421764\pi$
$854$	−24.0530	+	23.6705i	−0.823076	+	0.809989i
$855$	16.5845	−	2.79443i	0.567177	−	0.0955674i
$856$	4.37291	+	7.57410i	0.149463	+	0.258877i
$857$	3.59961	+	1.31015i	0.122960	+	0.0447540i	0.402768	−	0.915302i	$-0.368048\pi$
$857$	3.59961	+	1.31015i	0.122960	+	0.0447540i	−0.279807	+	0.960056i	$0.590271\pi$
$858$	−10.4814	+	1.84815i	−0.357827	+	0.0630946i
$859$	−19.4656	+	23.1982i	−0.664157	+	0.791512i	−0.987976	−	0.154607i	$-0.950589\pi$
$859$	−19.4656	+	23.1982i	−0.664157	+	0.791512i	0.323819	+	0.946119i	$0.395033\pi$
$860$	−7.04930	+	19.3678i	−0.240379	+	0.660436i
$861$	18.1538	−	1.44176i	0.618680	−	0.0491352i
$862$	15.2649	−	26.4396i	0.519925	−	0.900536i
$863$	27.1899	+	15.6981i	0.925554	+	0.534369i	0.885403	−	0.464825i	$-0.153883\pi$
$863$	27.1899	+	15.6981i	0.925554	+	0.534369i	0.0401515	+	0.999194i	$0.487216\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	1.01342	−	1.20775i	0.0344575	−	0.0410648i
$866$	11.5296	+	6.65662i	0.391792	+	0.226201i
$867$	−5.36845	+	9.29842i	−0.182322	+	0.315791i
$868$	7.89421	−	16.5810i	0.267947	−	0.562795i
$869$	26.8572	−	73.7894i	0.911067	−	2.50314i
$870$	−18.6684	+	22.2481i	−0.632918	+	0.754282i
$871$	−22.3169	+	3.93507i	−0.756179	+	0.133335i
$872$	15.8107	+	5.75462i	0.535417	+	0.194876i
$873$	8.67911	+	15.0327i	0.293743	+	0.508779i
$874$	−6.17537	+	16.5735i	−0.208885	+	0.560605i
$875$	13.2978	−	48.0834i	0.449548	−	1.62552i
$876$	0.843521	−	0.148736i	0.0284999	−	0.00502531i
$877$	8.44822	−	23.2113i	0.285276	−	0.783790i	−0.711435	−	0.702752i	$-0.751954\pi$
$877$	8.44822	−	23.2113i	0.285276	−	0.783790i	0.996711	−	0.0810376i	$-0.0258234\pi$
$878$	−7.95471	−	1.40263i	−0.268458	−	0.0473365i
$879$	−8.35324	+	7.00920i	−0.281748	+	0.236414i
$880$	21.5844	+	3.80591i	0.727610	+	0.128297i
$881$	−21.0912	−	12.1770i	−0.710581	−	0.410254i	0.100695	−	0.994917i	$-0.467893\pi$
$881$	−21.0912	−	12.1770i	−0.710581	−	0.410254i	−0.811276	+	0.584663i	$0.801227\pi$
$882$	3.59670	−	6.00531i	0.121107	−	0.202209i
$883$	−5.74901	+	32.6043i	−0.193470	+	1.09722i	0.721111	+	0.692819i	$0.243632\pi$
$883$	−5.74901	+	32.6043i	−0.193470	+	1.09722i	−0.914581	+	0.404402i	$0.867480\pi$
$884$	−3.37491	−	9.27249i	−0.113510	−	0.311867i
$885$			19.6696i			0.661185i
$886$	−10.0428	+	5.79821i	−0.337394	+	0.194795i
$887$	−9.77247	+	55.4224i	−0.328127	+	1.86090i	0.158591	+	0.987344i	$0.449305\pi$
$887$	−9.77247	+	55.4224i	−0.328127	+	1.86090i	−0.486718	+	0.873559i	$0.661806\pi$
$888$	−0.243378	−	0.0885825i	−0.00816724	−	0.00297263i
$889$	0.956326	+	12.0415i	0.0320741	+	0.403858i
$890$	14.2367	−	11.9460i	0.477217	−	0.400432i
$891$	−4.35149	+	3.65134i	−0.145781	+	0.122324i
$892$	5.88237	−	10.1886i	0.196956	−	0.341138i
$893$	0.145076	−	19.0775i	0.00485479	−	0.638406i
$894$	0.787765	−	0.454816i	0.0263468	−	0.0152113i
$895$	−13.3596	−	75.7661i	−0.446562	−	2.53258i
$896$	−1.53486	+	2.15504i	−0.0512760	+	0.0719949i
$897$	−7.14388	+	2.60016i	−0.238527	+	0.0868168i
$898$	3.22643	+	18.2980i	0.107667	+	0.610612i
$899$	−17.8695	−	49.0960i	−0.595981	−	1.63744i
$900$	−4.94352	−	8.56243i	−0.164784	−	0.285414i
$901$	−6.55034	+	11.3455i	−0.218223	+	0.377974i
$902$	−38.5053	−	6.78952i	−1.28208	−	0.226066i
$903$	−8.01341	−	11.6418i	−0.266670	−	0.387415i
$904$	4.24946	+	7.36028i	0.141335	+	0.244799i
$905$			67.2118i			2.23420i
$906$	8.03568	−	2.92475i	0.266968	−	0.0971682i
$907$	−6.49609	−	7.74174i	−0.215699	−	0.257060i	0.647335	−	0.762205i	$-0.275883\pi$
$907$	−6.49609	−	7.74174i	−0.215699	−	0.257060i	−0.863034	+	0.505145i	$0.831439\pi$
$908$	9.49449	+	7.96683i	0.315086	+	0.264388i
$909$	−3.96165	−	4.72131i	−0.131400	−	0.156596i
$910$	15.5791	+	11.0957i	0.516441	+	0.367818i
$911$		−	25.7621i		−	0.853536i	−0.904361	−	0.426768i	$-0.859652\pi$
$911$		−	25.7621i		−	0.853536i	0.904361	−	0.426768i	$-0.140348\pi$
$912$	2.20809	−	3.75823i	0.0731172	−	0.124448i
$913$	−26.4059	−	15.2455i	−0.873909	−	0.504551i
$914$	−0.111997	+	0.307710i	−0.00370454	+	0.0101781i
$915$	−46.2458	−	16.8321i	−1.52884	−	0.556452i
$916$	−3.93775	−	10.8189i	−0.130107	−	0.357465i
$917$	−1.47444	−	0.140911i	−0.0486903	−	0.00465330i
$918$	−4.03444	−	3.38529i	−0.133156	−	0.111731i
$919$	−4.11946			−0.135889			−0.0679443	−	0.997689i	$-0.521644\pi$
$919$	−4.11946			−0.135889			−0.0679443	+	0.997689i	$0.521644\pi$
$920$	15.6556			0.516151
$921$	−6.15809	−	5.16725i	−0.202916	−	0.170267i
$922$	20.3435	−	7.40444i	0.669978	−	0.243852i
$923$	5.75328	−	3.32166i	0.189371	−	0.109334i
$924$	−10.7120	+	10.5417i	−0.352399	+	0.346796i
$925$	1.64600	−	1.96163i	0.0541202	−	0.0644979i
$926$	−24.7370	+	4.36180i	−0.812909	+	0.143338i
$927$	2.09361	−	11.8734i	0.0687631	−	0.389975i
$928$	1.30709	+	7.41287i	0.0429073	+	0.243340i
$929$	14.5191	+	17.3031i	0.476355	+	0.567698i	0.949693	−	0.313183i	$-0.101395\pi$
$929$	14.5191	+	17.3031i	0.476355	+	0.567698i	−0.473338	+	0.880881i	$0.656951\pi$
$930$	26.7812			0.878189
$931$	−11.1104	+	28.4176i	−0.364129	+	0.931349i
$932$	−14.5997			−0.478230
$933$	−0.240435	−	0.286540i	−0.00787150	−	0.00938089i
$934$	2.19788	+	12.4648i	0.0719170	+	0.407861i
$935$	−20.0442	+	113.676i	−0.655514	+	3.71760i
$936$	1.84516	−	0.325351i	0.0603108	−	0.0106344i
$937$	−7.26109	+	8.65343i	−0.237209	+	0.282695i	−0.871496	−	0.490403i	$-0.836850\pi$
$937$	−7.26109	+	8.65343i	−0.237209	+	0.282695i	0.634286	+	0.773098i	$0.281294\pi$
$938$	−22.8080	+	22.4454i	−0.744708	+	0.732867i
$939$	17.9415	−	10.3585i	0.585498	−	0.338037i
$940$	−15.8689	+	5.77582i	−0.517588	+	0.188387i
$941$	−29.1555	−	24.4644i	−0.950442	−	0.797515i	0.0289302	−	0.999581i	$-0.490790\pi$
$941$	−29.1555	−	24.4644i	−0.950442	−	0.797515i	−0.979372	+	0.202066i	$0.935234\pi$
$942$	0.755431			0.0246133
$943$	−27.9287			−0.909484
$944$	3.90521	+	3.27686i	0.127104	+	0.106653i
$945$	10.1620	+	0.971175i	0.330570	+	0.0315923i
$946$	10.3783	+	28.5141i	0.337428	+	0.927075i
$947$	−36.7637	−	13.3809i	−1.19466	−	0.434821i	−0.333302	−	0.942820i	$-0.608163\pi$
$947$	−36.7637	−	13.3809i	−1.19466	−	0.434821i	−0.861357	+	0.508000i	$0.830385\pi$
$948$	−4.72798	+	12.9900i	−0.153558	+	0.421896i
$949$	−1.38981	−	0.802409i	−0.0451153	−	0.0260473i
$950$	27.4501	+	33.2236i	0.890599	+	1.07792i
$951$			2.56882i			0.0832998i
$952$	−11.3497	−	8.08346i	−0.367846	−	0.261987i
$953$	−0.945681	−	1.12702i	−0.0306336	−	0.0365077i	0.750510	−	0.660859i	$-0.229808\pi$
$953$	−0.945681	−	1.12702i	−0.0306336	−	0.0365077i	−0.781144	+	0.624351i	$0.785363\pi$
$954$	−1.90554	−	1.59894i	−0.0616943	−	0.0517676i
$955$	63.6261	+	75.8266i	2.05889	+	2.45369i
$956$	−8.95844	+	3.26060i	−0.289737	+	0.105455i
$957$			42.7582i			1.38218i
$958$	−8.25115	−	14.2914i	−0.266583	−	0.461735i
$959$	21.8206	+	31.7007i	0.704623	+	1.02367i
$960$	−3.79976	−	0.669999i	−0.122637	−	0.0216241i
$961$	−8.58911	+	14.8768i	−0.277068	+	0.479896i
$962$	0.242632	+	0.420250i	0.00782276	+	0.0135494i
$963$	−2.99125	−	8.21838i	−0.0963915	−	0.264834i
$964$	2.79537	+	15.8533i	0.0900327	+	0.510601i
$965$	25.8241	−	9.39919i	0.831306	−	0.302571i
$966$	−6.22781	+	8.74425i	−0.200376	+	0.281342i
$967$	4.63597	+	26.2919i	0.149083	+	0.845489i	0.963998	+	0.265910i	$0.0856722\pi$
$967$	4.63597	+	26.2919i	0.149083	+	0.845489i	−0.814915	+	0.579580i	$0.803217\pi$
$968$	18.4184	−	10.6339i	0.591990	−	0.341786i
$969$	19.7931	+	11.6291i	0.635844	+	0.373581i
$970$	−33.4872	+	58.0016i	−1.07521	+	1.86232i
$971$	30.8949	−	25.9239i	0.991465	−	0.831938i	0.00568609	−	0.999984i	$-0.498190\pi$
$971$	30.8949	−	25.9239i	0.991465	−	0.831938i	0.985779	+	0.168046i	$0.0537456\pi$
$972$	0.766044	−	0.642788i	0.0245709	−	0.0206174i
$973$	−4.70549	−	59.2487i	−0.150851	−	1.89943i
$974$	4.16353	+	1.51540i	0.133408	+	0.0485566i
$975$	−3.21676	+	18.2431i	−0.103019	+	0.584248i
$976$	−11.0462	+	6.37753i	−0.353580	+	0.204140i
$977$		−	5.55370i		−	0.177679i	−0.996046	−	0.0888393i	$-0.971684\pi$
$977$		−	5.55370i		−	0.177679i	0.996046	−	0.0888393i	$-0.0283158\pi$
$978$	4.35239	+	11.9581i	0.139174	+	0.382378i
$979$	4.75124	−	26.9456i	0.151850	−	0.861186i
$980$	27.0051	+	0.432848i	0.862648	+	0.0138268i
$981$	−14.5712	−	8.41269i	−0.465223	−	0.268596i
$982$	−19.3392	−	3.41002i	−0.617138	−	0.108818i
$983$	−31.4756	+	26.4112i	−1.00392	+	0.842385i	−0.987522	−	0.157480i	$-0.949663\pi$
$983$	−31.4756	+	26.4112i	−1.00392	+	0.842385i	−0.0163937	+	0.999866i	$0.505219\pi$
$984$	6.77853	+	1.19524i	0.216092	+	0.0381028i
$985$	9.33875	−	25.6580i	0.297557	−	0.817532i
$986$	−39.0405	+	6.88390i	−1.24330	+	0.219228i
$987$	3.08665	−	11.1610i	0.0982492	−	0.355259i
$988$	−7.69541	+	2.73481i	−0.244824	+	0.0870059i
$989$	10.8374	+	18.7710i	0.344611	+	0.596883i
$990$	−20.5956	−	7.49618i	−0.654571	−	0.238244i
$991$	2.17940	−	0.384287i	0.0692310	−	0.0122073i	−0.138925	−	0.990303i	$-0.544365\pi$
$991$	2.17940	−	0.384287i	0.0692310	−	0.0122073i	0.208156	+	0.978096i	$0.433254\pi$
$992$	4.46162	−	5.31716i	0.141657	−	0.168820i
$993$	−1.85606	+	5.09949i	−0.0589003	+	0.161827i
$994$	4.03261	−	8.47009i	0.127907	−	0.268655i
$995$	−48.9067	+	84.7089i	−1.55045	+	2.68545i
$996$	4.64855	+	2.68384i	0.147295	+	0.0850407i
$997$	28.0386	−	33.4151i	0.887992	−	1.05827i	−0.109937	−	0.993939i	$-0.535065\pi$
$997$	28.0386	−	33.4151i	0.887992	−	1.05827i	0.997929	−	0.0643288i	$-0.0204906\pi$
$998$	−23.5581	+	28.0755i	−0.745720	+	0.888714i
$999$	0.224299	+	0.129499i	0.00709650	+	0.00409716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.b.409.7	yes	84
7.5	odd	6		798.2.ca.b.523.7	yes	84
19.2	odd	18		798.2.ca.b.325.7	✓	84
133.40	even	18	inner	798.2.cj.b.439.7	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.325.7	✓	84	19.2	odd	18
798.2.ca.b.523.7	yes	84	7.5	odd	6
798.2.cj.b.409.7	yes	84	1.1	even	1	trivial
798.2.cj.b.439.7	yes	84	133.40	even	18	inner

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(3.79976 - 0.669999i) q^{5} +(-0.642788 + 0.766044i) q^{6} +(1.88576 - 1.85578i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-2.95569 - 2.48011i) q^{10} -5.68047 q^{11} +1.00000 q^{12} +(-1.43528 - 1.20434i) q^{13} +(-2.63375 - 0.251706i) q^{14} +(-1.31964 - 3.62568i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.80128 - 4.94897i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-4.08457 - 1.52194i) q^{19} +3.85837i q^{20} +(-2.15504 - 1.53486i) q^{21} +(3.65134 + 4.35149i) q^{22} +(3.10828 + 2.60816i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(9.29078 - 3.38157i) q^{25} +1.87362i q^{26} +(0.500000 + 0.866025i) q^{27} +(1.50012 + 2.17936i) q^{28} +(7.41287 + 1.30709i) q^{29} +(-1.92919 + 3.34145i) q^{30} +(-3.47053 - 6.01113i) q^{31} +(0.342020 + 0.939693i) q^{32} +(0.986403 + 5.59417i) q^{33} +(-4.94897 + 1.80128i) q^{34} +(5.92206 - 8.31496i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(0.224299 - 0.129499i) q^{37} +(1.45964 + 4.10724i) q^{38} +(-0.936810 + 1.62260i) q^{39} +(2.95569 - 2.48011i) q^{40} +(-5.27276 + 4.42437i) q^{41} +(0.209464 + 2.63745i) q^{42} +(5.01968 + 1.82701i) q^{43} +(0.986403 - 5.59417i) q^{44} +(-3.34145 + 1.92919i) q^{45} -4.05758i q^{46} +(1.49696 + 4.11286i) q^{47} +(-0.173648 + 0.984808i) q^{48} +(0.112184 - 6.99910i) q^{49} +(-8.56243 - 4.94352i) q^{50} +(-5.18657 - 0.914532i) q^{51} +(1.43528 - 1.20434i) q^{52} +(-2.44972 - 0.431952i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-21.5844 + 3.80591i) q^{55} +(0.705228 - 2.55003i) q^{56} +(-0.789536 + 4.28680i) q^{57} +(-3.76361 - 6.51877i) q^{58} +(-4.79045 - 1.74358i) q^{59} +(3.79976 - 0.669999i) q^{60} +(8.19879 - 9.77094i) q^{61} +(-2.37398 + 6.52246i) q^{62} +(-1.13732 + 2.38883i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.26060 - 3.61456i) q^{65} +(3.65134 - 4.35149i) q^{66} +(7.77442 - 9.26520i) q^{67} +(4.56099 + 2.63329i) q^{68} +(2.02879 - 3.51396i) q^{69} +(-10.1763 + 0.808191i) q^{70} +(-1.21270 + 3.33188i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(0.843521 - 0.148736i) q^{73} +(-0.243378 - 0.0885825i) q^{74} +(-4.94352 - 8.56243i) q^{75} +(2.20809 - 3.75823i) q^{76} +(-10.7120 + 10.5417i) q^{77} +(1.84516 - 0.325351i) q^{78} +(-4.72798 + 12.9900i) q^{79} +(-3.79976 - 0.669999i) q^{80} +(0.766044 - 0.642788i) q^{81} +(6.77853 + 1.19524i) q^{82} +(4.64855 + 2.68384i) q^{83} +(1.88576 - 1.85578i) q^{84} +(3.52861 - 20.0117i) q^{85} +(-1.82701 - 5.01968i) q^{86} -7.52723i q^{87} +(-4.91943 + 2.84024i) q^{88} +(-0.836416 + 4.74355i) q^{89} +(3.62568 + 1.31964i) q^{90} +(-4.94157 + 0.392456i) q^{91} +(-3.10828 + 2.60816i) q^{92} +(-5.31716 + 4.46162i) q^{93} +(2.18841 - 3.79043i) q^{94} +(-16.5401 - 3.04632i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-3.01422 - 17.0945i) q^{97} +(-5.43373 + 4.41300i) q^{98} +(5.33790 - 1.94284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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