LMFDB - Embedded newform 804.2.j.a.499.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.17
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00630957 - 1.41420i) q^{2} -1.00000 q^{3} +(-1.99992 - 0.0178460i) q^{4} +0.235538i q^{5} +(-0.00630957 + 1.41420i) q^{6} +(0.386363 - 0.669200i) q^{7} +(-0.0378564 + 2.82817i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.00630957 - 1.41420i) q^{2} -1.00000 q^{3} +(-1.99992 - 0.0178460i) q^{4} +0.235538i q^{5} +(-0.00630957 + 1.41420i) q^{6} +(0.386363 - 0.669200i) q^{7} +(-0.0378564 + 2.82817i) q^{8} +1.00000 q^{9} +(0.333097 + 0.00148614i) q^{10} +(-0.219298 + 0.379836i) q^{11} +(1.99992 + 0.0178460i) q^{12} +(-2.21475 + 1.27869i) q^{13} +(-0.943944 - 0.550616i) q^{14} -0.235538i q^{15} +(3.99936 + 0.0713811i) q^{16} +(3.20255 + 5.54697i) q^{17} +(0.00630957 - 1.41420i) q^{18} +(-0.0899060 + 0.0519073i) q^{19} +(0.00420340 - 0.471057i) q^{20} +(-0.386363 + 0.669200i) q^{21} +(0.535780 + 0.312528i) q^{22} +(1.71240 - 0.988656i) q^{23} +(0.0378564 - 2.82817i) q^{24} +4.94452 q^{25} +(1.79435 + 3.14017i) q^{26} -1.00000 q^{27} +(-0.784637 + 1.33145i) q^{28} +(4.68638 - 8.11705i) q^{29} +(-0.333097 - 0.00148614i) q^{30} +(-3.88084 + 6.72181i) q^{31} +(0.126181 - 5.65545i) q^{32} +(0.219298 - 0.379836i) q^{33} +(7.86473 - 4.49404i) q^{34} +(0.157622 + 0.0910030i) q^{35} +(-1.99992 - 0.0178460i) q^{36} +(1.98661 + 3.44091i) q^{37} +(0.0728400 + 0.127473i) q^{38} +(2.21475 - 1.27869i) q^{39} +(-0.666142 - 0.00891661i) q^{40} +(-3.90842 - 2.25653i) q^{41} +(0.943944 + 0.550616i) q^{42} +12.3543 q^{43} +(0.445358 - 0.755728i) q^{44} +0.235538i q^{45} +(-1.38735 - 2.42792i) q^{46} +(4.46727 + 2.57918i) q^{47} +(-3.99936 - 0.0713811i) q^{48} +(3.20145 + 5.54507i) q^{49} +(0.0311978 - 6.99254i) q^{50} +(-3.20255 - 5.54697i) q^{51} +(4.45215 - 2.51775i) q^{52} -13.6441i q^{53} +(-0.00630957 + 1.41420i) q^{54} +(-0.0894657 - 0.0516531i) q^{55} +(1.87799 + 1.11803i) q^{56} +(0.0899060 - 0.0519073i) q^{57} +(-11.4496 - 6.67869i) q^{58} +2.51516i q^{59} +(-0.00420340 + 0.471057i) q^{60} +(6.53767 - 3.77452i) q^{61} +(9.48149 + 5.53069i) q^{62} +(0.386363 - 0.669200i) q^{63} +(-7.99713 - 0.214129i) q^{64} +(-0.301179 - 0.521658i) q^{65} +(-0.535780 - 0.312528i) q^{66} +(6.75535 - 4.62226i) q^{67} +(-6.30584 - 11.1507i) q^{68} +(-1.71240 + 0.988656i) q^{69} +(0.129691 - 0.222335i) q^{70} +(-2.98439 - 1.72304i) q^{71} +(-0.0378564 + 2.82817i) q^{72} +(0.483410 + 0.837291i) q^{73} +(4.87866 - 2.78775i) q^{74} -4.94452 q^{75} +(0.180731 - 0.102206i) q^{76} +(0.169457 + 0.293509i) q^{77} +(-1.79435 - 3.14017i) q^{78} +(-6.49609 + 11.2516i) q^{79} +(-0.0168129 + 0.942001i) q^{80} +1.00000 q^{81} +(-3.21584 + 5.51305i) q^{82} +(-4.93531 + 2.84941i) q^{83} +(0.784637 - 1.33145i) q^{84} +(-1.30652 + 0.754320i) q^{85} +(0.0779505 - 17.4715i) q^{86} +(-4.68638 + 8.11705i) q^{87} +(-1.06594 - 0.634593i) q^{88} +10.5485 q^{89} +(0.333097 + 0.00148614i) q^{90} +1.97615i q^{91} +(-3.44231 + 1.94667i) q^{92} +(3.88084 - 6.72181i) q^{93} +(3.67566 - 6.30133i) q^{94} +(-0.0122261 - 0.0211763i) q^{95} +(-0.126181 + 5.65545i) q^{96} +(-15.3625 + 8.86953i) q^{97} +(7.86204 - 4.49250i) q^{98} +(-0.219298 + 0.379836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.00630957	−	1.41420i	0.00446154	−	0.999990i
$2$	0.00630957	−	1.41420i	0.00446154	−	0.999990i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.99992	−	0.0178460i	−0.999960	−	0.00892299i
$5$			0.235538i			0.105336i	0.998612	+	0.0526679i	$0.0167725\pi$
$5$			0.235538i			0.105336i	−0.998612	+	0.0526679i	$0.983228\pi$
$6$	−0.00630957	+	1.41420i	−0.00257587	+	0.577345i
$7$	0.386363	−	0.669200i	0.146031	−	0.252934i	−0.783726	−	0.621107i	$-0.786683\pi$
$7$	0.386363	−	0.669200i	0.146031	−	0.252934i	0.929757	+	0.368173i	$0.120017\pi$
$8$	−0.0378564	+	2.82817i	−0.0133843	+	0.999910i
$9$	1.00000			0.333333
$10$	0.333097	+	0.00148614i	0.105335	+	0.000469959i
$11$	−0.219298	+	0.379836i	−0.0661210	+	0.114525i	−0.897191	−	0.441643i	$-0.854396\pi$
$11$	−0.219298	+	0.379836i	−0.0661210	+	0.114525i	0.831070	+	0.556168i	$0.187729\pi$
$12$	1.99992	+	0.0178460i	0.577327	+	0.00515169i
$13$	−2.21475	+	1.27869i	−0.614262	+	0.354644i	−0.774632	−	0.632413i	$-0.782065\pi$
$13$	−2.21475	+	1.27869i	−0.614262	+	0.354644i	0.160370	+	0.987057i	$0.448731\pi$
$14$	−0.943944	−	0.550616i	−0.252280	−	0.147158i
$15$		−	0.235538i		−	0.0608156i
$16$	3.99936	+	0.0713811i	0.999841	+	0.0178453i
$17$	3.20255	+	5.54697i	0.776731	+	1.34534i	0.933816	+	0.357753i	$0.116457\pi$
$17$	3.20255	+	5.54697i	0.776731	+	1.34534i	−0.157085	+	0.987585i	$0.550210\pi$
$18$	0.00630957	−	1.41420i	0.00148718	−	0.333330i
$19$	−0.0899060	+	0.0519073i	−0.0206259	+	0.0119083i	−0.510277	−	0.860010i	$-0.670457\pi$
$19$	−0.0899060	+	0.0519073i	−0.0206259	+	0.0119083i	0.489652	+	0.871918i	$0.337124\pi$
$20$	0.00420340	−	0.471057i	0.000939909	−	0.105332i
$21$	−0.386363	+	0.669200i	−0.0843112	+	0.146031i
$22$	0.535780	+	0.312528i	0.114229	+	0.0666313i
$23$	1.71240	−	0.988656i	0.357061	−	0.206149i	−0.310730	−	0.950498i	$-0.600573\pi$
$23$	1.71240	−	0.988656i	0.357061	−	0.206149i	0.667791	+	0.744349i	$0.267240\pi$
$24$	0.0378564	−	2.82817i	0.00772741	−	0.577299i
$25$	4.94452			0.988904
$26$	1.79435	+	3.14017i	0.351900	+	0.615838i
$27$	−1.00000			−0.192450
$28$	−0.784637	+	1.33145i	−0.148282	+	0.251621i
$29$	4.68638	−	8.11705i	0.870239	−	1.50730i	0.00848887	−	0.999964i	$-0.497298\pi$
$29$	4.68638	−	8.11705i	0.870239	−	1.50730i	0.861750	−	0.507334i	$-0.169369\pi$
$30$	−0.333097	−	0.00148614i	−0.0608150	−	0.000271331i
$31$	−3.88084	+	6.72181i	−0.697019	+	1.20727i	0.272477	+	0.962162i	$0.412157\pi$
$31$	−3.88084	+	6.72181i	−0.697019	+	1.20727i	−0.969495	+	0.245110i	$0.921176\pi$
$32$	0.126181	−	5.65545i	0.0223059	−	0.999751i
$33$	0.219298	−	0.379836i	0.0381750	−	0.0661210i
$34$	7.86473	−	4.49404i	1.34879	−	0.770721i
$35$	0.157622	+	0.0910030i	0.0266430	+	0.0153823i
$36$	−1.99992	−	0.0178460i	−0.333320	−	0.00297433i
$37$	1.98661	+	3.44091i	0.326596	+	0.565682i	0.981834	−	0.189741i	$-0.0607649\pi$
$37$	1.98661	+	3.44091i	0.326596	+	0.565682i	−0.655238	+	0.755423i	$0.727432\pi$
$38$	0.0728400	+	0.127473i	0.0118162	+	0.0206788i
$39$	2.21475	−	1.27869i	0.354644	−	0.204754i
$40$	−0.666142	−	0.00891661i	−0.105326	−	0.00140984i
$41$	−3.90842	−	2.25653i	−0.610393	−	0.352411i	0.162726	−	0.986671i	$-0.447971\pi$
$41$	−3.90842	−	2.25653i	−0.610393	−	0.352411i	−0.773119	+	0.634261i	$0.781305\pi$
$42$	0.943944	+	0.550616i	0.145654	+	0.0849619i
$43$	12.3543			1.88402			0.942009	−	0.335589i	$-0.108935\pi$
$43$	12.3543			1.88402			0.942009	+	0.335589i	$0.108935\pi$
$44$	0.445358	−	0.755728i	0.0671402	−	0.113930i
$45$			0.235538i			0.0351119i
$46$	−1.38735	−	2.42792i	−0.204554	−	0.357977i
$47$	4.46727	+	2.57918i	0.651618	+	0.376212i	0.789076	−	0.614296i	$-0.210560\pi$
$47$	4.46727	+	2.57918i	0.651618	+	0.376212i	−0.137458	+	0.990508i	$0.543893\pi$
$48$	−3.99936	−	0.0713811i	−0.577258	−	0.0103030i
$49$	3.20145	+	5.54507i	0.457350	+	0.792153i
$50$	0.0311978	−	6.99254i	0.00441203	−	0.988895i
$51$	−3.20255	−	5.54697i	−0.448446	−	0.776731i
$52$	4.45215	−	2.51775i	0.617402	−	0.349149i
$53$		−	13.6441i		−	1.87416i	−0.349115	−	0.937080i	$-0.613518\pi$
$53$		−	13.6441i		−	1.87416i	0.349115	−	0.937080i	$-0.386482\pi$
$54$	−0.00630957	+	1.41420i	−0.000858623	+	0.192448i
$55$	−0.0894657	−	0.0516531i	−0.0120636	−	0.00696490i
$56$	1.87799	+	1.11803i	0.250957	+	0.149404i
$57$	0.0899060	−	0.0519073i	0.0119083	−	0.00687529i
$58$	−11.4496	−	6.67869i	−1.50340	−	0.876955i
$59$			2.51516i			0.327446i	0.986506	+	0.163723i	$0.0523503\pi$
$59$			2.51516i			0.327446i	−0.986506	+	0.163723i	$0.947650\pi$
$60$	−0.00420340	+	0.471057i	−0.000542657	+	0.0608132i
$61$	6.53767	−	3.77452i	0.837062	−	0.483278i	−0.0192022	−	0.999816i	$-0.506113\pi$
$61$	6.53767	−	3.77452i	0.837062	−	0.483278i	0.856265	+	0.516537i	$0.172779\pi$
$62$	9.48149	+	5.53069i	1.20415	+	0.702398i
$63$	0.386363	−	0.669200i	0.0486771	−	0.0843112i
$64$	−7.99713	−	0.214129i	−0.999642	−	0.0267661i
$65$	−0.301179	−	0.521658i	−0.0373567	−	0.0647037i
$66$	−0.535780	−	0.312528i	−0.0659500	−	0.0384696i
$67$	6.75535	−	4.62226i	0.825297	−	0.564699i
$67$	6.75535	−	4.62226i	0.825297	−	0.564699i
$68$	−6.30584	−	11.1507i	−0.764696	−	1.35222i
$69$	−1.71240	+	0.988656i	−0.206149	+	0.119020i
$70$	0.129691	−	0.222335i	0.0155010	−	0.0265741i
$71$	−2.98439	−	1.72304i	−0.354182	−	0.204487i	0.312344	−	0.949969i	$-0.398886\pi$
$71$	−2.98439	−	1.72304i	−0.354182	−	0.204487i	−0.666526	+	0.745482i	$0.732219\pi$
$72$	−0.0378564	+	2.82817i	−0.00446142	+	0.333303i
$73$	0.483410	+	0.837291i	0.0565789	+	0.0979975i	0.892928	−	0.450200i	$-0.148647\pi$
$73$	0.483410	+	0.837291i	0.0565789	+	0.0979975i	−0.836349	+	0.548198i	$0.815314\pi$
$74$	4.87866	−	2.78775i	0.567133	−	0.324069i
$75$	−4.94452			−0.570944
$76$	0.180731	−	0.102206i	0.0207313	−	0.0117238i
$77$	0.169457	+	0.293509i	0.0193115	+	0.0334484i
$78$	−1.79435	−	3.14017i	−0.203170	−	0.355554i
$79$	−6.49609	+	11.2516i	−0.730868	+	1.26590i	0.225645	+	0.974210i	$0.427551\pi$
$79$	−6.49609	+	11.2516i	−0.730868	+	1.26590i	−0.956513	+	0.291690i	$0.905782\pi$
$80$	−0.0168129	+	0.942001i	−0.00187974	+	0.105319i
$81$	1.00000			0.111111
$82$	−3.21584	+	5.51305i	−0.355130	+	0.608815i
$83$	−4.93531	+	2.84941i	−0.541721	+	0.312763i	−0.745776	−	0.666197i	$-0.767921\pi$
$83$	−4.93531	+	2.84941i	−0.541721	+	0.312763i	0.204055	+	0.978959i	$0.434588\pi$
$84$	0.784637	−	1.33145i	0.0856109	−	0.145273i
$85$	−1.30652	+	0.754320i	−0.141712	+	0.0818175i
$86$	0.0779505	−	17.4715i	0.00840561	−	1.88400i
$87$	−4.68638	+	8.11705i	−0.502433	+	0.870239i
$88$	−1.06594	−	0.634593i	−0.113630	−	0.0676479i
$89$	10.5485			1.11814			0.559070	−	0.829121i	$-0.311158\pi$
$89$	10.5485			1.11814			0.559070	+	0.829121i	$0.311158\pi$
$90$	0.333097	+	0.00148614i	0.0351116	+	0.000156653i
$91$			1.97615i			0.207157i
$92$	−3.44231	+	1.94667i	−0.358886	+	0.202955i
$93$	3.88084	−	6.72181i	0.402424	−	0.697019i
$94$	3.67566	−	6.30133i	0.379115	−	0.649933i
$95$	−0.0122261	−	0.0211763i	−0.00125437	−	0.00217264i
$96$	−0.126181	+	5.65545i	−0.0128783	+	0.577207i
$97$	−15.3625	+	8.86953i	−1.55982	+	0.900565i	−0.562551	+	0.826763i	$0.690180\pi$
$97$	−15.3625	+	8.86953i	−1.55982	+	0.900565i	−0.997273	+	0.0738017i	$0.976487\pi$
$98$	7.86204	−	4.49250i	0.794186	−	0.453811i
$99$	−0.219298	+	0.379836i	−0.0220403	+	0.0381750i
$100$	−9.88865	−	0.0882398i	−0.988865	−	0.00882398i
$101$	−4.36153	−	2.51813i	−0.433988	−	0.250563i	0.267056	−	0.963681i	$-0.413949\pi$
$101$	−4.36153	−	2.51813i	−0.433988	−	0.250563i	−0.701044	+	0.713118i	$0.747282\pi$
$102$	−7.86473	+	4.49404i	−0.778724	+	0.444976i
$103$	10.9112	+	6.29959i	1.07511	+	0.620717i	0.929574	−	0.368635i	$-0.120175\pi$
$103$	10.9112	+	6.29959i	1.07511	+	0.620717i	0.145540	+	0.989352i	$0.453508\pi$
$104$	−3.53251	−	6.31211i	−0.346391	−	0.618954i
$105$	−0.157622	−	0.0910030i	−0.0153823	−	0.00888098i
$106$	−19.2955	−	0.0860883i	−1.87414	−	0.00836164i
$107$			9.67494i			0.935311i	0.883911	+	0.467656i	$0.154901\pi$
$107$			9.67494i			0.935311i	−0.883911	+	0.467656i	$0.845099\pi$
$108$	1.99992	+	0.0178460i	0.192442	+	0.00171723i
$109$			13.7586i			1.31783i	0.752216	+	0.658917i	$0.228985\pi$
$109$			13.7586i			1.31783i	−0.752216	+	0.658917i	$0.771015\pi$
$110$	−0.0736122	+	0.126196i	−0.00701865	+	0.0120324i
$111$	−1.98661	−	3.44091i	−0.188561	−	0.326596i
$112$	1.59297	−	2.64879i	0.150522	−	0.250287i
$113$	0.509592	+	0.294213i	0.0479383	+	0.0276772i	0.523778	−	0.851855i	$-0.324522\pi$
$113$	0.509592	+	0.294213i	0.0479383	+	0.0276772i	−0.475839	+	0.879532i	$0.657856\pi$
$114$	−0.0728400	−	0.127473i	−0.00682209	−	0.0119389i
$115$	0.232866	+	0.403336i	0.0217149	+	0.0376112i
$116$	−9.51724	+	16.1498i	−0.883654	+	1.49947i
$117$	−2.21475	+	1.27869i	−0.204754	+	0.118215i
$118$	3.55694	+	0.0158696i	0.327443	+	0.00146091i
$119$	4.94937			0.453708
$120$	0.666142	+	0.00891661i	0.0608102	+	0.000813972i
$121$	5.40382	+	9.35968i	0.491256	+	0.850880i
$122$	−5.29668	−	9.26938i	−0.479539	−	0.839210i
$123$	3.90842	+	2.25653i	0.352411	+	0.203464i
$124$	7.88132	−	13.3738i	0.707764	−	1.20100i
$125$			2.34231i			0.209503i
$126$	−0.943944	−	0.550616i	−0.0840932	−	0.0490528i
$127$	0.686103	+	0.396122i	0.0608818	+	0.0351501i	0.530132	−	0.847915i	$-0.322142\pi$
$127$	0.686103	+	0.396122i	0.0608818	+	0.0351501i	−0.469250	+	0.883065i	$0.655476\pi$
$128$	−0.353280	+	11.3082i	−0.0312258	+	0.999512i
$129$	−12.3543			−1.08774
$130$	−0.739629	+	0.422636i	−0.0648697	+	0.0370677i
$131$			5.49980i			0.480520i	0.970709	+	0.240260i	$0.0772326\pi$
$131$			5.49980i			0.480520i	−0.970709	+	0.240260i	$0.922767\pi$
$132$	−0.445358	+	0.755728i	−0.0387634	+	0.0657777i
$133$			0.0802201i			0.00695597i
$134$	−6.49417	−	9.58257i	−0.561011	−	0.827808i
$135$		−	0.235538i		−	0.0202719i
$136$	−15.8090	+	8.84737i	−1.35561	+	0.758655i
$137$		−	20.4285i		−	1.74532i	−0.488325	−	0.872662i	$-0.662392\pi$
$137$		−	20.4285i		−	1.74532i	0.488325	−	0.872662i	$-0.337608\pi$
$138$	1.38735	+	2.42792i	0.118099	+	0.206678i
$139$	−0.381642			−0.0323704			−0.0161852	−	0.999869i	$-0.505152\pi$
$139$	−0.381642			−0.0323704			−0.0161852	+	0.999869i	$0.505152\pi$
$140$	−0.313607	−	0.184812i	−0.0265046	−	0.0156194i
$141$	−4.46727	−	2.57918i	−0.376212	−	0.217206i
$142$	−2.45555	+	4.20965i	−0.206065	+	0.353266i
$143$		−	1.12166i		−	0.0937977i
$144$	3.99936	+	0.0713811i	0.333280	+	0.00594842i
$145$	1.91187	+	1.10382i	0.158772	+	0.0916672i
$146$	1.18715	−	0.678355i	0.0982489	−	0.0561411i
$147$	−3.20145	−	5.54507i	−0.264051	−	0.457350i
$148$	−3.91165	−	6.91699i	−0.321536	−	0.568573i
$149$	18.2222			1.49282			0.746411	−	0.665485i	$-0.231775\pi$
$149$	18.2222			1.49282			0.746411	+	0.665485i	$0.231775\pi$
$150$	−0.0311978	+	6.99254i	−0.00254729	+	0.570939i
$151$	−7.82514	+	4.51784i	−0.636801	+	0.367657i	−0.783381	−	0.621542i	$-0.786507\pi$
$151$	−7.82514	+	4.51784i	−0.636801	+	0.367657i	0.146580	+	0.989199i	$0.453173\pi$
$152$	−0.143399	−	0.256235i	−0.0116312	−	0.0207834i
$153$	3.20255	+	5.54697i	0.258910	+	0.448446i
$154$	0.416149	−	0.237795i	0.0335343	−	0.0191620i
$155$	−1.58324	−	0.914084i	−0.127169	−	0.0734210i
$156$	−4.45215	+	2.51775i	−0.356457	+	0.201581i
$157$	−6.02859	−	10.4418i	−0.481134	−	0.833349i	0.518632	−	0.854998i	$-0.326442\pi$
$157$	−6.02859	−	10.4418i	−0.481134	−	0.833349i	−0.999766	+	0.0216492i	$0.993108\pi$
$158$	15.8710	+	9.25777i	1.26263	+	0.736508i
$159$			13.6441i			1.08205i
$160$	1.33207	+	0.0297205i	0.105310	+	0.00234961i
$161$		−	1.52792i		−	0.120417i
$162$	0.00630957	−	1.41420i	0.000495726	−	0.111110i
$163$	−1.97241	−	1.13877i	−0.154491	−	0.0891953i	0.420762	−	0.907171i	$-0.361763\pi$
$163$	−1.97241	−	1.13877i	−0.154491	−	0.0891953i	−0.575252	+	0.817976i	$0.695096\pi$
$164$	7.77626	+	4.58263i	0.607224	+	0.357843i
$165$	0.0894657	+	0.0516531i	0.00696490	+	0.00402119i
$166$	3.99849	+	6.99750i	0.310343	+	0.543111i
$167$	−7.66706	−	4.42658i	−0.593295	−	0.342539i	0.173104	−	0.984903i	$-0.444620\pi$
$167$	−7.66706	−	4.42658i	−0.593295	−	0.342539i	−0.766399	+	0.642365i	$0.777954\pi$
$168$	−1.87799	−	1.11803i	−0.144890	−	0.0862582i
$169$	−3.22991	+	5.59437i	−0.248455	+	0.430336i
$170$	1.05852	+	1.85244i	0.0811845	+	0.142076i
$171$	−0.0899060	+	0.0519073i	−0.00687529	+	0.00396945i
$172$	−24.7077	−	0.220475i	−1.88394	−	0.0168111i
$173$	4.68824	+	8.12027i	0.356440	+	0.617372i	0.987363	−	0.158473i	$-0.0506571\pi$
$173$	4.68824	+	8.12027i	0.356440	+	0.617372i	−0.630923	+	0.775845i	$0.717324\pi$
$174$	11.4496	+	6.67869i	0.867988	+	0.506310i
$175$	1.91038	−	3.30887i	0.144411	−	0.250127i
$176$	−0.904167	+	1.50345i	−0.0681542	+	0.113327i
$177$		−	2.51516i		−	0.189051i
$178$	0.0665565	−	14.9177i	0.00498862	−	1.11813i
$179$	11.6354			0.869668			0.434834	−	0.900511i	$-0.356807\pi$
$179$	11.6354			0.869668			0.434834	+	0.900511i	$0.356807\pi$
$180$	0.00420340	−	0.471057i	0.000313303	−	0.0351105i
$181$	−5.38478	+	9.32671i	−0.400247	+	0.693249i	−0.993756	−	0.111579i	$-0.964409\pi$
$181$	−5.38478	+	9.32671i	−0.400247	+	0.693249i	0.593508	+	0.804828i	$0.297742\pi$
$182$	2.79467	+	0.0124686i	0.207155	+	0.000924238i
$183$	−6.53767	+	3.77452i	−0.483278	+	0.279021i
$184$	2.73127	+	4.88040i	0.201352	+	0.359788i
$185$	−0.810464	+	0.467921i	−0.0595865	+	0.0344023i
$186$	−9.48149	−	5.53069i	−0.695216	−	0.405530i
$187$	−2.80925			−0.205433
$188$	−8.88815	−	5.23787i	−0.648235	−	0.382011i
$189$	−0.386363	+	0.669200i	−0.0281037	+	0.0486771i
$190$	−0.0300246	+	0.0171566i	−0.00217821	+	0.00124467i
$191$	8.14499	+	14.1075i	0.589351	+	1.02079i	0.994318	+	0.106454i	$0.0339498\pi$
$191$	8.14499	+	14.1075i	0.589351	+	1.02079i	−0.404967	+	0.914331i	$0.632717\pi$
$192$	7.99713	+	0.214129i	0.577143	+	0.0154534i
$193$	−9.98296			−0.718589			−0.359295	−	0.933224i	$-0.616983\pi$
$193$	−9.98296			−0.718589			−0.359295	+	0.933224i	$0.616983\pi$
$194$	12.4464	+	21.7816i	0.893596	+	1.56383i
$195$	0.301179	+	0.521658i	0.0215679	+	0.0373567i
$196$	−6.30368	−	11.1468i	−0.450263	−	0.796202i
$197$	−2.34882	−	1.35609i	−0.167347	−	0.0966177i	0.413987	−	0.910283i	$-0.364136\pi$
$197$	−2.34882	−	1.35609i	−0.167347	−	0.0966177i	−0.581334	+	0.813665i	$0.697469\pi$
$198$	0.535780	+	0.312528i	0.0380762	+	0.0222104i
$199$	12.1690	−	7.02579i	0.862639	−	0.498045i	−0.00225599	−	0.999997i	$-0.500718\pi$
$199$	12.1690	−	7.02579i	0.862639	−	0.498045i	0.864895	+	0.501952i	$0.167385\pi$
$200$	−0.187182	+	13.9840i	−0.0132358	+	0.988816i
$201$	−6.75535	+	4.62226i	−0.476486	+	0.326029i
$202$	−3.58865	+	6.15218i	−0.252497	+	0.432866i
$203$	−3.62128	−	6.27225i	−0.254164	−	0.440225i
$204$	6.30584	+	11.1507i	0.441497	+	0.780702i
$205$	0.531498	−	0.920581i	0.0371214	−	0.0642962i
$206$	8.97772	−	15.3909i	0.625508	−	1.07233i
$207$	1.71240	−	0.988656i	0.119020	−	0.0687164i
$208$	−8.94888	+	4.95585i	−0.620493	+	0.343626i
$209$		−	0.0455327i		−	0.00314956i
$210$	−0.129691	+	0.222335i	−0.00894952	+	0.0153425i
$211$	−6.45817	+	3.72863i	−0.444599	+	0.256689i	−0.705546	−	0.708664i	$-0.749298\pi$
$211$	−6.45817	+	3.72863i	−0.444599	+	0.256689i	0.260947	+	0.965353i	$0.415965\pi$
$212$	−0.243492	+	27.2871i	−0.0167231	+	1.87409i
$213$	2.98439	+	1.72304i	0.204487	+	0.118061i
$214$	13.6823	+	0.0610447i	0.935302	+	0.00417293i
$215$			2.90991i			0.198454i
$216$	0.0378564	−	2.82817i	0.00257580	−	0.192433i
$217$	2.99882	+	5.19411i	0.203573	+	0.352599i
$218$	19.4574	+	0.0868107i	1.31782	+	0.00587956i
$219$	−0.483410	−	0.837291i	−0.0326658	−	0.0565789i
$220$	0.178003	+	0.104899i	0.0120009	+	0.00707226i
$221$	−14.1857	−	8.19011i	−0.954233	−	0.550927i
$222$	−4.87866	+	2.78775i	−0.327434	+	0.187102i
$223$		−	25.5413i		−	1.71037i	−0.518319	−	0.855187i	$-0.673442\pi$
$223$		−	25.5413i		−	1.71037i	0.518319	−	0.855187i	$-0.326558\pi$
$224$	−3.73587	−	2.26949i	−0.249613	−	0.151637i
$225$	4.94452			0.329635
$226$	0.419291	−	0.718808i	0.0278908	−	0.0478144i
$227$	−17.4356	−	10.0665i	−1.15724	−	0.668134i	−0.206600	−	0.978425i	$-0.566240\pi$
$227$	−17.4356	−	10.0665i	−1.15724	−	0.668134i	−0.950641	+	0.310292i	$0.899573\pi$
$228$	−0.180731	+	0.102206i	−0.0119692	+	0.00676875i
$229$	4.88243	−	2.81887i	0.322640	−	0.186276i	−0.329929	−	0.944006i	$-0.607025\pi$
$229$	4.88243	−	2.81887i	0.322640	−	0.186276i	0.652569	+	0.757729i	$0.273691\pi$
$230$	0.571866	−	0.326774i	0.0377078	−	0.0215468i
$231$	−0.169457	−	0.293509i	−0.0111495	−	0.0193115i
$232$	22.7790	+	13.5612i	1.49552	+	0.890335i
$233$	−11.0308	−	6.36865i	−0.722654	−	0.417224i	0.0930750	−	0.995659i	$-0.470330\pi$
$233$	−11.0308	−	6.36865i	−0.722654	−	0.417224i	−0.815729	+	0.578435i	$0.803664\pi$
$234$	1.79435	+	3.14017i	0.117300	+	0.205279i
$235$	−0.607494	+	1.05221i	−0.0396285	+	0.0686386i
$236$	0.0448855	−	5.03012i	0.00292179	−	0.327433i
$237$	6.49609	−	11.2516i	0.421967	−	0.730868i
$238$	0.0312284	−	6.99940i	0.00202424	−	0.453704i
$239$	3.92936	−	6.80584i	0.254169	−	0.440233i	−0.710501	−	0.703697i	$-0.751531\pi$
$239$	3.92936	−	6.80584i	0.254169	−	0.440233i	0.964669	+	0.263463i	$0.0848648\pi$
$240$	0.0168129	−	0.942001i	0.00108527	−	0.0608059i
$241$	17.4787			1.12590			0.562952	−	0.826489i	$-0.309665\pi$
$241$	17.4787			1.12590			0.562952	+	0.826489i	$0.309665\pi$
$242$	13.2706	−	7.58302i	0.853064	−	0.487455i
$243$	−1.00000			−0.0641500
$244$	−13.1422	+	7.43208i	−0.841341	+	0.475790i
$245$	−1.30607	+	0.754062i	−0.0834420	+	0.0481753i
$246$	3.21584	−	5.51305i	0.205035	−	0.351499i
$247$	0.132746	−	0.229924i	0.00844645	−	0.0146297i
$248$	−18.8635	−	11.2301i	−1.19783	−	0.713115i
$249$	4.93531	−	2.84941i	0.312763	−	0.180574i
$250$	3.31249	+	0.0147790i	0.209501	+	0.000934704i
$251$	7.30855	+	12.6588i	0.461312	+	0.799015i	0.999027	−	0.0441113i	$-0.0140456\pi$
$251$	7.30855	+	12.6588i	0.461312	+	0.799015i	−0.537715	+	0.843127i	$0.680712\pi$
$252$	−0.784637	+	1.33145i	−0.0494275	+	0.0838735i
$253$			0.867243i			0.0545231i
$254$	0.564524	−	0.967787i	0.0354214	−	0.0607244i
$255$	1.30652	−	0.754320i	0.0818175	−	0.0472374i
$256$	15.9898	+	0.570958i	0.999363	+	0.0356848i
$257$	−2.48240	+	4.29964i	−0.154848	+	0.268204i	−0.933004	−	0.359867i	$-0.882822\pi$
$257$	−2.48240	+	4.29964i	−0.154848	+	0.268204i	0.778156	+	0.628071i	$0.216155\pi$
$258$	−0.0779505	+	17.4715i	−0.00485298	+	1.08773i
$259$	3.07020			0.190773
$260$	0.593025	+	1.04865i	0.0367779	+	0.0650345i
$261$	4.68638	−	8.11705i	0.290080	−	0.502433i
$262$	7.77781	+	0.0347013i	0.480515	+	0.00214386i
$263$			12.7373i			0.785418i	0.919663	+	0.392709i	$0.128462\pi$
$263$			12.7373i			0.785418i	−0.919663	+	0.392709i	$0.871538\pi$
$264$	1.06594	+	0.634593i	0.0656041	+	0.0390565i
$265$	3.21370			0.197416
$266$	0.113447		0.000506154i	0.00695590		3.10343e-5i
$267$	−10.5485			−0.645558
$268$	−13.5926	+	9.12359i	−0.830303	+	0.557312i
$269$	−4.96771			−0.302887			−0.151443	−	0.988466i	$-0.548392\pi$
$269$	−4.96771			−0.302887			−0.151443	+	0.988466i	$0.548392\pi$
$270$	−0.333097	−	0.00148614i	−0.0202717	−	9.04437e-5i
$271$	−5.78762			−0.351573			−0.175786	−	0.984428i	$-0.556247\pi$
$271$	−5.78762			−0.351573			−0.175786	+	0.984428i	$0.556247\pi$
$272$	12.4122	+	22.4130i	0.752600	+	1.35898i
$273$		−	1.97615i		−	0.119602i
$274$	−28.8900	−	0.128895i	−1.74531	−	0.00778683i
$275$	−1.08433	+	1.87811i	−0.0653873	+	0.113254i
$276$	3.44231	−	1.94667i	0.207203	−	0.117176i
$277$	10.9468			0.657728			0.328864	−	0.944377i	$-0.393334\pi$
$277$	10.9468			0.657728			0.328864	+	0.944377i	$0.393334\pi$
$278$	−0.00240799	+	0.539718i	−0.000144422	+	0.0323701i
$279$	−3.88084	+	6.72181i	−0.232340	+	0.402424i
$280$	−0.263339	+	0.442337i	−0.0157375	+	0.0264347i
$281$	1.05929	−	0.611579i	0.0631917	−	0.0364837i	−0.468071	−	0.883691i	$-0.655051\pi$
$281$	1.05929	−	0.611579i	0.0631917	−	0.0364837i	0.531263	+	0.847207i	$0.321718\pi$
$282$	−3.67566	+	6.30133i	−0.218882	+	0.375239i
$283$		−	27.8666i		−	1.65650i	−0.560360	−	0.828249i	$-0.689337\pi$
$283$		−	27.8666i		−	1.65650i	0.560360	−	0.828249i	$-0.310663\pi$
$284$	5.93779	+	3.49920i	0.352343	+	0.207639i
$285$	0.0122261	+	0.0211763i	0.000724213	+	0.00125437i
$286$	−1.58625	−	0.00707717i	−0.0937967	−	0.000418482i
$287$	−3.02014	+	1.74368i	−0.178273	+	0.102926i
$288$	0.126181	−	5.65545i	0.00743530	−	0.333250i
$289$	−12.0126	+	20.8064i	−0.706623	+	1.22391i
$290$	1.57308	−	2.69680i	0.0923747	−	0.158362i
$291$	15.3625	−	8.86953i	0.900565	−	0.519941i
$292$	−0.951839	−	1.68314i	−0.0557022	−	0.0984984i
$293$	−24.4695			−1.42952			−0.714762	−	0.699368i	$-0.753465\pi$
$293$	−24.4695			−1.42952			−0.714762	+	0.699368i	$0.753465\pi$
$294$	−7.86204	+	4.49250i	−0.458523	+	0.262008i
$295$	−0.592415			−0.0344917
$296$	−9.80669	+	5.48821i	−0.570002	+	0.318996i
$297$	0.219298	−	0.379836i	0.0127250	−	0.0220403i
$298$	0.114974	−	25.7699i	0.00666029	−	1.49281i
$299$	−2.52837	+	4.37926i	−0.146219	+	0.253259i
$300$	9.88865	+	0.0882398i	0.570921	+	0.00509453i
$301$	4.77325	−	8.26751i	0.275126	−	0.476531i
$302$	6.33976	+	11.0948i	0.364812	+	0.638435i
$303$	4.36153	+	2.51813i	0.250563	+	0.144663i
$304$	−0.363272	+	0.201178i	−0.0208351	+	0.0115384i
$305$	0.889043	+	1.53987i	0.0509065	+	0.0881726i
$306$	7.86473	−	4.49404i	0.449597	−	0.256907i
$307$	−18.4346	+	10.6432i	−1.05212	+	0.607442i	−0.923242	−	0.384219i	$-0.874471\pi$
$307$	−18.4346	+	10.6432i	−1.05212	+	0.607442i	−0.128878	+	0.991660i	$0.541138\pi$
$308$	−0.333663	−	0.590018i	−0.0190122	−	0.0336194i
$309$	−10.9112	−	6.29959i	−0.620717	−	0.358371i
$310$	−1.30269	+	2.23325i	−0.0739876	+	0.126840i
$311$	−24.3836			−1.38267			−0.691334	−	0.722536i	$-0.742977\pi$
$311$	−24.3836			−1.38267			−0.691334	+	0.722536i	$0.742977\pi$
$312$	3.53251	+	6.31211i	0.199989	+	0.357353i
$313$			20.6206i			1.16555i	0.812635	+	0.582774i	$0.198033\pi$
$313$			20.6206i			1.16555i	−0.812635	+	0.582774i	$0.801967\pi$
$314$	−14.8049	+	8.45975i	−0.835487	+	0.477411i
$315$	0.157622	+	0.0910030i	0.00888098	+	0.00512744i
$316$	13.1925	−	22.3863i	0.742134	−	1.25933i
$317$	−14.2500	−	24.6817i	−0.800360	−	1.38626i	−0.919380	−	0.393372i	$-0.871309\pi$
$317$	−14.2500	−	24.6817i	−0.800360	−	1.38626i	0.119020	−	0.992892i	$-0.462025\pi$
$318$	19.2955	+	0.0860883i	1.08204	+	0.00482759i
$319$	2.05543	+	3.56011i	0.115082	+	0.199328i
$320$	0.0504355	−	1.88363i	0.00281943	−	0.105298i
$321$		−	9.67494i		−	0.540002i
$322$	−2.16078	−	0.00964051i	−0.120416	−	0.000537245i
$323$	−0.575856	−	0.332471i	−0.0320415	−	0.0184992i
$324$	−1.99992	−	0.0178460i	−0.111107	−	0.000991443i
$325$	−10.9509	+	6.32250i	−0.607446	+	0.350709i
$326$	−1.62289	+	2.78219i	−0.0898837	+	0.154091i
$327$		−	13.7586i		−	0.760852i
$328$	6.52981	−	10.9683i	0.360549	−	0.605622i
$329$	3.45197	−	1.99300i	0.190313	−	0.109877i
$330$	0.0736122	−	0.126196i	0.00405222	−	0.00694689i
$331$	7.96649	−	13.7984i	0.437878	−	0.758427i	−0.559648	−	0.828731i	$-0.689064\pi$
$331$	7.96649	−	13.7984i	0.437878	−	0.758427i	0.997526	+	0.0703039i	$0.0223969\pi$
$332$	9.92109	−	5.61051i	0.544490	−	0.307917i
$333$	1.98661	+	3.44091i	0.108865	+	0.188561i
$334$	−6.30844	+	10.8148i	−0.345182	+	0.591761i
$335$	1.08872	+	1.59114i	0.0594829	+	0.0869333i
$336$	−1.59297	+	2.64879i	−0.0869038	+	0.144504i
$337$	15.6568	−	9.03946i	0.852881	−	0.492411i	−0.00874108	−	0.999962i	$-0.502782\pi$
$337$	15.6568	−	9.03946i	0.852881	−	0.492411i	0.861622	+	0.507551i	$0.169449\pi$
$338$	7.89118	+	4.60304i	0.429224	+	0.250372i
$339$	−0.509592	−	0.294213i	−0.0276772	−	0.0159794i
$340$	2.62640	−	1.48526i	0.142437	−	0.0805498i
$341$	−1.70212	−	2.94816i	−0.0921751	−	0.159652i
$342$	0.0728400	+	0.127473i	0.00393873	+	0.00689293i
$343$	10.3568			0.559212
$344$	−0.467690	+	34.9402i	−0.0252162	+	1.88385i
$345$	−0.232866	−	0.403336i	−0.0125371	−	0.0217149i
$346$	11.5133	−	6.57887i	0.618956	−	0.353682i
$347$	18.0388	−	31.2441i	0.968372	−	1.67727i	0.268104	−	0.963390i	$-0.413603\pi$
$347$	18.0388	−	31.2441i	0.968372	−	1.67727i	0.700268	−	0.713880i	$-0.253064\pi$
$348$	9.51724	−	16.1498i	0.510178	−	0.865721i
$349$	2.68028			0.143472			0.0717361	−	0.997424i	$-0.477146\pi$
$349$	2.68028			0.143472			0.0717361	+	0.997424i	$0.477146\pi$
$350$	−4.66735	−	2.72253i	−0.249480	−	0.145526i
$351$	2.21475	−	1.27869i	0.118215	−	0.0682513i
$352$	2.12047	+	1.28816i	0.113021	+	0.0686591i
$353$	2.40465	−	1.38833i	0.127987	−	0.0738932i	−0.434640	−	0.900604i	$-0.643124\pi$
$353$	2.40465	−	1.38833i	0.127987	−	0.0738932i	0.562626	+	0.826711i	$0.309791\pi$
$354$	−3.55694	−	0.0158696i	−0.189049	−	0.000843458i
$355$	0.405841	−	0.702937i	0.0215398	−	0.0373080i
$356$	−21.0962	−	0.188248i	−1.11809	−	0.00997714i
$357$	−4.94937			−0.261949
$358$	0.0734141	−	16.4547i	0.00388006	−	0.869659i
$359$		−	23.9590i		−	1.26451i	−0.774761	−	0.632254i	$-0.782130\pi$
$359$		−	23.9590i		−	1.26451i	0.774761	−	0.632254i	$-0.217870\pi$
$360$	−0.666142	−	0.00891661i	−0.0351088	−	0.000469947i
$361$	−9.49461	+	16.4451i	−0.499716	+	0.865534i
$362$	13.1559	+	7.67400i	0.691456	+	0.403336i
$363$	−5.40382	−	9.35968i	−0.283627	−	0.491256i
$364$	0.0352663	−	3.95214i	0.00184846	−	0.207148i
$365$	−0.197214	+	0.113861i	−0.0103226	+	0.00595978i
$366$	5.29668	+	9.26938i	0.276862	+	0.484518i
$367$	2.06299	−	3.57320i	0.107687	−	0.186520i	−0.807146	−	0.590352i	$-0.798989\pi$
$367$	2.06299	−	3.57320i	0.107687	−	0.186520i	0.914833	+	0.403833i	$0.132322\pi$
$368$	6.91909	−	3.83176i	0.360683	−	0.199744i
$369$	−3.90842	−	2.25653i	−0.203464	−	0.117470i
$370$	0.656621	+	1.14911i	0.0341361	+	0.0597394i
$371$	−9.13062	−	5.27157i	−0.474038	−	0.273686i
$372$	−7.88132	+	13.3738i	−0.408627	+	0.693400i
$373$	−10.1152	−	5.84000i	−0.523744	−	0.302383i	0.214721	−	0.976675i	$-0.431116\pi$
$373$	−10.1152	−	5.84000i	−0.523744	−	0.302383i	−0.738465	+	0.674292i	$0.764449\pi$
$374$	−0.0177252	+	3.97284i	−0.000916546	+	0.205431i
$375$		−	2.34231i		−	0.120956i
$376$	−7.46348	+	12.5366i	−0.384899	+	0.646524i
$377$			23.9697i			1.23450i
$378$	0.943944	+	0.550616i	0.0485512	+	0.0283206i
$379$	−9.15149	−	15.8509i	−0.470081	−	0.814204i	0.529334	−	0.848414i	$-0.322442\pi$
$379$	−9.15149	−	15.8509i	−0.470081	−	0.814204i	−0.999415	+	0.0342099i	$0.989109\pi$
$380$	0.0240734	+	0.0425690i	0.00123494	+	0.00218375i
$381$	−0.686103	−	0.396122i	−0.0351501	−	0.0202939i
$382$	20.0023	−	11.4296i	1.02340	−	0.584791i
$383$	−15.8188	−	27.3989i	−0.808301	−	1.40002i	−0.914040	−	0.405624i	$-0.867054\pi$
$383$	−15.8188	−	27.3989i	−0.808301	−	1.40002i	0.105739	−	0.994394i	$-0.466279\pi$
$384$	0.353280	−	11.3082i	0.0180282	−	0.577069i
$385$	−0.0691324	+	0.0399136i	−0.00352331	+	0.00203419i
$386$	−0.0629882	+	14.1179i	−0.00320601	+	0.718582i
$387$	12.3543			0.628006
$388$	30.8820	−	17.4642i	1.56780	−	0.886610i
$389$	−3.91304	−	6.77758i	−0.198399	−	0.343637i	0.749611	−	0.661879i	$-0.230241\pi$
$389$	−3.91304	−	6.77758i	−0.198399	−	0.343637i	−0.948009	+	0.318242i	$0.896907\pi$
$390$	0.739629	−	0.422636i	0.0374526	−	0.0214010i
$391$	10.9681	+	6.33243i	0.554680	+	0.320245i
$392$	−15.8036	+	8.84433i	−0.798203	+	0.446706i
$393$		−	5.49980i		−	0.277428i
$394$	−1.93261	+	3.31315i	−0.0973633	+	0.166914i
$395$	−2.65017	−	1.53008i	−0.133344	−	0.0769865i
$396$	0.445358	−	0.755728i	0.0223801	−	0.0379768i
$397$	−17.3823			−0.872395			−0.436197	−	0.899851i	$-0.643675\pi$
$397$	−17.3823			−0.872395			−0.436197	+	0.899851i	$0.643675\pi$
$398$	−9.85909	−	17.2538i	−0.494191	−	0.864853i
$399$		−	0.0802201i		−	0.00401603i
$400$	19.7749	+	0.352945i	0.988747	+	0.0176473i
$401$			11.5229i			0.575425i	0.957717	+	0.287713i	$0.0928948\pi$
$401$			11.5229i			0.575425i	−0.957717	+	0.287713i	$0.907105\pi$
$402$	6.49417	+	9.58257i	0.323900	+	0.477935i
$403$		−	19.8495i		−	0.988775i
$404$	8.67777	+	5.11389i	0.431735	+	0.254426i
$405$			0.235538i			0.0117040i
$406$	−8.89305	+	5.08164i	−0.441355	+	0.252198i
$407$	−1.74264			−0.0863795
$408$	15.8090	−	8.84737i	0.782664	−	0.438010i
$409$	9.52431	+	5.49886i	0.470947	+	0.271901i	0.716636	−	0.697447i	$-0.245681\pi$
$409$	9.52431	+	5.49886i	0.470947	+	0.271901i	−0.245689	+	0.969349i	$0.579014\pi$
$410$	−1.29853	−	0.757453i	−0.0641299	−	0.0374079i
$411$			20.4285i			1.00766i
$412$	−21.7091	−	12.7934i	−1.06953	−	0.630286i
$413$	1.68314	+	0.971763i	0.0828221	+	0.0478173i
$414$	−1.38735	−	2.42792i	−0.0681847	−	0.119326i
$415$	−0.671143	−	1.16245i	−0.0329451	−	0.0570626i
$416$	6.95209	+	12.6868i	0.340854	+	0.622020i
$417$	0.381642			0.0186891
$418$	−0.0643924		0.000287292i	−0.00314953		1.40519e-5i
$419$	18.7533	−	10.8272i	0.916158	−	0.528944i	0.0337506	−	0.999430i	$-0.489255\pi$
$419$	18.7533	−	10.8272i	0.916158	−	0.528944i	0.882407	+	0.470486i	$0.155921\pi$
$420$	0.313607	+	0.184812i	0.0153025	+	0.00901789i
$421$	−16.4213	−	28.4425i	−0.800324	−	1.38620i	−0.919403	−	0.393317i	$-0.871327\pi$
$421$	−16.4213	−	28.4425i	−0.800324	−	1.38620i	0.119079	−	0.992885i	$-0.462006\pi$
$422$	5.23228	+	9.15667i	0.254703	+	0.445740i
$423$	4.46727	+	2.57918i	0.217206	+	0.125404i
$424$	38.5879	+	0.516516i	1.87399	+	0.0250842i
$425$	15.8351	+	27.4271i	0.768113	+	1.33041i
$426$	2.45555	−	4.20965i	0.118972	−	0.203958i
$427$		−	5.83334i		−	0.282295i
$428$	0.172659	−	19.3491i	0.00834577	−	0.935274i
$429$			1.12166i			0.0541541i
$430$	4.11519	+	0.0183603i	0.198452	+	0.000885411i
$431$	−1.12319	−	0.648473i	−0.0541021	−	0.0312359i	0.472705	−	0.881221i	$-0.343278\pi$
$431$	−1.12319	−	0.648473i	−0.0541021	−	0.0312359i	−0.526807	+	0.849985i	$0.676611\pi$
$432$	−3.99936	−	0.0713811i	−0.192419	−	0.00343432i
$433$	−22.5711	−	13.0315i	−1.08470	−	0.626252i	−0.152539	−	0.988297i	$-0.548745\pi$
$433$	−22.5711	−	13.0315i	−1.08470	−	0.626252i	−0.932160	+	0.362046i	$0.882078\pi$
$434$	7.36443	−	4.20816i	0.353504	−	0.201998i
$435$	−1.91187	−	1.10382i	−0.0916672	−	0.0529241i
$436$	0.245535	−	27.5161i	0.0117590	−	1.31778i
$437$	−0.102637	+	0.177772i	−0.00490979	+	0.00850400i
$438$	−1.18715	+	0.678355i	−0.0567240	+	0.0324131i
$439$	29.2364	−	16.8796i	1.39538	−	0.805621i	0.401473	−	0.915871i	$-0.368498\pi$
$439$	29.2364	−	16.8796i	1.39538	−	0.805621i	0.993904	+	0.110250i	$0.0351651\pi$
$440$	0.149471	−	0.251069i	0.00712574	−	0.0119693i
$441$	3.20145	+	5.54507i	0.152450	+	0.264051i
$442$	−11.6720	+	20.0097i	−0.555178	+	0.951765i
$443$	−12.9749	+	22.4732i	−0.616457	+	1.06773i	0.373670	+	0.927562i	$0.378099\pi$
$443$	−12.9749	+	22.4732i	−0.616457	+	1.06773i	−0.990127	+	0.140173i	$0.955234\pi$
$444$	3.91165	+	6.91699i	0.185639	+	0.328266i
$445$			2.48457i			0.117780i
$446$	−36.1205	−	0.161155i	−1.71036	−	0.00763090i
$447$	−18.2222			−0.861882
$448$	−3.23309	+	5.26895i	−0.152749	+	0.248934i
$449$	−2.27705	+	3.94396i	−0.107460	+	0.186127i	−0.914741	−	0.404041i	$-0.867605\pi$
$449$	−2.27705	+	3.94396i	−0.107460	+	0.186127i	0.807280	+	0.590168i	$0.200939\pi$
$450$	0.0311978	−	6.99254i	0.00147068	−	0.329632i
$451$	1.71422	−	0.989706i	0.0807195	−	0.0466035i
$452$	−1.01389	−	0.597496i	−0.0476895	−	0.0281039i
$453$	7.82514	−	4.51784i	0.367657	−	0.212267i
$454$	−14.3460	+	24.5939i	−0.673290	+	1.15425i
$455$	−0.465458			−0.0218210
$456$	0.143399	+	0.256235i	0.00671529	+	0.0119993i
$457$	4.83856	−	8.38064i	0.226338	−	0.392030i	−0.730382	−	0.683039i	$-0.760658\pi$
$457$	4.83856	−	8.38064i	0.226338	−	0.392030i	0.956720	+	0.291009i	$0.0939911\pi$
$458$	−3.95564	−	6.92252i	−0.184835	−	0.323468i
$459$	−3.20255	−	5.54697i	−0.149482	−	0.258910i
$460$	−0.458515	−	0.810795i	−0.0213784	−	0.0378035i
$461$	3.62518			0.168841			0.0844207	−	0.996430i	$-0.473096\pi$
$461$	3.62518			0.168841			0.0844207	+	0.996430i	$0.473096\pi$
$462$	−0.416149	+	0.237795i	−0.0193610	+	0.0110632i
$463$	−2.06236	−	3.57212i	−0.0958462	−	0.166010i	0.814115	−	0.580703i	$-0.197222\pi$
$463$	−2.06236	−	3.57212i	−0.0958462	−	0.166010i	−0.909961	+	0.414693i	$0.863889\pi$
$464$	19.3219	−	32.1285i	0.896998	−	1.49153i
$465$	1.58324	+	0.914084i	0.0734210	+	0.0423896i
$466$	−9.07614	+	15.5596i	−0.420444	+	0.720785i
$467$	17.9240	−	10.3484i	0.829424	−	0.478868i	−0.0242315	−	0.999706i	$-0.507714\pi$
$467$	17.9240	−	10.3484i	0.829424	−	0.478868i	0.853655	+	0.520838i	$0.174381\pi$
$468$	4.45215	−	2.51775i	0.205801	−	0.116383i
$469$	−0.483199	−	6.30654i	−0.0223121	−	0.291209i
$470$	1.48420	+	0.865756i	0.0684611	+	0.0399344i
$471$	6.02859	+	10.4418i	0.277783	+	0.481134i
$472$	−7.11331	−	0.0952149i	−0.327416	−	0.00438262i
$473$	−2.70928	+	4.69262i	−0.124573	+	0.215767i
$474$	−15.8710	−	9.25777i	−0.728978	−	0.425223i
$475$	−0.444542	+	0.256657i	−0.0203970	+	0.0117762i
$476$	−9.89835	−	0.0883264i	−0.453690	−	0.00404843i
$477$		−	13.6441i		−	0.624720i
$478$	−9.60003	−	5.59983i	−0.439095	−	0.256130i
$479$	24.1386	−	13.9365i	1.10292	−	0.636773i	0.165936	−	0.986137i	$-0.446936\pi$
$479$	24.1386	−	13.9365i	1.10292	−	0.636773i	0.936987	+	0.349364i	$0.113602\pi$
$480$	−1.33207	−	0.0297205i	−0.0608005	−	0.00135655i
$481$	−8.79969	−	5.08051i	−0.401231	−	0.231651i
$482$	0.110283	−	24.7184i	0.00502327	−	1.12589i
$483$			1.52792i			0.0695227i
$484$	−10.6402	−	18.8151i	−0.483644	−	0.855230i
$485$	−2.08911	−	3.61845i	−0.0948616	−	0.164305i
$486$	−0.00630957	+	1.41420i	−0.000286208	+	0.0641494i
$487$	9.47493	+	16.4111i	0.429350	+	0.743656i	0.996816	−	0.0797412i	$-0.0254094\pi$
$487$	9.47493	+	16.4111i	0.429350	+	0.743656i	−0.567466	+	0.823397i	$0.692076\pi$
$488$	10.4275	+	18.6325i	0.472031	+	0.843456i
$489$	1.97241	+	1.13877i	0.0891953	+	0.0514969i
$490$	1.05815	+	1.85181i	0.0478025	+	0.0836561i
$491$			22.7513i			1.02675i	0.858164	+	0.513375i	$0.171605\pi$
$491$			22.7513i			1.02675i	−0.858164	+	0.513375i	$0.828395\pi$
$492$	−7.77626	−	4.58263i	−0.350581	−	0.206601i
$493$	60.0334			2.70377
$494$	−0.324320	−	0.189181i	−0.0145919	−	0.00851164i
$495$	−0.0894657	−	0.0516531i	−0.00402119	−	0.00232163i
$496$	−16.0007	+	26.6059i	−0.718452	+	1.19464i
$497$	−2.30611	+	1.33144i	−0.103443	+	0.0597230i
$498$	−3.99849	−	6.99750i	−0.179177	−	0.313565i
$499$	−0.514306	−	0.890803i	−0.0230235	−	0.0398778i	0.854284	−	0.519806i	$-0.173996\pi$
$499$	−0.514306	−	0.890803i	−0.0230235	−	0.0398778i	−0.877308	+	0.479929i	$0.840663\pi$
$500$	0.0418008	−	4.68444i	0.00186939	−	0.209494i
$501$	7.66706	+	4.42658i	0.342539	+	0.197765i
$502$	17.9482	−	10.2559i	0.801066	−	0.457742i
$503$	22.1213	−	38.3152i	0.986341	−	1.70839i	0.350520	−	0.936555i	$-0.386005\pi$
$503$	22.1213	−	38.3152i	0.986341	−	1.70839i	0.635821	−	0.771837i	$-0.280662\pi$
$504$	1.87799	+	1.11803i	0.0836522	+	0.0498012i
$505$	0.593114	−	1.02730i	0.0263932	−	0.0457144i
$506$	1.22645	+	0.00547193i	0.0545226	+	0.000243257i
$507$	3.22991	−	5.59437i	0.143445	−	0.248455i
$508$	−1.36508	−	0.804456i	−0.0605657	−	0.0356920i
$509$	16.4857			0.730715			0.365358	−	0.930867i	$-0.380947\pi$
$509$	16.4857			0.730715			0.365358	+	0.930867i	$0.380947\pi$
$510$	−1.05852	−	1.85244i	−0.0468719	−	0.0820275i
$511$	0.747086			0.0330492
$512$	0.908337	−	22.6092i	0.0401432	−	0.999194i
$513$	0.0899060	−	0.0519073i	0.00396945	−	0.00229176i
$514$	6.06489	+	3.53774i	0.267511	+	0.156043i
$515$	−1.48379	+	2.57000i	−0.0653837	+	0.113248i
$516$	24.7077	+	0.220475i	1.08769	+	0.00970587i
$517$	−1.95933	+	1.13122i	−0.0861712	+	0.0497509i
$518$	0.0193717	−	4.34188i	0.000851142	−	0.190771i
$519$	−4.68824	−	8.12027i	−0.205791	−	0.356440i
$520$	1.48674	−	0.832040i	0.0651979	−	0.0364874i
$521$			31.9182i			1.39836i	0.714945	+	0.699181i	$0.246452\pi$
$521$			31.9182i			1.39836i	−0.714945	+	0.699181i	$0.753548\pi$
$522$	−11.4496	−	6.67869i	−0.501133	−	0.292318i
$523$	14.9663	−	8.64079i	0.654430	−	0.377835i	−0.135721	−	0.990747i	$-0.543335\pi$
$523$	14.9663	−	8.64079i	0.654430	−	0.377835i	0.790151	+	0.612912i	$0.210002\pi$
$524$	0.0981493	−	10.9992i	0.00428767	−	0.480500i
$525$	−1.91038	+	3.30887i	−0.0833757	+	0.144411i
$526$	18.0132	+	0.0803672i	0.785411	+	0.00350417i
$527$	−49.7142			−2.16559
$528$	0.904167	−	1.50345i	0.0393488	−	0.0654292i
$529$	−9.54512	+	16.5326i	−0.415005	+	0.718810i
$530$	0.0202771	−	4.54481i	0.000880779	−	0.197414i
$531$			2.51516i			0.109149i
$532$	0.00143161	−	0.160434i	6.20680e−5	−	0.00695569i
$533$	11.5416			0.499922
$534$	−0.0665565	+	14.9177i	−0.00288018	+	0.645552i
$535$	−2.27881			−0.0985217
$536$	12.8168	+	19.2803i	0.553602	+	0.832781i
$537$	−11.6354			−0.502103
$538$	−0.0313441	+	7.02534i	−0.00135134	+	0.302884i
$539$	−2.80829			−0.120962
$540$	−0.00420340	+	0.471057i	−0.000180886	+	0.0202711i
$541$		−	5.91311i		−	0.254224i	−0.991888	−	0.127112i	$-0.959429\pi$
$541$		−	5.91311i		−	0.254224i	0.991888	−	0.127112i	$-0.0405708\pi$
$542$	−0.0365174	+	8.18484i	−0.00156855	+	0.351569i
$543$	5.38478	−	9.32671i	0.231083	−	0.400247i
$544$	31.7747	−	17.4119i	1.36233	−	0.746529i
$545$	−3.24067			−0.138815
$546$	−2.79467	−	0.0124686i	−0.119601	−	0.000533609i
$547$	−19.9632	+	34.5772i	−0.853563	+	1.47841i	0.0244089	+	0.999702i	$0.492230\pi$
$547$	−19.9632	+	34.5772i	−0.853563	+	1.47841i	−0.877972	+	0.478712i	$0.841104\pi$
$548$	−0.364566	+	40.8554i	−0.0155735	+	1.74525i
$549$	6.53767	−	3.77452i	0.279021	−	0.161093i
$550$	2.64918	+	1.54530i	0.112961	+	0.0658919i
$551$			0.973029i			0.0414524i
$552$	−2.73127	−	4.88040i	−0.116250	−	0.207724i
$553$	5.01970	+	8.69437i	0.213459	+	0.369722i
$554$	0.0690695	−	15.4809i	0.00293448	−	0.657722i
$555$	0.810464	−	0.467921i	0.0344023	−	0.0198622i
$556$	0.763253	+	0.00681077i	0.0323691	+	0.000288841i
$557$	−5.49146	+	9.51149i	−0.232681	+	0.403015i	−0.958596	−	0.284769i	$-0.908083\pi$
$557$	−5.49146	+	9.51149i	−0.232681	+	0.403015i	0.725915	+	0.687784i	$0.241416\pi$
$558$	9.48149	+	5.53069i	0.401383	+	0.234133i
$559$	−27.3618	+	15.7973i	−1.15728	+	0.668156i
$560$	0.623891	+	0.375205i	0.0263642	+	0.0158553i
$561$	2.80925			0.118607
$562$	−0.858211	−	1.50190i	−0.0362014	−	0.0633538i
$563$	−20.7630			−0.875057			−0.437528	−	0.899205i	$-0.644146\pi$
$563$	−20.7630			−0.875057			−0.437528	+	0.899205i	$0.644146\pi$
$564$	8.88815	+	5.23787i	0.374259	+	0.220554i
$565$	−0.0692983	+	0.120028i	−0.00291540	+	0.00504962i
$566$	−39.4090	−	0.175826i	−1.65648	−	0.00739053i
$567$	0.386363	−	0.669200i	0.0162257	−	0.0281037i
$568$	4.98603	−	8.37515i	0.209209	−	0.351413i
$569$	−1.16827	+	2.02349i	−0.0489762	+	0.0848293i	−0.889474	−	0.456985i	$-0.848929\pi$
$569$	−1.16827	+	2.02349i	−0.0489762	+	0.0848293i	0.840498	+	0.541815i	$0.182263\pi$
$570$	0.0300246	−	0.0171566i	0.00125759	−	0.000718610i
$571$	31.2607	+	18.0484i	1.30822	+	0.755301i	0.981799	−	0.189923i	$-0.0608239\pi$
$571$	31.2607	+	18.0484i	1.30822	+	0.755301i	0.326421	+	0.945224i	$0.394157\pi$
$572$	−0.0200171	+	2.24322i	−0.000836955	+	0.0937939i
$573$	−8.14499	−	14.1075i	−0.340262	−	0.589351i
$574$	2.44685	+	4.28208i	0.102130	+	0.178730i
$575$	8.46701	−	4.88843i	0.353099	−	0.203862i
$576$	−7.99713	−	0.214129i	−0.333214	−	0.00892204i
$577$	2.70657	+	1.56264i	0.112676	+	0.0650534i	0.555279	−	0.831664i	$-0.312612\pi$
$577$	2.70657	+	1.56264i	0.112676	+	0.0650534i	−0.442603	+	0.896718i	$0.645945\pi$
$578$	29.3486	+	17.1195i	1.22074	+	0.712076i
$579$	9.98296			0.414878
$580$	−3.80389	−	2.24167i	−0.157948	−	0.0930803i
$581$			4.40361i			0.182693i
$582$	−12.4464	−	21.7816i	−0.515918	−	0.902875i
$583$	5.18252	+	2.99213i	0.214638	+	0.123921i
$584$	−2.38630	+	1.33547i	−0.0987460	+	0.0552622i
$585$	−0.301179	−	0.521658i	−0.0124522	−	0.0215679i
$586$	−0.154392	+	34.6048i	−0.00637788	+	1.42951i
$587$	−1.56979	−	2.71896i	−0.0647923	−	0.112223i	0.831810	−	0.555061i	$-0.187305\pi$
$587$	−1.56979	−	2.71896i	−0.0647923	−	0.112223i	−0.896602	+	0.442838i	$0.853972\pi$
$588$	6.30368	+	11.1468i	0.259960	+	0.459688i
$589$		−	0.805775i		−	0.0332014i
$590$	−0.00373788	+	0.837793i	−0.000153886	+	0.0344914i
$591$	2.34882	+	1.35609i	0.0966177	+	0.0557822i
$592$	7.69955	+	13.9032i	0.316450	+	0.571420i
$593$	−8.50733	+	4.91171i	−0.349354	+	0.201700i	−0.664401	−	0.747376i	$-0.731313\pi$
$593$	−8.50733	+	4.91171i	−0.349354	+	0.201700i	0.315047	+	0.949076i	$0.397980\pi$
$594$	−0.535780	−	0.312528i	−0.0219833	−	0.0128232i
$595$			1.16576i			0.0477917i
$596$	−36.4430	−	0.325193i	−1.49276	−	0.0133204i
$597$	−12.1690	+	7.02579i	−0.498045	+	0.287546i
$598$	6.17719	+	3.60325i	0.252604	+	0.147348i
$599$	−13.2496	+	22.9490i	−0.541364	+	0.937670i	0.457462	+	0.889229i	$0.348759\pi$
$599$	−13.2496	+	22.9490i	−0.541364	+	0.937670i	−0.998826	+	0.0484411i	$0.984575\pi$
$600$	0.187182	−	13.9840i	0.00764166	−	0.570893i
$601$	10.3630	+	17.9492i	0.422715	+	0.732164i	0.996204	−	0.0870491i	$-0.0277437\pi$
$601$	10.3630	+	17.9492i	0.422715	+	0.732164i	−0.573489	+	0.819213i	$0.694410\pi$
$602$	−11.6618	−	6.80249i	−0.475299	−	0.277249i
$603$	6.75535	−	4.62226i	0.275099	−	0.188233i
$604$	15.7303	−	8.89568i	0.640056	−	0.361960i
$605$	−2.20456	+	1.27280i	−0.0896281	+	0.0517468i
$606$	3.58865	−	6.15218i	0.145779	−	0.249915i
$607$	18.1975	+	10.5063i	0.738614	+	0.426439i	0.821565	−	0.570115i	$-0.193101\pi$
$607$	18.1975	+	10.5063i	0.738614	+	0.426439i	−0.0829512	+	0.996554i	$0.526435\pi$
$608$	0.282214	+	0.515009i	0.0114453	+	0.0208864i
$609$	3.62128	+	6.27225i	0.146742	+	0.254164i
$610$	2.18329	−	1.24757i	0.0883988	−	0.0505126i
$611$	−13.1919			−0.533685
$612$	−6.30584	−	11.1507i	−0.254899	−	0.450738i
$613$	10.7627	+	18.6415i	0.434700	+	0.752922i	0.997271	−	0.0738266i	$-0.0235211\pi$
$613$	10.7627	+	18.6415i	0.434700	+	0.752922i	−0.562571	+	0.826749i	$0.690188\pi$
$614$	14.9354	+	26.1374i	0.602742	+	1.05482i
$615$	−0.531498	+	0.920581i	−0.0214321	+	0.0371214i
$616$	−0.836509	+	0.468144i	−0.0337039	+	0.0188620i
$617$	27.0638			1.08955			0.544774	−	0.838583i	$-0.316615\pi$
$617$	27.0638			1.08955			0.544774	+	0.838583i	$0.316615\pi$
$618$	−8.97772	+	15.3909i	−0.361137	+	0.619112i
$619$	−4.34615	+	2.50925i	−0.174686	+	0.100855i	−0.584794	−	0.811182i	$-0.698825\pi$
$619$	−4.34615	+	2.50925i	−0.174686	+	0.100855i	0.410107	+	0.912037i	$0.365491\pi$
$620$	3.15004	+	1.85635i	0.126509	+	0.0745528i
$621$	−1.71240	+	0.988656i	−0.0687164	+	0.0396734i
$622$	−0.153850	+	34.4833i	−0.00616882	+	1.38265i
$623$	4.07555	−	7.05906i	0.163283	−	0.282815i
$624$	8.94888	−	4.95585i	0.358242	−	0.198393i
$625$	24.1709			0.966836
$626$	29.1617	+	0.130107i	1.16554	+	0.00520013i
$627$			0.0455327i			0.00181840i
$628$	11.8704	+	20.9904i	0.473679	+	0.837609i
$629$	−12.7244	+	22.0393i	−0.507355	+	0.878765i
$630$	0.129691	−	0.222335i	0.00516701	−	0.00885802i
$631$	5.06075	+	8.76548i	0.201465	+	0.348948i	0.949001	−	0.315274i	$-0.102096\pi$
$631$	5.06075	+	8.76548i	0.201465	+	0.348948i	−0.747535	+	0.664222i	$0.768763\pi$
$632$	−31.5755	−	18.7980i	−1.25600	−	0.747745i
$633$	6.45817	−	3.72863i	0.256689	−	0.148200i
$634$	−34.9948	+	19.9966i	−1.38982	+	0.794167i
$635$	−0.0933016	+	0.161603i	−0.00370256	+	0.00641303i
$636$	0.243492	−	27.2871i	0.00965509	−	1.08200i
$637$	−14.1808	−	8.18731i	−0.561865	−	0.324393i
$638$	5.04767	−	2.88433i	0.199839	−	0.114192i
$639$	−2.98439	−	1.72304i	−0.118061	−	0.0681623i
$640$	−2.66351	−	0.0832107i	−0.105284	−	0.00328919i
$641$	−35.5903	−	20.5481i	−1.40573	−	0.811599i	−0.410758	−	0.911744i	$-0.634736\pi$
$641$	−35.5903	−	20.5481i	−1.40573	−	0.811599i	−0.994973	+	0.100145i	$0.968069\pi$
$642$	−13.6823	−	0.0610447i	−0.539997	−	0.00240924i
$643$			34.2763i			1.35172i	0.737028	+	0.675862i	$0.236229\pi$
$643$			34.2763i			1.35172i	−0.737028	+	0.675862i	$0.763771\pi$
$644$	−0.0272672	+	3.05572i	−0.00107448	+	0.120412i
$645$		−	2.90991i		−	0.114578i
$646$	−0.473813	+	0.812278i	−0.0186419	+	0.0319586i
$647$	−1.41443	−	2.44986i	−0.0556069	−	0.0963140i	0.836882	−	0.547383i	$-0.184376\pi$
$647$	−1.41443	−	2.44986i	−0.0556069	−	0.0963140i	−0.892489	+	0.451069i	$0.851043\pi$
$648$	−0.0378564	+	2.82817i	−0.00148714	+	0.111101i
$649$	−0.955348	−	0.551570i	−0.0375007	−	0.0216510i
$650$	8.87218	+	15.5266i	0.347996	+	0.609005i
$651$	−2.99882	−	5.19411i	−0.117533	−	0.203573i
$652$	3.92433	+	2.31265i	0.153689	+	0.0905703i
$653$	15.7072	−	9.06853i	0.614669	−	0.354879i	−0.160122	−	0.987097i	$-0.551189\pi$
$653$	15.7072	−	9.06853i	0.614669	−	0.354879i	0.774790	+	0.632218i	$0.217855\pi$
$654$	−19.4574	−	0.0868107i	−0.760844	−	0.00339457i
$655$	−1.29541			−0.0506159
$656$	−15.4701	−	9.30367i	−0.604007	−	0.363247i
$657$	0.483410	+	0.837291i	0.0188596	+	0.0326658i
$658$	−2.79671	−	4.89435i	−0.109027	−	0.190802i
$659$	−22.7850	−	13.1549i	−0.887578	−	0.512444i	−0.0144288	−	0.999896i	$-0.504593\pi$
$659$	−22.7850	−	13.1549i	−0.887578	−	0.512444i	−0.873150	+	0.487452i	$0.837926\pi$
$660$	−0.178003	−	0.104899i	−0.00692874	−	0.00408317i
$661$		−	23.8031i		−	0.925834i	−0.886402	−	0.462917i	$-0.846803\pi$
$661$		−	23.8031i		−	0.925834i	0.886402	−	0.462917i	$-0.153197\pi$
$662$	−19.4634	−	11.3533i	−0.756466	−	0.441257i
$663$	14.1857	+	8.19011i	0.550927	+	0.318078i
$664$	−7.87178	−	14.0658i	−0.305484	−	0.545859i
$665$	−0.0188949			−0.000732712
$666$	4.87866	−	2.78775i	0.189044	−	0.108023i
$667$		−	18.5329i		−	0.717596i
$668$	15.2545	+	8.98963i	0.590215	+	0.347819i
$669$			25.5413i			0.987485i
$670$	2.25706	−	1.52962i	0.0871978	−	0.0590945i
$671$			3.31099i			0.127819i
$672$	3.73587	+	2.26949i	0.144114	+	0.0875476i
$673$		−	17.2202i		−	0.663791i	−0.943316	−	0.331895i	$-0.892312\pi$
$673$		−	17.2202i		−	0.663791i	0.943316	−	0.331895i	$-0.107688\pi$
$674$	−12.6848	−	22.1989i	−0.488601	−	0.855069i
$675$	−4.94452			−0.190315
$676$	6.55941	−	11.1307i	0.252285	−	0.428102i
$677$	−22.1381	−	12.7814i	−0.850835	−	0.491230i	0.0100972	−	0.999949i	$-0.496786\pi$
$677$	−22.1381	−	12.7814i	−0.850835	−	0.491230i	−0.860933	+	0.508719i	$0.830119\pi$
$678$	−0.419291	+	0.718808i	−0.0161028	+	0.0276056i
$679$			13.7074i			0.526043i
$680$	−2.08389	−	3.72363i	−0.0799135	−	0.142795i
$681$	17.4356	+	10.0665i	0.668134	+	0.385747i
$682$	−4.18003	+	2.38854i	−0.160062	+	0.0914619i
$683$	16.9821	+	29.4138i	0.649801	+	1.12549i	0.983170	+	0.182692i	$0.0584812\pi$
$683$	16.9821	+	29.4138i	0.649801	+	1.12549i	−0.333369	+	0.942796i	$0.608185\pi$
$684$	0.180731	−	0.102206i	0.00691043	−	0.00390794i
$685$	4.81168			0.183845
$686$	0.0653466	−	14.6465i	0.00249495	−	0.559207i
$687$	−4.88243	+	2.81887i	−0.186276	+	0.107547i
$688$	49.4094	+	0.881865i	1.88372	+	0.0336208i
$689$	17.4465	+	30.2183i	0.664660	+	1.15123i
$690$	−0.571866	+	0.326774i	−0.0217706	+	0.0124401i
$691$	−24.6273	−	14.2186i	−0.936867	−	0.540901i	−0.0478904	−	0.998853i	$-0.515250\pi$
$691$	−24.6273	−	14.2186i	−0.936867	−	0.540901i	−0.888977	+	0.457952i	$0.848583\pi$
$692$	−9.23119	−	16.3236i	−0.350917	−	0.620528i
$693$	0.169457	+	0.293509i	0.00643715	+	0.0111495i
$694$	−44.0715	−	25.7076i	−1.67293	−	0.975846i
$695$		−	0.0898911i		−	0.00340976i
$696$	−22.7790	−	13.5612i	−0.863436	−	0.514035i
$697$		−	28.9065i		−	1.09491i
$698$	0.0169114	−	3.79045i	0.000640107	−	0.143471i
$699$	11.0308	+	6.36865i	0.417224	+	0.240885i
$700$	−3.87965	+	6.58339i	−0.146637	+	0.248829i
$701$	17.8098	+	10.2825i	0.672668	+	0.388365i	0.797087	−	0.603865i	$-0.206373\pi$
$701$	17.8098	+	10.2825i	0.672668	+	0.388365i	−0.124419	+	0.992230i	$0.539707\pi$
$702$	−1.79435	−	3.14017i	−0.0677232	−	0.118518i
$703$	−0.357216	−	0.206239i	−0.0134727	−	0.00777845i
$704$	1.83509	−	2.99064i	0.0691626	−	0.112714i
$705$	0.607494	−	1.05221i	0.0228795	−	0.0396285i
$706$	−1.94820	−	3.40942i	−0.0733214	−	0.128315i
$707$	−3.37026	+	1.94582i	−0.126752	+	0.0731801i
$708$	−0.0448855	+	5.03012i	−0.00168690	+	0.189043i
$709$	−18.7936	−	32.5515i	−0.705808	−	1.22250i	−0.966399	−	0.257046i	$-0.917251\pi$
$709$	−18.7936	−	32.5515i	−0.705808	−	1.22250i	0.260591	−	0.965449i	$-0.416083\pi$
$710$	−0.991532	−	0.578375i	−0.0372115	−	0.0217060i
$711$	−6.49609	+	11.2516i	−0.243623	+	0.421967i
$712$	−0.399328	+	29.8330i	−0.0149655	+	1.11804i
$713$			15.3473i			0.574759i
$714$	−0.0312284	+	6.99940i	−0.00116869	+	0.261946i
$715$	0.264193			0.00988025
$716$	−23.2698	−	0.207644i	−0.869634	−	0.00776004i
$717$	−3.92936	+	6.80584i	−0.146744	+	0.254169i
$718$	−33.8828	−	0.151171i	−1.26450	−	0.00564165i
$719$	−15.6061	+	9.01017i	−0.582008	+	0.336023i	−0.761931	−	0.647658i	$-0.775748\pi$
$719$	−15.6061	+	9.01017i	−0.582008	+	0.336023i	0.179923	+	0.983681i	$0.442415\pi$
$720$	−0.0168129	+	0.942001i	−0.000626581	+	0.0351063i
$721$	8.43137	−	4.86785i	0.314001	−	0.181288i
$722$	23.1968	+	13.5310i	0.863296	+	0.503573i
$723$	−17.4787			−0.650041
$724$	10.9356	−	18.5566i	0.406417	−	0.689650i
$725$	23.1719	−	40.1349i	0.860583	−	1.49057i
$726$	−13.2706	+	7.58302i	−0.492517	+	0.281432i
$727$	6.60429	+	11.4390i	0.244939	+	0.424247i	0.962115	−	0.272645i	$-0.0878986\pi$
$727$	6.60429	+	11.4390i	0.244939	+	0.424247i	−0.717175	+	0.696893i	$0.754565\pi$
$728$	−5.58889	−	0.0748099i	−0.207138	−	0.00277264i
$729$	1.00000			0.0370370
$730$	0.159778	+	0.279618i	0.00591366	+	0.0103491i
$731$	39.5653	+	68.5291i	1.46337	+	2.53464i
$732$	13.1422	−	7.43208i	0.485749	−	0.274697i
$733$	−28.0544	−	16.1972i	−1.03621	−	0.598258i	−0.117455	−	0.993078i	$-0.537474\pi$
$733$	−28.0544	−	16.1972i	−1.03621	−	0.598258i	−0.918759	+	0.394820i	$0.870807\pi$
$734$	−5.04020	−	2.94002i	−0.186037	−	0.108518i
$735$	1.30607	−	0.754062i	0.0481753	−	0.0278140i
$736$	−5.37522	−	9.80915i	−0.198133	−	0.361570i
$737$	0.274263	+	3.57958i	0.0101026	+	0.131855i
$738$	−3.21584	+	5.51305i	−0.118377	+	0.202938i
$739$	−17.6286	−	30.5336i	−0.648478	−	1.12320i	−0.983486	−	0.180982i	$-0.942072\pi$
$739$	−17.6286	−	30.5336i	−0.648478	−	1.12320i	0.335008	−	0.942215i	$-0.391261\pi$
$740$	1.62921	−	0.921342i	0.0598911	−	0.0338692i
$741$	−0.132746	+	0.229924i	−0.00487656	+	0.00844645i
$742$	−7.51266	+	12.8793i	−0.275798	+	0.472812i
$743$	19.7273	−	11.3896i	0.723725	−	0.417843i	−0.0923971	−	0.995722i	$-0.529453\pi$
$743$	19.7273	−	11.3896i	0.723725	−	0.417843i	0.816122	+	0.577879i	$0.196120\pi$
$744$	18.8635	+	11.2301i	0.691570	+	0.411717i
$745$			4.29202i			0.157248i
$746$	−8.32274	+	14.2680i	−0.304717	+	0.522389i
$747$	−4.93531	+	2.84941i	−0.180574	+	0.104254i
$748$	5.61828	+	0.0501338i	0.205425	+	0.00183307i
$749$	6.47446	+	3.73803i	0.236572	+	0.136585i
$750$	−3.31249	−	0.0147790i	−0.120955	−	0.000539652i
$751$			6.87322i			0.250807i	0.992106	+	0.125404i	$0.0400226\pi$
$751$			6.87322i			0.250807i	−0.992106	+	0.125404i	$0.959977\pi$
$752$	17.6821	+	10.6339i	0.644800	+	0.387780i
$753$	−7.30855	−	12.6588i	−0.266338	−	0.461312i
$754$	33.8979	+	0.151238i	1.23449	+	0.00550777i
$755$	−1.06412	−	1.84312i	−0.0387274	−	0.0670778i
$756$	0.784637	−	1.33145i	0.0285370	−	0.0484244i
$757$	−23.6556	−	13.6576i	−0.859779	−	0.496394i	0.00415914	−	0.999991i	$-0.498676\pi$
$757$	−23.6556	−	13.6576i	−0.859779	−	0.496394i	−0.863938	+	0.503598i	$0.832009\pi$
$758$	−22.4740	+	12.8420i	−0.816293	+	0.466443i
$759$		−	0.867243i		−	0.0314789i
$760$	0.0603530	−	0.0337760i	0.00218923	−	0.00122518i
$761$	−12.4427			−0.451048			−0.225524	−	0.974238i	$-0.572409\pi$
$761$	−12.4427			−0.451048			−0.225524	+	0.974238i	$0.572409\pi$
$762$	−0.564524	+	0.967787i	−0.0204506	+	0.0350592i
$763$	9.20724	+	5.31580i	0.333324	+	0.192445i
$764$	−16.0376	−	28.3593i	−0.580219	−	1.02600i
$765$	−1.30652	+	0.754320i	−0.0472374	+	0.0272725i
$766$	−38.8473	+	22.1980i	−1.40361	+	0.802046i
$767$	−3.21610	−	5.57046i	−0.116127	−	0.201137i
$768$	−15.9898	−	0.570958i	−0.576983	−	0.0206027i
$769$	24.7824	+	14.3081i	0.893674	+	0.515963i	0.875143	−	0.483865i	$-0.160767\pi$
$769$	24.7824	+	14.3081i	0.893674	+	0.515963i	0.0185318	+	0.999828i	$0.494101\pi$
$770$	0.0560096	+	0.0980189i	0.00201845	+	0.00353236i
$771$	2.48240	−	4.29964i	0.0894015	−	0.154848i
$772$	19.9651	+	0.178156i	0.718561	+	0.00641196i
$773$	3.43711	−	5.95325i	0.123624	−	0.214123i	−0.797570	−	0.603226i	$-0.793882\pi$
$773$	3.43711	−	5.95325i	0.123624	−	0.214123i	0.921194	+	0.389103i	$0.127215\pi$
$774$	0.0779505	−	17.4715i	0.00280187	−	0.627999i
$775$	−19.1889	+	33.2361i	−0.689285	+	1.19388i
$776$	−24.5030	−	43.7835i	−0.879607	−	1.57174i
$777$	−3.07020			−0.110143
$778$	−9.60954	+	5.49105i	−0.344519	+	0.196864i
$779$	0.468521			0.0167865
$780$	−0.593025	−	1.04865i	−0.0212337	−	0.0375477i
$781$	1.30894	−	0.755719i	0.0468377	−	0.0270418i
$782$	9.02453	−	15.4711i	0.322716	−	0.553246i
$783$	−4.68638	+	8.11705i	−0.167478	+	0.290080i
$784$	12.4079	+	22.4053i	0.443141	+	0.800188i
$785$	2.45945	−	1.41996i	0.0877814	−	0.0506806i
$786$	−7.77781	−	0.0347013i	−0.277425	−	0.00123776i
$787$	22.4242	+	38.8399i	0.799336	+	1.38449i	0.920049	+	0.391804i	$0.128149\pi$
$787$	22.4242	+	38.8399i	0.799336	+	1.38449i	−0.120713	+	0.992688i	$0.538518\pi$
$788$	4.67326	+	2.75400i	0.166478	+	0.0981071i
$789$		−	12.7373i		−	0.453462i
$790$	−2.18055	+	3.73821i	−0.0775806	+	0.133000i
$791$	0.393774	−	0.227346i	0.0140010	−	0.00808348i
$792$	−1.06594	−	0.634593i	−0.0378765	−	0.0225493i
$793$	−9.65288	+	16.7193i	−0.342784	+	0.593719i
$794$	−0.109675	+	24.5821i	−0.00389222	+	0.872386i
$795$	−3.21370			−0.113978
$796$	−24.4625	+	13.8339i	−0.867049	+	0.490328i
$797$	−2.78510	+	4.82394i	−0.0986535	+	0.170873i	−0.911128	−	0.412125i	$-0.864787\pi$
$797$	−2.78510	+	4.82394i	−0.0986535	+	0.170873i	0.812474	+	0.582997i	$0.198120\pi$
$798$	−0.113447		0.000506154i	−0.00401599		1.79177e-5i
$799$			33.0397i			1.16886i
$800$	0.623906	−	27.9635i	0.0220584	−	0.988658i
$801$	10.5485			0.372713
$802$	16.2957	+	0.0727044i	0.575420	+	0.00256728i
$803$	−0.424044			−0.0149642
$804$	13.5926	−	9.12359i	0.479376	−	0.321764i
$805$	0.359883			0.0126842
$806$	−28.0712	−	0.125242i	−0.988765	−	0.00441146i
$807$	4.96771			0.174872
$808$	7.28682	−	12.2398i	0.256349	−	0.430596i
$809$			21.9394i			0.771350i	0.922635	+	0.385675i	$0.126031\pi$
$809$			21.9394i			0.771350i	−0.922635	+	0.385675i	$0.873969\pi$
$810$	0.333097	+	0.00148614i	0.0117039	+	5.22177e-5i
$811$	−18.0978	+	31.3463i	−0.635500	+	1.10072i	0.350909	+	0.936410i	$0.385873\pi$
$811$	−18.0978	+	31.3463i	−0.635500	+	1.10072i	−0.986409	+	0.164309i	$0.947461\pi$
$812$	7.13034	+	12.6086i	0.250226	+	0.442476i
$813$	5.78762			0.202981
$814$	−0.0109953	+	2.46444i	−0.000385385	+	0.0863786i
$815$	0.268223	−	0.464576i	0.00939545	−	0.0162734i
$816$	−12.4122	−	22.4130i	−0.434514	−	0.784610i
$817$	−1.11073	+	0.641279i	−0.0388595	+	0.0224355i
$818$	7.83658	−	13.4346i	0.274000	−	0.469729i
$819$			1.97615i			0.0690522i
$820$	−1.07938	+	1.83160i	−0.0376937	+	0.0639624i
$821$	−18.6201	−	32.2510i	−0.649846	−	1.12557i	−0.983159	−	0.182750i	$-0.941500\pi$
$821$	−18.6201	−	32.2510i	−0.649846	−	1.12557i	0.333314	−	0.942816i	$-0.391833\pi$
$822$	28.8900	+	0.128895i	1.00765	+	0.00449573i
$823$	−0.977222	+	0.564199i	−0.0340638	+	0.0196668i	−0.516935	−	0.856025i	$-0.672927\pi$
$823$	−0.977222	+	0.564199i	−0.0340638	+	0.0196668i	0.482871	+	0.875691i	$0.339594\pi$
$824$	−18.2294	+	30.6203i	−0.635051	+	1.06671i
$825$	1.08433	−	1.87811i	0.0377514	−	0.0653873i
$826$	1.38489	−	2.37417i	0.0481864	−	0.0826079i
$827$	−37.1435	+	21.4448i	−1.29161	+	0.745709i	−0.978939	−	0.204154i	$-0.934556\pi$
$827$	−37.1435	+	21.4448i	−1.29161	+	0.745709i	−0.312667	+	0.949863i	$0.601222\pi$
$828$	−3.44231	+	1.94667i	−0.119629	+	0.0676516i
$829$	5.65712			0.196480			0.0982400	−	0.995163i	$-0.468679\pi$
$829$	5.65712			0.196480			0.0982400	+	0.995163i	$0.468679\pi$
$830$	−1.64818	+	0.941795i	−0.0572090	+	0.0326902i
$831$	−10.9468			−0.379740
$832$	17.9855	−	9.75160i	0.623534	−	0.338076i
$833$	−20.5056	+	35.5167i	−0.710476	+	1.23058i
$834$	0.00240799	−	0.539718i	8.33820e−5	−	0.0186889i
$835$	1.04263	−	1.80588i	0.0360816	−	0.0624951i
$836$	−0.000812576		0.0910618i	−2.81035e−5		0.00314944i
$837$	3.88084	−	6.72181i	0.134141	−	0.232340i
$838$	−15.1935	−	26.5892i	−0.524851	−	0.918509i
$839$	−28.2110	−	16.2877i	−0.973953	−	0.562312i	−0.0735142	−	0.997294i	$-0.523421\pi$
$839$	−28.2110	−	16.2877i	−0.973953	−	0.562312i	−0.900439	+	0.434982i	$0.856755\pi$
$840$	0.263339	−	0.442337i	0.00908607	−	0.0152621i
$841$	−29.4243	−	50.9644i	−1.01463	−	1.75739i
$842$	−40.3270	+	23.0435i	−1.38976	+	0.794132i
$843$	−1.05929	+	0.611579i	−0.0364837	+	0.0210639i
$844$	12.9824	−	7.34171i	0.446872	−	0.252712i
$845$	−1.31769	−	0.760767i	−0.0453298	−	0.0261712i
$846$	3.67566	−	6.30133i	0.126372	−	0.216644i
$847$	8.35133			0.286955
$848$	0.973930	−	54.5677i	0.0334449	−	1.87386i
$849$			27.8666i			0.956380i
$850$	38.8873	−	22.2209i	1.33382	−	0.762170i
$851$	6.80375	+	3.92815i	0.233229	+	0.134655i
$852$	−5.93779	−	3.49920i	−0.203425	−	0.119881i
$853$	−9.89061	−	17.1310i	−0.338648	−	0.586556i	0.645531	−	0.763734i	$-0.276636\pi$
$853$	−9.89061	−	17.1310i	−0.338648	−	0.586556i	−0.984179	+	0.177179i	$0.943303\pi$
$854$	−8.24951	−	0.0368058i	−0.282292	−	0.00125947i
$855$	−0.0122261	−	0.0211763i	−0.000418125	−	0.000724213i
$856$	−27.3624	−	0.366258i	−0.935228	−	0.0125184i
$857$		−	54.5851i		−	1.86459i	−0.361698	−	0.932295i	$-0.617803\pi$
$857$		−	54.5851i		−	1.86459i	0.361698	−	0.932295i	$-0.382197\pi$
$858$	1.58625	+	0.00707717i	0.0541536	+	0.000241611i
$859$	−38.1152	−	22.0058i	−1.30047	−	0.750829i	−0.319989	−	0.947421i	$-0.603679\pi$
$859$	−38.1152	−	22.0058i	−1.30047	−	0.750829i	−0.980485	+	0.196592i	$0.937013\pi$
$860$	0.0519302	−	5.81959i	0.00177080	−	0.198446i
$861$	3.02014	−	1.74368i	0.102926	−	0.0594243i
$862$	−0.924158	+	1.58432i	−0.0314769	+	0.0539622i
$863$		−	7.66276i		−	0.260843i	−0.991459	−	0.130422i	$-0.958367\pi$
$863$		−	7.66276i		−	0.260843i	0.991459	−	0.130422i	$-0.0416331\pi$
$864$	−0.126181	+	5.65545i	−0.00429278	+	0.192402i
$865$	−1.91263	+	1.10426i	−0.0650314	+	0.0375459i
$866$	−18.5715	+	31.8379i	−0.631085	+	1.08189i
$867$	12.0126	−	20.8064i	0.407969	−	0.706623i
$868$	−5.90471	−	10.4413i	−0.200419	−	0.354402i
$869$	−2.84917	−	4.93490i	−0.0966513	−	0.167405i
$870$	−1.57308	+	2.69680i	−0.0533325	+	0.0914302i
$871$	−9.05100	+	18.8751i	−0.306681	+	0.639560i
$872$	−38.9117	−	0.520851i	−1.31772	−	0.0176382i
$873$	−15.3625	+	8.86953i	−0.519941	+	0.300188i
$874$	0.250758	+	0.146271i	0.00848201	+	0.00494768i
$875$	1.56747	+	0.904981i	0.0529903	+	0.0305940i
$876$	0.951839	+	1.68314i	0.0321597	+	0.0568681i
$877$	−6.09111	−	10.5501i	−0.205682	−	0.356252i	0.744668	−	0.667435i	$-0.232608\pi$
$877$	−6.09111	−	10.5501i	−0.205682	−	0.356252i	−0.950350	+	0.311183i	$0.899275\pi$
$878$	−23.6867	−	41.4526i	−0.799387	−	1.39896i
$879$	24.4695			0.825336
$880$	−0.354119	−	0.212966i	−0.0119373	−	0.00717907i
$881$	5.50899	+	9.54186i	0.185603	+	0.321473i	0.943779	−	0.330576i	$-0.107243\pi$
$881$	5.50899	+	9.54186i	0.185603	+	0.321473i	−0.758177	+	0.652049i	$0.773910\pi$
$882$	7.86204	−	4.49250i	0.264729	−	0.151270i
$883$	11.7814	−	20.4059i	0.396475	−	0.686714i	−0.596813	−	0.802380i	$-0.703567\pi$
$883$	11.7814	−	20.4059i	0.396475	−	0.686714i	0.993288	+	0.115666i	$0.0369001\pi$
$884$	28.2241	+	16.6327i	0.949279	+	0.559419i
$885$	0.592415			0.0199138
$886$	31.6997	+	18.4909i	1.06497	+	0.621214i
$887$	15.4320	−	8.90969i	0.518157	−	0.299158i	−0.218023	−	0.975944i	$-0.569961\pi$
$887$	15.4320	−	8.90969i	0.518157	−	0.299158i	0.736180	+	0.676786i	$0.236628\pi$
$888$	9.80669	−	5.48821i	0.329091	−	0.184172i
$889$	0.530169	−	0.306093i	0.0177813	−	0.0102660i
$890$	3.51368	+	0.0156766i	0.117779	+	0.000525480i
$891$	−0.219298	+	0.379836i	−0.00734677	+	0.0127250i
$892$	−0.455810	+	51.0806i	−0.0152616	+	1.71031i
$893$	−0.535512			−0.0179202
$894$	−0.114974	+	25.7699i	−0.00384532	+	0.861873i
$895$			2.74057i			0.0916071i
$896$	7.43094	+	4.60548i	0.248250	+	0.153858i
$897$	2.52837	−	4.37926i	0.0844197	−	0.146219i
$898$	5.56318	+	3.24508i	0.185646	+	0.108290i
$899$	36.3741	+	63.0019i	1.21315	+	2.10123i
$900$	−9.88865	−	0.0882398i	−0.329622	−	0.00294133i
$901$	75.6834	−	43.6958i	2.52138	−	1.45572i
$902$	−1.38883	−	2.43050i	−0.0462429	−	0.0809267i
$903$	−4.77325	+	8.26751i	−0.158844	+	0.275126i
$904$	−0.851376	+	1.43008i	−0.0283164	+	0.0475636i
$905$	−2.19679	−	1.26832i	−0.0730239	−	0.0421603i
$906$	−6.33976	−	11.0948i	−0.210624	−	0.368600i
$907$	42.0300	+	24.2660i	1.39558	+	0.805740i	0.993926	−	0.110050i	$-0.0351012\pi$
$907$	42.0300	+	24.2660i	1.39558	+	0.805740i	0.401657	+	0.915790i	$0.368434\pi$
$908$	34.6902	+	20.4433i	1.15123	+	0.678433i
$909$	−4.36153	−	2.51813i	−0.144663	−	0.0835210i
$910$	−0.00293684	+	0.658250i	−9.73552e−5	+	0.0218208i
$911$			34.9228i			1.15704i	0.815667	+	0.578521i	$0.196370\pi$
$911$			34.9228i			1.15704i	−0.815667	+	0.578521i	$0.803630\pi$
$912$	0.363272	−	0.201178i	0.0120291	−	0.00666168i
$913$		−	2.49948i		−	0.0827207i
$914$	−11.8214	−	6.89557i	−0.391016	−	0.228085i
$915$	−0.889043	−	1.53987i	−0.0293909	−	0.0509065i
$916$	−9.81478	+	5.55039i	−0.324289	+	0.183390i
$917$	3.68046	+	2.12492i	0.121540	+	0.0701709i
$918$	−7.86473	+	4.49404i	−0.259575	+	0.148325i
$919$	−18.8634	−	32.6724i	−0.622247	−	1.07776i	−0.989066	−	0.147472i	$-0.952886\pi$
$919$	−18.8634	−	32.6724i	−0.622247	−	1.07776i	0.366819	−	0.930292i	$-0.380447\pi$
$920$	−1.14952	+	0.643317i	−0.0378985	+	0.0212095i
$921$	18.4346	−	10.6432i	0.607442	−	0.350707i
$922$	0.0228733	−	5.12673i	0.000753293	−	0.168840i
$923$	8.81291			0.290081
$924$	0.333663	+	0.590018i	0.0109767	+	0.0194102i
$925$	9.82283	+	17.0136i	0.322973	+	0.559405i
$926$	−5.06470	+	2.89405i	−0.166436	+	0.0951045i
$927$	10.9112	+	6.29959i	0.358371	+	0.206906i
$928$	−45.3142	−	27.5278i	−1.48751	−	0.903644i
$929$			0.646765i			0.0212197i	0.999944	+	0.0106098i	$0.00337728\pi$
$929$			0.646765i			0.0212197i	−0.999944	+	0.0106098i	$0.996623\pi$
$930$	1.30269	−	2.23325i	0.0427168	−	0.0732311i
$931$	−0.575659	−	0.332357i	−0.0188665	−	0.0108926i
$932$	21.9471	+	12.9337i	0.718902	+	0.423656i
$933$	24.3836			0.798283
$934$	−14.5216	−	25.4134i	−0.475163	−	0.831552i
$935$		−	0.661685i		−	0.0216394i
$936$	−3.53251	−	6.31211i	−0.115464	−	0.206318i
$937$			26.2860i			0.858728i	0.903132	+	0.429364i	$0.141262\pi$
$937$			26.2860i			0.858728i	−0.903132	+	0.429364i	$0.858738\pi$
$938$	−8.92176	+	0.643549i	−0.291306	+	0.0210126i
$939$		−	20.6206i		−	0.672929i
$940$	1.23372	−	2.09349i	0.0402394	−	0.0682823i
$941$			40.5703i			1.32255i	0.750141	+	0.661277i	$0.229985\pi$
$941$			40.5703i			1.32255i	−0.750141	+	0.661277i	$0.770015\pi$
$942$	14.8049	−	8.45975i	0.482369	−	0.275633i
$943$	−8.92373			−0.290597
$944$	−0.179535	+	10.0590i	−0.00584336	+	0.327394i
$945$	−0.157622	−	0.0910030i	−0.00512744	−	0.00296033i
$946$	6.61920	+	3.86108i	0.215209	+	0.125534i
$947$		−	15.7233i		−	0.510937i	−0.966817	−	0.255469i	$-0.917770\pi$
$947$		−	15.7233i		−	0.510937i	0.966817	−	0.255469i	$-0.0822297\pi$
$948$	−13.1925	+	22.3863i	−0.428471	+	0.727073i
$949$	−2.14127	−	1.23626i	−0.0695085	−	0.0401307i
$950$	0.360159	+	0.630291i	0.0116851	+	0.0204493i
$951$	14.2500	+	24.6817i	0.462088	+	0.800360i
$952$	−0.187365	+	13.9977i	−0.00607255	+	0.453668i
$953$	11.4464			0.370787			0.185393	−	0.982664i	$-0.440644\pi$
$953$	11.4464			0.370787			0.185393	+	0.982664i	$0.440644\pi$
$954$	−19.2955	−	0.0860883i	−0.624714	−	0.00278721i
$955$	−3.32286	+	1.91845i	−0.107525	+	0.0620797i
$956$	−7.97985	+	13.5410i	−0.258087	+	0.437948i
$957$	−2.05543	−	3.56011i	−0.0664426	−	0.115082i
$958$	−19.5566	−	34.2248i	−0.631846	−	1.10575i
$959$	−13.6707	−	7.89281i	−0.441451	−	0.254872i
$960$	−0.0504355	+	1.88363i	−0.00162780	+	0.0607938i
$961$	−14.6218	−	25.3257i	−0.471670	−	0.816957i
$962$	−7.24037	+	12.4125i	−0.233439	+	0.400194i
$963$			9.67494i			0.311770i
$964$	−34.9561	−	0.311925i	−1.12586	−	0.0100464i
$965$		−	2.35136i		−	0.0756931i
$966$	2.16078	+	0.00964051i	0.0695220	+	0.000310178i
$967$	−51.7483	−	29.8769i	−1.66411	−	0.960776i	−0.970719	−	0.240216i	$-0.922782\pi$
$967$	−51.7483	−	29.8769i	−1.66411	−	0.960776i	−0.693393	−	0.720559i	$-0.743885\pi$
$968$	−26.6754	+	14.9286i	−0.857379	+	0.479824i
$969$	0.575856	+	0.332471i	0.0184992	+	0.0106805i
$970$	−5.13038	+	2.93159i	−0.164727	+	0.0941276i
$971$	31.5763	+	18.2306i	1.01333	+	0.585047i	0.912165	−	0.409822i	$-0.134409\pi$
$971$	31.5763	+	18.2306i	1.01333	+	0.585047i	0.101166	+	0.994870i	$0.467743\pi$
$972$	1.99992	+	0.0178460i	0.0641475	+	0.000572410i
$973$	−0.147452	+	0.255395i	−0.00472710	+	0.00818757i
$974$	23.2683	−	13.2959i	0.745564	−	0.426028i
$975$	10.9509	−	6.32250i	0.350709	−	0.202482i
$976$	26.4159	−	14.6290i	0.845553	−	0.468264i
$977$	−18.8852	−	32.7101i	−0.604190	−	1.04649i	−0.992179	−	0.124824i	$-0.960163\pi$
$977$	−18.8852	−	32.7101i	−0.604190	−	1.04649i	0.387989	−	0.921664i	$-0.373170\pi$
$978$	1.62289	−	2.78219i	0.0518944	−	0.0889647i
$979$	−2.31327	+	4.00670i	−0.0739324	+	0.128055i
$980$	2.62550	−	1.48476i	0.0838685	−	0.0474288i
$981$			13.7586i			0.439278i
$982$	32.1748	+	0.143551i	1.02674	+	0.00458088i
$983$	31.6686			1.01007			0.505036	−	0.863098i	$-0.331479\pi$
$983$	31.6686			1.01007			0.505036	+	0.863098i	$0.331479\pi$
$984$	−6.52981	+	10.9683i	−0.208163	+	0.349656i
$985$	0.319411	−	0.553237i	0.0101773	−	0.0176276i
$986$	0.378784	−	84.8991i	0.0120630	−	2.70374i
$987$	−3.45197	+	1.99300i	−0.109877	+	0.0634377i
$988$	−0.269586	+	0.457460i	−0.00857666	+	0.0145537i
$989$	21.1556	−	12.2142i	0.672708	−	0.388388i
$990$	−0.0736122	+	0.126196i	−0.00233955	+	0.00401079i
$991$	−36.5519			−1.16111			−0.580555	−	0.814221i	$-0.697164\pi$
$991$	−36.5519			−1.16111			−0.580555	+	0.814221i	$0.697164\pi$
$992$	37.5251	+	22.7960i	1.19142	+	0.723775i
$993$	−7.96649	+	13.7984i	−0.252809	+	0.437878i
$994$	1.86836	+	3.26970i	0.0592609	+	0.103709i
$995$	1.65484	+	2.86627i	0.0524619	+	0.0908667i
$996$	−9.92109	+	5.61051i	−0.314362	+	0.177776i
$997$	−28.9669			−0.917391			−0.458696	−	0.888593i	$-0.651683\pi$
$997$	−28.9669			−0.917391			−0.458696	+	0.888593i	$0.651683\pi$
$998$	−1.26302	+	0.721710i	−0.0399802	+	0.0228453i
$999$	−1.98661	−	3.44091i	−0.0628535	−	0.108865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.17	✓	68
4.3	odd	2		804.2.j.b.499.29	yes	68
67.38	odd	6		804.2.j.b.775.29	yes	68
268.239	even	6	inner	804.2.j.a.775.17	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.17	✓	68	1.1	even	1	trivial
804.2.j.a.775.17	yes	68	268.239	even	6	inner
804.2.j.b.499.29	yes	68	4.3	odd	2
804.2.j.b.775.29	yes	68	67.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00630957 - 1.41420i) q^{2} -1.00000 q^{3} +(-1.99992 - 0.0178460i) q^{4} +0.235538i q^{5} +(-0.00630957 + 1.41420i) q^{6} +(0.386363 - 0.669200i) q^{7} +(-0.0378564 + 2.82817i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.00630957 - 1.41420i) q^{2} -1.00000 q^{3} +(-1.99992 - 0.0178460i) q^{4} +0.235538i q^{5} +(-0.00630957 + 1.41420i) q^{6} +(0.386363 - 0.669200i) q^{7} +(-0.0378564 + 2.82817i) q^{8} +1.00000 q^{9} +(0.333097 + 0.00148614i) q^{10} +(-0.219298 + 0.379836i) q^{11} +(1.99992 + 0.0178460i) q^{12} +(-2.21475 + 1.27869i) q^{13} +(-0.943944 - 0.550616i) q^{14} -0.235538i q^{15} +(3.99936 + 0.0713811i) q^{16} +(3.20255 + 5.54697i) q^{17} +(0.00630957 - 1.41420i) q^{18} +(-0.0899060 + 0.0519073i) q^{19} +(0.00420340 - 0.471057i) q^{20} +(-0.386363 + 0.669200i) q^{21} +(0.535780 + 0.312528i) q^{22} +(1.71240 - 0.988656i) q^{23} +(0.0378564 - 2.82817i) q^{24} +4.94452 q^{25} +(1.79435 + 3.14017i) q^{26} -1.00000 q^{27} +(-0.784637 + 1.33145i) q^{28} +(4.68638 - 8.11705i) q^{29} +(-0.333097 - 0.00148614i) q^{30} +(-3.88084 + 6.72181i) q^{31} +(0.126181 - 5.65545i) q^{32} +(0.219298 - 0.379836i) q^{33} +(7.86473 - 4.49404i) q^{34} +(0.157622 + 0.0910030i) q^{35} +(-1.99992 - 0.0178460i) q^{36} +(1.98661 + 3.44091i) q^{37} +(0.0728400 + 0.127473i) q^{38} +(2.21475 - 1.27869i) q^{39} +(-0.666142 - 0.00891661i) q^{40} +(-3.90842 - 2.25653i) q^{41} +(0.943944 + 0.550616i) q^{42} +12.3543 q^{43} +(0.445358 - 0.755728i) q^{44} +0.235538i q^{45} +(-1.38735 - 2.42792i) q^{46} +(4.46727 + 2.57918i) q^{47} +(-3.99936 - 0.0713811i) q^{48} +(3.20145 + 5.54507i) q^{49} +(0.0311978 - 6.99254i) q^{50} +(-3.20255 - 5.54697i) q^{51} +(4.45215 - 2.51775i) q^{52} -13.6441i q^{53} +(-0.00630957 + 1.41420i) q^{54} +(-0.0894657 - 0.0516531i) q^{55} +(1.87799 + 1.11803i) q^{56} +(0.0899060 - 0.0519073i) q^{57} +(-11.4496 - 6.67869i) q^{58} +2.51516i q^{59} +(-0.00420340 + 0.471057i) q^{60} +(6.53767 - 3.77452i) q^{61} +(9.48149 + 5.53069i) q^{62} +(0.386363 - 0.669200i) q^{63} +(-7.99713 - 0.214129i) q^{64} +(-0.301179 - 0.521658i) q^{65} +(-0.535780 - 0.312528i) q^{66} +(6.75535 - 4.62226i) q^{67} +(-6.30584 - 11.1507i) q^{68} +(-1.71240 + 0.988656i) q^{69} +(0.129691 - 0.222335i) q^{70} +(-2.98439 - 1.72304i) q^{71} +(-0.0378564 + 2.82817i) q^{72} +(0.483410 + 0.837291i) q^{73} +(4.87866 - 2.78775i) q^{74} -4.94452 q^{75} +(0.180731 - 0.102206i) q^{76} +(0.169457 + 0.293509i) q^{77} +(-1.79435 - 3.14017i) q^{78} +(-6.49609 + 11.2516i) q^{79} +(-0.0168129 + 0.942001i) q^{80} +1.00000 q^{81} +(-3.21584 + 5.51305i) q^{82} +(-4.93531 + 2.84941i) q^{83} +(0.784637 - 1.33145i) q^{84} +(-1.30652 + 0.754320i) q^{85} +(0.0779505 - 17.4715i) q^{86} +(-4.68638 + 8.11705i) q^{87} +(-1.06594 - 0.634593i) q^{88} +10.5485 q^{89} +(0.333097 + 0.00148614i) q^{90} +1.97615i q^{91} +(-3.44231 + 1.94667i) q^{92} +(3.88084 - 6.72181i) q^{93} +(3.67566 - 6.30133i) q^{94} +(-0.0122261 - 0.0211763i) q^{95} +(-0.126181 + 5.65545i) q^{96} +(-15.3625 + 8.86953i) q^{97} +(7.86204 - 4.49250i) q^{98} +(-0.219298 + 0.379836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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