LMFDB - Embedded newform 630.2.bi.b.479.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(479,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.479"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.18
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.b.509.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.13785 + 1.30587i) q^{3} +1.00000 q^{4} +(1.67933 + 1.47644i) q^{5} +(1.13785 + 1.30587i) q^{6} +(-2.41546 + 1.07960i) q^{7} +1.00000 q^{8} +(-0.410606 + 2.97177i) q^{9} +(1.67933 + 1.47644i) q^{10} +(5.13649 - 2.96556i) q^{11} +(1.13785 + 1.30587i) q^{12} +(-2.57957 - 4.46794i) q^{13} +(-2.41546 + 1.07960i) q^{14} +(-0.0172195 + 3.87295i) q^{15} +1.00000 q^{16} +(1.62025 + 0.935454i) q^{17} +(-0.410606 + 2.97177i) q^{18} +(-1.51165 + 0.872754i) q^{19} +(1.67933 + 1.47644i) q^{20} +(-4.15825 - 1.92587i) q^{21} +(5.13649 - 2.96556i) q^{22} +(-3.20885 + 5.55790i) q^{23} +(1.13785 + 1.30587i) q^{24} +(0.640274 + 4.95884i) q^{25} +(-2.57957 - 4.46794i) q^{26} +(-4.34796 + 2.84522i) q^{27} +(-2.41546 + 1.07960i) q^{28} +(-2.16663 - 1.25090i) q^{29} +(-0.0172195 + 3.87295i) q^{30} -4.36743i q^{31} +1.00000 q^{32} +(9.71719 + 3.33326i) q^{33} +(1.62025 + 0.935454i) q^{34} +(-5.65031 - 1.75328i) q^{35} +(-0.410606 + 2.97177i) q^{36} +(-1.17895 + 0.680668i) q^{37} +(-1.51165 + 0.872754i) q^{38} +(2.89941 - 8.45243i) q^{39} +(1.67933 + 1.47644i) q^{40} +(-3.79398 - 6.57136i) q^{41} +(-4.15825 - 1.92587i) q^{42} +(4.07460 + 2.35247i) q^{43} +(5.13649 - 2.96556i) q^{44} +(-5.07717 + 4.38433i) q^{45} +(-3.20885 + 5.55790i) q^{46} -9.74722i q^{47} +(1.13785 + 1.30587i) q^{48} +(4.66893 - 5.21547i) q^{49} +(0.640274 + 4.95884i) q^{50} +(0.622018 + 3.18025i) q^{51} +(-2.57957 - 4.46794i) q^{52} +(0.628956 - 1.08938i) q^{53} +(-4.34796 + 2.84522i) q^{54} +(13.0043 + 2.60357i) q^{55} +(-2.41546 + 1.07960i) q^{56} +(-2.85974 - 0.980967i) q^{57} +(-2.16663 - 1.25090i) q^{58} -1.30033 q^{59} +(-0.0172195 + 3.87295i) q^{60} -11.4604i q^{61} -4.36743i q^{62} +(-2.21652 - 7.62149i) q^{63} +1.00000 q^{64} +(2.26470 - 11.3117i) q^{65} +(9.71719 + 3.33326i) q^{66} +15.0907i q^{67} +(1.62025 + 0.935454i) q^{68} +(-10.9091 + 2.13369i) q^{69} +(-5.65031 - 1.75328i) q^{70} -2.88706i q^{71} +(-0.410606 + 2.97177i) q^{72} +(1.79824 - 3.11464i) q^{73} +(-1.17895 + 0.680668i) q^{74} +(-5.74707 + 6.47852i) q^{75} +(-1.51165 + 0.872754i) q^{76} +(-9.20540 + 12.7086i) q^{77} +(2.89941 - 8.45243i) q^{78} +8.42064 q^{79} +(1.67933 + 1.47644i) q^{80} +(-8.66281 - 2.44045i) q^{81} +(-3.79398 - 6.57136i) q^{82} +(2.43978 + 1.40861i) q^{83} +(-4.15825 - 1.92587i) q^{84} +(1.33980 + 3.96313i) q^{85} +(4.07460 + 2.35247i) q^{86} +(-0.831773 - 4.25268i) q^{87} +(5.13649 - 2.96556i) q^{88} +(8.92096 + 15.4516i) q^{89} +(-5.07717 + 4.38433i) q^{90} +(11.0544 + 8.00725i) q^{91} +(-3.20885 + 5.55790i) q^{92} +(5.70331 - 4.96947i) q^{93} -9.74722i q^{94} +(-3.82713 - 0.766222i) q^{95} +(1.13785 + 1.30587i) q^{96} +(1.23514 - 2.13933i) q^{97} +(4.66893 - 5.21547i) q^{98} +(6.70387 + 16.4821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.13785	+	1.30587i	0.656937	+	0.753946i
$3$	1.13785	+	1.30587i	0.656937	+	0.753946i
$4$	1.00000			0.500000
$5$	1.67933	+	1.47644i	0.751018	+	0.660282i
$5$	1.67933	+	1.47644i	0.751018	+	0.660282i
$6$	1.13785	+	1.30587i	0.464524	+	0.533120i
$7$	−2.41546	+	1.07960i	−0.912959	+	0.408050i
$7$	−2.41546	+	1.07960i	−0.912959	+	0.408050i
$8$	1.00000			0.353553
$9$	−0.410606	+	2.97177i	−0.136869	+	0.990589i
$10$	1.67933	+	1.47644i	0.531050	+	0.466890i
$11$	5.13649	−	2.96556i	1.54871	−	0.894149i	0.550471	−	0.834854i	$-0.314448\pi$
$11$	5.13649	−	2.96556i	1.54871	−	0.894149i	0.998241	−	0.0592945i	$-0.0188851\pi$
$12$	1.13785	+	1.30587i	0.328468	+	0.376973i
$13$	−2.57957	−	4.46794i	−0.715444	−	1.23918i	−0.962788	−	0.270257i	$-0.912891\pi$
$13$	−2.57957	−	4.46794i	−0.715444	−	1.23918i	0.247344	−	0.968928i	$-0.420442\pi$
$14$	−2.41546	+	1.07960i	−0.645560	+	0.288535i
$15$	−0.0172195	+	3.87295i	−0.00444607	+	0.999990i
$16$	1.00000			0.250000
$17$	1.62025	+	0.935454i	0.392969	+	0.226881i	0.683446	−	0.730001i	$-0.260481\pi$
$17$	1.62025	+	0.935454i	0.392969	+	0.226881i	−0.290477	+	0.956882i	$0.593814\pi$
$18$	−0.410606	+	2.97177i	−0.0967807	+	0.700452i
$19$	−1.51165	+	0.872754i	−0.346797	+	0.200224i	−0.663274	−	0.748377i	$-0.730833\pi$
$19$	−1.51165	+	0.872754i	−0.346797	+	0.200224i	0.316476	+	0.948600i	$0.397500\pi$
$20$	1.67933	+	1.47644i	0.375509	+	0.330141i
$21$	−4.15825	−	1.92587i	−0.907404	−	0.420259i
$22$	5.13649	−	2.96556i	1.09510	−	0.632259i
$23$	−3.20885	+	5.55790i	−0.669092	+	1.15890i	0.309066	+	0.951041i	$0.399984\pi$
$23$	−3.20885	+	5.55790i	−0.669092	+	1.15890i	−0.978158	+	0.207861i	$0.933350\pi$
$24$	1.13785	+	1.30587i	0.232262	+	0.266560i
$25$	0.640274	+	4.95884i	0.128055	+	0.991767i
$26$	−2.57957	−	4.46794i	−0.505895	−	0.876236i
$27$	−4.34796	+	2.84522i	−0.836765	+	0.547563i
$28$	−2.41546	+	1.07960i	−0.456480	+	0.204025i
$29$	−2.16663	−	1.25090i	−0.402333	−	0.232287i	0.285157	−	0.958481i	$-0.407954\pi$
$29$	−2.16663	−	1.25090i	−0.402333	−	0.232287i	−0.687490	+	0.726194i	$0.741288\pi$
$30$	−0.0172195	+	3.87295i	−0.00314384	+	0.707100i
$31$		−	4.36743i		−	0.784413i	−0.919877	−	0.392207i	$-0.871712\pi$
$31$		−	4.36743i		−	0.784413i	0.919877	−	0.392207i	$-0.128288\pi$
$32$	1.00000			0.176777
$33$	9.71719	+	3.33326i	1.69155	+	0.580245i
$34$	1.62025	+	0.935454i	0.277871	+	0.160429i
$35$	−5.65031	−	1.75328i	−0.955077	−	0.296358i
$36$	−0.410606	+	2.97177i	−0.0684343	+	0.495295i
$37$	−1.17895	+	0.680668i	−0.193818	+	0.111901i	−0.593769	−	0.804636i	$-0.702361\pi$
$37$	−1.17895	+	0.680668i	−0.193818	+	0.111901i	0.399950	+	0.916537i	$0.369027\pi$
$38$	−1.51165	+	0.872754i	−0.245223	+	0.141579i
$39$	2.89941	−	8.45243i	0.464277	−	1.35347i
$40$	1.67933	+	1.47644i	0.265525	+	0.233445i
$41$	−3.79398	−	6.57136i	−0.592520	−	1.02627i	−0.993892	−	0.110359i	$-0.964800\pi$
$41$	−3.79398	−	6.57136i	−0.592520	−	1.02627i	0.401372	−	0.915915i	$-0.368533\pi$
$42$	−4.15825	−	1.92587i	−0.641632	−	0.297168i
$43$	4.07460	+	2.35247i	0.621370	+	0.358748i	0.777402	−	0.629004i	$-0.216537\pi$
$43$	4.07460	+	2.35247i	0.621370	+	0.358748i	−0.156032	+	0.987752i	$0.549870\pi$
$44$	5.13649	−	2.96556i	0.774356	−	0.447074i
$45$	−5.07717	+	4.38433i	−0.756859	+	0.653578i
$46$	−3.20885	+	5.55790i	−0.473120	+	0.819467i
$47$		−	9.74722i		−	1.42178i	−0.703304	−	0.710889i	$-0.748293\pi$
$47$		−	9.74722i		−	1.42178i	0.703304	−	0.710889i	$-0.251707\pi$
$48$	1.13785	+	1.30587i	0.164234	+	0.188486i
$49$	4.66893	−	5.21547i	0.666990	−	0.745067i
$50$	0.640274	+	4.95884i	0.0905484	+	0.701285i
$51$	0.622018	+	3.18025i	0.0871000	+	0.445324i
$52$	−2.57957	−	4.46794i	−0.357722	−	0.619592i
$53$	0.628956	−	1.08938i	0.0863938	−	0.149638i	−0.819591	−	0.572950i	$-0.805799\pi$
$53$	0.628956	−	1.08938i	0.0863938	−	0.149638i	0.905984	+	0.423311i	$0.139132\pi$
$54$	−4.34796	+	2.84522i	−0.591682	+	0.387185i
$55$	13.0043	+	2.60357i	1.75350	+	0.351065i
$56$	−2.41546	+	1.07960i	−0.322780	+	0.144268i
$57$	−2.85974	−	0.980967i	−0.378782	−	0.129932i
$58$	−2.16663	−	1.25090i	−0.284492	−	0.164252i
$59$	−1.30033			−0.169289			−0.0846443	−	0.996411i	$-0.526975\pi$
$59$	−1.30033			−0.169289			−0.0846443	+	0.996411i	$0.526975\pi$
$60$	−0.0172195	+	3.87295i	−0.00222303	+	0.499995i
$61$		−	11.4604i		−	1.46735i	−0.679499	−	0.733677i	$-0.737803\pi$
$61$		−	11.4604i		−	1.46735i	0.679499	−	0.733677i	$-0.262197\pi$
$62$		−	4.36743i		−	0.554664i
$63$	−2.21652	−	7.62149i	−0.279255	−	0.960217i
$64$	1.00000			0.125000
$65$	2.26470	−	11.3117i	0.280901	−	1.40304i
$66$	9.71719	+	3.33326i	1.19610	+	0.410295i
$67$			15.0907i			1.84362i	0.387641	+	0.921810i	$0.373290\pi$
$67$			15.0907i			1.84362i	−0.387641	+	0.921810i	$0.626710\pi$
$68$	1.62025	+	0.935454i	0.196485	+	0.113440i
$69$	−10.9091	+	2.13369i	−1.31330	+	0.256866i
$70$	−5.65031	−	1.75328i	−0.675341	−	0.209557i
$71$		−	2.88706i		−	0.342631i	−0.985216	−	0.171315i	$-0.945198\pi$
$71$		−	2.88706i		−	0.342631i	0.985216	−	0.171315i	$-0.0548017\pi$
$72$	−0.410606	+	2.97177i	−0.0483904	+	0.350226i
$73$	1.79824	−	3.11464i	0.210468	−	0.364541i	−0.741393	−	0.671071i	$-0.765835\pi$
$73$	1.79824	−	3.11464i	0.210468	−	0.364541i	0.951861	+	0.306530i	$0.0991680\pi$
$74$	−1.17895	+	0.680668i	−0.137050	+	0.0791260i
$75$	−5.74707	+	6.47852i	−0.663615	+	0.748074i
$76$	−1.51165	+	0.872754i	−0.173399	+	0.100112i
$77$	−9.20540	+	12.7086i	−1.04905	+	1.44827i
$78$	2.89941	−	8.45243i	0.328293	−	0.957049i
$79$	8.42064			0.947396			0.473698	−	0.880687i	$-0.342919\pi$
$79$	8.42064			0.947396			0.473698	+	0.880687i	$0.342919\pi$
$80$	1.67933	+	1.47644i	0.187754	+	0.165071i
$81$	−8.66281	−	2.44045i	−0.962534	−	0.271161i
$82$	−3.79398	−	6.57136i	−0.418975	−	0.725686i
$83$	2.43978	+	1.40861i	0.267801	+	0.154615i	0.627888	−	0.778304i	$-0.283920\pi$
$83$	2.43978	+	1.40861i	0.267801	+	0.154615i	−0.360087	+	0.932919i	$0.617253\pi$
$84$	−4.15825	−	1.92587i	−0.453702	−	0.210129i
$85$	1.33980	+	3.96313i	0.145321	+	0.429862i
$86$	4.07460	+	2.35247i	0.439375	+	0.253673i
$87$	−0.831773	−	4.25268i	−0.0891754	−	0.455935i
$88$	5.13649	−	2.96556i	0.547552	−	0.316129i
$89$	8.92096	+	15.4516i	0.945620	+	1.63786i	0.754506	+	0.656293i	$0.227877\pi$
$89$	8.92096	+	15.4516i	0.945620	+	1.63786i	0.191113	+	0.981568i	$0.438790\pi$
$90$	−5.07717	+	4.38433i	−0.535180	+	0.462149i
$91$	11.0544	+	8.00725i	1.15882	+	0.839388i
$92$	−3.20885	+	5.55790i	−0.334546	+	0.579451i
$93$	5.70331	−	4.96947i	0.591405	−	0.515310i
$94$		−	9.74722i		−	1.00535i
$95$	−3.82713	−	0.766222i	−0.392655	−	0.0786127i
$96$	1.13785	+	1.30587i	0.116131	+	0.133280i
$97$	1.23514	−	2.13933i	0.125410	−	0.217216i	−0.796483	−	0.604661i	$-0.793309\pi$
$97$	1.23514	−	2.13933i	0.125410	−	0.217216i	0.921893	+	0.387444i	$0.126642\pi$
$98$	4.66893	−	5.21547i	0.471633	−	0.526842i
$99$	6.70387	+	16.4821i	0.673764	+	1.65652i
$100$	0.640274	+	4.95884i	0.0640274	+	0.495884i
$101$	−6.90957	−	11.9677i	−0.687528	−	1.19083i	−0.972635	−	0.232337i	$-0.925363\pi$
$101$	−6.90957	−	11.9677i	−0.687528	−	1.19083i	0.285108	−	0.958496i	$-0.407971\pi$
$102$	0.622018	+	3.18025i	0.0615890	+	0.314891i
$103$	−0.712859	+	1.23471i	−0.0702400	+	0.121659i	−0.899006	−	0.437935i	$-0.855710\pi$
$103$	−0.712859	+	1.23471i	−0.0702400	+	0.121659i	0.828766	+	0.559595i	$0.189043\pi$
$104$	−2.57957	−	4.46794i	−0.252948	−	0.438118i
$105$	−4.13964	−	9.37355i	−0.403987	−	0.914765i
$106$	0.628956	−	1.08938i	0.0610896	−	0.105810i
$107$	−1.67000	−	2.89252i	−0.161445	−	0.279630i	0.773942	−	0.633256i	$-0.218282\pi$
$107$	−1.67000	−	2.89252i	−0.161445	−	0.279630i	−0.935387	+	0.353626i	$0.884949\pi$
$108$	−4.34796	+	2.84522i	−0.418382	+	0.273781i
$109$	4.42125	−	7.65783i	0.423479	−	0.733487i	−0.572798	−	0.819696i	$-0.694142\pi$
$109$	4.42125	−	7.65783i	0.423479	−	0.733487i	0.996277	+	0.0862097i	$0.0274755\pi$
$110$	13.0043	+	2.60357i	1.23991	+	0.248240i
$111$	−2.23033	−	0.765064i	−0.211694	−	0.0726167i
$112$	−2.41546	+	1.07960i	−0.228240	+	0.102013i
$113$	−8.87845	−	15.3779i	−0.835215	−	1.44663i	−0.893855	−	0.448355i	$-0.852010\pi$
$113$	−8.87845	−	15.3779i	−0.835215	−	1.44663i	0.0586408	−	0.998279i	$-0.481323\pi$
$114$	−2.85974	−	0.980967i	−0.267839	−	0.0918760i
$115$	−13.5946	+	4.59586i	−1.26770	+	0.428566i
$116$	−2.16663	−	1.25090i	−0.201166	−	0.116143i
$117$	14.3369	−	5.83132i	1.32544	−	0.539105i
$118$	−1.30033			−0.119705
$119$	−4.92358	−	0.510329i	−0.451344	−	0.0467817i
$120$	−0.0172195	+	3.87295i	−0.00157192	+	0.353550i
$121$	12.0891	−	20.9388i	1.09900	−	1.90353i
$122$		−	11.4604i		−	1.03758i
$123$	4.26439	−	12.4317i	0.384507	−	1.12093i
$124$		−	4.36743i		−	0.392207i
$125$	−6.24617	+	9.27283i	−0.558675	+	0.829387i
$126$	−2.21652	−	7.62149i	−0.197463	−	0.678976i
$127$		−	8.49642i		−	0.753936i	−0.926226	−	0.376968i	$-0.876967\pi$
$127$		−	8.49642i		−	0.753936i	0.926226	−	0.376968i	$-0.123033\pi$
$128$	1.00000			0.0883883
$129$	1.56424	+	7.99766i	0.137724	+	0.704154i
$130$	2.26470	−	11.3117i	0.198627	−	0.992102i
$131$	−1.98718	+	3.44190i	−0.173621	+	0.300720i	−0.939683	−	0.342046i	$-0.888880\pi$
$131$	−1.98718	+	3.44190i	−0.173621	+	0.300720i	0.766062	+	0.642766i	$0.222213\pi$
$132$	9.71719	+	3.33326i	0.845773	+	0.290123i
$133$	2.70912	−	3.74009i	0.234911	−	0.324307i
$134$			15.0907i			1.30364i
$135$	−11.5024	−	1.64143i	−0.989971	−	0.141271i
$136$	1.62025	+	0.935454i	0.138936	+	0.0802145i
$137$	4.85327	+	8.40611i	0.414643	+	0.718182i	0.995391	−	0.0959011i	$-0.0305733\pi$
$137$	4.85327	+	8.40611i	0.414643	+	0.718182i	−0.580748	+	0.814083i	$0.697240\pi$
$138$	−10.9091	+	2.13369i	−0.928644	+	0.181631i
$139$	−17.4411	+	10.0696i	−1.47933	+	0.854092i	−0.999726	−	0.0233924i	$-0.992553\pi$
$139$	−17.4411	+	10.0696i	−1.47933	+	0.854092i	−0.479605	+	0.877485i	$0.659220\pi$
$140$	−5.65031	−	1.75328i	−0.477539	−	0.148179i
$141$	12.7286	−	11.0908i	1.07194	−	0.934018i
$142$		−	2.88706i		−	0.242276i
$143$	−26.4999	−	15.2997i	−2.21603	−	1.27943i
$144$	−0.410606	+	2.97177i	−0.0342171	+	0.247647i
$145$	−1.79160	−	5.29956i	−0.148784	−	0.440105i
$146$	1.79824	−	3.11464i	0.148823	−	0.257769i
$147$	12.1233	+	0.162614i	0.999910	+	0.0134122i
$148$	−1.17895	+	0.680668i	−0.0969092	+	0.0559506i
$149$	−2.64213	−	1.52543i	−0.216452	−	0.124968i	0.387855	−	0.921721i	$-0.373216\pi$
$149$	−2.64213	−	1.52543i	−0.216452	−	0.124968i	−0.604306	+	0.796752i	$0.706550\pi$
$150$	−5.74707	+	6.47852i	−0.469246	+	0.528969i
$151$	8.45186	+	14.6390i	0.687803	+	1.19131i	0.972547	+	0.232706i	$0.0747578\pi$
$151$	8.45186	+	14.6390i	0.687803	+	1.19131i	−0.284745	+	0.958603i	$0.591909\pi$
$152$	−1.51165	+	0.872754i	−0.122611	+	0.0707897i
$153$	−3.44524	+	4.43091i	−0.278531	+	0.358218i
$154$	−9.20540	+	12.7086i	−0.741792	+	1.02408i
$155$	6.44823	−	7.33434i	0.517934	−	0.589108i
$156$	2.89941	−	8.45243i	0.232139	−	0.676736i
$157$	−4.95836			−0.395720			−0.197860	−	0.980230i	$-0.563399\pi$
$157$	−4.95836			−0.395720			−0.197860	+	0.980230i	$0.563399\pi$
$158$	8.42064			0.669910
$159$	2.13825	−	0.418216i	0.169574	−	0.0331667i
$160$	1.67933	+	1.47644i	0.132762	+	0.116723i
$161$	1.75056	−	16.8892i	0.137964	−	1.33105i
$162$	−8.66281	−	2.44045i	−0.680614	−	0.191740i
$163$	−5.11733	+	2.95449i	−0.400820	+	0.231413i	−0.686838	−	0.726811i	$-0.741002\pi$
$163$	−5.11733	+	2.95449i	−0.400820	+	0.231413i	0.286018	+	0.958224i	$0.407668\pi$
$164$	−3.79398	−	6.57136i	−0.296260	−	0.513137i
$165$	11.3970	+	19.9444i	0.887254	+	1.55267i
$166$	2.43978	+	1.40861i	0.189364	+	0.109329i
$167$	−9.07327	+	5.23846i	−0.702111	+	0.405364i	−0.808133	−	0.589000i	$-0.799522\pi$
$167$	−9.07327	+	5.23846i	−0.702111	+	0.405364i	0.106022	+	0.994364i	$0.466189\pi$
$168$	−4.15825	−	1.92587i	−0.320816	−	0.148584i
$169$	−6.80835	+	11.7924i	−0.523720	+	0.907109i
$170$	1.33980	+	3.96313i	0.102758	+	0.303958i
$171$	−1.97293	−	4.85064i	−0.150874	−	0.370938i
$172$	4.07460	+	2.35247i	0.310685	+	0.179374i
$173$			8.60028i			0.653867i	0.945047	+	0.326933i	$0.106015\pi$
$173$			8.60028i			0.653867i	−0.945047	+	0.326933i	$0.893985\pi$
$174$	−0.831773	−	4.25268i	−0.0630565	−	0.322395i
$175$	−6.90012	−	11.2866i	−0.521600	−	0.853190i
$176$	5.13649	−	2.96556i	0.387178	−	0.223537i
$177$	−1.47958	−	1.69807i	−0.111212	−	0.127634i
$178$	8.92096	+	15.4516i	0.668654	+	1.15814i
$179$	−2.31384	−	1.33590i	−0.172945	−	0.0998497i	0.411029	−	0.911622i	$-0.365170\pi$
$179$	−2.31384	−	1.33590i	−0.172945	−	0.0998497i	−0.583974	+	0.811773i	$0.698503\pi$
$180$	−5.07717	+	4.38433i	−0.378430	+	0.326789i
$181$			7.92990i			0.589425i	0.955586	+	0.294712i	$0.0952238\pi$
$181$			7.92990i			0.589425i	−0.955586	+	0.294712i	$0.904776\pi$
$182$	11.0544	+	8.00725i	0.819410	+	0.593537i
$183$	14.9658	−	13.0402i	1.10630	−	0.963958i
$184$	−3.20885	+	5.55790i	−0.236560	+	0.409734i
$185$	−2.98481	−	0.597583i	−0.219447	−	0.0439352i
$186$	5.70331	−	4.96947i	0.418187	−	0.364379i
$187$	11.0966			0.811461
$188$		−	9.74722i		−	0.710889i
$189$	7.43063	−	11.5666i	0.540499	−	0.841345i
$190$	−3.82713	−	0.766222i	−0.277649	−	0.0555876i
$191$			11.8760i			0.859321i	0.902991	+	0.429660i	$0.141367\pi$
$191$			11.8760i			0.859321i	−0.902991	+	0.429660i	$0.858633\pi$
$192$	1.13785	+	1.30587i	0.0821171	+	0.0942432i
$193$			15.3218i			1.10288i	0.834213	+	0.551442i	$0.185922\pi$
$193$			15.3218i			1.10288i	−0.834213	+	0.551442i	$0.814078\pi$
$194$	1.23514	−	2.13933i	0.0886781	−	0.153595i
$195$	17.3485	−	9.91359i	1.24235	−	0.709927i
$196$	4.66893	−	5.21547i	0.333495	−	0.372534i
$197$	9.02678			0.643131			0.321566	−	0.946887i	$-0.395791\pi$
$197$	9.02678			0.643131			0.321566	+	0.946887i	$0.395791\pi$
$198$	6.70387	+	16.4821i	0.476423	+	1.17133i
$199$	10.4835	+	6.05268i	0.743159	+	0.429063i	0.823217	−	0.567727i	$-0.192177\pi$
$199$	10.4835	+	6.05268i	0.743159	+	0.429063i	−0.0800578	+	0.996790i	$0.525510\pi$
$200$	0.640274	+	4.95884i	0.0452742	+	0.350643i
$201$	−19.7065	+	17.1709i	−1.38999	+	1.21114i
$202$	−6.90957	−	11.9677i	−0.486155	−	0.842046i
$203$	6.58389	+	0.682419i	0.462098	+	0.0478965i
$204$	0.622018	+	3.18025i	0.0435500	+	0.222662i
$205$	3.33087	−	16.6370i	0.232638	−	1.16198i
$206$	−0.712859	+	1.23471i	−0.0496672	+	0.0860261i
$207$	−15.1992	−	11.8181i	−1.05642	−	0.821413i
$208$	−2.57957	−	4.46794i	−0.178861	−	0.309796i
$209$	−5.17640	+	8.96579i	−0.358059	+	0.620177i
$210$	−4.13964	−	9.37355i	−0.285662	−	0.646836i
$211$	4.28556	+	7.42280i	0.295030	+	0.511007i	0.974992	−	0.222241i	$-0.0713370\pi$
$211$	4.28556	+	7.42280i	0.295030	+	0.511007i	−0.679962	+	0.733247i	$0.738004\pi$
$212$	0.628956	−	1.08938i	0.0431969	−	0.0748192i
$213$	3.77013	−	3.28503i	0.258325	−	0.225087i
$214$	−1.67000	−	2.89252i	−0.114159	−	0.197729i
$215$	3.36931	+	9.96644i	0.229785	+	0.679706i
$216$	−4.34796	+	2.84522i	−0.295841	+	0.193593i
$217$	4.71508	+	10.5494i	0.320080	+	0.716138i
$218$	4.42125	−	7.65783i	0.299445	−	0.518653i
$219$	6.11344	−	1.19572i	0.413108	−	0.0807990i
$220$	13.0043	+	2.60357i	0.876750	+	0.175533i
$221$		−	9.65227i		−	0.649282i
$222$	−2.23033	−	0.765064i	−0.149690	−	0.0513477i
$223$	−10.2042	+	17.6741i	−0.683322	+	1.18355i	0.290639	+	0.956833i	$0.406132\pi$
$223$	−10.2042	+	17.6741i	−0.683322	+	1.18355i	−0.973961	+	0.226716i	$0.927201\pi$
$224$	−2.41546	+	1.07960i	−0.161390	+	0.0721338i
$225$	−14.9994	−	0.133381i	−0.999960	−	0.00889205i
$226$	−8.87845	−	15.3779i	−0.590586	−	1.02292i
$227$	−19.9142	+	11.4974i	−1.32175	+	0.763112i	−0.984008	−	0.178127i	$-0.942996\pi$
$227$	−19.9142	+	11.4974i	−1.32175	+	0.763112i	−0.337741	+	0.941239i	$0.609663\pi$
$228$	−2.85974	−	0.980967i	−0.189391	−	0.0649661i
$229$	−18.0144	−	10.4006i	−1.19043	−	0.687292i	−0.232022	−	0.972710i	$-0.574534\pi$
$229$	−18.0144	−	10.4006i	−1.19043	−	0.687292i	−0.958403	+	0.285418i	$0.907868\pi$
$230$	−13.5946	+	4.59586i	−0.896401	+	0.303042i
$231$	−27.0701	+	2.43932i	−1.78108	+	0.160495i
$232$	−2.16663	−	1.25090i	−0.142246	−	0.0821258i
$233$	−13.6638	−	23.6663i	−0.895143	−	1.55043i	−0.833627	−	0.552327i	$-0.813740\pi$
$233$	−13.6638	−	23.6663i	−0.895143	−	1.55043i	−0.0615156	−	0.998106i	$-0.519593\pi$
$234$	14.3369	−	5.83132i	0.937231	−	0.381205i
$235$	14.3911	−	16.3688i	0.938774	−	1.06778i
$236$	−1.30033			−0.0846443
$237$	9.58141	+	10.9963i	0.622379	+	0.714286i
$238$	−4.92358	−	0.510329i	−0.319148	−	0.0330797i
$239$	−15.6608	+	9.04177i	−1.01301	+	0.584864i	−0.912073	−	0.410029i	$-0.865519\pi$
$239$	−15.6608	+	9.04177i	−1.01301	+	0.584864i	−0.100941	+	0.994892i	$0.532185\pi$
$240$	−0.0172195	+	3.87295i	−0.00111152	+	0.249998i
$241$	2.31790	−	1.33824i	0.149309	−	0.0862037i	−0.423484	−	0.905903i	$-0.639193\pi$
$241$	2.31790	−	1.33824i	0.149309	−	0.0862037i	0.572793	+	0.819700i	$0.305860\pi$
$242$	12.0891	−	20.9388i	0.777114	−	1.34600i
$243$	−6.67004	−	14.0894i	−0.427883	−	0.903834i
$244$		−	11.4604i		−	0.733677i
$245$	15.5410	−	1.86510i	0.992875	−	0.119157i
$246$	4.26439	−	12.4317i	0.271888	−	0.792614i
$247$	7.79883	+	4.50266i	0.496228	+	0.286497i
$248$		−	4.36743i		−	0.277332i
$249$	0.936637	+	4.78883i	0.0593570	+	0.303480i
$250$	−6.24617	+	9.27283i	−0.395043	+	0.586465i
$251$	0.220993			0.0139490			0.00697448	−	0.999976i	$-0.497780\pi$
$251$	0.220993			0.0139490			0.00697448	+	0.999976i	$0.497780\pi$
$252$	−2.21652	−	7.62149i	−0.139627	−	0.480108i
$253$			38.0642i			2.39307i
$254$		−	8.49642i		−	0.533113i
$255$	−3.65086	+	6.25904i	−0.228626	+	0.391957i
$256$	1.00000			0.0625000
$257$	−14.7049	−	8.48987i	−0.917265	−	0.529583i	−0.0345037	−	0.999405i	$-0.510985\pi$
$257$	−14.7049	−	8.48987i	−0.917265	−	0.529583i	−0.882762	+	0.469821i	$0.844318\pi$
$258$	1.56424	+	7.99766i	0.0973856	+	0.497912i
$259$	2.11287	−	2.91692i	0.131287	−	0.181249i
$260$	2.26470	−	11.3117i	0.140450	−	0.701522i
$261$	4.60702	−	5.92509i	0.285168	−	0.366754i
$262$	−1.98718	+	3.44190i	−0.122768	+	0.212641i
$263$	5.28060	+	9.14626i	0.325615	+	0.563983i	0.981637	−	0.190760i	$-0.0610952\pi$
$263$	5.28060	+	9.14626i	0.325615	+	0.563983i	−0.656021	+	0.754742i	$0.727762\pi$
$264$	9.71719	+	3.33326i	0.598051	+	0.205148i
$265$	2.66463	−	0.900818i	0.163687	−	0.0553368i
$266$	2.70912	−	3.74009i	0.166107	−	0.229319i
$267$	−10.0271	+	29.2311i	−0.613646	+	1.78892i
$268$			15.0907i			0.921810i
$269$	1.54717	−	2.67977i	0.0943324	−	0.163388i	−0.814997	−	0.579465i	$-0.803262\pi$
$269$	1.54717	−	2.67977i	0.0943324	−	0.163388i	0.909330	+	0.416076i	$0.136595\pi$
$270$	−11.5024	−	1.64143i	−0.700015	−	0.0998940i
$271$	15.2570	−	8.80863i	0.926797	−	0.535086i	0.0409997	−	0.999159i	$-0.486946\pi$
$271$	15.2570	−	8.80863i	0.926797	−	0.535086i	0.885797	+	0.464073i	$0.153612\pi$
$272$	1.62025	+	0.935454i	0.0982423	+	0.0567202i
$273$	2.12182	+	23.5467i	0.128419	+	1.42511i
$274$	4.85327	+	8.40611i	0.293197	+	0.507831i
$275$	17.9945	+	23.5723i	1.08511	+	1.42146i
$276$	−10.9091	+	2.13369i	−0.656650	+	0.128433i
$277$	−2.43071	+	1.40337i	−0.146047	+	0.0843204i	−0.571243	−	0.820781i	$-0.693539\pi$
$277$	−2.43071	+	1.40337i	−0.146047	+	0.0843204i	0.425196	+	0.905101i	$0.360205\pi$
$278$	−17.4411	+	10.0696i	−1.04605	+	0.603934i
$279$	12.9790	+	1.79329i	0.777032	+	0.107362i
$280$	−5.65031	−	1.75328i	−0.337671	−	0.104778i
$281$	6.77309	+	3.91045i	0.404049	+	0.233278i	0.688229	−	0.725493i	$-0.258388\pi$
$281$	6.77309	+	3.91045i	0.404049	+	0.233278i	−0.284181	+	0.958771i	$0.591722\pi$
$282$	12.7286	−	11.0908i	0.757978	−	0.660450i
$283$	26.6702			1.58538			0.792691	−	0.609624i	$-0.208679\pi$
$283$	26.6702			1.58538			0.792691	+	0.609624i	$0.208679\pi$
$284$		−	2.88706i		−	0.171315i
$285$	−3.35410	−	5.86958i	−0.198680	−	0.347684i
$286$	−26.4999	−	15.2997i	−1.56697	−	0.904691i
$287$	16.2587	+	11.7769i	0.959718	+	0.695169i
$288$	−0.410606	+	2.97177i	−0.0241952	+	0.175113i
$289$	−6.74985	−	11.6911i	−0.397050	−	0.687711i
$290$	−1.79160	−	5.29956i	−0.105206	−	0.311201i
$291$	4.19910	−	0.821293i	0.246156	−	0.0481451i
$292$	1.79824	−	3.11464i	0.105234	−	0.182270i
$293$	−28.0362	+	16.1867i	−1.63789	+	0.945638i	−0.656335	+	0.754469i	$0.727894\pi$
$293$	−28.0362	+	16.1867i	−1.63789	+	0.945638i	−0.981557	+	0.191168i	$0.938772\pi$
$294$	12.1233	+	0.162614i	0.707043	+	0.00948387i
$295$	−2.18368	−	1.91986i	−0.127139	−	0.111778i
$296$	−1.17895	+	0.680668i	−0.0685252	+	0.0395630i
$297$	−13.8956	+	27.5086i	−0.806304	+	1.59621i
$298$	−2.64213	−	1.52543i	−0.153054	−	0.0883660i
$299$	33.1098			1.91479
$300$	−5.74707	+	6.47852i	−0.331807	+	0.374037i
$301$	−12.3818	−	1.28337i	−0.713673	−	0.0739722i
$302$	8.45186	+	14.6390i	0.486350	+	0.842383i
$303$	7.76628	−	22.6405i	0.446161	−	1.30066i
$304$	−1.51165	+	0.872754i	−0.0866993	+	0.0500559i
$305$	16.9205	−	19.2457i	0.968867	−	1.10201i
$306$	−3.44524	+	4.43091i	−0.196951	+	0.253298i
$307$	1.43218			0.0817386			0.0408693	−	0.999165i	$-0.486987\pi$
$307$	1.43218			0.0817386			0.0408693	+	0.999165i	$0.486987\pi$
$308$	−9.20540	+	12.7086i	−0.524526	+	0.724137i
$309$	−2.42349	+	0.474006i	−0.137868	+	0.0269653i
$310$	6.44823	−	7.33434i	0.366235	−	0.416562i
$311$	10.0729			0.571182			0.285591	−	0.958352i	$-0.407810\pi$
$311$	10.0729			0.571182			0.285591	+	0.958352i	$0.407810\pi$
$312$	2.89941	−	8.45243i	0.164147	−	0.478525i
$313$	15.5516			0.879031			0.439516	−	0.898235i	$-0.355150\pi$
$313$	15.5516			0.879031			0.439516	+	0.898235i	$0.355150\pi$
$314$	−4.95836			−0.279816
$315$	7.53038	−	16.0715i	0.424289	−	0.905527i
$316$	8.42064			0.473698
$317$	27.9352			1.56899			0.784497	−	0.620132i	$-0.212921\pi$
$317$	27.9352			1.56899			0.784497	+	0.620132i	$0.212921\pi$
$318$	2.13825	−	0.418216i	0.119907	−	0.0234524i
$319$	−14.8385			−0.830797
$320$	1.67933	+	1.47644i	0.0938772	+	0.0825353i
$321$	1.87706	−	5.47205i	0.104767	−	0.305420i
$322$	1.75056	−	16.8892i	0.0975550	−	0.941197i
$323$	−3.26568			−0.181708
$324$	−8.66281	−	2.44045i	−0.481267	−	0.135581i
$325$	20.5042	−	15.6524i	1.13737	−	0.868237i
$326$	−5.11733	+	2.95449i	−0.283422	+	0.163634i
$327$	15.0309	−	2.93985i	0.831208	−	0.162574i
$328$	−3.79398	−	6.57136i	−0.209487	−	0.362843i
$329$	10.5231	+	23.5440i	0.580157	+	1.29803i
$330$	11.3970	+	19.9444i	0.627384	+	1.09790i
$331$	−2.18531			−0.120116			−0.0600578	−	0.998195i	$-0.519128\pi$
$331$	−2.18531			−0.120116			−0.0600578	+	0.998195i	$0.519128\pi$
$332$	2.43978	+	1.40861i	0.133900	+	0.0773075i
$333$	−1.53870	−	3.78306i	−0.0843204	−	0.207310i
$334$	−9.07327	+	5.23846i	−0.496467	+	0.286636i
$335$	−22.2804	+	25.3422i	−1.21731	+	1.38459i
$336$	−4.15825	−	1.92587i	−0.226851	−	0.105065i
$337$	0.212414	−	0.122637i	0.0115709	−	0.00668047i	−0.494203	−	0.869346i	$-0.664540\pi$
$337$	0.212414	−	0.122637i	0.0115709	−	0.00668047i	0.505774	+	0.862666i	$0.331207\pi$
$338$	−6.80835	+	11.7924i	−0.370326	+	0.641423i
$339$	9.97929	−	29.0919i	0.542001	−	1.58005i
$340$	1.33980	+	3.96313i	0.0726607	+	0.214931i
$341$	−12.9519	−	22.4333i	−0.701382	−	1.21483i
$342$	−1.97293	−	4.85064i	−0.106684	−	0.262293i
$343$	−5.64700	+	17.6383i	−0.304909	+	0.952381i
$344$	4.07460	+	2.35247i	0.219688	+	0.126837i
$345$	−21.4702	−	12.5234i	−1.15592	−	0.674238i
$346$			8.60028i			0.462354i
$347$	−6.03454			−0.323951			−0.161976	−	0.986795i	$-0.551787\pi$
$347$	−6.03454			−0.323951			−0.161976	+	0.986795i	$0.551787\pi$
$348$	−0.831773	−	4.25268i	−0.0445877	−	0.227967i
$349$	6.70174	+	3.86925i	0.358736	+	0.207116i	0.668526	−	0.743689i	$-0.266925\pi$
$349$	6.70174	+	3.86925i	0.358736	+	0.207116i	−0.309790	+	0.950805i	$0.600259\pi$
$350$	−6.90012	−	11.2866i	−0.368827	−	0.603297i
$351$	23.9281	+	12.0870i	1.27719	+	0.645156i
$352$	5.13649	−	2.96556i	0.273776	−	0.158065i
$353$	12.4114	−	7.16571i	0.660591	−	0.381392i	−0.131911	−	0.991262i	$-0.542111\pi$
$353$	12.4114	−	7.16571i	0.660591	−	0.381392i	0.792502	+	0.609869i	$0.208778\pi$
$354$	−1.47958	−	1.69807i	−0.0786387	−	0.0902512i
$355$	4.26256	−	4.84831i	0.226233	−	0.257322i
$356$	8.92096	+	15.4516i	0.472810	+	0.818931i
$357$	−4.93586	−	7.01024i	−0.261233	−	0.371021i
$358$	−2.31384	−	1.33590i	−0.122290	−	0.0706044i
$359$	−14.4007	+	8.31423i	−0.760039	+	0.438808i	−0.829310	−	0.558789i	$-0.811266\pi$
$359$	−14.4007	+	8.31423i	−0.760039	+	0.438808i	0.0692710	+	0.997598i	$0.477933\pi$
$360$	−5.07717	+	4.38433i	−0.267590	+	0.231075i
$361$	−7.97660	+	13.8159i	−0.419821	+	0.727151i
$362$			7.92990i			0.416786i
$363$	41.0990	−	8.03846i	2.15714	−	0.421910i
$364$	11.0544	+	8.00725i	0.579411	+	0.419694i
$365$	7.61839	−	2.57551i	0.398765	−	0.134808i
$366$	14.9658	−	13.0402i	0.782276	−	0.681621i
$367$	16.5694	+	28.6990i	0.864914	+	1.49807i	0.867133	+	0.498077i	$0.165960\pi$
$367$	16.5694	+	28.6990i	0.864914	+	1.49807i	−0.00221888	+	0.999998i	$0.500706\pi$
$368$	−3.20885	+	5.55790i	−0.167273	+	0.289725i
$369$	21.0864	−	8.57658i	1.09771	−	0.446479i
$370$	−2.98481	−	0.597583i	−0.155173	−	0.0310668i
$371$	−0.343121	+	3.31039i	−0.0178140	+	0.171867i
$372$	5.70331	−	4.96947i	0.295703	−	0.257655i
$373$	−18.2835	−	10.5560i	−0.946682	−	0.546567i	−0.0546330	−	0.998507i	$-0.517399\pi$
$373$	−18.2835	−	10.5560i	−0.946682	−	0.546567i	−0.892048	+	0.451940i	$0.850732\pi$
$374$	11.0966			0.573790
$375$	−19.2163	+	2.39436i	−0.992327	+	0.123644i
$376$		−	9.74722i		−	0.502674i
$377$			12.9072i			0.664753i
$378$	7.43063	−	11.5666i	0.382190	−	0.594921i
$379$	−12.8226			−0.658651			−0.329325	−	0.944217i	$-0.606821\pi$
$379$	−12.8226			−0.658651			−0.329325	+	0.944217i	$0.606821\pi$
$380$	−3.82713	−	0.766222i	−0.196327	−	0.0393064i
$381$	11.0952	−	9.66764i	0.568427	−	0.495288i
$382$			11.8760i			0.607631i
$383$	−14.1368	−	8.16190i	−0.722358	−	0.417054i	0.0932617	−	0.995642i	$-0.470271\pi$
$383$	−14.1368	−	8.16190i	−0.722358	−	0.417054i	−0.815620	+	0.578588i	$0.803604\pi$
$384$	1.13785	+	1.30587i	0.0580655	+	0.0666400i
$385$	−34.2222	+	7.75063i	−1.74413	+	0.395008i
$386$			15.3218i			0.779857i
$387$	−8.66405	+	11.1428i	−0.440418	+	0.566421i
$388$	1.23514	−	2.13933i	0.0627049	−	0.108608i
$389$	−9.64090	+	5.56618i	−0.488813	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$389$	−9.64090	+	5.56618i	−0.488813	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$390$	17.3485	−	9.91359i	0.878477	−	0.501994i
$391$	−10.3983	+	6.00347i	−0.525865	+	0.303608i
$392$	4.66893	−	5.21547i	0.235816	−	0.263421i
$393$	−6.75579	+	1.32135i	−0.340784	+	0.0666533i
$394$	9.02678			0.454763
$395$	14.1410	+	12.4325i	0.711511	+	0.625549i
$396$	6.70387	+	16.4821i	0.336882	+	0.828259i
$397$	−10.7572	−	18.6321i	−0.539891	−	0.935118i	−0.998909	−	0.0466914i	$-0.985132\pi$
$397$	−10.7572	−	18.6321i	−0.539891	−	0.935118i	0.459019	−	0.888427i	$-0.348201\pi$
$398$	10.4835	+	6.05268i	0.525493	+	0.303393i
$399$	7.96664	−	0.717884i	0.398831	−	0.0359392i
$400$	0.640274	+	4.95884i	0.0320137	+	0.247942i
$401$	11.7705	+	6.79568i	0.587789	+	0.339360i	0.764223	−	0.644953i	$-0.223123\pi$
$401$	11.7705	+	6.79568i	0.587789	+	0.339360i	−0.176434	+	0.984312i	$0.556456\pi$
$402$	−19.7065	+	17.1709i	−0.982872	+	0.856407i
$403$	−19.5134	+	11.2661i	−0.972033	+	0.561204i
$404$	−6.90957	−	11.9677i	−0.343764	−	0.595416i
$405$	−10.9445	−	16.8884i	−0.543837	−	0.839191i
$406$	6.58389	+	0.682419i	0.326753	+	0.0338679i
$407$	−4.03712	+	6.99249i	−0.200113	+	0.346605i
$408$	0.622018	+	3.18025i	0.0307945	+	0.157446i
$409$			6.31246i			0.312131i	0.987747	+	0.156066i	$0.0498811\pi$
$409$			6.31246i			0.312131i	−0.987747	+	0.156066i	$0.950119\pi$
$410$	3.33087	−	16.6370i	0.164500	−	0.821644i
$411$	−5.45502	+	15.9026i	−0.269076	+	0.784418i
$412$	−0.712859	+	1.23471i	−0.0351200	+	0.0608297i
$413$	3.14090	−	1.40384i	0.154554	−	0.0690783i
$414$	−15.1992	−	11.8181i	−0.747000	−	0.580827i
$415$	2.01747	+	5.96770i	0.0990337	+	0.292943i
$416$	−2.57957	−	4.46794i	−0.126474	−	0.219059i
$417$	−32.9949	−	11.3181i	−1.61577	−	0.554251i
$418$	−5.17640	+	8.96579i	−0.253186	+	0.438531i
$419$	10.2076	+	17.6802i	0.498676	+	0.863732i	0.999999	−	0.00152816i	$-0.000486427\pi$
$419$	10.2076	+	17.6802i	0.498676	+	0.863732i	−0.501323	+	0.865260i	$0.667153\pi$
$420$	−4.13964	−	9.37355i	−0.201994	−	0.457382i
$421$	−15.4045	+	26.6814i	−0.750769	+	1.30037i	0.196681	+	0.980467i	$0.436984\pi$
$421$	−15.4045	+	26.6814i	−0.750769	+	1.30037i	−0.947450	+	0.319903i	$0.896350\pi$
$422$	4.28556	+	7.42280i	0.208618	+	0.361336i
$423$	28.9665	+	4.00226i	1.40840	+	0.194597i
$424$	0.628956	−	1.08938i	0.0305448	−	0.0529052i
$425$	−3.60135	+	8.63352i	−0.174691	+	0.418787i
$426$	3.77013	−	3.28503i	0.182663	−	0.159160i
$427$	12.3726	+	27.6822i	0.598754	+	1.33963i
$428$	−1.67000	−	2.89252i	−0.0807224	−	0.139815i
$429$	−10.1734	−	52.0142i	−0.491174	−	2.51127i
$430$	3.36931	+	9.96644i	0.162482	+	0.480625i
$431$	29.8217	+	17.2176i	1.43646	+	0.829342i	0.997602	−	0.0692140i	$-0.0220491\pi$
$431$	29.8217	+	17.2176i	1.43646	+	0.829342i	0.438860	+	0.898556i	$0.355382\pi$
$432$	−4.34796	+	2.84522i	−0.209191	+	0.136891i
$433$	−5.86503			−0.281855			−0.140928	−	0.990020i	$-0.545008\pi$
$433$	−5.86503			−0.281855			−0.140928	+	0.990020i	$0.545008\pi$
$434$	4.71508	+	10.5494i	0.226331	+	0.506386i
$435$	4.88199	−	8.36969i	0.234073	−	0.401296i
$436$	4.42125	−	7.65783i	0.211739	−	0.366743i
$437$		−	11.2022i		−	0.535872i
$438$	6.11344	−	1.19572i	0.292112	−	0.0571335i
$439$		−	0.0933769i		−	0.00445664i	−0.999998	−	0.00222832i	$-0.999291\pi$
$439$		−	0.0933769i		−	0.00445664i	0.999998	−	0.00222832i	$-0.000709296\pi$
$440$	13.0043	+	2.60357i	0.619956	+	0.124120i
$441$	13.5821	+	16.0165i	0.646765	+	0.762689i
$442$		−	9.65227i		−	0.459112i
$443$	1.69982			0.0807610			0.0403805	−	0.999184i	$-0.487143\pi$
$443$	1.69982			0.0807610			0.0403805	+	0.999184i	$0.487143\pi$
$444$	−2.23033	−	0.765064i	−0.105847	−	0.0363083i
$445$	−7.83203	+	39.1194i	−0.371274	+	1.85444i
$446$	−10.2042	+	17.6741i	−0.483182	+	0.836895i
$447$	−1.01432	−	5.18599i	−0.0479756	−	0.245289i
$448$	−2.41546	+	1.07960i	−0.114120	+	0.0510063i
$449$		−	1.98554i		−	0.0937035i	−0.998902	−	0.0468518i	$-0.985081\pi$
$449$		−	1.98554i		−	0.0937035i	0.998902	−	0.0468518i	$-0.0149188\pi$
$450$	−14.9994	−	0.133381i	−0.707079	−	0.00628763i
$451$	−38.9755	−	22.5025i	−1.83528	−	1.05960i
$452$	−8.87845	−	15.3779i	−0.417607	−	0.723317i
$453$	−9.49980	+	27.6941i	−0.446340	+	1.30118i
$454$	−19.9142	+	11.4974i	−0.934618	+	0.539602i
$455$	6.74183	+	29.7680i	0.316062	+	1.39554i
$456$	−2.85974	−	0.980967i	−0.133919	−	0.0459380i
$457$		−	24.5551i		−	1.14864i	−0.818631	−	0.574320i	$-0.805266\pi$
$457$		−	24.5551i		−	1.14864i	0.818631	−	0.574320i	$-0.194734\pi$
$458$	−18.0144	−	10.4006i	−0.841758	−	0.485989i
$459$	−9.70636	+	0.542665i	−0.453054	+	0.0253294i
$460$	−13.5946	+	4.59586i	−0.633851	+	0.214283i
$461$	16.3946	−	28.3963i	0.763574	−	1.32255i	−0.177423	−	0.984135i	$-0.556776\pi$
$461$	16.3946	−	28.3963i	0.763574	−	1.32255i	0.940997	−	0.338415i	$-0.109891\pi$
$462$	−27.0701	+	2.43932i	−1.25941	+	0.113487i
$463$	19.1444	−	11.0530i	0.889717	−	0.513678i	0.0158669	−	0.999874i	$-0.494949\pi$
$463$	19.1444	−	11.0530i	0.889717	−	0.513678i	0.873850	+	0.486196i	$0.161616\pi$
$464$	−2.16663	−	1.25090i	−0.100583	−	0.0580717i
$465$	16.9148	+	0.0752051i	0.784406	+	0.00348756i
$466$	−13.6638	−	23.6663i	−0.632962	−	1.09632i
$467$	30.9099	−	17.8459i	1.43034	−	0.825808i	0.433195	−	0.901300i	$-0.357386\pi$
$467$	30.9099	−	17.8459i	1.43034	−	0.825808i	0.997146	+	0.0754924i	$0.0240529\pi$
$468$	14.3369	−	5.83132i	0.662722	−	0.269553i
$469$	−16.2919	−	36.4510i	−0.752290	−	1.68315i
$470$	14.3911	−	16.3688i	0.663814	−	0.755034i
$471$	−5.64185	−	6.47498i	−0.259963	−	0.298351i
$472$	−1.30033			−0.0598526
$473$	27.9055			1.28310
$474$	9.58141	+	10.9963i	0.440089	+	0.505076i
$475$	−5.29572	−	6.93724i	−0.242984	−	0.318303i
$476$	−4.92358	−	0.510329i	−0.225672	−	0.0233909i
$477$	2.97914	+	2.31642i	0.136406	+	0.106062i
$478$	−15.6608	+	9.04177i	−0.716309	+	0.413561i
$479$	−1.92319	−	3.33106i	−0.0878727	−	0.152200i	0.818739	−	0.574166i	$-0.194674\pi$
$479$	−1.92319	−	3.33106i	−0.0878727	−	0.152200i	−0.906612	+	0.421966i	$0.861340\pi$
$480$	−0.0172195	+	3.87295i	−0.000785961	+	0.176775i
$481$	6.08237	+	3.51166i	0.277332	+	0.160118i
$482$	2.31790	−	1.33824i	0.105578	−	0.0609552i
$483$	24.0470	−	16.9313i	1.09418	−	0.770401i
$484$	12.0891	−	20.9388i	0.549502	−	0.951766i
$485$	5.23279	−	1.76903i	0.237609	−	0.0803273i
$486$	−6.67004	−	14.0894i	−0.302559	−	0.639107i
$487$	−17.1992	−	9.92995i	−0.779369	−	0.449969i	0.0568378	−	0.998383i	$-0.481898\pi$
$487$	−17.1992	−	9.92995i	−0.779369	−	0.449969i	−0.836207	+	0.548415i	$0.815232\pi$
$488$		−	11.4604i		−	0.518788i
$489$	−9.68092	−	3.32082i	−0.437786	−	0.150172i
$490$	15.5410	−	1.86510i	0.702069	−	0.0842568i
$491$	7.14924	−	4.12761i	0.322641	−	0.186277i	−0.329928	−	0.944006i	$-0.607025\pi$
$491$	7.14924	−	4.12761i	0.322641	−	0.186277i	0.652569	+	0.757729i	$0.273691\pi$
$492$	4.26439	−	12.4317i	0.192254	−	0.560463i
$493$	−2.34032	−	4.05356i	−0.105403	−	0.182563i
$494$	7.79883	+	4.50266i	0.350886	+	0.202584i
$495$	−13.0768	+	37.5767i	−0.587760	+	1.68895i
$496$		−	4.36743i		−	0.196103i
$497$	3.11687	+	6.97358i	0.139811	+	0.312808i
$498$	0.936637	+	4.78883i	0.0419717	+	0.214593i
$499$	−15.9868	+	27.6900i	−0.715668	+	1.23957i	0.247033	+	0.969007i	$0.420544\pi$
$499$	−15.9868	+	27.6900i	−0.715668	+	1.23957i	−0.962701	+	0.270567i	$0.912789\pi$
$500$	−6.24617	+	9.27283i	−0.279337	+	0.414693i
$501$	−17.1648	−	5.88797i	−0.766865	−	0.263055i
$502$	0.220993			0.00986341
$503$		−	3.78755i		−	0.168878i	−0.996429	−	0.0844392i	$-0.973090\pi$
$503$		−	3.78755i		−	0.168878i	0.996429	−	0.0844392i	$-0.0269099\pi$
$504$	−2.21652	−	7.62149i	−0.0987315	−	0.339488i
$505$	6.06616	−	30.2992i	0.269940	−	1.34830i
$506$			38.0642i			1.69216i
$507$	−23.1463	+	4.52713i	−1.02796	+	0.201057i
$508$		−	8.49642i		−	0.376968i
$509$	−6.04054	+	10.4625i	−0.267742	+	0.463743i	−0.968278	−	0.249874i	$-0.919611\pi$
$509$	−6.04054	+	10.4625i	−0.267742	+	0.463743i	0.700536	+	0.713617i	$0.252944\pi$
$510$	−3.65086	+	6.25904i	−0.161663	+	0.277155i
$511$	−0.981013	+	9.46467i	−0.0433974	+	0.418693i
$512$	1.00000			0.0441942
$513$	4.08943	−	8.09569i	0.180553	−	0.357433i
$514$	−14.7049	−	8.48987i	−0.648605	−	0.374472i
$515$	−3.02009	+	1.02099i	−0.133081	+	0.0449900i
$516$	1.56424	+	7.99766i	0.0688620	+	0.352077i
$517$	−28.9059	−	50.0665i	−1.27128	−	2.20192i
$518$	2.11287	−	2.91692i	0.0928340	−	0.128162i
$519$	−11.2309	+	9.78580i	−0.492980	+	0.429549i
$520$	2.26470	−	11.3117i	0.0993135	−	0.496051i
$521$	−19.2169	+	33.2847i	−0.841910	+	1.45823i	0.0463687	+	0.998924i	$0.485235\pi$
$521$	−19.2169	+	33.2847i	−0.841910	+	1.45823i	−0.888278	+	0.459306i	$0.848098\pi$
$522$	4.60702	−	5.92509i	0.201644	−	0.259334i
$523$	5.25006	+	9.09336i	0.229569	+	0.397625i	0.957680	−	0.287834i	$-0.0929350\pi$
$523$	5.25006	+	9.09336i	0.229569	+	0.397625i	−0.728111	+	0.685459i	$0.759602\pi$
$524$	−1.98718	+	3.44190i	−0.0868104	+	0.150360i
$525$	6.88764	−	21.8532i	0.300601	−	0.953750i
$526$	5.28060	+	9.14626i	0.230245	+	0.398796i
$527$	4.08553	−	7.07634i	0.177968	−	0.308250i
$528$	9.71719	+	3.33326i	0.422886	+	0.145061i
$529$	−9.09349	−	15.7504i	−0.395369	−	0.684799i
$530$	2.66463	−	0.900818i	0.115744	−	0.0391290i
$531$	0.533923	−	3.86428i	0.0231703	−	0.167696i
$532$	2.70912	−	3.74009i	0.117455	−	0.162153i
$533$	−19.5737	+	33.9026i	−0.847829	+	1.46848i
$534$	−10.0271	+	29.2311i	−0.433914	+	1.26496i
$535$	1.46615	−	7.32313i	0.0633872	−	0.316607i
$536$			15.0907i			0.651818i
$537$	−0.888288	−	4.54163i	−0.0383325	−	0.195986i
$538$	1.54717	−	2.67977i	0.0667031	−	0.115533i
$539$	8.51515	−	40.6352i	0.366773	−	1.75028i
$540$	−11.5024	−	1.64143i	−0.494985	−	0.0706357i
$541$	17.0100	+	29.4622i	0.731316	+	1.26668i	0.956321	+	0.292319i	$0.0944270\pi$
$541$	17.0100	+	29.4622i	0.731316	+	1.26668i	−0.225004	+	0.974358i	$0.572240\pi$
$542$	15.2570	−	8.80863i	0.655344	−	0.378363i
$543$	−10.3554	+	9.02302i	−0.444394	+	0.387215i
$544$	1.62025	+	0.935454i	0.0694678	+	0.0401072i
$545$	18.7310	−	6.33230i	0.802348	−	0.271246i
$546$	2.12182	+	23.5467i	0.0908057	+	1.00771i
$547$	−22.5807	−	13.0370i	−0.965482	−	0.557422i	−0.0676264	−	0.997711i	$-0.521543\pi$
$547$	−22.5807	−	13.0370i	−0.965482	−	0.557422i	−0.897856	+	0.440289i	$0.854876\pi$
$548$	4.85327	+	8.40611i	0.207321	+	0.359091i
$549$	34.0576	+	4.70570i	1.45354	+	0.200835i
$550$	17.9945	+	23.5723i	0.767287	+	1.00512i
$551$	4.36692			0.186037
$552$	−10.9091	+	2.13369i	−0.464322	+	0.0908157i
$553$	−20.3398	+	9.09093i	−0.864934	+	0.386586i
$554$	−2.43071	+	1.40337i	−0.103271	+	0.0596235i
$555$	−2.61589	−	4.57774i	−0.111038	−	0.194314i
$556$	−17.4411	+	10.0696i	−0.739666	+	0.427046i
$557$	9.87249	−	17.0997i	0.418311	−	0.724535i	−0.577459	−	0.816420i	$-0.695956\pi$
$557$	9.87249	−	17.0997i	0.418311	−	0.724535i	0.995770	+	0.0918842i	$0.0292890\pi$
$558$	12.9790	+	1.79329i	0.549444	+	0.0759161i
$559$		−	24.2734i		−	1.02666i
$560$	−5.65031	−	1.75328i	−0.238769	−	0.0740894i
$561$	12.6262	+	14.4907i	0.533078	+	0.611798i
$562$	6.77309	+	3.91045i	0.285706	+	0.164952i
$563$		−	26.5207i		−	1.11771i	−0.829264	−	0.558857i	$-0.811240\pi$
$563$		−	26.5207i		−	1.11771i	0.829264	−	0.558857i	$-0.188760\pi$
$564$	12.7286	−	11.0908i	0.535972	−	0.467009i
$565$	7.79471	−	38.9330i	0.327926	−	1.63793i
$566$	26.6702			1.12103
$567$	23.5594	−	3.45755i	0.989402	−	0.145203i
$568$		−	2.88706i		−	0.121138i
$569$			4.44062i			0.186160i	0.995659	+	0.0930802i	$0.0296713\pi$
$569$			4.44062i			0.186160i	−0.995659	+	0.0930802i	$0.970329\pi$
$570$	−3.35410	−	5.86958i	−0.140488	−	0.245850i
$571$	34.4566			1.44196			0.720982	−	0.692954i	$-0.243691\pi$
$571$	34.4566			1.44196			0.720982	+	0.692954i	$0.243691\pi$
$572$	−26.4999	−	15.2997i	−1.10802	−	0.639713i
$573$	−15.5086	+	13.5131i	−0.647881	+	0.564519i
$574$	16.2587	+	11.7769i	0.678623	+	0.491559i
$575$	−29.6152	−	12.3536i	−1.23504	−	0.515181i
$576$	−0.410606	+	2.97177i	−0.0171086	+	0.123824i
$577$	10.7016	−	18.5357i	0.445513	−	0.771651i	−0.552575	−	0.833463i	$-0.686355\pi$
$577$	10.7016	−	18.5357i	0.445513	−	0.771651i	0.998088	+	0.0618122i	$0.0196880\pi$
$578$	−6.74985	−	11.6911i	−0.280757	−	0.486285i
$579$	−20.0083	+	17.4338i	−0.831516	+	0.724526i
$580$	−1.79160	−	5.29956i	−0.0743920	−	0.220052i
$581$	−7.41394	−	0.768454i	−0.307582	−	0.0318809i
$582$	4.19910	−	0.821293i	0.174058	−	0.0340437i
$583$		−	7.46082i		−	0.308996i
$584$	1.79824	−	3.11464i	0.0744116	−	0.128885i
$585$	32.6859	+	11.3748i	1.35139	+	0.470290i
$586$	−28.0362	+	16.1867i	−1.15816	+	0.668667i
$587$	4.73587	+	2.73426i	0.195470	+	0.112855i	0.594541	−	0.804065i	$-0.297334\pi$
$587$	4.73587	+	2.73426i	0.195470	+	0.112855i	−0.399071	+	0.916920i	$0.630667\pi$
$588$	12.1233	+	0.162614i	0.499955	+	0.00670611i
$589$	3.81169	+	6.60204i	0.157058	+	0.272032i
$590$	−2.18368	−	1.91986i	−0.0899007	−	0.0790392i
$591$	10.2711	+	11.7878i	0.422497	+	0.484886i
$592$	−1.17895	+	0.680668i	−0.0484546	+	0.0279753i
$593$	−5.02625	+	2.90190i	−0.206403	+	0.119167i	−0.599639	−	0.800271i	$-0.704689\pi$
$593$	−5.02625	+	2.90190i	−0.206403	+	0.119167i	0.393236	+	0.919438i	$0.371356\pi$
$594$	−13.8956	+	27.5086i	−0.570143	+	1.12869i
$595$	−7.51483	−	8.12636i	−0.308078	−	0.333148i
$596$	−2.64213	−	1.52543i	−0.108226	−	0.0624842i
$597$	4.02465	+	20.5772i	0.164718	+	0.842169i
$598$	33.1098			1.35396
$599$		−	18.0350i		−	0.736888i	−0.929650	−	0.368444i	$-0.879891\pi$
$599$		−	18.0350i		−	0.736888i	0.929650	−	0.368444i	$-0.120109\pi$
$600$	−5.74707	+	6.47852i	−0.234623	+	0.264484i
$601$	2.29768	+	1.32656i	0.0937242	+	0.0541117i	0.546130	−	0.837701i	$-0.316101\pi$
$601$	2.29768	+	1.32656i	0.0937242	+	0.0541117i	−0.452405	+	0.891812i	$0.649434\pi$
$602$	−12.3818	−	1.28337i	−0.504643	−	0.0523062i
$603$	−44.8460	−	6.19632i	−1.82627	−	0.252334i
$604$	8.45186	+	14.6390i	0.343901	+	0.595654i
$605$	51.2163	−	17.3145i	2.08224	−	0.703933i
$606$	7.76628	−	22.6405i	0.315484	−	0.919706i
$607$	4.83260	−	8.37031i	0.196149	−	0.339740i	−0.751128	−	0.660157i	$-0.770490\pi$
$607$	4.83260	−	8.37031i	0.196149	−	0.339740i	0.947277	+	0.320417i	$0.103823\pi$
$608$	−1.51165	+	0.872754i	−0.0613057	+	0.0353949i
$609$	6.60031	+	9.37421i	0.267458	+	0.379862i
$610$	16.9205	−	19.2457i	0.685093	−	0.779237i
$611$	−43.5500	+	25.1436i	−1.76185	+	1.01720i
$612$	−3.44524	+	4.43091i	−0.139265	+	0.179109i
$613$	−0.262890	−	0.151780i	−0.0106180	−	0.00613033i	0.494682	−	0.869074i	$-0.335285\pi$
$613$	−0.262890	−	0.151780i	−0.0106180	−	0.00613033i	−0.505300	+	0.862944i	$0.668618\pi$
$614$	1.43218			0.0577979
$615$	25.5159	−	14.5807i	1.02890	−	0.587951i
$616$	−9.20540	+	12.7086i	−0.370896	+	0.512042i
$617$	−3.49093	−	6.04647i	−0.140540	−	0.243422i	0.787160	−	0.616748i	$-0.211550\pi$
$617$	−3.49093	−	6.04647i	−0.140540	−	0.243422i	−0.927700	+	0.373327i	$0.878217\pi$
$618$	−2.42349	+	0.474006i	−0.0974873	+	0.0190673i
$619$	15.3880	−	8.88428i	0.618497	−	0.357089i	−0.157787	−	0.987473i	$-0.550436\pi$
$619$	15.3880	−	8.88428i	0.618497	−	0.357089i	0.776284	+	0.630384i	$0.217102\pi$
$620$	6.44823	−	7.33434i	0.258967	−	0.294554i
$621$	−1.86149	−	33.2954i	−0.0746988	−	1.33610i
$622$	10.0729			0.403887
$623$	−38.2297	−	27.6916i	−1.53164	−	1.10944i
$624$	2.89941	−	8.45243i	0.116069	−	0.338368i
$625$	−24.1801	+	6.35003i	−0.967204	+	0.254001i
$626$	15.5516			0.621569
$627$	−17.5981	+	3.44198i	−0.702802	+	0.137460i
$628$	−4.95836			−0.197860
$629$	−2.54693			−0.101553
$630$	7.53038	−	16.0715i	0.300017	−	0.640304i
$631$	12.0365			0.479167			0.239583	−	0.970876i	$-0.422989\pi$
$631$	12.0365			0.479167			0.239583	+	0.970876i	$0.422989\pi$
$632$	8.42064			0.334955
$633$	−4.81692	+	14.0424i	−0.191455	+	0.558136i
$634$	27.9352			1.10945
$635$	12.5444	−	14.2683i	0.497810	−	0.566219i
$636$	2.13825	−	0.418216i	0.0847872	−	0.0165834i
$637$	−35.3462	−	7.40685i	−1.40047	−	0.293470i
$638$	−14.8385			−0.587462
$639$	8.57966	+	1.18544i	0.339406	+	0.0468954i
$640$	1.67933	+	1.47644i	0.0663812	+	0.0583613i
$641$	−14.6690	+	8.46918i	−0.579392	+	0.334512i	−0.760892	−	0.648879i	$-0.775238\pi$
$641$	−14.6690	+	8.46918i	−0.579392	+	0.334512i	0.181499	+	0.983391i	$0.441905\pi$
$642$	1.87706	−	5.47205i	0.0740817	−	0.215965i
$643$	−12.5911	−	21.8084i	−0.496545	−	0.860041i	0.503447	−	0.864026i	$-0.332065\pi$
$643$	−12.5911	−	21.8084i	−0.496545	−	0.860041i	−0.999992	+	0.00398491i	$0.998732\pi$
$644$	1.75056	−	16.8892i	0.0689818	−	0.665527i
$645$	−9.18115	+	15.7402i	−0.361507	+	0.619769i
$646$	−3.26568			−0.128487
$647$	−21.6450	−	12.4967i	−0.850951	−	0.491297i	0.0100203	−	0.999950i	$-0.496810\pi$
$647$	−21.6450	−	12.4967i	−0.850951	−	0.491297i	−0.860972	+	0.508653i	$0.830144\pi$
$648$	−8.66281	−	2.44045i	−0.340307	−	0.0958699i
$649$	−6.67914	+	3.85621i	−0.262179	+	0.151369i
$650$	20.5042	−	15.6524i	0.804240	−	0.613936i
$651$	−8.41109	+	18.1609i	−0.329656	+	0.711780i
$652$	−5.11733	+	2.95449i	−0.200410	+	0.115707i
$653$	10.8541	−	18.7998i	0.424753	−	0.735694i	−0.571644	−	0.820502i	$-0.693694\pi$
$653$	10.8541	−	18.7998i	0.424753	−	0.735694i	0.996397	+	0.0848077i	$0.0270276\pi$
$654$	15.0309	−	2.93985i	0.587753	−	0.114957i
$655$	−8.41887	+	2.84612i	−0.328952	+	0.111207i
$656$	−3.79398	−	6.57136i	−0.148130	−	0.256569i
$657$	8.51762	+	6.62283i	0.332304	+	0.258381i
$658$	10.5231	+	23.5440i	0.410233	+	0.917842i
$659$	−6.26940	−	3.61964i	−0.244221	−	0.141001i	0.372894	−	0.927874i	$-0.378365\pi$
$659$	−6.26940	−	3.61964i	−0.244221	−	0.141001i	−0.617115	+	0.786873i	$0.711699\pi$
$660$	11.3970	+	19.9444i	0.443627	+	0.776336i
$661$			27.7010i			1.07744i	0.842484	+	0.538721i	$0.181092\pi$
$661$			27.7010i			1.07744i	−0.842484	+	0.538721i	$0.818908\pi$
$662$	−2.18531			−0.0849345
$663$	12.6046	−	10.9828i	0.489523	−	0.426537i
$664$	2.43978	+	1.40861i	0.0946820	+	0.0546646i
$665$	10.0715	−	2.28099i	0.390556	−	0.0884528i
$666$	−1.53870	−	3.78306i	−0.0596235	−	0.146590i
$667$	13.9048	−	8.02793i	0.538396	−	0.310843i
$668$	−9.07327	+	5.23846i	−0.351055	+	0.202682i
$669$	−34.6910	+	6.78514i	−1.34123	+	0.262329i
$670$	−22.2804	+	25.3422i	−0.860768	+	0.979054i
$671$	−33.9865	−	58.8663i	−1.31203	−	2.27251i
$672$	−4.15825	−	1.92587i	−0.160408	−	0.0742919i
$673$	40.2514	+	23.2391i	1.55158	+	0.895803i	0.998014	+	0.0629944i	$0.0200650\pi$
$673$	40.2514	+	23.2391i	1.55158	+	0.895803i	0.553562	+	0.832808i	$0.313268\pi$
$674$	0.212414	−	0.122637i	0.00818187	−	0.00472381i
$675$	−16.8929	−	19.7391i	−0.650207	−	0.759758i
$676$	−6.80835	+	11.7924i	−0.261860	+	0.453554i
$677$			1.40767i			0.0541012i	0.999634	+	0.0270506i	$0.00861152\pi$
$677$			1.40767i			0.0541012i	−0.999634	+	0.0270506i	$0.991388\pi$
$678$	9.97929	−	29.0919i	0.383252	−	1.11727i
$679$	−0.673822	+	6.50094i	−0.0258589	+	0.249483i
$680$	1.33980	+	3.96313i	0.0513789	+	0.151979i
$681$	−37.6735	−	12.9230i	−1.44365	−	0.495211i
$682$	−12.9519	−	22.4333i	−0.495952	−	0.859015i
$683$	18.2234	−	31.5639i	0.697300	−	1.20776i	−0.272099	−	0.962269i	$-0.587718\pi$
$683$	18.2234	−	31.5639i	0.697300	−	1.20776i	0.969399	−	0.245490i	$-0.0789487\pi$
$684$	−1.97293	−	4.85064i	−0.0754368	−	0.185469i
$685$	−4.26086	+	21.2821i	−0.162799	+	0.813149i
$686$	−5.64700	+	17.6383i	−0.215604	+	0.673435i
$687$	−6.91576	−	35.3588i	−0.263853	−	1.34902i
$688$	4.07460	+	2.35247i	0.155343	+	0.0896871i
$689$	−6.48974			−0.247240
$690$	−21.4702	−	12.5234i	−0.817356	−	0.476758i
$691$			41.4523i			1.57692i	0.615086	+	0.788460i	$0.289121\pi$
$691$			41.4523i			1.57692i	−0.615086	+	0.788460i	$0.710879\pi$
$692$			8.60028i			0.326933i
$693$	−33.9871	−	32.5745i	−1.29106	−	1.23740i
$694$	−6.03454			−0.229068
$695$	−44.1563	−	8.84046i	−1.67495	−	0.335338i
$696$	−0.831773	−	4.25268i	−0.0315283	−	0.161197i
$697$		−	14.1964i		−	0.537726i
$698$	6.70174	+	3.86925i	0.253665	+	0.146453i
$699$	15.3579	−	44.7718i	0.580890	−	1.69343i
$700$	−6.90012	−	11.2866i	−0.260800	−	0.426595i
$701$		−	9.85600i		−	0.372256i	−0.982526	−	0.186128i	$-0.940406\pi$
$701$		−	9.85600i		−	0.372256i	0.982526	−	0.186128i	$-0.0595939\pi$
$702$	23.9281	+	12.0870i	0.903109	+	0.456194i
$703$	1.18811	−	2.05787i	0.0448105	−	0.0776140i
$704$	5.13649	−	2.96556i	0.193589	−	0.111769i
$705$	37.7504	+	0.167843i	1.42176	+	0.00632132i
$706$	12.4114	−	7.16571i	0.467108	−	0.269685i
$707$	29.6102	+	21.4480i	1.11360	+	0.806636i
$708$	−1.47958	−	1.69807i	−0.0556060	−	0.0638172i
$709$	4.54234			0.170591			0.0852957	−	0.996356i	$-0.472817\pi$
$709$	4.54234			0.170591			0.0852957	+	0.996356i	$0.472817\pi$
$710$	4.26256	−	4.84831i	0.159971	−	0.181954i
$711$	−3.45756	+	25.0242i	−0.129669	+	0.938481i
$712$	8.92096	+	15.4516i	0.334327	+	0.579071i
$713$	24.2737	+	14.0144i	0.909058	+	0.524845i
$714$	−4.93586	−	7.01024i	−0.184720	−	0.262352i
$715$	−21.9129	−	64.8186i	−0.819496	−	2.42408i
$716$	−2.31384	−	1.33590i	−0.0864724	−	0.0499248i
$717$	−29.6270	−	10.1629i	−1.10644	−	0.379539i
$718$	−14.4007	+	8.31423i	−0.537428	+	0.310284i
$719$	−20.9595	−	36.3030i	−0.781659	−	1.35387i	−0.930975	−	0.365083i	$-0.881040\pi$
$719$	−20.9595	−	36.3030i	−0.781659	−	1.35387i	0.149316	−	0.988790i	$-0.452293\pi$
$720$	−5.07717	+	4.38433i	−0.189215	+	0.163395i
$721$	0.388894	−	3.75199i	0.0144832	−	0.139732i
$722$	−7.97660	+	13.8159i	−0.296858	+	0.514174i
$723$	4.38499	+	1.50417i	0.163080	+	0.0559407i
$724$			7.92990i			0.294712i
$725$	4.81579	−	11.5449i	0.178854	−	0.428766i
$726$	41.0990	−	8.03846i	1.52533	−	0.298335i
$727$	5.40633	−	9.36404i	0.200510	−	0.347293i	−0.748183	−	0.663492i	$-0.769074\pi$
$727$	5.40633	−	9.36404i	0.200510	−	0.347293i	0.948693	+	0.316199i	$0.102407\pi$
$728$	11.0544	+	8.00725i	0.409705	+	0.296769i
$729$	10.8094	−	24.7418i	0.400350	−	0.916362i
$730$	7.61839	−	2.57551i	0.281969	−	0.0953240i
$731$	4.40125	+	7.62319i	0.162786	+	0.281954i
$732$	14.9658	−	13.0402i	0.553152	−	0.481979i
$733$	6.82458	−	11.8205i	0.252072	−	0.436601i	−0.712024	−	0.702155i	$-0.752221\pi$
$733$	6.82458	−	11.8205i	0.252072	−	0.436601i	0.964096	+	0.265554i	$0.0855548\pi$
$734$	16.5694	+	28.6990i	0.611586	+	1.05930i
$735$	20.1188	+	18.1723i	0.742094	+	0.670296i
$736$	−3.20885	+	5.55790i	−0.118280	+	0.204867i
$737$	44.7523	+	77.5132i	1.64847	+	2.85524i
$738$	21.0864	−	8.57658i	0.776201	−	0.315708i
$739$	15.6035	−	27.0261i	0.573985	−	0.994171i	−0.422166	−	0.906519i	$-0.638730\pi$
$739$	15.6035	−	27.0261i	0.573985	−	0.994171i	0.996151	−	0.0876529i	$-0.0279366\pi$
$740$	−2.98481	−	0.597583i	−0.109724	−	0.0219676i
$741$	2.99399	+	15.3076i	0.109987	+	0.562340i
$742$	−0.343121	+	3.31039i	−0.0125964	+	0.121528i
$743$	−3.52550	−	6.10635i	−0.129338	−	0.224020i	0.794082	−	0.607810i	$-0.207952\pi$
$743$	−3.52550	−	6.10635i	−0.129338	−	0.224020i	−0.923420	+	0.383790i	$0.874619\pi$
$744$	5.70331	−	4.96947i	0.209093	−	0.182190i
$745$	−2.18479	−	6.46263i	−0.0800445	−	0.236773i
$746$	−18.2835	−	10.5560i	−0.669405	−	0.386481i
$747$	−5.18785	+	6.67209i	−0.189813	+	0.244119i
$748$	11.0966			0.405731
$749$	7.15658	+	5.18385i	0.261496	+	0.189414i
$750$	−19.2163	+	2.39436i	−0.701681	+	0.0874296i
$751$	16.2419	−	28.1318i	0.592675	−	1.02654i	−0.401196	−	0.915992i	$-0.631405\pi$
$751$	16.2419	−	28.1318i	0.592675	−	1.02654i	0.993871	−	0.110550i	$-0.0352613\pi$
$752$		−	9.74722i		−	0.355444i
$753$	0.251457	+	0.288589i	0.00916359	+	0.0105168i
$754$			12.9072i			0.470051i
$755$	−7.42019	+	37.0624i	−0.270048	+	1.34884i
$756$	7.43063	−	11.5666i	0.270249	−	0.420672i
$757$			4.96180i			0.180340i	0.995926	+	0.0901699i	$0.0287410\pi$
$757$			4.96180i			0.180340i	−0.995926	+	0.0901699i	$0.971259\pi$
$758$	−12.8226			−0.465736
$759$	−49.7069	+	43.3112i	−1.80425	+	1.57210i
$760$	−3.82713	−	0.766222i	−0.138824	−	0.0277938i
$761$	−14.0123	+	24.2700i	−0.507944	+	0.879785i	0.492014	+	0.870588i	$0.336261\pi$
$761$	−14.0123	+	24.2700i	−0.507944	+	0.879785i	−0.999958	+	0.00919753i	$0.997072\pi$
$762$	11.0952	−	9.66764i	0.401938	−	0.350222i
$763$	−2.41197	+	23.2704i	−0.0873193	+	0.842444i
$764$			11.8760i			0.429660i
$765$	−12.3276	+	2.35428i	−0.445707	+	0.0851192i
$766$	−14.1368	−	8.16190i	−0.510784	−	0.294902i
$767$	3.35429	+	5.80981i	0.121117	+	0.209780i
$768$	1.13785	+	1.30587i	0.0410585	+	0.0471216i
$769$	22.5043	−	12.9928i	0.811524	−	0.468534i	−0.0359606	−	0.999353i	$-0.511449\pi$
$769$	22.5043	−	12.9928i	0.811524	−	0.468534i	0.847485	+	0.530819i	$0.178116\pi$
$770$	−34.2222	+	7.75063i	−1.23328	+	0.279313i
$771$	−5.64523	−	28.8629i	−0.203308	−	1.03947i
$772$			15.3218i			0.551442i
$773$	−44.5726	−	25.7340i	−1.60317	−	0.925589i	−0.990849	−	0.134977i	$-0.956904\pi$
$773$	−44.5726	−	25.7340i	−1.60317	−	0.925589i	−0.612318	−	0.790612i	$-0.709763\pi$
$774$	−8.66405	+	11.1428i	−0.311423	+	0.400520i
$775$	21.6574	−	2.79635i	0.777955	−	0.100448i
$776$	1.23514	−	2.13933i	0.0443391	−	0.0767975i
$777$	6.21325	−	0.559884i	0.222899	−	0.0200857i
$778$	−9.64090	+	5.56618i	−0.345643	+	0.199557i
$779$	11.4704	+	6.62242i	0.410969	+	0.237273i
$780$	17.3485	−	9.91359i	0.621177	−	0.354964i
$781$	−8.56173	−	14.8294i	−0.306363	−	0.530636i
$782$	−10.3983	+	6.00347i	−0.371843	+	0.214684i
$783$	12.9795	−	0.725661i	0.463850	−	0.0259330i
$784$	4.66893	−	5.21547i	0.166747	−	0.186267i
$785$	−8.32670	−	7.32069i	−0.297193	−	0.261287i
$786$	−6.75579	+	1.32135i	−0.240971	+	0.0471310i
$787$	14.4239			0.514156			0.257078	−	0.966391i	$-0.417240\pi$
$787$	14.4239			0.514156			0.257078	+	0.966391i	$0.417240\pi$
$788$	9.02678			0.321566
$789$	−5.93534	+	17.3028i	−0.211304	+	0.615997i
$790$	14.1410	+	12.4325i	0.503115	+	0.442330i
$791$	38.0476	+	27.5597i	1.35282	+	0.979909i
$792$	6.70387	+	16.4821i	0.238212	+	0.585667i
$793$	−51.2044	+	29.5629i	−1.81832	+	1.04981i
$794$	−10.7572	−	18.6321i	−0.381760	−	0.661228i
$795$	4.20829	+	2.45467i	0.149253	+	0.0870582i
$796$	10.4835	+	6.05268i	0.371580	+	0.214532i
$797$	−18.3241	+	10.5794i	−0.649072	+	0.374742i	−0.788101	−	0.615546i	$-0.788935\pi$
$797$	−18.3241	+	10.5794i	−0.649072	+	0.374742i	0.139029	+	0.990288i	$0.455602\pi$
$798$	7.96664	−	0.717884i	0.282016	−	0.0254128i
$799$	9.11807	−	15.7930i	0.322574	−	0.558715i
$800$	0.640274	+	4.95884i	0.0226371	+	0.175321i
$801$	−49.5814	+	20.1665i	−1.75187	+	0.712549i
$802$	11.7705	+	6.79568i	0.415629	+	0.239964i
$803$		−	21.3311i		−	0.752758i
$804$	−19.7065	+	17.1709i	−0.694995	+	0.605571i
$805$	27.8756	−	25.7779i	0.982484	−	0.908550i
$806$	−19.5134	+	11.2661i	−0.687331	+	0.396831i
$807$	5.25988	−	1.02877i	0.185156	−	0.0362144i
$808$	−6.90957	−	11.9677i	−0.243078	−	0.421023i
$809$	14.1543	+	8.17201i	0.497640	+	0.287312i	0.727738	−	0.685855i	$-0.240572\pi$
$809$	14.1543	+	8.17201i	0.497640	+	0.287312i	−0.230099	+	0.973167i	$0.573905\pi$
$810$	−10.9445	−	16.8884i	−0.384551	−	0.593398i
$811$			2.77152i			0.0973212i	0.998815	+	0.0486606i	$0.0154953\pi$
$811$			2.77152i			0.0973212i	−0.998815	+	0.0486606i	$0.984505\pi$
$812$	6.58389	+	0.682419i	0.231049	+	0.0239482i
$813$	28.8631	+	9.90082i	1.01227	+	0.347237i
$814$	−4.03712	+	6.99249i	−0.141501	+	0.245087i
$815$	−12.9558	−	2.59385i	−0.453821	−	0.0908586i
$816$	0.622018	+	3.18025i	0.0217750	+	0.111331i
$817$	−8.21251			−0.287319
$818$			6.31246i			0.220710i
$819$	−28.3347	+	29.5634i	−0.990095	+	1.03303i
$820$	3.33087	−	16.6370i	0.116319	−	0.580990i
$821$		−	41.5518i		−	1.45017i	−0.688660	−	0.725085i	$-0.741801\pi$
$821$		−	41.5518i		−	1.45017i	0.688660	−	0.725085i	$-0.258199\pi$
$822$	−5.45502	+	15.9026i	−0.190266	+	0.554667i
$823$			40.0405i			1.39572i	0.716232	+	0.697862i	$0.245865\pi$
$823$			40.0405i			1.39572i	−0.716232	+	0.697862i	$0.754135\pi$
$824$	−0.712859	+	1.23471i	−0.0248336	+	0.0430131i
$825$	−10.3074	+	50.3201i	−0.358858	+	1.75192i
$826$	3.14090	−	1.40384i	0.109286	−	0.0488458i
$827$	−44.7684			−1.55675			−0.778376	−	0.627799i	$-0.783956\pi$
$827$	−44.7684			−1.55675			−0.778376	+	0.627799i	$0.783956\pi$
$828$	−15.1992	−	11.8181i	−0.528209	−	0.410706i
$829$	12.4094	+	7.16460i	0.430998	+	0.248837i	0.699772	−	0.714367i	$-0.253285\pi$
$829$	12.4094	+	7.16460i	0.430998	+	0.248837i	−0.268774	+	0.963203i	$0.586618\pi$
$830$	2.01747	+	5.96770i	0.0700274	+	0.207142i
$831$	−4.59840	−	1.57737i	−0.159517	−	0.0547185i
$832$	−2.57957	−	4.46794i	−0.0894305	−	0.154898i
$833$	12.4437	−	4.08282i	0.431148	−	0.141461i
$834$	−32.9949	−	11.3181i	−1.14252	−	0.391915i
$835$	−22.9712	−	4.59903i	−0.794952	−	0.159156i
$836$	−5.17640	+	8.96579i	−0.179030	+	0.310088i
$837$	12.4263	+	18.9894i	0.429516	+	0.656369i
$838$	10.2076	+	17.6802i	0.352617	+	0.610751i
$839$	6.70519	−	11.6137i	0.231489	−	0.400951i	−0.726758	−	0.686894i	$-0.758974\pi$
$839$	6.70519	−	11.6137i	0.231489	−	0.400951i	0.958246	+	0.285943i	$0.0923070\pi$
$840$	−4.13964	−	9.37355i	−0.142831	−	0.323418i
$841$	−11.3705	−	19.6942i	−0.392086	−	0.679112i
$842$	−15.4045	+	26.6814i	−0.530874	+	0.919501i
$843$	2.60020	+	13.2943i	0.0895557	+	0.457879i
$844$	4.28556	+	7.42280i	0.147515	+	0.255503i
$845$	−28.8442	+	9.75121i	−0.992270	+	0.335452i
$846$	28.9665	+	4.00226i	0.995887	+	0.137601i
$847$	−6.59508	+	63.6284i	−0.226609	+	2.18630i
$848$	0.628956	−	1.08938i	0.0215984	−	0.0374096i
$849$	30.3467	+	34.8279i	1.04150	+	1.19529i
$850$	−3.60135	+	8.63352i	−0.123525	+	0.296127i
$851$		−	8.73666i		−	0.299489i
$852$	3.77013	−	3.28503i	0.129162	−	0.112543i
$853$	−6.92038	+	11.9865i	−0.236949	+	0.410408i	−0.959837	−	0.280557i	$-0.909481\pi$
$853$	−6.92038	+	11.9865i	−0.236949	+	0.410408i	0.722888	+	0.690965i	$0.242814\pi$
$854$	12.3726	+	27.6822i	0.423383	+	0.947264i
$855$	3.84847	−	11.0587i	0.131615	−	0.378200i
$856$	−1.67000	−	2.89252i	−0.0570793	−	0.0988643i
$857$	−9.97559	+	5.75941i	−0.340760	+	0.196738i	−0.660608	−	0.750731i	$-0.729701\pi$
$857$	−9.97559	+	5.75941i	−0.340760	+	0.196738i	0.319848	+	0.947469i	$0.396368\pi$
$858$	−10.1734	−	52.0142i	−0.347313	−	1.77574i
$859$	0.710391	+	0.410145i	0.0242382	+	0.0139940i	0.512070	−	0.858944i	$-0.328879\pi$
$859$	0.710391	+	0.410145i	0.0242382	+	0.0139940i	−0.487832	+	0.872938i	$0.662212\pi$
$860$	3.36931	+	9.96644i	0.114892	+	0.339853i
$861$	3.12074	+	34.6321i	0.106354	+	1.18026i
$862$	29.8217	+	17.2176i	1.01573	+	0.586433i
$863$	−0.390428	−	0.676242i	−0.0132903	−	0.0230195i	0.859304	−	0.511466i	$-0.170897\pi$
$863$	−0.390428	−	0.676242i	−0.0132903	−	0.0230195i	−0.872594	+	0.488446i	$0.837564\pi$
$864$	−4.34796	+	2.84522i	−0.147920	+	0.0967963i
$865$	−12.6978	+	14.4427i	−0.431737	+	0.491066i
$866$	−5.86503			−0.199302
$867$	7.58677	−	22.1171i	0.257660	−	0.751137i
$868$	4.71508	+	10.5494i	0.160040	+	0.358069i
$869$	43.2526	−	24.9719i	1.46724	−	0.847114i
$870$	4.88199	−	8.36969i	0.165515	−	0.283759i
$871$	67.4244	−	38.9275i	2.28459	−	1.31901i
$872$	4.42125	−	7.65783i	0.149722	−	0.259327i
$873$	5.85044	+	4.54898i	0.198007	+	0.153960i
$874$		−	11.2022i		−	0.378919i
$875$	5.07646	−	29.1415i	0.171616	−	0.985164i
$876$	6.11344	−	1.19572i	0.206554	−	0.0403995i
$877$	24.1988	+	13.9712i	0.817137	+	0.471774i	0.849428	−	0.527704i	$-0.176947\pi$
$877$	24.1988	+	13.9712i	0.817137	+	0.471774i	−0.0322912	+	0.999479i	$0.510280\pi$
$878$		−	0.0933769i		−	0.00315132i
$879$	−53.0387	−	18.1937i	−1.78895	−	0.613658i
$880$	13.0043	+	2.60357i	0.438375	+	0.0877663i
$881$	32.6360			1.09953			0.549767	−	0.835318i	$-0.314716\pi$
$881$	32.6360			1.09953			0.549767	+	0.835318i	$0.314716\pi$
$882$	13.5821	+	16.0165i	0.457332	+	0.539303i
$883$		−	45.5409i		−	1.53257i	−0.642499	−	0.766287i	$-0.722102\pi$
$883$		−	45.5409i		−	1.53257i	0.642499	−	0.766287i	$-0.277898\pi$
$884$		−	9.65227i		−	0.324641i
$885$	0.0223911	−	5.03611i	0.000752669	−	0.169287i
$886$	1.69982			0.0571066
$887$	15.8391	+	9.14469i	0.531824	+	0.307049i	0.741759	−	0.670667i	$-0.233992\pi$
$887$	15.8391	+	9.14469i	0.531824	+	0.307049i	−0.209935	+	0.977715i	$0.567325\pi$
$888$	−2.23033	−	0.765064i	−0.0748451	−	0.0256739i
$889$	9.17274	+	20.5228i	0.307644	+	0.688313i
$890$	−7.83203	+	39.1194i	−0.262530	+	1.31129i
$891$	−51.7337	+	13.1547i	−1.73315	+	0.440698i
$892$	−10.2042	+	17.6741i	−0.341661	+	0.591774i
$893$	8.50692	+	14.7344i	0.284673	+	0.493069i
$894$	−1.01432	−	5.18599i	−0.0339239	−	0.173446i
$895$	−1.91333	−	5.65965i	−0.0639556	−	0.189181i
$896$	−2.41546	+	1.07960i	−0.0806950	+	0.0360669i
$897$	37.6740	+	43.2372i	1.25790	+	1.44365i
$898$		−	1.98554i		−	0.0662584i
$899$	−5.46323	+	9.46260i	−0.182209	+	0.315595i
$900$	−14.9994	−	0.133381i	−0.499980	−	0.00444602i
$901$	2.03814	−	1.17672i	0.0679002	−	0.0392022i
$902$	−38.9755	−	22.5025i	−1.29774	−	0.749252i
$903$	−12.4126	−	17.6293i	−0.413067	−	0.586666i
$904$	−8.87845	−	15.3779i	−0.295293	−	0.511462i
$905$	−11.7080	+	13.3169i	−0.389187	+	0.442668i
$906$	−9.49980	+	27.6941i	−0.315610	+	0.920073i
$907$	25.0843	−	14.4825i	0.832912	−	0.480882i	−0.0219368	−	0.999759i	$-0.506983\pi$
$907$	25.0843	−	14.4825i	0.832912	−	0.480882i	0.854849	+	0.518877i	$0.173650\pi$
$908$	−19.9142	+	11.4974i	−0.660874	+	0.381556i
$909$	38.4024	−	15.6196i	1.27373	−	0.518070i
$910$	6.74183	+	29.7680i	0.223489	+	0.986799i
$911$	−47.8771	−	27.6419i	−1.58624	−	0.915816i	−0.993919	−	0.110114i	$-0.964878\pi$
$911$	−47.8771	−	27.6419i	−1.58624	−	0.915816i	−0.592321	−	0.805702i	$-0.701788\pi$
$912$	−2.85974	−	0.980967i	−0.0946954	−	0.0324831i
$913$	16.7092			0.552995
$914$		−	24.5551i		−	0.812211i
$915$	44.3855	+	0.197343i	1.46734	+	0.00652395i
$916$	−18.0144	−	10.4006i	−0.595213	−	0.343646i
$917$	1.08409	−	10.4591i	0.0357998	−	0.345391i
$918$	−9.70636	+	0.542665i	−0.320358	+	0.0179106i
$919$	−5.45039	−	9.44036i	−0.179792	−	0.311409i	0.762017	−	0.647557i	$-0.224209\pi$
$919$	−5.45039	−	9.44036i	−0.179792	−	0.311409i	−0.941809	+	0.336148i	$0.890876\pi$
$920$	−13.5946	+	4.59586i	−0.448200	+	0.151521i
$921$	1.62960	+	1.87024i	0.0536971	+	0.0616265i
$922$	16.3946	−	28.3963i	0.539929	−	0.935184i
$923$	−12.8992	+	7.44736i	−0.424583	+	0.245133i
$924$	−27.0701	+	2.43932i	−0.890541	+	0.0802477i
$925$	−4.13017	−	5.41041i	−0.135799	−	0.177893i
$926$	19.1444	−	11.0530i	0.629125	−	0.363225i
$927$	−3.37656	−	2.62543i	−0.110901	−	0.0862304i
$928$	−2.16663	−	1.25090i	−0.0711231	−	0.0410629i
$929$	28.3585			0.930411			0.465205	−	0.885203i	$-0.345980\pi$
$929$	28.3585			0.930411			0.465205	+	0.885203i	$0.345980\pi$
$930$	16.9148	+	0.0752051i	0.554659	+	0.00246607i
$931$	−2.50598	+	11.9588i	−0.0821303	+	0.391934i
$932$	−13.6638	−	23.6663i	−0.447572	−	0.775217i
$933$	11.4614	+	13.1539i	0.375231	+	0.430641i
$934$	30.9099	−	17.8459i	1.01140	−	0.583934i
$935$	18.6348	+	16.3834i	0.609422	+	0.535793i
$936$	14.3369	−	5.83132i	0.468616	−	0.190603i
$937$	−7.70498			−0.251711			−0.125855	−	0.992049i	$-0.540168\pi$
$937$	−7.70498			−0.251711			−0.125855	+	0.992049i	$0.540168\pi$
$938$	−16.2919	−	36.4510i	−0.531950	−	1.19017i
$939$	17.6954	+	20.3085i	0.577468	+	0.662742i
$940$	14.3911	−	16.3688i	0.469387	−	0.533890i
$941$	−44.4748			−1.44984			−0.724919	−	0.688834i	$-0.758123\pi$
$941$	−44.4748			−1.44984			−0.724919	+	0.688834i	$0.758123\pi$
$942$	−5.64185	−	6.47498i	−0.183821	−	0.210966i
$943$	48.6973			1.58580
$944$	−1.30033			−0.0423222
$945$	29.5558	−	8.45321i	0.961449	−	0.274983i
$946$	27.9055			0.907287
$947$	−48.7565			−1.58437			−0.792187	−	0.610279i	$-0.791058\pi$
$947$	−48.7565			−1.58437			−0.792187	+	0.610279i	$0.791058\pi$
$948$	9.58141	+	10.9963i	0.311190	+	0.357143i
$949$	−18.5547			−0.602311
$950$	−5.29572	−	6.93724i	−0.171816	−	0.225074i
$951$	31.7859	+	36.4797i	1.03073	+	1.18294i
$952$	−4.92358	−	0.510329i	−0.159574	−	0.0165398i
$953$	52.5200			1.70129			0.850644	−	0.525742i	$-0.176212\pi$
$953$	52.5200			1.70129			0.850644	+	0.525742i	$0.176212\pi$
$954$	2.97914	+	2.31642i	0.0964533	+	0.0749968i
$955$	−17.5342	+	19.9438i	−0.567394	+	0.645365i
$956$	−15.6608	+	9.04177i	−0.506507	+	0.292432i
$957$	−16.8840	−	19.3772i	−0.545781	−	0.626376i
$958$	−1.92319	−	3.33106i	−0.0621354	−	0.107622i
$959$	−20.7981	−	15.0651i	−0.671606	−	0.486476i
$960$	−0.0172195	+	3.87295i	−0.000555758	+	0.124999i
$961$	11.9256			0.384696
$962$	6.08237	+	3.51166i	0.196104	+	0.113220i
$963$	9.28161	−	3.77516i	0.299096	−	0.121653i
$964$	2.31790	−	1.33824i	0.0746546	−	0.0431018i
$965$	−22.6216	+	25.7302i	−0.728215	+	0.828286i
$966$	24.0470	−	16.9313i	0.773699	−	0.544756i
$967$	−22.4676	+	12.9717i	−0.722510	+	0.417141i	−0.815676	−	0.578509i	$-0.803635\pi$
$967$	−22.4676	+	12.9717i	−0.722510	+	0.417141i	0.0931658	+	0.995651i	$0.470301\pi$
$968$	12.0891	−	20.9388i	0.388557	−	0.673000i
$969$	−3.71585	−	4.26457i	−0.119370	−	0.136998i
$970$	5.23279	−	1.76903i	0.168015	−	0.0568000i
$971$	22.7435	+	39.3929i	0.729875	+	1.26418i	0.956936	+	0.290299i	$0.0937549\pi$
$971$	22.7435	+	39.3929i	0.729875	+	1.26418i	−0.227061	+	0.973880i	$0.572912\pi$
$972$	−6.67004	−	14.0894i	−0.213942	−	0.451917i
$973$	31.2571	−	43.1521i	1.00206	−	1.38339i
$974$	−17.1992	−	9.92995i	−0.551097	−	0.318176i
$975$	43.7706	+	8.96582i	1.40178	+	0.287136i
$976$		−	11.4604i		−	0.366838i
$977$	46.0077			1.47192			0.735958	−	0.677027i	$-0.236732\pi$
$977$	46.0077			1.47192			0.735958	+	0.677027i	$0.236732\pi$
$978$	−9.68092	−	3.32082i	−0.309562	−	0.106188i
$979$	91.6449	+	52.9112i	2.92898	+	1.69105i
$980$	15.5410	−	1.86510i	0.496438	−	0.0595785i
$981$	20.9419	+	16.2833i	0.668623	+	0.519885i
$982$	7.14924	−	4.12761i	0.228141	−	0.131717i
$983$	−26.7395	+	15.4381i	−0.852858	+	0.492398i	−0.861614	−	0.507564i	$-0.830546\pi$
$983$	−26.7395	+	15.4381i	−0.852858	+	0.492398i	0.00875587	+	0.999962i	$0.497213\pi$
$984$	4.26439	−	12.4317i	0.135944	−	0.396307i
$985$	15.1589	+	13.3275i	0.483003	+	0.424648i
$986$	−2.34032	−	4.05356i	−0.0745311	−	0.129092i
$987$	−18.7718	+	40.5314i	−0.597514	+	1.29013i
$988$	7.79883	+	4.50266i	0.248114	+	0.143249i
$989$	−26.1496	+	15.0975i	−0.831508	+	0.480071i
$990$	−13.0768	+	37.5767i	−0.415609	+	1.19427i
$991$	−12.4227	+	21.5168i	−0.394621	+	0.683504i	−0.993053	−	0.117670i	$-0.962457\pi$
$991$	−12.4227	+	21.5168i	−0.394621	+	0.683504i	0.598432	+	0.801174i	$0.295791\pi$
$992$		−	4.36743i		−	0.138666i
$993$	−2.48655	−	2.85374i	−0.0789083	−	0.0905606i
$994$	3.11687	+	6.97358i	0.0988610	+	0.221189i
$995$	8.66891	+	25.6427i	0.274823	+	0.812929i
$996$	0.936637	+	4.78883i	0.0296785	+	0.151740i
$997$	14.0068	+	24.2604i	0.443599	+	0.768336i	0.997953	−	0.0639447i	$-0.0203681\pi$
$997$	14.0068	+	24.2604i	0.443599	+	0.768336i	−0.554354	+	0.832281i	$0.687035\pi$
$998$	−15.9868	+	27.6900i	−0.506054	+	0.876511i
$999$	3.18938	−	6.31389i	0.100908	−	0.199763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.479.18	yes	48
3.2	odd	2		1890.2.bi.a.899.5		48
5.4	even	2		630.2.bi.a.479.7	yes	48
7.5	odd	6		630.2.r.a.299.23	yes	48
9.4	even	3		1890.2.r.a.1529.14		48
9.5	odd	6		630.2.r.b.59.2	yes	48
15.14	odd	2		1890.2.bi.b.899.22		48
21.5	even	6		1890.2.r.b.89.14		48
35.19	odd	6		630.2.r.b.299.2	yes	48
45.4	even	6		1890.2.r.b.1529.14		48
45.14	odd	6		630.2.r.a.59.23	✓	48
63.5	even	6		630.2.bi.a.509.7	yes	48
63.40	odd	6		1890.2.bi.b.719.22		48
105.89	even	6		1890.2.r.a.89.14		48
315.194	even	6	inner	630.2.bi.b.509.18	yes	48
315.229	odd	6		1890.2.bi.a.719.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.23	✓	48	45.14	odd	6
630.2.r.a.299.23	yes	48	7.5	odd	6
630.2.r.b.59.2	yes	48	9.5	odd	6
630.2.r.b.299.2	yes	48	35.19	odd	6
630.2.bi.a.479.7	yes	48	5.4	even	2
630.2.bi.a.509.7	yes	48	63.5	even	6
630.2.bi.b.479.18	yes	48	1.1	even	1	trivial
630.2.bi.b.509.18	yes	48	315.194	even	6	inner
1890.2.r.a.89.14		48	105.89	even	6
1890.2.r.a.1529.14		48	9.4	even	3
1890.2.r.b.89.14		48	21.5	even	6
1890.2.r.b.1529.14		48	45.4	even	6
1890.2.bi.a.719.5		48	315.229	odd	6
1890.2.bi.a.899.5		48	3.2	odd	2
1890.2.bi.b.719.22		48	63.40	odd	6
1890.2.bi.b.899.22		48	15.14	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.13785 + 1.30587i) q^{3} +1.00000 q^{4} +(1.67933 + 1.47644i) q^{5} +(1.13785 + 1.30587i) q^{6} +(-2.41546 + 1.07960i) q^{7} +1.00000 q^{8} +(-0.410606 + 2.97177i) q^{9} +(1.67933 + 1.47644i) q^{10} +(5.13649 - 2.96556i) q^{11} +(1.13785 + 1.30587i) q^{12} +(-2.57957 - 4.46794i) q^{13} +(-2.41546 + 1.07960i) q^{14} +(-0.0172195 + 3.87295i) q^{15} +1.00000 q^{16} +(1.62025 + 0.935454i) q^{17} +(-0.410606 + 2.97177i) q^{18} +(-1.51165 + 0.872754i) q^{19} +(1.67933 + 1.47644i) q^{20} +(-4.15825 - 1.92587i) q^{21} +(5.13649 - 2.96556i) q^{22} +(-3.20885 + 5.55790i) q^{23} +(1.13785 + 1.30587i) q^{24} +(0.640274 + 4.95884i) q^{25} +(-2.57957 - 4.46794i) q^{26} +(-4.34796 + 2.84522i) q^{27} +(-2.41546 + 1.07960i) q^{28} +(-2.16663 - 1.25090i) q^{29} +(-0.0172195 + 3.87295i) q^{30} -4.36743i q^{31} +1.00000 q^{32} +(9.71719 + 3.33326i) q^{33} +(1.62025 + 0.935454i) q^{34} +(-5.65031 - 1.75328i) q^{35} +(-0.410606 + 2.97177i) q^{36} +(-1.17895 + 0.680668i) q^{37} +(-1.51165 + 0.872754i) q^{38} +(2.89941 - 8.45243i) q^{39} +(1.67933 + 1.47644i) q^{40} +(-3.79398 - 6.57136i) q^{41} +(-4.15825 - 1.92587i) q^{42} +(4.07460 + 2.35247i) q^{43} +(5.13649 - 2.96556i) q^{44} +(-5.07717 + 4.38433i) q^{45} +(-3.20885 + 5.55790i) q^{46} -9.74722i q^{47} +(1.13785 + 1.30587i) q^{48} +(4.66893 - 5.21547i) q^{49} +(0.640274 + 4.95884i) q^{50} +(0.622018 + 3.18025i) q^{51} +(-2.57957 - 4.46794i) q^{52} +(0.628956 - 1.08938i) q^{53} +(-4.34796 + 2.84522i) q^{54} +(13.0043 + 2.60357i) q^{55} +(-2.41546 + 1.07960i) q^{56} +(-2.85974 - 0.980967i) q^{57} +(-2.16663 - 1.25090i) q^{58} -1.30033 q^{59} +(-0.0172195 + 3.87295i) q^{60} -11.4604i q^{61} -4.36743i q^{62} +(-2.21652 - 7.62149i) q^{63} +1.00000 q^{64} +(2.26470 - 11.3117i) q^{65} +(9.71719 + 3.33326i) q^{66} +15.0907i q^{67} +(1.62025 + 0.935454i) q^{68} +(-10.9091 + 2.13369i) q^{69} +(-5.65031 - 1.75328i) q^{70} -2.88706i q^{71} +(-0.410606 + 2.97177i) q^{72} +(1.79824 - 3.11464i) q^{73} +(-1.17895 + 0.680668i) q^{74} +(-5.74707 + 6.47852i) q^{75} +(-1.51165 + 0.872754i) q^{76} +(-9.20540 + 12.7086i) q^{77} +(2.89941 - 8.45243i) q^{78} +8.42064 q^{79} +(1.67933 + 1.47644i) q^{80} +(-8.66281 - 2.44045i) q^{81} +(-3.79398 - 6.57136i) q^{82} +(2.43978 + 1.40861i) q^{83} +(-4.15825 - 1.92587i) q^{84} +(1.33980 + 3.96313i) q^{85} +(4.07460 + 2.35247i) q^{86} +(-0.831773 - 4.25268i) q^{87} +(5.13649 - 2.96556i) q^{88} +(8.92096 + 15.4516i) q^{89} +(-5.07717 + 4.38433i) q^{90} +(11.0544 + 8.00725i) q^{91} +(-3.20885 + 5.55790i) q^{92} +(5.70331 - 4.96947i) q^{93} -9.74722i q^{94} +(-3.82713 - 0.766222i) q^{95} +(1.13785 + 1.30587i) q^{96} +(1.23514 - 2.13933i) q^{97} +(4.66893 - 5.21547i) q^{98} +(6.70387 + 16.4821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

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