LMFDB - Embedded newform 133.2.o.d.75.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [133,2,Mod(75,133)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("133.75"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(133, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-9] 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			75.1
Root			$1.56632 - 2.71294i$ of defining polynomial
Character	$\chi$	$=$	133.75
Dual form			133.2.o.d.94.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.06632 - 1.84692i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.90671 - 1.67819i) q^{5} +3.69384i q^{6} +(1.84039 + 1.90078i) q^{7} +1.73205i q^{8} +(-0.774071 + 1.34073i) q^{9} +(2.90671 + 5.03457i) q^{10} +(-0.566319 - 0.980893i) q^{11} +(1.06632 - 1.84692i) q^{12} -0.680780 q^{13} +(-1.11446 - 4.44499i) q^{14} +7.15794i q^{15} +(2.50000 - 4.33013i) q^{16} +(-4.40671 + 2.54421i) q^{17} +(2.32221 - 1.34073i) q^{18} +(-4.35857 - 0.0538617i) q^{19} -3.35638i q^{20} +(1.54814 - 5.42589i) q^{21} +1.96179i q^{22} +(0.840390 - 1.45560i) q^{23} +(3.19896 - 1.84692i) q^{24} +(3.13264 + 5.42589i) q^{25} +(1.02117 + 0.589573i) q^{26} -3.09629 q^{27} +(-0.725929 + 2.54421i) q^{28} -4.64325i q^{29} +(6.19896 - 10.7369i) q^{30} +(-4.06632 - 7.04307i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(-1.20775 + 2.09189i) q^{33} +8.81342 q^{34} +(-2.15961 - 8.61354i) q^{35} -1.54814 q^{36} +(1.02117 + 0.589573i) q^{37} +(6.49120 + 3.85542i) q^{38} +(0.725929 + 1.25735i) q^{39} +(2.90671 - 5.03457i) q^{40} +11.6268 q^{41} +(-7.02117 + 6.79810i) q^{42} -5.94606 q^{43} +(0.566319 - 0.980893i) q^{44} +(4.50000 - 2.59808i) q^{45} +(-2.52117 + 1.45560i) q^{46} +(-2.70775 - 1.56332i) q^{47} -10.6632 q^{48} +(-0.225929 + 6.99635i) q^{49} -10.8518i q^{50} +(9.39791 + 5.42589i) q^{51} +(-0.340390 - 0.589573i) q^{52} +(-10.4191 + 6.01546i) q^{53} +(4.64443 + 2.68146i) q^{54} +3.80156i q^{55} +(-3.29225 + 3.18765i) q^{56} +(4.54814 + 8.10735i) q^{57} +(-4.02117 + 6.96487i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-6.19896 + 3.57897i) q^{60} +(0.0932912 + 0.0538617i) q^{61} +14.0861i q^{62} +(-3.97303 + 0.996129i) q^{63} -1.00000 q^{64} +(1.97883 + 1.14248i) q^{65} +(3.62326 - 2.09189i) q^{66} +(9.39791 - 5.42589i) q^{67} +(-4.40671 - 2.54421i) q^{68} -3.58449 q^{69} +(-4.22013 + 14.7906i) q^{70} +0.229735i q^{71} +(-2.32221 - 1.34073i) q^{72} +(7.89791 - 4.55986i) q^{73} +(-1.02117 - 1.76872i) q^{74} +(6.68078 - 11.5715i) q^{75} +(-2.13264 - 3.80156i) q^{76} +(0.822214 - 2.88167i) q^{77} -2.51469i q^{78} +(-12.5969 - 7.27281i) q^{79} +(-14.5335 + 8.39095i) q^{80} +(5.62384 + 9.74078i) q^{81} +(-17.4403 - 10.0691i) q^{82} -13.0290i q^{83} +(5.47303 - 1.37221i) q^{84} +17.0787 q^{85} +(8.91908 + 5.14943i) q^{86} +(-8.57570 + 4.95118i) q^{87} +(1.69896 - 0.980893i) q^{88} +(1.79225 - 3.10426i) q^{89} -9.00000 q^{90} +(-1.25290 - 1.29401i) q^{91} +1.68078 q^{92} +(-8.67198 + 15.0203i) q^{93} +(2.70775 + 4.68997i) q^{94} +(12.5787 + 7.47106i) q^{95} +(9.59687 + 5.54075i) q^{96} -2.90371 q^{97} +(6.39791 - 10.2989i) q^{98} +1.75348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{2} + 2 q^{3} + 3 q^{4} - 3 q^{5} + 5 q^{7} - 7 q^{9} + 3 q^{10} + 5 q^{11} - 2 q^{12} + 8 q^{13} - 3 q^{14} + 15 q^{16} - 12 q^{17} + 21 q^{18} - 7 q^{19} + 14 q^{21} - q^{23} - 6 q^{24} + 2 q^{25}+ \cdots - 54 q^{99}+O(q^{100}) $ 6 * q - 9 * q^2 + 2 * q^3 + 3 * q^4 - 3 * q^5 + 5 * q^7 - 7 * q^9 + 3 * q^10 + 5 * q^11 - 2 * q^12 + 8 * q^13 - 3 * q^14 + 15 * q^16 - 12 * q^17 + 21 * q^18 - 7 * q^19 + 14 * q^21 - q^23 - 6 * q^24 + 2 * q^25 - 12 * q^26 - 28 * q^27 - 2 * q^28 + 12 * q^30 - 16 * q^31 - 27 * q^32 - 18 * q^33 + 24 * q^34 - 19 * q^35 - 14 * q^36 - 12 * q^37 + 3 * q^38 + 2 * q^39 + 3 * q^40 + 12 * q^41 - 24 * q^42 + 10 * q^43 - 5 * q^44 + 27 * q^45 + 3 * q^46 - 27 * q^47 + 20 * q^48 + q^49 + 6 * q^51 + 4 * q^52 + 6 * q^53 + 42 * q^54 - 9 * q^56 + 32 * q^57 - 6 * q^58 - 18 * q^59 - 12 * q^60 + 15 * q^61 - q^63 - 6 * q^64 + 30 * q^65 + 54 * q^66 + 6 * q^67 - 12 * q^68 + 18 * q^70 - 21 * q^72 - 3 * q^73 + 12 * q^74 + 28 * q^75 + 4 * q^76 + 12 * q^77 - 15 * q^80 - 19 * q^81 - 18 * q^82 + 10 * q^84 + 40 * q^85 - 15 * q^86 + 6 * q^87 - 15 * q^88 - 54 * q^90 - 28 * q^91 - 2 * q^92 - 4 * q^93 + 27 * q^94 + 13 * q^95 - 18 * q^96 - 8 * q^97 - 12 * q^98 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−1.06632	−	1.84692i	−0.615639	−	1.06632i	−0.990272	−	0.139145i	$-0.955564\pi$
$3$	−1.06632	−	1.84692i	−0.615639	−	1.06632i	0.374633	−	0.927173i	$-0.377769\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.90671	−	1.67819i	−1.29992	−	0.750509i	−0.319530	−	0.947576i	$-0.603525\pi$
$5$	−2.90671	−	1.67819i	−1.29992	−	0.750509i	−0.980390	+	0.197067i	$0.936858\pi$
$6$			3.69384i			1.50800i
$7$	1.84039	+	1.90078i	0.695602	+	0.718427i
$7$	1.84039	+	1.90078i	0.695602	+	0.718427i
$8$			1.73205i			0.612372i
$9$	−0.774071	+	1.34073i	−0.258024	+	0.446910i
$10$	2.90671	+	5.03457i	0.919182	+	1.59207i
$11$	−0.566319	−	0.980893i	−0.170752	−	0.295750i	0.767931	−	0.640532i	$-0.221286\pi$
$11$	−0.566319	−	0.980893i	−0.170752	−	0.295750i	−0.938683	+	0.344782i	$0.887953\pi$
$12$	1.06632	−	1.84692i	0.307820	−	0.533159i
$13$	−0.680780			−0.188814			−0.0944072	−	0.995534i	$-0.530096\pi$
$13$	−0.680780			−0.188814			−0.0944072	+	0.995534i	$0.530096\pi$
$14$	−1.11446	−	4.44499i	−0.297852	−	1.18797i
$15$			7.15794i			1.84817i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−4.40671	+	2.54421i	−1.06878	+	0.617063i	−0.927849	−	0.372956i	$-0.878344\pi$
$17$	−4.40671	+	2.54421i	−1.06878	+	0.617063i	−0.140935	+	0.990019i	$0.545011\pi$
$18$	2.32221	−	1.34073i	0.547351	−	0.316013i
$19$	−4.35857	−	0.0538617i	−0.999924	−	0.0123567i
$19$	−4.35857	−	0.0538617i	−0.999924	−	0.0123567i
$20$		−	3.35638i		−	0.750509i
$21$	1.54814	−	5.42589i	0.337832	−	1.18403i
$22$			1.96179i			0.418254i
$23$	0.840390	−	1.45560i	0.175233	−	0.303513i	−0.765009	−	0.644020i	$-0.777265\pi$
$23$	0.840390	−	1.45560i	0.175233	−	0.303513i	0.940242	+	0.340507i	$0.110599\pi$
$24$	3.19896	−	1.84692i	0.652984	−	0.377001i
$25$	3.13264	+	5.42589i	0.626527	+	1.08518i
$26$	1.02117	+	0.589573i	0.200268	+	0.115625i
$27$	−3.09629			−0.595880
$28$	−0.725929	+	2.54421i	−0.137188	+	0.480811i
$29$		−	4.64325i		−	0.862229i	−0.902297	−	0.431115i	$-0.858120\pi$
$29$		−	4.64325i		−	0.862229i	0.902297	−	0.431115i	$-0.141880\pi$
$30$	6.19896	−	10.7369i	1.13177	−	1.96028i
$31$	−4.06632	−	7.04307i	−0.730332	−	1.26497i	−0.956741	−	0.290940i	$-0.906032\pi$
$31$	−4.06632	−	7.04307i	−0.730332	−	1.26497i	0.226409	−	0.974032i	$-0.427301\pi$
$32$	−4.50000	+	2.59808i	−0.795495	+	0.459279i
$33$	−1.20775	+	2.09189i	−0.210243	+	0.364151i
$34$	8.81342			1.51149
$35$	−2.15961	−	8.61354i	−0.365041	−	1.45595i
$36$	−1.54814			−0.258024
$37$	1.02117	+	0.589573i	0.167879	+	0.0969252i	0.581586	−	0.813485i	$-0.302433\pi$
$37$	1.02117	+	0.589573i	0.167879	+	0.0969252i	−0.413706	+	0.910410i	$0.635766\pi$
$38$	6.49120	+	3.85542i	1.05301	+	0.625432i
$39$	0.725929	+	1.25735i	0.116242	+	0.201336i
$40$	2.90671	−	5.03457i	0.459591	−	0.796035i
$41$	11.6268			1.81581			0.907903	−	0.419180i	$-0.137682\pi$
$41$	11.6268			1.81581			0.907903	+	0.419180i	$0.137682\pi$
$42$	−7.02117	+	6.79810i	−1.08339	+	1.04897i
$43$	−5.94606			−0.906765			−0.453382	−	0.891316i	$-0.649783\pi$
$43$	−5.94606			−0.906765			−0.453382	+	0.891316i	$0.649783\pi$
$44$	0.566319	−	0.980893i	0.0853758	−	0.147875i
$45$	4.50000	−	2.59808i	0.670820	−	0.387298i
$46$	−2.52117	+	1.45560i	−0.371726	+	0.214616i
$47$	−2.70775	−	1.56332i	−0.394966	−	0.228034i	0.289343	−	0.957225i	$-0.406563\pi$
$47$	−2.70775	−	1.56332i	−0.394966	−	0.228034i	−0.684310	+	0.729191i	$0.739896\pi$
$48$	−10.6632			−1.53910
$49$	−0.225929	+	6.99635i	−0.0322755	+	0.999479i
$50$		−	10.8518i		−	1.53467i
$51$	9.39791	+	5.42589i	1.31597	+	0.759776i
$52$	−0.340390	−	0.589573i	−0.0472036	−	0.0817591i
$53$	−10.4191	+	6.01546i	−1.43117	+	0.826287i	−0.997210	−	0.0746447i	$-0.976218\pi$
$53$	−10.4191	+	6.01546i	−1.43117	+	0.826287i	−0.433961	+	0.900932i	$0.642884\pi$
$54$	4.64443	+	2.68146i	0.632027	+	0.364901i
$55$			3.80156i			0.512602i
$56$	−3.29225	+	3.18765i	−0.439945	+	0.425968i
$57$	4.54814	+	8.10735i	0.602416	+	1.07384i
$58$	−4.02117	+	6.96487i	−0.528006	+	0.914532i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−6.19896	+	3.57897i	−0.800282	+	0.462043i
$61$	0.0932912	+	0.0538617i	0.0119447	+	0.00689628i	0.505960	−	0.862557i	$-0.331138\pi$
$61$	0.0932912	+	0.0538617i	0.0119447	+	0.00689628i	−0.494016	+	0.869453i	$0.664471\pi$
$62$			14.0861i			1.78894i
$63$	−3.97303	+	0.996129i	−0.500554	+	0.125500i
$64$	−1.00000			−0.125000
$65$	1.97883	+	1.14248i	0.245444	+	0.141707i
$66$	3.62326	−	2.09189i	0.445992	−	0.257494i
$67$	9.39791	−	5.42589i	1.14814	−	0.662878i	0.199705	−	0.979856i	$-0.436002\pi$
$67$	9.39791	−	5.42589i	1.14814	−	0.662878i	0.948433	+	0.316978i	$0.102668\pi$
$68$	−4.40671	−	2.54421i	−0.534392	−	0.308531i
$69$	−3.58449			−0.431522
$70$	−4.22013	+	14.7906i	−0.504402	+	1.76781i
$71$			0.229735i			0.0272645i	0.999907	+	0.0136323i	$0.00433942\pi$
$71$			0.229735i			0.0272645i	−0.999907	+	0.0136323i	$0.995661\pi$
$72$	−2.32221	−	1.34073i	−0.273676	−	0.158007i
$73$	7.89791	−	4.55986i	0.924381	−	0.533691i	0.0393507	−	0.999225i	$-0.487471\pi$
$73$	7.89791	−	4.55986i	0.924381	−	0.533691i	0.885030	+	0.465534i	$0.154138\pi$
$74$	−1.02117	−	1.76872i	−0.118709	−	0.205609i
$75$	6.68078	−	11.5715i	0.771430	−	1.33616i
$76$	−2.13264	−	3.80156i	−0.244630	−	0.436069i
$77$	0.822214	−	2.88167i	0.0937000	−	0.328397i
$78$		−	2.51469i		−	0.284733i
$79$	−12.5969	−	7.27281i	−1.41726	−	0.818255i	−0.421201	−	0.906967i	$-0.638391\pi$
$79$	−12.5969	−	7.27281i	−1.41726	−	0.818255i	−0.996057	+	0.0887127i	$0.971725\pi$
$80$	−14.5335	+	8.39095i	−1.62490	+	0.938136i
$81$	5.62384	+	9.74078i	0.624871	+	1.08231i
$82$	−17.4403	−	10.0691i	−1.92595	−	1.11195i
$83$		−	13.0290i		−	1.43012i	−0.699063	−	0.715060i	$-0.746400\pi$
$83$		−	13.0290i		−	1.43012i	0.699063	−	0.715060i	$-0.253600\pi$
$84$	5.47303	−	1.37221i	0.597156	−	0.149721i
$85$	17.0787			1.85244
$86$	8.91908	+	5.14943i	0.961769	+	0.555278i
$87$	−8.57570	+	4.95118i	−0.919411	+	0.530822i
$88$	1.69896	−	0.980893i	0.181109	−	0.104564i
$89$	1.79225	−	3.10426i	0.189978	−	0.329051i	−0.755265	−	0.655420i	$-0.772492\pi$
$89$	1.79225	−	3.10426i	0.189978	−	0.329051i	0.945243	+	0.326369i	$0.105825\pi$
$90$	−9.00000			−0.948683
$91$	−1.25290	−	1.29401i	−0.131340	−	0.135649i
$92$	1.68078			0.175233
$93$	−8.67198	+	15.0203i	−0.899243	+	1.55753i
$94$	2.70775	+	4.68997i	0.279283	+	0.483733i
$95$	12.5787	+	7.47106i	1.29055	+	0.766514i
$96$	9.59687	+	5.54075i	0.979476	+	0.565501i
$97$	−2.90371			−0.294828			−0.147414	−	0.989075i	$-0.547095\pi$
$97$	−2.90371			−0.294828			−0.147414	+	0.989075i	$0.547095\pi$
$98$	6.39791	−	10.2989i	0.646287	−	1.04034i
$99$	1.75348			0.176232
$100$	−3.13264	+	5.42589i	−0.313264	+	0.542589i
$101$	12.3046	−	7.10408i	1.22436	−	0.706882i	0.258512	−	0.966008i	$-0.416768\pi$
$101$	12.3046	−	7.10408i	1.22436	−	0.706882i	0.965844	+	0.259126i	$0.0834345\pi$
$102$	−9.39791	−	16.2777i	−0.930532	−	1.61173i
$103$	−8.13264	+	14.0861i	−0.801333	+	1.38795i	0.117407	+	0.993084i	$0.462542\pi$
$103$	−8.13264	+	14.0861i	−0.801333	+	1.38795i	−0.918739	+	0.394865i	$0.870791\pi$
$104$		−	1.17915i		−	0.115625i
$105$	−13.6057	+	13.1734i	−1.32778	+	1.28559i
$106$	20.8382			2.02398
$107$	9.19896	+	5.31102i	0.889297	+	0.513436i	0.873712	−	0.486443i	$-0.161706\pi$
$107$	9.19896	+	5.31102i	0.889297	+	0.513436i	0.0155843	+	0.999879i	$0.495039\pi$
$108$	−1.54814	−	2.68146i	−0.148970	−	0.258024i
$109$	3.00000	−	1.73205i	0.287348	−	0.165900i	−0.349397	−	0.936975i	$-0.613614\pi$
$109$	3.00000	−	1.73205i	0.287348	−	0.165900i	0.636745	+	0.771074i	$0.280280\pi$
$110$	3.29225	−	5.70234i	0.313903	−	0.543697i
$111$		−	2.51469i		−	0.238684i
$112$	12.8316	−	3.21717i	1.21247	−	0.303994i
$113$		−	8.10735i		−	0.762675i	−0.924436	−	0.381338i	$-0.875464\pi$
$113$		−	8.10735i		−	0.762675i	0.924436	−	0.381338i	$-0.124536\pi$
$114$	0.198956	−	16.0998i	0.0186340	−	1.50789i
$115$	−4.88554	+	2.82067i	−0.455579	+	0.263029i
$116$	4.02117	−	2.32162i	0.373356	−	0.215557i
$117$	0.526972	−	0.912743i	0.0487186	−	0.0843831i
$118$			10.3923i			0.956689i
$119$	−12.9461	−	3.69384i	−1.18676	−	0.338613i
$120$	−12.3979			−1.13177
$121$	4.85857	−	8.41528i	0.441688	−	0.765026i
$122$	−0.0932912	−	0.161585i	−0.00844619	−	0.0146292i
$123$	−12.3979	−	21.4738i	−1.11788	−	1.93623i
$124$	4.06632	−	7.04307i	0.365166	−	0.632486i
$125$		−	4.24674i		−	0.379840i
$126$	6.82221	+	1.94655i	0.607771	+	0.173412i
$127$		−	14.5456i		−	1.29071i	−0.763881	−	0.645357i	$-0.776709\pi$
$127$		−	14.5456i		−	1.29071i	0.763881	−	0.645357i	$-0.223291\pi$
$128$	10.5000	+	6.06218i	0.928078	+	0.535826i
$129$	6.34039	+	10.9819i	0.558240	+	0.966900i
$130$	−1.97883	−	3.42743i	−0.173555	−	0.300606i
$131$	8.62684	+	4.98071i	0.753730	+	0.435166i	0.827040	−	0.562143i	$-0.190023\pi$
$131$	8.62684	+	4.98071i	0.753730	+	0.435166i	−0.0733100	+	0.997309i	$0.523356\pi$
$132$	−2.41551			−0.210243
$133$	−7.91908	−	8.38380i	−0.686672	−	0.726968i
$134$	−18.7958			−1.62371
$135$	9.00000	+	5.19615i	0.774597	+	0.447214i
$136$	−4.40671	−	7.63264i	−0.377872	−	0.654494i
$137$	−1.03935	−	1.80020i	−0.0887973	−	0.153802i	0.818206	−	0.574926i	$-0.194969\pi$
$137$	−1.03935	−	1.80020i	−0.0887973	−	0.153802i	−0.907003	+	0.421124i	$0.861636\pi$
$138$	5.37674	+	3.10426i	0.457699	+	0.264252i
$139$		−	11.6792i		−	0.990615i	−0.868718	−	0.495307i	$-0.835055\pi$
$139$		−	11.6792i		−	0.990615i	0.868718	−	0.495307i	$-0.164945\pi$
$140$	6.37974	−	6.17705i	0.539186	−	0.522056i
$141$			6.66800i			0.561547i
$142$	0.198956	−	0.344602i	0.0166960	−	0.0289184i
$143$	0.385539	+	0.667772i	0.0322404	+	0.0558419i
$144$	3.87036	+	6.70365i	0.322530	+	0.558638i
$145$	−7.79225	+	13.4966i	−0.647111	+	1.12083i
$146$	−15.7958			−1.30727
$147$	13.1626	−	7.04307i	1.08563	−	0.580903i
$148$			1.17915i			0.0969252i
$149$	−6.21713	+	10.7684i	−0.509327	+	0.882181i	0.490614	+	0.871377i	$0.336772\pi$
$149$	−6.21713	+	10.7684i	−0.509327	+	0.882181i	−0.999942	+	0.0108040i	$0.996561\pi$
$150$	−20.0423	+	11.5715i	−1.63645	+	0.944805i
$151$	1.35557	−	0.782640i	0.110315	−	0.0636903i	−0.443827	−	0.896112i	$-0.646380\pi$
$151$	1.35557	−	0.782640i	0.110315	−	0.0636903i	0.554142	+	0.832422i	$0.313046\pi$
$152$	0.0932912	−	7.54926i	0.00756691	−	0.612326i
$153$		−	7.87761i		−	0.636867i
$154$	−3.72892	+	3.61045i	−0.300485	+	0.290938i
$155$			27.2962i			2.19248i
$156$	−0.725929	+	1.25735i	−0.0581208	+	0.100668i
$157$	2.08449	−	1.20348i	0.166361	−	0.0960485i	−0.414508	−	0.910046i	$-0.636046\pi$
$157$	2.08449	−	1.20348i	0.166361	−	0.0960485i	0.580869	+	0.813997i	$0.302713\pi$
$158$	12.5969	+	21.8184i	1.00215	+	1.73578i
$159$	22.2201	+	12.8288i	1.76217	+	1.01739i
$160$	17.4403			1.37877
$161$	4.31342	−	1.08147i	0.339945	−	0.0852319i
$162$		−	19.4816i		−	1.53062i
$163$	6.06052	−	10.4971i	0.474696	−	0.822198i	−0.524884	−	0.851174i	$-0.675891\pi$
$163$	6.06052	−	10.4971i	0.474696	−	0.822198i	0.999580	+	0.0289758i	$0.00922457\pi$
$164$	5.81342	+	10.0691i	0.453952	+	0.786267i
$165$	7.02117	−	4.05367i	0.546597	−	0.315578i
$166$	−11.2835	+	19.5435i	−0.875766	+	1.51687i
$167$	−5.22892			−0.404626			−0.202313	−	0.979321i	$-0.564846\pi$
$167$	−5.22892			−0.404626			−0.202313	+	0.979321i	$0.564846\pi$
$168$	9.39791	+	2.68146i	0.725065	+	0.206879i
$169$	−12.5365			−0.964349
$170$	−25.6180	−	14.7906i	−1.96481	−	1.13439i
$171$	3.44606	−	5.80197i	0.263526	−	0.443688i
$172$	−2.97303	−	5.14943i	−0.226691	−	0.392641i
$173$	−8.81342	+	15.2653i	−0.670072	+	1.16060i	0.307812	+	0.951447i	$0.400403\pi$
$173$	−8.81342	+	15.2653i	−0.670072	+	1.16060i	−0.977883	+	0.209151i	$0.932930\pi$
$174$	17.1514			1.30024
$175$	−4.54814	+	15.9402i	−0.343807	+	1.20497i
$176$	−5.66319			−0.426879
$177$	−6.39791	+	11.0815i	−0.480897	+	0.832937i
$178$	−5.37674	+	3.10426i	−0.403004	+	0.232674i
$179$	−4.35557	+	2.51469i	−0.325551	+	0.187957i	−0.653864	−	0.756612i	$-0.726853\pi$
$179$	−4.35557	+	2.51469i	−0.325551	+	0.187957i	0.328313	+	0.944569i	$0.393520\pi$
$180$	4.50000	+	2.59808i	0.335410	+	0.193649i
$181$	2.22293			0.165229			0.0826147	−	0.996582i	$-0.473673\pi$
$181$	2.22293			0.165229			0.0826147	+	0.996582i	$0.473673\pi$
$182$	0.758703	+	3.02606i	0.0562388	+	0.224307i
$183$		−	0.229735i		−	0.0169825i
$184$	2.52117	+	1.45560i	0.185863	+	0.107308i
$185$	−1.97883	−	3.42743i	−0.145486	−	0.251990i
$186$	26.0160	−	15.0203i	1.90758	−	1.10134i
$187$	4.99120	+	2.88167i	0.364993	+	0.210729i
$188$		−	3.12664i		−	0.228034i
$189$	−5.69837	−	5.88536i	−0.414496	−	0.428097i
$190$	−12.3979	−	22.1001i	−0.899439	−	1.60331i
$191$	−3.56632	+	6.17705i	−0.258050	+	0.446955i	−0.965719	−	0.259588i	$-0.916413\pi$
$191$	−3.56632	+	6.17705i	−0.258050	+	0.446955i	0.707670	+	0.706543i	$0.249747\pi$
$192$	1.06632	+	1.84692i	0.0769549	+	0.133290i
$193$	4.02117	−	2.32162i	0.289450	−	0.167114i	−0.348244	−	0.937404i	$-0.613222\pi$
$193$	4.02117	−	2.32162i	0.289450	−	0.167114i	0.637694	+	0.770290i	$0.279888\pi$
$194$	4.35557	+	2.51469i	0.312712	+	0.180544i
$195$		−	4.87298i		−	0.348962i
$196$	−6.17198	+	3.30252i	−0.440856	+	0.235894i
$197$	3.17498			0.226208			0.113104	−	0.993583i	$-0.463921\pi$
$197$	3.17498			0.226208			0.113104	+	0.993583i	$0.463921\pi$
$198$	−2.63023	−	1.51856i	−0.186922	−	0.107920i
$199$	−8.91908	+	5.14943i	−0.632257	+	0.365034i	−0.781626	−	0.623748i	$-0.785609\pi$
$199$	−8.91908	+	5.14943i	−0.632257	+	0.365034i	0.149369	+	0.988782i	$0.452276\pi$
$200$	−9.39791	+	5.42589i	−0.664533	+	0.383668i
$201$	−20.0423	−	11.5715i	−1.41368	−	0.816187i
$202$	−24.6092			−1.73150
$203$	8.82579	−	8.54539i	0.619449	−	0.599769i
$204$			10.8518i			0.759776i
$205$	−33.7958	−	19.5120i	−2.36040	−	1.36278i
$206$	24.3979	−	14.0861i	1.69988	−	0.981428i
$207$	1.30104	+	2.25347i	0.0904288	+	0.156627i
$208$	−1.70195	+	2.94786i	−0.118009	+	0.204398i
$209$	2.41551	+	4.30579i	0.167084	+	0.297838i
$210$	31.8170	−	7.97725i	2.19558	−	0.550482i
$211$			1.56528i			0.107758i	0.998547	+	0.0538791i	$0.0171586\pi$
$211$			1.56528i			0.107758i	−0.998547	+	0.0538791i	$0.982841\pi$
$212$	−10.4191	−	6.01546i	−0.715586	−	0.413144i
$213$	0.424302	−	0.244971i	0.0290727	−	0.0167851i
$214$	−9.19896	−	15.9331i	−0.628828	−	1.08916i
$215$	17.2835	+	9.97861i	1.17872	+	0.680535i
$216$		−	5.36292i		−	0.364901i
$217$	5.90371	−	20.6912i	0.400770	−	1.40461i
$218$	−6.00000			−0.406371
$219$	−16.8434	−	9.72453i	−1.13817	−	0.657123i
$220$	−3.29225	+	1.90078i	−0.221963	+	0.128151i
$221$	3.00000	−	1.73205i	0.201802	−	0.116510i
$222$	−2.17779	+	3.77204i	−0.146163	+	0.253162i
$223$	14.9285			0.999684			0.499842	−	0.866117i	$-0.333391\pi$
$223$	14.9285			0.999684			0.499842	+	0.866117i	$0.333391\pi$
$224$	−13.2201	−	3.77204i	−0.883307	−	0.252030i
$225$	−9.69954			−0.646636
$226$	−7.02117	+	12.1610i	−0.467041	+	0.808939i
$227$	6.38554	+	11.0601i	0.423823	+	0.734083i	0.996310	−	0.0858309i	$-0.0273545\pi$
$227$	6.38554	+	11.0601i	0.423823	+	0.734083i	−0.572487	+	0.819914i	$0.694021\pi$
$228$	−4.74710	+	7.99248i	−0.314384	+	0.529315i
$229$	−1.99120	−	1.14962i	−0.131582	−	0.0759692i	0.432764	−	0.901507i	$-0.357538\pi$
$229$	−1.99120	−	1.14962i	−0.131582	−	0.0759692i	−0.564346	+	0.825538i	$0.690872\pi$
$230$	9.77108			0.644286
$231$	−6.19896	+	1.55422i	−0.407861	+	0.102260i
$232$	8.04234			0.528006
$233$	−8.72593	+	15.1138i	−0.571655	+	0.990135i	0.424742	+	0.905315i	$0.360365\pi$
$233$	−8.72593	+	15.1138i	−0.571655	+	0.990135i	−0.996396	+	0.0848202i	$0.972968\pi$
$234$	−1.58092	+	0.912743i	−0.103348	+	0.0596679i
$235$	5.24710	+	9.08824i	0.342283	+	0.592852i
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$			31.0205i			2.01500i
$238$	16.2201	+	16.7524i	1.05139	+	1.08589i
$239$	5.45186			0.352651			0.176326	−	0.984332i	$-0.443579\pi$
$239$	5.45186			0.352651			0.176326	+	0.984332i	$0.443579\pi$
$240$	30.9948	+	17.8948i	2.00070	+	1.15511i
$241$	4.70195	+	8.14402i	0.302879	+	0.524602i	0.976787	−	0.214213i	$-0.0687188\pi$
$241$	4.70195	+	8.14402i	0.302879	+	0.524602i	−0.673908	+	0.738816i	$0.735385\pi$
$242$	−14.5757	+	8.41528i	−0.936961	+	0.540955i
$243$	7.34919	−	12.7292i	0.471451	−	0.816576i
$244$			0.107723i			0.00689628i
$245$	12.3979	−	19.9572i	0.792074	−	1.27502i
$246$			42.9476i			2.73824i
$247$	2.96723	+	0.0366680i	0.188800	+	0.00233313i
$248$	12.1990	−	7.04307i	0.774634	−	0.447235i
$249$	−24.0635	+	13.8931i	−1.52496	+	0.880438i
$250$	−3.67779	+	6.37011i	−0.232604	+	0.402881i
$251$			7.50968i			0.474007i	0.971509	+	0.237004i	$0.0761653\pi$
$251$			7.50968i			0.474007i	−0.971509	+	0.237004i	$0.923835\pi$
$252$	−2.84919	−	2.94268i	−0.179482	−	0.185371i
$253$	−1.90371			−0.119686
$254$	−12.5969	+	21.8184i	−0.790398	+	1.36901i
$255$	−18.2113	−	31.5429i	−1.14044	−	1.97530i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	11.8134	−	20.4614i	0.736901	−	1.27635i	−0.216984	−	0.976175i	$-0.569622\pi$
$257$	11.8134	−	20.4614i	0.736901	−	1.27635i	0.953884	−	0.300174i	$-0.0970448\pi$
$258$		−	21.9638i		−	1.36740i
$259$	0.758703	+	3.02606i	0.0471435	+	0.188030i
$260$			2.28496i			0.141707i
$261$	6.22535	+	3.59420i	0.385339	+	0.222476i
$262$	−8.62684	−	14.9421i	−0.532968	−	0.923127i
$263$	−13.4942	−	23.3726i	−0.832088	−	1.44122i	−0.896380	−	0.443287i	$-0.853812\pi$
$263$	−13.4942	−	23.3726i	−0.832088	−	1.44122i	0.0642917	−	0.997931i	$-0.479521\pi$
$264$	−3.62326	−	2.09189i	−0.222996	−	0.128747i
$265$	40.3803			2.48054
$266$	4.61804	+	19.4338i	0.283150	+	1.19156i
$267$	−7.64443			−0.467831
$268$	9.39791	+	5.42589i	0.574069	+	0.331439i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	−9.00000	−	15.5885i	−0.547723	−	0.948683i
$271$	−14.4948	−	8.36857i	−0.880495	−	0.508354i	−0.00967358	−	0.999953i	$-0.503079\pi$
$271$	−14.4948	−	8.36857i	−0.880495	−	0.508354i	−0.870822	+	0.491599i	$0.836413\pi$
$272$			25.4421i			1.54266i
$273$	−1.05394	+	3.69384i	−0.0637876	+	0.223561i
$274$			3.60040i			0.217508i
$275$	3.54814	−	6.14556i	0.213961	−	0.370591i
$276$	−1.79225	−	3.10426i	−0.107881	−	0.186855i
$277$	−3.58749	−	6.21371i	−0.215551	−	0.373346i	0.737892	−	0.674919i	$-0.235822\pi$
$277$	−3.58749	−	6.21371i	−0.215551	−	0.373346i	−0.953443	+	0.301573i	$0.902488\pi$
$278$	−10.1145	+	17.5188i	−0.606625	+	1.05071i
$279$	12.5905			0.753773
$280$	14.9191	−	3.74055i	0.891586	−	0.223541i
$281$		−	5.56219i		−	0.331812i	−0.986142	−	0.165906i	$-0.946945\pi$
$281$		−	5.56219i		−	0.331812i	0.986142	−	0.165906i	$-0.0530549\pi$
$282$	5.77465	−	10.0020i	0.343876	−	0.595610i
$283$	−8.65662	+	4.99790i	−0.514582	+	0.297094i	−0.734715	−	0.678376i	$-0.762684\pi$
$283$	−8.65662	+	4.99790i	−0.514582	+	0.297094i	0.220133	+	0.975470i	$0.429351\pi$
$284$	−0.198956	+	0.114867i	−0.0118059	+	0.00681613i
$285$	0.385539	−	31.1983i	0.0228373	−	1.84803i
$286$		−	1.33554i		−	0.0789724i
$287$	21.3979	+	22.1001i	1.26308	+	1.30453i
$288$		−	8.04439i		−	0.474020i
$289$	4.44606	−	7.70079i	0.261533	−	0.452988i
$290$	23.3767	−	13.4966i	1.37273	−	0.792546i
$291$	3.09629	+	5.36292i	0.181507	+	0.314380i
$292$	7.89791	+	4.55986i	0.462190	+	0.266846i
$293$	5.25367			0.306923			0.153461	−	0.988155i	$-0.450958\pi$
$293$	5.25367			0.306923			0.153461	+	0.988155i	$0.450958\pi$
$294$	−25.8434	−	0.834544i	−1.50722	−	0.0486716i
$295$			20.1383i			1.17250i
$296$	−1.02117	+	1.76872i	−0.0593543	+	0.102805i
$297$	1.75348	+	3.03712i	0.101747	+	0.176232i
$298$	18.6514	−	10.7684i	1.08045	−	0.623796i
$299$	−0.572121	+	0.990942i	−0.0330866	+	0.0573077i
$300$	13.3616			0.771430
$301$	−10.9431	−	11.3021i	−0.630748	−	0.651445i
$302$	−2.71114			−0.156009
$303$	−26.2413	−	15.1504i	−1.50752	−	0.870369i
$304$	−11.1296	+	18.7385i	−0.638329	+	1.07473i
$305$	−0.180780	−	0.313120i	−0.0103514	−	0.0179292i
$306$	−6.82221	+	11.8164i	−0.390000	+	0.675500i
$307$	−9.09629			−0.519152			−0.259576	−	0.965723i	$-0.583583\pi$
$307$	−9.09629			−0.519152			−0.259576	+	0.965723i	$0.583583\pi$
$308$	2.90671	−	0.728778i	0.165625	−	0.0415260i
$309$	34.6879			1.97333
$310$	23.6392	−	40.9443i	1.34262	−	2.32548i
$311$	−2.22892	+	1.28687i	−0.126391	+	0.0729717i	−0.561862	−	0.827231i	$-0.689915\pi$
$311$	−2.22892	+	1.28687i	−0.126391	+	0.0729717i	0.435472	+	0.900202i	$0.356582\pi$
$312$	−2.17779	+	1.25735i	−0.123293	+	0.0711832i
$313$	28.5247	+	16.4688i	1.61231	+	0.930870i	0.988832	+	0.149032i	$0.0476158\pi$
$313$	28.5247	+	16.4688i	1.61231	+	0.930870i	0.623482	+	0.781838i	$0.285718\pi$
$314$	−4.16899			−0.235270
$315$	13.2201	+	3.77204i	0.744870	+	0.212530i
$316$		−	14.5456i		−	0.818255i
$317$	−19.8170	−	11.4413i	−1.11303	−	0.642610i	−0.173420	−	0.984848i	$-0.555482\pi$
$317$	−19.8170	−	11.4413i	−1.11303	−	0.642610i	−0.939613	+	0.342238i	$0.888815\pi$
$318$	−22.2201	−	38.4864i	−1.24604	−	2.15821i
$319$	−4.55453	+	2.62956i	−0.255005	+	0.147227i
$320$	2.90671	+	1.67819i	0.162490	+	0.0938136i
$321$		−	22.6530i		−	1.26436i
$322$	−7.40671	−	2.11332i	−0.412760	−	0.117771i
$323$	19.3440	−	10.8518i	1.07633	−	0.603809i
$324$	−5.62384	+	9.74078i	−0.312436	+	0.541154i
$325$	−2.13264	−	3.69384i	−0.118297	−	0.204897i
$326$	−18.1815	+	10.4971i	−1.00698	+	0.581382i
$327$	−6.39791	−	3.69384i	−0.353805	−	0.204270i
$328$			20.1383i			1.11195i
$329$	−2.01179	−	8.02396i	−0.110914	−	0.442375i
$330$	−14.0423			−0.773005
$331$	9.00000	+	5.19615i	0.494685	+	0.285606i	0.726516	−	0.687150i	$-0.241138\pi$
$331$	9.00000	+	5.19615i	0.494685	+	0.285606i	−0.231831	+	0.972756i	$0.574472\pi$
$332$	11.2835	−	6.51450i	0.619260	−	0.357530i
$333$	−1.58092	+	0.912743i	−0.0866337	+	0.0500180i
$334$	7.84338	+	4.52838i	0.429171	+	0.247782i
$335$	−36.4227			−1.98998
$336$	−19.6244	−	20.2684i	−1.07060	−	1.10573i
$337$		−	16.6008i		−	0.904305i	−0.891941	−	0.452152i	$-0.850656\pi$
$337$		−	16.6008i		−	0.904305i	0.891941	−	0.452152i	$-0.149344\pi$
$338$	18.8048	+	10.8570i	1.02285	+	0.590541i
$339$	−14.9736	+	8.64502i	−0.813255	+	0.469533i
$340$	8.53935	+	14.7906i	0.463111	+	0.802132i
$341$	−4.60567	+	7.97725i	−0.249411	+	0.431992i
$342$	−10.1937	+	5.71859i	−0.551214	+	0.309226i
$343$	−13.7143	+	12.4466i	−0.740504	+	0.672052i
$344$		−	10.2989i		−	0.555278i
$345$	10.4191	+	6.01546i	0.560945	+	0.323861i
$346$	26.4403	−	15.2653i	1.42144	−	0.820667i
$347$	−2.34619	−	4.06372i	−0.125950	−	0.218152i	0.796154	−	0.605094i	$-0.206865\pi$
$347$	−2.34619	−	4.06372i	−0.125950	−	0.218152i	−0.922104	+	0.386942i	$0.873531\pi$
$348$	−8.57570	−	4.95118i	−0.459706	−	0.265411i
$349$			10.2359i			0.547915i	0.961742	+	0.273958i	$0.0883328\pi$
$349$			10.2359i			0.547915i	−0.961742	+	0.273958i	$0.911667\pi$
$350$	20.6268	−	19.9715i	1.10255	−	1.06752i
$351$	2.10789			0.112511
$352$	5.09687	+	2.94268i	0.271664	+	0.156845i
$353$	−9.23772	+	5.33340i	−0.491674	+	0.283868i	−0.725269	−	0.688466i	$-0.758284\pi$
$353$	−9.23772	+	5.33340i	−0.491674	+	0.283868i	0.233595	+	0.972334i	$0.424951\pi$
$354$	19.1937	−	11.0815i	1.02014	−	0.588976i
$355$	0.385539	−	0.667772i	0.0204623	−	0.0354417i
$356$	3.58449			0.189978
$357$	6.98241	+	27.8491i	0.369548	+	1.47393i
$358$	8.71114			0.460398
$359$	15.3797	−	26.6385i	0.811711	−	1.40593i	−0.0999539	−	0.994992i	$-0.531870\pi$
$359$	15.3797	−	26.6385i	0.811711	−	1.40593i	0.911665	−	0.410933i	$-0.134797\pi$
$360$	4.50000	+	7.79423i	0.237171	+	0.410792i
$361$	18.9942	+	0.469519i	0.999695	+	0.0247115i
$362$	−3.33440	−	1.92512i	−0.175252	−	0.101182i
$363$	−20.7231			−1.08768
$364$	0.494198	−	1.73205i	0.0259030	−	0.0907841i
$365$	−30.6092			−1.60216
$366$	−0.198956	+	0.344602i	−0.0103996	+	0.0180127i
$367$	−21.6604	+	12.5056i	−1.13066	+	0.652788i	−0.944101	−	0.329655i	$-0.893068\pi$
$367$	−21.6604	+	12.5056i	−1.13066	+	0.652788i	−0.186561	+	0.982443i	$0.559734\pi$
$368$	−4.20195	−	7.27799i	−0.219042	−	0.379392i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$			6.85487i			0.356368i
$371$	−30.6092	−	8.73359i	−1.58915	−	0.453425i
$372$	−17.3440			−0.899243
$373$	21.3979	+	12.3541i	1.10794	+	0.639671i	0.938296	−	0.345834i	$-0.112404\pi$
$373$	21.3979	+	12.3541i	1.10794	+	0.639671i	0.169646	+	0.985505i	$0.445737\pi$
$374$	−4.99120	−	8.64502i	−0.258089	−	0.447023i
$375$	−7.84338	+	4.52838i	−0.405031	+	0.233845i
$376$	2.70775	−	4.68997i	0.139642	−	0.241866i
$377$			3.16103i			0.162801i
$378$	3.45069	+	13.7630i	0.177484	+	0.707891i
$379$			29.6545i			1.52325i	0.648018	+	0.761625i	$0.275598\pi$
$379$			29.6545i			1.52325i	−0.648018	+	0.761625i	$0.724402\pi$
$380$	−0.180780	+	14.6290i	−0.00927383	+	0.750452i
$381$	−26.8646	+	15.5103i	−1.37631	+	0.794615i
$382$	10.6990	−	6.17705i	0.547406	−	0.316045i
$383$	12.7835	−	22.1416i	0.653204	−	1.13138i	−0.329137	−	0.944282i	$-0.606758\pi$
$383$	12.7835	−	22.1416i	0.653204	−	1.13138i	0.982341	−	0.187100i	$-0.0599089\pi$
$384$		−	25.8569i		−	1.31950i
$385$	−7.22593	+	6.99635i	−0.368267	+	0.356567i
$386$	−8.04234			−0.409344
$387$	4.60267	−	7.97206i	0.233967	−	0.405243i
$388$	−1.45186	−	2.51469i	−0.0737069	−	0.127664i
$389$	9.67198	+	16.7524i	0.490389	+	0.849379i	0.999939	−	0.0110624i	$-0.00352136\pi$
$389$	9.67198	+	16.7524i	0.490389	+	0.849379i	−0.509550	+	0.860441i	$0.670188\pi$
$390$	−4.22013	+	7.30947i	−0.213694	+	0.370130i
$391$			8.55253i			0.432520i
$392$	−12.1180	−	0.391320i	−0.612053	−	0.0197646i
$393$		−	21.2441i		−	1.07162i
$394$	−4.76247	−	2.74961i	−0.239930	−	0.138523i
$395$	24.4103	+	42.2799i	1.22821	+	2.12733i
$396$	0.876742	+	1.51856i	0.0440580	+	0.0763106i
$397$	6.39791	+	3.69384i	0.321102	+	0.185388i	0.651884	−	0.758319i	$-0.273979\pi$
$397$	6.39791	+	3.69384i	0.321102	+	0.185388i	−0.330782	+	0.943707i	$0.607312\pi$
$398$	17.8382			0.894146
$399$	−7.03993	+	23.5657i	−0.352437	+	1.17976i
$400$	31.3264			1.56632
$401$	7.35557	+	4.24674i	0.367320	+	0.212072i	0.672287	−	0.740291i	$-0.265312\pi$
$401$	7.35557	+	4.24674i	0.367320	+	0.212072i	−0.304967	+	0.952363i	$0.598645\pi$
$402$	20.0423	+	34.7144i	0.999621	+	1.73139i
$403$	2.76827	+	4.79478i	0.137897	+	0.238845i
$404$	12.3046	+	7.10408i	0.612178	+	0.353441i
$405$		−	37.7515i		−	1.87589i
$406$	−20.6392	+	5.17472i	−1.02431	+	0.256817i
$407$		−	1.33554i		−	0.0662005i
$408$	−9.39791	+	16.2777i	−0.465266	+	0.805864i
$409$	11.3192	+	19.6055i	0.559699	+	0.969428i	0.997521	+	0.0703660i	$0.0224167\pi$
$409$	11.3192	+	19.6055i	0.559699	+	0.969428i	−0.437822	+	0.899062i	$0.644250\pi$
$410$	33.7958	+	58.5361i	1.66906	+	2.89089i
$411$	−2.21655	+	3.83918i	−0.109334	+	0.189373i
$412$	−16.2653			−0.801333
$413$	4.35557	−	15.2653i	0.214324	−	0.751156i
$414$		−	4.50695i		−	0.221504i
$415$	−21.8651	+	37.8715i	−1.07332	+	1.85904i
$416$	3.06351	−	1.76872i	0.150201	−	0.0867186i
$417$	−21.5705	+	12.4537i	−1.05631	+	0.609861i
$418$	0.105665	−	8.55057i	0.00516825	−	0.418222i
$419$		−	10.0548i		−	0.491211i	−0.969370	−	0.245606i	$-0.921013\pi$
$419$		−	10.0548i		−	0.491211i	0.969370	−	0.245606i	$-0.0789868\pi$
$420$	−18.2113	−	5.19615i	−0.888622	−	0.253546i
$421$			0.386134i			0.0188190i	0.999956	+	0.00940951i	$0.00299518\pi$
$421$			0.386134i			0.0188190i	−0.999956	+	0.00940951i	$0.997005\pi$
$422$	1.35557	−	2.34792i	0.0659882	−	0.114295i
$423$	4.19199	−	2.42025i	0.203821	−	0.117676i
$424$	−10.4191	−	18.0464i	−0.505995	−	0.876410i
$425$	−27.6092	−	15.9402i	−1.33924	−	0.773213i
$426$	−0.848603			−0.0411150
$427$	0.0693129	+	0.276452i	0.00335429	+	0.0133785i
$428$			10.6220i			0.513436i
$429$	0.822214	−	1.42412i	0.0396969	−	0.0687570i
$430$	−17.2835	−	29.9358i	−0.833482	−	1.44363i
$431$	−9.59687	+	5.54075i	−0.462265	+	0.266889i	−0.712996	−	0.701168i	$-0.752662\pi$
$431$	−9.59687	+	5.54075i	−0.462265	+	0.266889i	0.250731	+	0.968057i	$0.419329\pi$
$432$	−7.74071	+	13.4073i	−0.372425	+	0.645059i
$433$	−27.3264			−1.31322			−0.656611	−	0.754230i	$-0.728011\pi$
$433$	−27.3264			−1.31322			−0.656611	+	0.754230i	$0.728011\pi$
$434$	−26.7747	+	25.9240i	−1.28522	+	1.24439i
$435$	33.2361			1.59355
$436$	3.00000	+	1.73205i	0.143674	+	0.0829502i
$437$	−3.74130	+	6.29906i	−0.178970	+	0.301325i
$438$	16.8434	+	29.1736i	0.804808	+	1.39397i
$439$	3.77707	−	6.54207i	0.180270	−	0.312236i	−0.761703	−	0.647927i	$-0.775636\pi$
$439$	3.77707	−	6.54207i	0.180270	−	0.312236i	0.941972	+	0.335691i	$0.108970\pi$
$440$	−6.58449			−0.313903
$441$	−9.20534	−	5.71859i	−0.438350	−	0.272314i
$442$	−6.00000			−0.285391
$443$	−7.49420	+	12.9803i	−0.356060	+	0.616714i	−0.987299	−	0.158874i	$-0.949213\pi$
$443$	−7.49420	+	12.9803i	−0.356060	+	0.616714i	0.631239	+	0.775589i	$0.282547\pi$
$444$	2.17779	−	1.25735i	0.103353	−	0.0596710i
$445$	−10.4191	+	6.01546i	−0.493912	+	0.285160i
$446$	−22.3927	−	12.9284i	−1.06032	−	0.612179i
$447$	26.5178			1.25425
$448$	−1.84039	−	1.90078i	−0.0869503	−	0.0898034i
$449$		−	30.1970i		−	1.42509i	−0.701628	−	0.712543i	$-0.747543\pi$
$449$		−	30.1970i		−	1.42509i	0.701628	−	0.712543i	$-0.252457\pi$
$450$	14.5493	+	8.40005i	0.685861	+	0.395982i
$451$	−6.58449	−	11.4047i	−0.310052	−	0.537025i
$452$	7.02117	−	4.05367i	0.330248	−	0.190669i
$453$	−2.89094	−	1.66909i	−0.135828	−	0.0784206i
$454$		−	22.1202i		−	1.03815i
$455$	1.47022	+	5.86392i	0.0689250	+	0.274905i
$456$	−14.0423	+	7.87761i	−0.657593	+	0.368903i
$457$	18.9942	−	32.8989i	0.888511	−	1.53895i	0.0468754	−	0.998901i	$-0.485074\pi$
$457$	18.9942	−	32.8989i	0.888511	−	1.53895i	0.841636	−	0.540046i	$-0.181593\pi$
$458$	1.99120	+	3.44887i	0.0930428	+	0.161155i
$459$	13.6444	−	7.87761i	0.636867	−	0.367696i
$460$	−4.88554	−	2.82067i	−0.227789	−	0.131514i
$461$			21.2928i			0.991702i	0.868407	+	0.495851i	$0.165144\pi$
$461$			21.2928i			0.991702i	−0.868407	+	0.495851i	$0.834856\pi$
$462$	10.6444	+	3.03712i	0.495224	+	0.141300i
$463$	1.31323			0.0610310			0.0305155	−	0.999534i	$-0.490285\pi$
$463$	1.31323			0.0610310			0.0305155	+	0.999534i	$0.490285\pi$
$464$	−20.1059	−	11.6081i	−0.933391	−	0.538893i
$465$	50.4139	−	29.1065i	2.33789	−	1.34978i
$466$	26.1778	−	15.1138i	1.21266	−	0.700131i
$467$	−8.70775	−	5.02742i	−0.402947	−	0.232641i	0.284808	−	0.958585i	$-0.408070\pi$
$467$	−8.70775	−	5.02742i	−0.402947	−	0.232641i	−0.687755	+	0.725943i	$0.741404\pi$
$468$	1.05394			0.0487186
$469$	27.6092	+	7.87761i	1.27488	+	0.363754i
$470$		−	18.1765i		−	0.838419i
$471$	−4.44547	−	2.56659i	−0.204837	−	0.118262i
$472$	9.00000	−	5.19615i	0.414259	−	0.239172i
$473$	3.36736	+	5.83244i	0.154831	+	0.268176i
$474$	26.8646	−	46.5308i	1.23393	−	2.13723i
$475$	−13.3616	−	23.8178i	−0.613070	−	1.09284i
$476$	−3.27407	−	13.0585i	−0.150067	−	0.598537i
$477$		−	18.6256i		−	0.852807i
$478$	−8.17779	−	4.72145i	−0.374043	−	0.215954i
$479$	32.3082	−	18.6531i	1.47620	−	0.852284i	0.476560	−	0.879142i	$-0.341883\pi$
$479$	32.3082	−	18.6531i	1.47620	−	0.852284i	0.999639	+	0.0268579i	$0.00855016\pi$
$480$	−18.5969	−	32.2107i	−0.848827	−	1.47021i
$481$	−0.695192	−	0.401370i	−0.0316980	−	0.0183009i
$482$		−	16.2880i		−	0.741900i
$483$	−6.59687	−	6.81334i	−0.300168	−	0.310018i
$484$	9.71713			0.441688
$485$	8.44025	+	4.87298i	0.383252	+	0.221271i
$486$	−22.0476	+	12.7292i	−1.00010	+	0.577407i
$487$	−30.3979	+	17.5502i	−1.37746	+	0.795277i	−0.991853	−	0.127385i	$-0.959341\pi$
$487$	−30.3979	+	17.5502i	−1.37746	+	0.795277i	−0.385608	+	0.922663i	$0.626008\pi$
$488$	−0.0932912	+	0.161585i	−0.00422309	+	0.00731461i
$489$	−25.8498			−1.16897
$490$	−35.8803	+	19.1989i	−1.62091	+	0.867318i
$491$	1.30762			0.0590119			0.0295059	−	0.999565i	$-0.490607\pi$
$491$	1.30762			0.0590119			0.0295059	+	0.999565i	$0.490607\pi$
$492$	12.3979	−	21.4738i	0.558941	−	0.968114i
$493$	11.8134	+	20.4614i	0.532050	+	0.921537i
$494$	−4.41908	−	2.62469i	−0.198824	−	0.118091i
$495$	−5.09687	−	2.94268i	−0.229087	−	0.132264i
$496$	−40.6632			−1.82583
$497$	−0.436675	+	0.422802i	−0.0195876	+	0.0189653i
$498$	48.1270			2.15662
$499$	19.9554	−	34.5638i	0.893328	−	1.54729i	0.0574675	−	0.998347i	$-0.481697\pi$
$499$	19.9554	−	34.5638i	0.893328	−	1.54729i	0.835860	−	0.548942i	$-0.184969\pi$
$500$	3.67779	−	2.12337i	0.164476	−	0.0949600i
$501$	5.57570	+	9.65739i	0.249104	+	0.431461i
$502$	6.50358	−	11.2645i	0.290269	−	0.502760i
$503$		−	2.17723i		−	0.0970780i	−0.998821	−	0.0485390i	$-0.984543\pi$
$503$		−	2.17723i		−	0.0970780i	0.998821	−	0.0485390i	$-0.0154565\pi$
$504$	−1.72535	−	6.88149i	−0.0768530	−	0.306526i
$505$	−47.6879			−2.12209
$506$	2.85557	+	1.64867i	0.126946	+	0.0732921i
$507$	13.3679	+	23.1540i	0.593691	+	1.02830i
$508$	12.5969	−	7.27281i	0.558896	−	0.322679i
$509$	15.9824	−	27.6823i	0.708408	−	1.22700i	−0.257040	−	0.966401i	$-0.582747\pi$
$509$	15.9824	−	27.6823i	0.708408	−	1.22700i	0.965448	−	0.260597i	$-0.0839195\pi$
$510$			63.0859i			2.79349i
$511$	23.2025	+	6.62027i	1.02642	+	0.292863i
$512$			8.66025i			0.382733i
$513$	13.4954	+	0.166771i	0.595835	+	0.00736313i
$514$	−35.4403	+	20.4614i	−1.56320	+	0.902515i
$515$	47.2784	−	27.2962i	2.08334	−	1.20281i
$516$	−6.34039	+	10.9819i	−0.279120	+	0.483450i
$517$			3.54135i			0.155749i
$518$	1.48259	−	5.19615i	0.0651414	−	0.228306i
$519$	37.5916			1.65009
$520$	−1.97883	+	3.42743i	−0.0867774	+	0.150303i
$521$	−6.43668	−	11.1486i	−0.281996	−	0.488431i	0.689880	−	0.723923i	$-0.257663\pi$
$521$	−6.43668	−	11.1486i	−0.281996	−	0.488431i	−0.971876	+	0.235492i	$0.924330\pi$
$522$	−6.22535	−	10.7826i	−0.272476	−	0.471942i
$523$	−8.90970	+	15.4321i	−0.389594	+	0.674797i	−0.992395	−	0.123095i	$-0.960718\pi$
$523$	−8.90970	+	15.4321i	−0.389594	+	0.674797i	0.602801	+	0.797892i	$0.294051\pi$
$524$			9.96141i			0.435166i
$525$	34.2900	−	8.59729i	1.49654	−	0.375217i
$526$			46.7453i			2.03819i
$527$	35.8382	+	20.6912i	1.56114	+	0.901322i
$528$	6.03876	+	10.4594i	0.262803	+	0.455189i
$529$	10.0875	+	17.4720i	0.438586	+	0.759654i
$530$	−60.5705	−	34.9704i	−2.63101	−	1.51902i
$531$	9.28886			0.403102
$532$	3.30104	−	11.0500i	0.143118	−	0.479079i
$533$	−7.91532			−0.342851
$534$	11.4666	+	6.62027i	0.496210	+	0.286487i
$535$	−17.8258	−	30.8752i	−0.770676	−	1.33485i
$536$	9.39791	+	16.2777i	0.405928	+	0.703088i
$537$	9.28886	+	5.36292i	0.400844	+	0.231427i
$538$		−	10.3923i		−	0.448044i
$539$	6.99062	−	3.74055i	0.301107	−	0.161117i
$540$			10.3923i			0.447214i
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$	14.4948	+	25.1057i	0.622604	+	1.07838i
$543$	−2.37036	−	4.10558i	−0.101722	−	0.176187i
$544$	13.2201	−	22.8979i	0.566808	−	0.981741i
$545$	−11.6268			−0.498039
$546$	4.77987	−	4.62801i	0.204560	−	0.198061i
$547$		−	11.4151i		−	0.488072i	−0.969766	−	0.244036i	$-0.921528\pi$
$547$		−	11.4151i		−	0.488072i	0.969766	−	0.244036i	$-0.0784716\pi$
$548$	1.03935	−	1.80020i	0.0443987	−	0.0769008i
$549$	−0.144428	+	0.0833856i	−0.00616404	+	0.00355881i
$550$	−10.6444	+	6.14556i	−0.453880	+	0.262048i
$551$	−0.250093	+	20.2379i	−0.0106543	+	0.862164i
$552$		−	6.20853i		−	0.264252i
$553$	−9.35915	−	37.3287i	−0.397992	−	1.58738i
$554$			12.4274i			0.527991i
$555$	−4.22013	+	7.30947i	−0.179134	+	0.310270i
$556$	10.1145	−	5.83959i	0.428949	−	0.247654i
$557$	−10.1632	−	17.6032i	−0.430628	−	0.745870i	0.566299	−	0.824200i	$-0.308375\pi$
$557$	−10.1632	−	17.6032i	−0.430628	−	0.745870i	−0.996927	+	0.0783299i	$0.975041\pi$
$558$	−18.8857	−	10.9037i	−0.799496	−	0.461590i
$559$	4.04796			0.171210
$560$	−42.6967	−	12.1825i	−1.80427	−	0.514803i
$561$		−	12.2911i		−	0.518932i
$562$	−4.81700	+	8.34328i	−0.203193	+	0.351940i
$563$	−9.97003	−	17.2686i	−0.420187	−	0.727785i	0.575771	−	0.817611i	$-0.304702\pi$
$563$	−9.97003	−	17.2686i	−0.420187	−	0.727785i	−0.995957	+	0.0898264i	$0.971369\pi$
$564$	−5.77465	+	3.33400i	−0.243157	+	0.140387i
$565$	−13.6057	+	23.5657i	−0.572395	+	0.991417i
$566$	17.3132			0.727729
$567$	−8.16501	+	28.6165i	−0.342898	+	1.20178i
$568$	−0.397912			−0.0166960
$569$	−25.7535	−	14.8688i	−1.07964	−	0.623332i	−0.148842	−	0.988861i	$-0.547555\pi$
$569$	−25.7535	−	14.8688i	−1.07964	−	0.623332i	−0.930800	+	0.365529i	$0.880888\pi$
$570$	−27.5969	+	46.4636i	−1.15591	+	1.94615i
$571$	9.42488	+	16.3244i	0.394419	+	0.683154i	0.993027	−	0.117888i	$-0.0376125\pi$
$571$	9.42488	+	16.3244i	0.394419	+	0.683154i	−0.598608	+	0.801042i	$0.704279\pi$
$572$	−0.385539	+	0.667772i	−0.0161202	+	0.0279210i
$573$	15.2113			0.635462
$574$	−12.9577	−	51.6812i	−0.540842	−	2.15713i
$575$	10.5305			0.439154
$576$	0.774071	−	1.34073i	0.0322530	−	0.0558638i
$577$	13.3134	−	7.68651i	0.554245	−	0.319993i	−0.196587	−	0.980486i	$-0.562986\pi$
$577$	13.3134	−	7.68651i	0.554245	−	0.319993i	0.750832	+	0.660493i	$0.229653\pi$
$578$	−13.3382	+	7.70079i	−0.554795	+	0.320311i
$579$	−8.57570	−	4.95118i	−0.356394	−	0.205764i
$580$	−15.5845			−0.647111
$581$	24.7653	−	23.9785i	1.02744	−	0.994794i
$582$		−	10.7258i		−	0.444601i
$583$	11.8010	+	6.81334i	0.488749	+	0.282180i
$584$	7.89791	+	13.6796i	0.326818	+	0.566065i
$585$	−3.06351	+	1.76872i	−0.126661	+	0.0731275i
$586$	−7.88051	−	4.54981i	−0.325541	−	0.187951i
$587$		−	15.6962i		−	0.647851i	−0.946083	−	0.323925i	$-0.894997\pi$
$587$		−	15.6962i		−	0.647851i	0.946083	−	0.323925i	$-0.105003\pi$
$588$	12.6808	+	7.87761i	0.522947	+	0.324867i
$589$	17.3440	+	30.9167i	0.714646	+	1.27390i
$590$	17.4403	−	30.2074i	0.718004	−	1.24362i
$591$	−3.38554	−	5.86392i	−0.139262	−	0.241210i
$592$	5.10585	−	2.94786i	0.209849	−	0.121156i
$593$	15.9914	+	9.23263i	0.656688	+	0.379139i	0.791014	−	0.611798i	$-0.209554\pi$
$593$	15.9914	+	9.23263i	0.656688	+	0.379139i	−0.134326	+	0.990937i	$0.542887\pi$
$594$		−	6.07425i		−	0.249229i
$595$	31.4315	+	32.4628i	1.28856	+	1.33085i
$596$	−12.4343			−0.509327
$597$	19.0212	+	10.9819i	0.778485	+	0.449458i
$598$	1.71636	−	0.990942i	0.0701873	−	0.0405227i
$599$	−14.2413	+	8.22222i	−0.581884	+	0.335951i	−0.761882	−	0.647716i	$-0.775724\pi$
$599$	−14.2413	+	8.22222i	−0.581884	+	0.335951i	0.179998	+	0.983667i	$0.442391\pi$
$600$	20.0423	+	11.5715i	0.818225	+	0.472402i
$601$	19.4766			0.794467			0.397234	−	0.917718i	$-0.369970\pi$
$601$	19.4766			0.794467			0.397234	+	0.917718i	$0.369970\pi$
$602$	6.62665	+	26.4302i	0.270082	+	1.07721i
$603$			16.8001i			0.684153i
$604$	1.35557	+	0.782640i	0.0551574	+	0.0318452i
$605$	−28.2449	+	16.3072i	−1.14832	+	0.662981i
$606$	26.2413	+	45.4513i	1.06598	+	1.84633i
$607$	7.65081	−	13.2516i	0.310537	−	0.537866i	−0.667942	−	0.744214i	$-0.732824\pi$
$607$	7.65081	−	13.2516i	0.310537	−	0.537866i	0.978479	+	0.206348i	$0.0661578\pi$
$608$	19.7535	−	11.0815i	0.801110	−	0.449415i
$609$	−25.1937	−	7.18841i	−1.02090	−	0.291289i
$610$			0.626241i			0.0253558i
$611$	1.84338	+	1.06428i	0.0745753	+	0.0430561i
$612$	6.82221	−	3.93881i	0.275772	−	0.159217i
$613$	−18.0699	−	31.2980i	−0.729836	−	1.26411i	−0.956952	−	0.290246i	$-0.906263\pi$
$613$	−18.0699	−	31.2980i	−0.729836	−	1.26411i	0.227116	−	0.973868i	$-0.427070\pi$
$614$	13.6444	+	7.87761i	0.550644	+	0.317915i
$615$			83.2242i			3.35592i
$616$	4.99120	+	1.42412i	0.201101	+	0.0573793i
$617$	−33.9708			−1.36761			−0.683807	−	0.729663i	$-0.739677\pi$
$617$	−33.9708			−1.36761			−0.683807	+	0.729663i	$0.739677\pi$
$618$	−52.0319	−	30.0406i	−2.09303	−	1.20841i
$619$	−3.66541	+	2.11623i	−0.147325	+	0.0850583i	−0.571851	−	0.820358i	$-0.693774\pi$
$619$	−3.66541	+	2.11623i	−0.147325	+	0.0850583i	0.424525	+	0.905416i	$0.360441\pi$
$620$	−23.6392	+	13.6481i	−0.949373	+	0.548121i
$621$	−2.60209	+	4.50695i	−0.104418	+	0.180858i
$622$	4.45785			0.178743
$623$	9.19896	−	2.30639i	0.368548	−	0.0924035i
$624$	7.25929			0.290604
$625$	8.53635	−	14.7854i	0.341454	−	0.591416i
$626$	−28.5247	−	49.4063i	−1.14008	−	1.97467i
$627$	5.37674	−	9.05258i	0.214726	−	0.361525i
$628$	2.08449	+	1.20348i	0.0831804	+	0.0480242i
$629$	−6.00000			−0.239236
$630$	−16.5635	−	17.1070i	−0.659906	−	0.681560i
$631$	−12.9169			−0.514212			−0.257106	−	0.966383i	$-0.582769\pi$
$631$	−12.9169			−0.514212			−0.257106	+	0.966383i	$0.582769\pi$
$632$	12.5969	−	21.8184i	0.501077	−	0.867890i
$633$	2.89094	−	1.66909i	0.114905	−	0.0663403i
$634$	19.8170	+	34.3240i	0.787033	+	1.36318i
$635$	−24.4103	+	42.2799i	−0.968693	+	1.67782i
$636$			25.6576i			1.01739i
$637$	0.153808	−	4.76298i	0.00609409	−	0.188716i
$638$	9.10906			0.360631
$639$	−0.308013	−	0.177831i	−0.0121848	−	0.00703489i
$640$	−20.3470	−	35.2420i	−0.804284	−	1.39306i
$641$	−16.6444	+	9.60967i	−0.657415	+	0.379559i	−0.791291	−	0.611439i	$-0.790591\pi$
$641$	−16.6444	+	9.60967i	−0.657415	+	0.379559i	0.133876	+	0.990998i	$0.457258\pi$
$642$	−19.6180	+	33.9794i	−0.774262	+	1.34106i
$643$		−	6.74133i		−	0.265852i	−0.991126	−	0.132926i	$-0.957563\pi$
$643$		−	6.74133i		−	0.265852i	0.991126	−	0.132926i	$-0.0424373\pi$
$644$	3.09329	+	3.19479i	0.121893	+	0.125892i
$645$		−	42.5615i		−	1.67586i
$646$	−38.4139	−	0.474705i	−1.51137	−	0.0186770i
$647$	15.0214	−	8.67258i	0.590550	−	0.340954i	−0.174765	−	0.984610i	$-0.555916\pi$
$647$	15.0214	−	8.67258i	0.590550	−	0.340954i	0.765315	+	0.643656i	$0.222583\pi$
$648$	−16.8715	+	9.74078i	−0.662776	+	0.382654i
$649$	−3.39791	+	5.88536i	−0.133380	+	0.231020i
$650$			7.38767i			0.289768i
$651$	−44.5101	+	11.1597i	−1.74449	+	0.437383i
$652$	12.1210			0.474696
$653$	5.31641	−	9.20830i	0.208047	−	0.360348i	−0.743052	−	0.669234i	$-0.766623\pi$
$653$	5.31641	−	9.20830i	0.208047	−	0.360348i	0.951099	+	0.308885i	$0.0999559\pi$
$654$	6.39791	+	11.0815i	0.250178	+	0.433321i
$655$	−16.7171	−	28.9549i	−0.653192	−	1.13136i
$656$	29.0671	−	50.3457i	1.13488	−	1.96567i
$657$			14.1186i			0.550820i
$658$	−3.93127	+	13.7782i	−0.153257	+	0.537130i
$659$		−	14.5456i		−	0.566617i	−0.959029	−	0.283308i	$-0.908568\pi$
$659$		−	14.5456i		−	0.566617i	0.959029	−	0.283308i	$-0.0914320\pi$
$660$	7.02117	+	4.05367i	0.273299	+	0.157789i
$661$	−11.0751	−	19.1827i	−0.430772	−	0.746119i	0.566168	−	0.824290i	$-0.308425\pi$
$661$	−11.0751	−	19.1827i	−0.430772	−	0.746119i	−0.996940	+	0.0781708i	$0.975092\pi$
$662$	−9.00000	−	15.5885i	−0.349795	−	0.605863i
$663$	−6.39791	−	3.69384i	−0.248474	−	0.143457i
$664$	22.5669			0.875766
$665$	8.94886	+	37.6590i	0.347022	+	1.46035i
$666$	3.16183			0.122519
$667$	−6.75870	−	3.90214i	−0.261698	−	0.151091i
$668$	−2.61446	−	4.52838i	−0.101157	−	0.175208i
$669$	−15.9185	−	27.5716i	−0.615445	−	1.06598i
$670$	54.6340	+	31.5429i	2.11070	+	1.21861i
$671$		−	0.122012i		−	0.00471020i
$672$	7.13023	+	28.4387i	0.275054	+	1.09705i
$673$			28.6318i			1.10367i	0.833952	+	0.551836i	$0.186073\pi$
$673$			28.6318i			1.10367i	−0.833952	+	0.551836i	$0.813927\pi$
$674$	−14.3767	+	24.9012i	−0.553771	+	0.959160i
$675$	−9.69954	−	16.8001i	−0.373335	−	0.646636i
$676$	−6.26827	−	10.8570i	−0.241087	−	0.417575i
$677$	−0.771077	+	1.33554i	−0.0296349	+	0.0513292i	−0.880462	−	0.474116i	$-0.842768\pi$
$677$	−0.771077	+	1.33554i	−0.0296349	+	0.0513292i	0.850828	+	0.525445i	$0.176101\pi$
$678$	29.9472			1.15012
$679$	−5.34397	−	5.51932i	−0.205083	−	0.211812i
$680$			29.5812i			1.13439i
$681$	13.6180	−	23.5871i	0.521844	−	0.903861i
$682$	13.8170	−	7.97725i	0.529080	−	0.305465i
$683$	19.4826	−	11.2483i	0.745481	−	0.430403i	−0.0785779	−	0.996908i	$-0.525038\pi$
$683$	19.4826	−	11.2483i	0.745481	−	0.430403i	0.824059	+	0.566504i	$0.191705\pi$
$684$	6.74768	+	0.0833856i	0.258004	+	0.00318833i
$685$			6.97688i			0.266573i
$686$	31.3505	−	6.79291i	1.19697	−	0.259355i
$687$			4.90345i			0.187078i
$688$	−14.8651	+	25.7472i	−0.566728	+	0.981602i
$689$	7.09310	−	4.09521i	0.270226	−	0.156015i
$690$	−10.4191	−	18.0464i	−0.396648	−	0.687014i
$691$	−4.50898	−	2.60326i	−0.171530	−	0.0990328i	0.411777	−	0.911285i	$-0.364908\pi$
$691$	−4.50898	−	2.60326i	−0.171530	−	0.0990328i	−0.583307	+	0.812252i	$0.698242\pi$
$692$	−17.6268			−0.670072
$693$	3.22710	+	3.33299i	0.122587	+	0.126610i
$694$			8.12745i			0.308514i
$695$	−19.5999	+	33.9480i	−0.743465	+	1.28772i
$696$	−8.57570	−	14.8535i	−0.325061	−	0.563022i
$697$	−51.2361	+	29.5812i	−1.94070	+	1.12047i
$698$	8.86455	−	15.3539i	0.335528	−	0.581152i
$699$	37.2185			1.40773
$700$	−16.0787	+	4.03129i	−0.607717	+	0.152369i
$701$	−39.8685			−1.50581			−0.752907	−	0.658127i	$-0.771349\pi$
$701$	−39.8685			−1.50581			−0.752907	+	0.658127i	$0.771349\pi$
$702$	−3.16183	−	1.82549i	−0.119336	−	0.0688985i
$703$	−4.41908	−	2.62469i	−0.166669	−	0.0989922i
$704$	0.566319	+	0.980893i	0.0213439	+	0.0369688i
$705$	11.1902	−	19.3819i	0.421446	−	0.729966i
$706$	18.4754			0.695332
$707$	36.1486	+	10.3141i	1.35951	+	0.387902i
$708$	−12.7958			−0.480897
$709$	−13.7201	+	23.7640i	−0.515270	+	0.892474i	0.484573	+	0.874751i	$0.338975\pi$
$709$	−13.7201	+	23.7640i	−0.515270	+	0.892474i	−0.999843	+	0.0177232i	$0.994358\pi$
$710$	−1.15662	+	0.667772i	−0.0434070	+	0.0250611i
$711$	19.5018	−	11.2593i	0.731373	−	0.422258i
$712$	5.37674	+	3.10426i	0.201502	+	0.116337i
$713$	−13.6692			−0.511915
$714$	13.6444	−	47.8206i	0.510630	−	1.78964i
$715$		−	2.58803i		−	0.0967867i
$716$	−4.35557	−	2.51469i	−0.162775	−	0.0939784i
$717$	−5.81342	−	10.0691i	−0.217106	−	0.376039i
$718$	−46.1392	+	26.6385i	−1.72190	+	0.994139i
$719$	24.5845	+	14.1939i	0.916847	+	0.529342i	0.882628	−	0.470073i	$-0.155772\pi$
$719$	24.5845	+	14.1939i	0.916847	+	0.529342i	0.0342192	+	0.999414i	$0.489106\pi$
$720$		−	25.9808i		−	0.968246i
$721$	−41.7419	+	10.4656i	−1.55455	+	0.389761i
$722$	−28.0847	−	17.1537i	−1.04520	−	0.638396i
$723$	10.0276	−	17.3682i	0.372929	−	0.645932i
$724$	1.11147	+	1.92512i	0.0413074	+	0.0715464i
$725$	25.1937	−	14.5456i	0.935672	−	0.540210i
$726$	31.0847	+	17.9467i	1.15366	+	0.666066i
$727$		−	23.5394i		−	0.873028i	−0.899697	−	0.436514i	$-0.856213\pi$
$727$		−	23.5394i		−	0.873028i	0.899697	−	0.436514i	$-0.143787\pi$
$728$	2.24130	−	2.17009i	0.0830680	−	0.0804288i
$729$	2.39675			0.0887684
$730$	45.9139	+	26.5084i	1.69935	+	0.981119i
$731$	26.2025	−	15.1280i	0.969136	−	0.559531i
$732$	0.198956	−	0.114867i	0.00735363	−	0.00424562i
$733$	−26.0160	−	15.0203i	−0.960921	−	0.554788i	−0.0644647	−	0.997920i	$-0.520534\pi$
$733$	−26.0160	−	15.0203i	−0.960921	−	0.554788i	−0.896456	+	0.443132i	$0.853867\pi$
$734$	43.3208			1.59900
$735$	−50.0795	−	1.61718i	−1.84721	−	0.0596507i
$736$			8.73359i			0.321924i
$737$	−10.6444	−	6.14556i	−0.392093	−	0.226375i
$738$	27.0000	−	15.5885i	0.993884	−	0.573819i
$739$	8.37036	+	14.4979i	0.307909	+	0.533313i	0.977905	−	0.209051i	$-0.0670376\pi$
$739$	8.37036	+	14.4979i	0.307909	+	0.533313i	−0.669996	+	0.742365i	$0.733704\pi$
$740$	1.97883	−	3.42743i	0.0727432	−	0.125995i
$741$	−3.09629	−	5.51932i	−0.113745	−	0.202757i
$742$	38.3504	+	39.6088i	1.40789	+	1.45408i
$743$			21.1403i			0.775561i	0.921752	+	0.387781i	$0.126758\pi$
$743$			21.1403i			0.775561i	−0.921752	+	0.387781i	$0.873242\pi$
$744$	−26.0160	−	15.0203i	−0.953791	−	0.550672i
$745$	36.1428	−	20.8670i	1.32417	−	0.764509i
$746$	−21.3979	−	37.0623i	−0.783433	−	1.35695i
$747$	17.4684	+	10.0854i	0.639135	+	0.369005i
$748$			5.76335i			0.210729i
$749$	6.83459	+	27.2595i	0.249730	+	0.996042i
$750$	15.6868			0.572800
$751$	19.1937	+	11.0815i	0.700389	+	0.404370i	0.807492	−	0.589878i	$-0.200824\pi$
$751$	19.1937	+	11.0815i	0.700389	+	0.404370i	−0.107103	+	0.994248i	$0.534157\pi$
$752$	−13.5388	+	7.81661i	−0.493708	+	0.285042i
$753$	13.8698	−	8.00772i	0.505443	−	0.291817i
$754$	2.73753	−	4.74155i	0.0996951	−	0.172677i
$755$	−5.25367			−0.191201
$756$	2.24768	−	7.87761i	0.0817474	−	0.286506i
$757$	−4.73473			−0.172087			−0.0860433	−	0.996291i	$-0.527422\pi$
$757$	−4.73473			−0.172087			−0.0860433	+	0.996291i	$0.527422\pi$
$758$	25.6815	−	44.4817i	0.932796	−	1.61565i
$759$	2.02997	+	3.51601i	0.0736831	+	0.127623i
$760$	−12.9403	+	21.7869i	−0.469392	+	0.790295i
$761$	−36.5671	−	21.1120i	−1.32556	−	0.765310i	−0.340947	−	0.940082i	$-0.610748\pi$
$761$	−36.5671	−	21.1120i	−1.32556	−	0.765310i	−0.984609	+	0.174772i	$0.944081\pi$
$762$	53.7291			1.94640
$763$	8.81342	+	2.51469i	0.319067	+	0.0910379i
$764$	−7.13264			−0.258050
$765$	−13.2201	+	22.8979i	−0.477975	+	0.827876i
$766$	−38.3504	+	22.1416i	−1.38565	+	0.800008i
$767$	2.04234	+	3.53744i	0.0737446	+	0.127729i
$768$	−20.2601	+	35.0914i	−0.731072	+	1.26625i
$769$			22.5452i			0.813002i	0.913650	+	0.406501i	$0.133251\pi$
$769$			22.5452i			0.813002i	−0.913650	+	0.406501i	$0.866749\pi$
$770$	16.8979	−	4.23669i	0.608958	−	0.152680i
$771$	−50.3875			−1.81466
$772$	4.02117	+	2.32162i	0.144725	+	0.0835571i
$773$	8.37674	+	14.5089i	0.301290	+	0.521850i	0.976429	−	0.215841i	$-0.0692493\pi$
$773$	8.37674	+	14.5089i	0.301290	+	0.521850i	−0.675138	+	0.737691i	$0.735916\pi$
$774$	−13.8080	+	7.97206i	−0.496319	+	0.286550i
$775$	25.4766	−	44.1268i	0.915147	−	1.58508i
$776$		−	5.02938i		−	0.180544i
$777$	4.77987	−	4.62801i	0.171477	−	0.166029i
$778$		−	33.5047i		−	1.20120i
$779$	−50.6763	−	0.626241i	−1.81567	−	0.0224374i
$780$	4.22013	−	2.43649i	0.151105	−	0.0872404i
$781$	0.225345	−	0.130103i	0.00806349	−	0.00465546i
$782$	7.40671	−	12.8288i	0.264863	−	0.458757i
$783$			14.3768i			0.513786i
$784$	29.7303	+	18.4692i	1.06180	+	0.659614i
$785$	−8.07869			−0.288341
$786$	−18.3979	+	31.8661i	−0.656232	+	1.13663i
$787$	25.1874	+	43.6258i	0.897832	+	1.55509i	0.830260	+	0.557376i	$0.188192\pi$
$787$	25.1874	+	43.6258i	0.897832	+	1.55509i	0.0675723	+	0.997714i	$0.478475\pi$
$788$	1.58749	+	2.74961i	0.0565520	+	0.0979509i
$789$	−28.7782	+	49.8454i	−1.02453	+	1.77454i
$790$		−	84.5597i		−	3.00850i
$791$	15.4103	−	14.9207i	0.547927	−	0.530518i
$792$			3.03712i			0.107920i
$793$	−0.0635108	−	0.0366680i	−0.00225533	−	0.00130212i
$794$	−6.39791	−	11.0815i	−0.227053	−	0.393268i
$795$	−43.0583	−	74.5791i	−1.52712	−	2.64505i
$796$	−8.91908	−	5.14943i	−0.316129	−	0.182517i
$797$	−32.0918			−1.13675			−0.568376	−	0.822769i	$-0.692428\pi$
$797$	−32.0918			−1.13675			−0.568376	+	0.822769i	$0.692428\pi$
$798$	30.9684	−	29.2518i	1.09627	−	1.03550i
$799$	15.9097			0.562845
$800$	−28.1937	−	16.2777i	−0.996799	−	0.575502i
$801$	2.77465	+	4.80584i	0.0980376	+	0.169806i
$802$	−7.35557	−	12.7402i	−0.259734	−	0.449873i
$803$	−8.94547	−	5.16467i	−0.315679	−	0.182257i
$804$		−	23.1429i		−	0.816187i
$805$	−14.3528	−	4.09521i	−0.505868	−	0.144337i
$806$		−	9.58957i		−	0.337778i
$807$	6.39791	−	11.0815i	0.225217	−	0.390088i
$808$	12.3046	+	21.3122i	0.432875	+	0.749762i
$809$	28.4373	+	49.2548i	0.999801	+	1.73171i	0.517186	+	0.855873i	$0.326979\pi$
$809$	28.4373	+	49.2548i	0.999801	+	1.73171i	0.482614	+	0.875833i	$0.339687\pi$
$810$	−32.6937	+	56.6272i	−1.14874	+	1.98968i
$811$	22.6384			0.794943			0.397472	−	0.917614i	$-0.369888\pi$
$811$	22.6384			0.794943			0.397472	+	0.917614i	$0.369888\pi$
$812$	11.8134	+	3.37067i	0.414570	+	0.118287i
$813$			35.6942i			1.25185i
$814$	−1.15662	+	2.00332i	−0.0405394	+	0.0702162i
$815$	−35.2323	+	20.3414i	−1.23413	+	0.712528i
$816$	46.9896	−	27.1294i	1.64496	−	0.949720i
$817$	25.9163	+	0.320265i	0.906696	+	0.0112046i
$818$		−	39.2109i		−	1.37098i
$819$	2.70476	−	0.678145i	0.0945119	−	0.0236963i
$820$		−	39.0241i		−	1.36278i
$821$	4.40091	−	7.62259i	0.153593	−	0.266030i	−0.778953	−	0.627082i	$-0.784249\pi$
$821$	4.40091	−	7.62259i	0.153593	−	0.266030i	0.932546	+	0.361052i	$0.117582\pi$
$822$	6.64965	−	3.83918i	0.231933	−	0.133907i
$823$	−10.9554	−	18.9754i	−0.381882	−	0.661440i	0.609449	−	0.792825i	$-0.291391\pi$
$823$	−10.9554	−	18.9754i	−0.381882	−	0.661440i	−0.991331	+	0.131386i	$0.958057\pi$
$824$	−24.3979	−	14.0861i	−0.849942	−	0.490714i
$825$	−15.1338			−0.526891
$826$	−19.7535	+	19.1259i	−0.687312	+	0.665475i
$827$		−	22.3499i		−	0.777182i	−0.921410	−	0.388591i	$-0.872962\pi$
$827$		−	22.3499i		−	0.777182i	0.921410	−	0.388591i	$-0.127038\pi$
$828$	−1.30104	+	2.25347i	−0.0452144	+	0.0783136i
$829$	1.07869	+	1.86835i	0.0374645	+	0.0648905i	0.884150	−	0.467204i	$-0.154739\pi$
$829$	1.07869	+	1.86835i	0.0374645	+	0.0648905i	−0.846685	+	0.532094i	$0.821405\pi$
$830$	65.5954	−	37.8715i	2.27685	−	1.31454i
$831$	−7.65081	+	13.2516i	−0.265404	+	0.459693i
$832$	0.680780			0.0236018
$833$	−16.8046	−	31.4057i	−0.582246	−	1.08814i
$834$	43.1410			1.49385
$835$	15.1990	+	8.77512i	0.525982	+	0.303676i
$836$	−2.52117	+	4.24478i	−0.0871965	+	0.146809i
$837$	12.5905	+	21.8074i	0.435191	+	0.753773i
$838$	−8.70775	+	15.0823i	−0.300804	+	0.521008i
$839$	−41.6268			−1.43712			−0.718559	−	0.695466i	$-0.755198\pi$
$839$	−41.6268			−1.43712			−0.718559	+	0.695466i	$0.755198\pi$
$840$	−22.8170	−	23.5657i	−0.787261	−	0.813094i
$841$	7.44025			0.256560
$842$	0.334402	−	0.579201i	0.0115242	−	0.0199606i
$843$	−10.2729	+	5.93106i	−0.353818	+	0.204277i
$844$	−1.35557	+	0.782640i	−0.0466607	+	0.0269396i
$845$	36.4401	+	21.0387i	1.25358	+	0.723753i
$846$	−8.38397			−0.288247
$847$	24.9373	−	6.25234i	0.856854	−	0.214833i
$848$			60.1546i			2.06572i
$849$	18.4614	+	10.6587i	0.633594	+	0.365806i
$850$	27.6092	+	47.8206i	0.946989	+	1.64023i
$851$	1.71636	−	0.990942i	0.0588362	−	0.0339691i
$852$	0.424302	+	0.244971i	0.0145363	+	0.00839255i
$853$			42.9275i			1.46981i	0.678170	+	0.734905i	$0.262773\pi$
$853$			42.9275i			1.46981i	−0.678170	+	0.734905i	$0.737227\pi$
$854$	0.135445	−	0.474705i	0.00463485	−	0.0162441i
$855$	−19.7535	+	11.0815i	−0.675555	+	0.378980i
$856$	−9.19896	+	15.9331i	−0.314414	+	0.544581i
$857$	−7.75348	−	13.4294i	−0.264854	−	0.458741i	0.702671	−	0.711515i	$-0.251990\pi$
$857$	−7.75348	−	13.4294i	−0.264854	−	0.458741i	−0.967525	+	0.252774i	$0.918657\pi$
$858$	−2.46664	+	1.42412i	−0.0842098	+	0.0486185i
$859$	−40.3505	−	23.2964i	−1.37674	−	0.794863i	−0.384977	−	0.922926i	$-0.625791\pi$
$859$	−40.3505	−	23.2964i	−1.37674	−	0.794863i	−0.991766	+	0.128064i	$0.959124\pi$
$860$			19.9572i			0.680535i
$861$	18.0000	−	63.0859i	0.613438	−	2.14996i
$862$	19.1937			0.653741
$863$	−7.95244	−	4.59134i	−0.270704	−	0.156291i	0.358503	−	0.933528i	$-0.383287\pi$
$863$	−7.95244	−	4.59134i	−0.270704	−	0.156291i	−0.629208	+	0.777237i	$0.716620\pi$
$864$	13.9333	−	8.04439i	0.474020	−	0.273676i
$865$	51.2361	−	29.5812i	1.74208	−	1.00579i
$866$	40.9896	+	23.6653i	1.39288	+	0.804181i
$867$	−18.9636			−0.644039
$868$	20.8709	−	5.23282i	0.708406	−	0.177613i
$869$			16.4749i			0.558873i
$870$	−49.8541	−	28.7833i	−1.69021	−	0.975845i
$871$	−6.39791	+	3.69384i	−0.216785	+	0.125161i
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$	2.24768	−	3.89310i	0.0760725	−	0.131761i
$874$	11.0671	−	6.20853i	0.374350	−	0.210007i
$875$	8.07212	−	7.81566i	0.272887	−	0.264218i
$876$		−	19.4491i		−	0.657123i
$877$	−29.1059	−	16.8043i	−0.982835	−	0.567440i	−0.0797100	−	0.996818i	$-0.525399\pi$
$877$	−29.1059	−	16.8043i	−0.982835	−	0.567440i	−0.903125	+	0.429378i	$0.858733\pi$
$878$	−11.3312	+	6.54207i	−0.382409	+	0.220784i
$879$	−5.60209	−	9.70310i	−0.188954	−	0.327277i
$880$	16.4612	+	9.50390i	0.554908	+	0.320376i
$881$		−	26.8206i		−	0.903607i	−0.892117	−	0.451804i	$-0.850781\pi$
$881$		−	26.8206i		−	0.903607i	0.892117	−	0.451804i	$-0.149219\pi$
$882$	8.85557	+	16.5499i	0.298183	+	0.557265i
$883$	−14.9037			−0.501550			−0.250775	−	0.968045i	$-0.580685\pi$
$883$	−14.9037			−0.501550			−0.250775	+	0.968045i	$0.580685\pi$
$884$	3.00000	+	1.73205i	0.100901	+	0.0582552i
$885$	37.1937	−	21.4738i	1.25025	−	0.721834i
$886$	22.4826	−	12.9803i	0.755318	−	0.436083i
$887$	−22.7535	+	39.4102i	−0.763987	+	1.32326i	0.176793	+	0.984248i	$0.443428\pi$
$887$	−22.7535	+	39.4102i	−0.763987	+	1.32326i	−0.940780	+	0.339017i	$0.889906\pi$
$888$	4.35557			0.146163
$889$	27.6480	−	26.7696i	0.927284	−	0.897824i
$890$	20.8382			0.698497
$891$	6.36977	−	11.0328i	0.213395	−	0.369612i
$892$	7.46423	+	12.9284i	0.249921	+	0.432876i
$893$	11.7177	+	6.95969i	0.392118	+	0.232897i
$894$	−39.7767	−	22.9651i	−1.33033	−	0.768067i
$895$	16.8805			0.564253
$896$	7.80123	+	31.1150i	0.260621	+	1.03948i
$897$	2.44025			0.0814777
$898$	−26.1514	+	45.2955i	−0.872683	+	1.51153i
$899$	−32.7027	+	18.8809i	−1.09070	+	0.629714i
$900$	−4.84977	−	8.40005i	−0.161659	−	0.280002i
$901$	30.6092	−	53.0168i	1.01974	−	1.76624i
$902$			22.8094i			0.759469i
$903$	−9.20534	+	32.2626i	−0.306335	+	1.07363i
$904$	14.0423			0.467041
$905$	−6.46142	−	3.73050i	−0.214785	−	0.124006i
$906$	2.89094	+	5.00726i	0.0960452	+	0.166355i
$907$	33.3260	−	19.2408i	1.10657	−	0.638879i	0.168632	−	0.985679i	$-0.446065\pi$
$907$	33.3260	−	19.2408i	1.10657	−	0.638879i	0.937939	+	0.346800i	$0.112732\pi$
$908$	−6.38554	+	11.0601i	−0.211912	+	0.367042i
$909$			21.9962i			0.729569i
$910$	2.87298	−	10.0691i	0.0952383	−	0.333789i
$911$		−	38.1480i		−	1.26390i	−0.775010	−	0.631950i	$-0.782255\pi$
$911$		−	38.1480i		−	1.26390i	0.775010	−	0.631950i	$-0.217745\pi$
$912$	46.4762	+	0.574337i	1.53898	+	0.0190182i
$913$	−12.7801	+	7.37857i	−0.422958	+	0.244195i
$914$	−56.9826	+	32.8989i	−1.88482	+	1.08820i
$915$	−0.385539	+	0.667772i	−0.0127455	+	0.0220759i
$916$		−	2.29924i		−	0.0759692i
$917$	6.40952	+	25.5642i	0.211661	+	0.844203i
$918$	−27.2889			−0.900666
$919$	3.52398	−	6.10371i	0.116245	−	0.201343i	−0.802032	−	0.597282i	$-0.796247\pi$
$919$	3.52398	−	6.10371i	0.116245	−	0.201343i	0.918277	+	0.395939i	$0.129581\pi$
$920$	−4.88554	−	8.46200i	−0.161071	−	0.278984i
$921$	9.69954	+	16.8001i	0.319611	+	0.553582i
$922$	18.4401	−	31.9391i	0.607291	−	1.05186i
$923$		−	0.156399i		−	0.00514793i
$924$	−4.44547	−	4.59134i	−0.146245	−	0.151044i
$925$			7.38767i			0.242905i
$926$	−1.96985	−	1.13729i	−0.0647332	−	0.0373737i
$927$	−12.5905	−	21.8074i	−0.413526	−	0.716248i
$928$	12.0635	+	20.8946i	0.396004	+	0.685899i
$929$	25.6866	+	14.8302i	0.842749	+	0.486562i	0.858198	−	0.513319i	$-0.171584\pi$
$929$	25.6866	+	14.8302i	0.842749	+	0.486562i	−0.0154484	+	0.999881i	$0.504918\pi$
$930$	−100.828			−3.30627
$931$	1.36156	−	30.4819i	0.0446233	−	0.999004i
$932$	−17.4519			−0.571655
$933$	4.75348	+	2.74443i	0.155622	+	0.0898485i
$934$	8.70775	+	15.0823i	0.284926	+	0.493507i
$935$	−9.67198	−	16.7524i	−0.316308	−	0.547861i
$936$	1.58092	+	0.912743i	0.0516739	+	0.0298339i
$937$			11.1749i			0.365070i	0.983199	+	0.182535i	$0.0584302\pi$
$937$			11.1749i			0.365070i	−0.983199	+	0.182535i	$0.941570\pi$
$938$	−34.5916	−	35.7267i	−1.12946	−	1.16652i
$939$		−	70.2438i		−	2.29232i
$940$	−5.24710	+	9.08824i	−0.171141	+	0.296426i
$941$	−21.3591	−	36.9951i	−0.696288	−	1.20601i	−0.969744	−	0.244122i	$-0.921500\pi$
$941$	−21.3591	−	36.9951i	−0.696288	−	1.20601i	0.273456	−	0.961884i	$-0.411833\pi$
$942$	4.44547	+	7.69978i	0.144841	+	0.250872i
$943$	9.77108	−	16.9240i	0.318190	−	0.551121i
$944$	−30.0000			−0.976417
$945$	6.68677	+	26.6700i	0.217521	+	0.867574i
$946$		−	11.6649i		−	0.379258i
$947$	10.3704	−	17.9620i	0.336991	−	0.583686i	−0.646874	−	0.762597i	$-0.723924\pi$
$947$	10.3704	−	17.9620i	0.336991	−	0.583686i	0.983865	+	0.178911i	$0.0572574\pi$
$948$	−26.8646	+	15.5103i	−0.872520	+	0.503750i
$949$	−5.37674	+	3.10426i	−0.174536	+	0.100769i
$950$	−0.584495	+	47.2982i	−0.0189635	+	1.53456i
$951$			48.8005i			1.58246i
$952$	6.39791	−	22.4232i	0.207358	−	0.726741i
$953$		−	10.5916i		−	0.343095i	−0.985176	−	0.171547i	$-0.945123\pi$
$953$		−	10.5916i		−	0.343095i	0.985176	−	0.171547i	$-0.0548766\pi$
$954$	−16.1302	+	27.9384i	−0.522235	+	0.904538i
$955$	20.7325	−	11.9699i	0.670888	−	0.387337i
$956$	2.72593	+	4.72145i	0.0881628	+	0.152703i
$957$	9.71316	+	5.60789i	0.313982	+	0.181277i
$958$	−64.6164			−2.08766
$959$	1.50898	−	5.28864i	0.0487276	−	0.170779i
$960$		−	7.15794i		−	0.231021i
$961$	−17.5699	+	30.4320i	−0.566771	+	0.981676i
$962$	0.695192	+	1.20411i	0.0224139	+	0.0388220i
$963$	−14.2413	+	8.22222i	−0.458919	+	0.264957i
$964$	−4.70195	+	8.14402i	−0.151440	+	0.262301i
$965$	−15.5845			−0.501683
$966$	3.99478	+	15.9331i	0.128530	+	0.512638i
$967$	−42.6033			−1.37003			−0.685014	−	0.728530i	$-0.740204\pi$
$967$	−42.6033			−1.37003			−0.685014	+	0.728530i	$0.740204\pi$
$968$	14.5757	+	8.41528i	0.468481	+	0.270477i
$969$	−40.6692	−	24.1553i	−1.30648	−	0.775979i
$970$	−8.44025	−	14.6189i	−0.271000	−	0.469386i
$971$	−8.05471	+	13.9512i	−0.258488	+	0.447714i	−0.965837	−	0.259150i	$-0.916558\pi$
$971$	−8.05471	+	13.9512i	−0.258488	+	0.447714i	0.707349	+	0.706864i	$0.249891\pi$
$972$	14.6984			0.471451
$973$	22.1995	−	21.4942i	0.711685	−	0.689074i
$974$	60.7958			1.94802
$975$	−4.54814	+	7.87761i	−0.145657	+	0.252286i
$976$	0.466456	−	0.269308i	0.0149309	−	0.00862035i
$977$	20.0423	−	11.5715i	0.641211	−	0.370204i	−0.143870	−	0.989597i	$-0.545955\pi$
$977$	20.0423	−	11.5715i	0.641211	−	0.370204i	0.785081	+	0.619393i	$0.212621\pi$
$978$	38.7747	+	22.3866i	1.23988	+	0.715843i
$979$	−4.05993			−0.129756
$980$	23.4824	+	0.758302i	0.750118	+	0.0242231i
$981$			5.36292i			0.171225i
$982$	−1.96142	−	1.13243i	−0.0625915	−	0.0361372i
$983$	−16.8558	−	29.1950i	−0.537615	−	0.931177i	−0.999032	−	0.0439933i	$-0.985992\pi$
$983$	−16.8558	−	29.1950i	−0.537615	−	0.931177i	0.461417	−	0.887184i	$-0.347341\pi$
$984$	37.1937	−	21.4738i	1.18569	−	0.684560i
$985$	−9.22874	−	5.32821i	−0.294052	−	0.169771i
$986$		−	40.9229i		−	1.30325i
$987$	−12.6744	+	12.2717i	−0.403430	+	0.390613i
$988$	1.45186	+	2.58803i	0.0461897	+	0.0823361i
$989$	−4.99701	+	8.65507i	−0.158896	+	0.275215i
$990$	5.09687	+	8.82804i	0.161989	+	0.280573i
$991$	−36.1270	+	20.8579i	−1.14761	+	0.662574i	−0.948304	−	0.317362i	$-0.897203\pi$
$991$	−36.1270	+	20.8579i	−1.14761	+	0.662574i	−0.199308	+	0.979937i	$0.563870\pi$
$992$	36.5969	+	21.1292i	1.16195	+	0.670853i
$993$		−	22.1630i		−	0.703322i
$994$	1.02117	−	0.256031i	0.0323896	−	0.00812080i
$995$	34.5669			1.09584
$996$	−24.0635	−	13.8931i	−0.762482	−	0.440219i
$997$	5.15304	−	2.97511i	0.163198	−	0.0942226i	−0.416176	−	0.909284i	$-0.636630\pi$
$997$	5.15304	−	2.97511i	0.163198	−	0.0942226i	0.579375	+	0.815061i	$0.303297\pi$
$998$	−59.8663	+	34.5638i	−1.89503	+	1.09410i
$999$	−3.16183	−	1.82549i	−0.100036	−	0.0577558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.o.d.75.1	✓	6
7.2	even	3		931.2.c.d.930.6		6
7.3	odd	6		133.2.o.e.94.3	yes	6
7.4	even	3		931.2.o.f.227.1		6
7.5	odd	6		931.2.c.e.930.4		6
7.6	odd	2		931.2.o.e.607.3		6
19.18	odd	2		133.2.o.e.75.3	yes	6
133.18	odd	6		931.2.o.e.227.3		6
133.37	odd	6		931.2.c.e.930.1		6
133.75	even	6		931.2.c.d.930.3		6
133.94	even	6	inner	133.2.o.d.94.1	yes	6
133.132	even	2		931.2.o.f.607.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.o.d.75.1	✓	6	1.1	even	1	trivial
133.2.o.d.94.1	yes	6	133.94	even	6	inner
133.2.o.e.75.3	yes	6	19.18	odd	2
133.2.o.e.94.3	yes	6	7.3	odd	6
931.2.c.d.930.3		6	133.75	even	6
931.2.c.d.930.6		6	7.2	even	3
931.2.c.e.930.1		6	133.37	odd	6
931.2.c.e.930.4		6	7.5	odd	6
931.2.o.e.227.3		6	133.18	odd	6
931.2.o.e.607.3		6	7.6	odd	2
931.2.o.f.227.1		6	7.4	even	3
931.2.o.f.607.1		6	133.132	even	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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.06632 - 1.84692i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.90671 - 1.67819i) q^{5} +3.69384i q^{6} +(1.84039 + 1.90078i) q^{7} +1.73205i q^{8} +(-0.774071 + 1.34073i) q^{9} +(2.90671 + 5.03457i) q^{10} +(-0.566319 - 0.980893i) q^{11} +(1.06632 - 1.84692i) q^{12} -0.680780 q^{13} +(-1.11446 - 4.44499i) q^{14} +7.15794i q^{15} +(2.50000 - 4.33013i) q^{16} +(-4.40671 + 2.54421i) q^{17} +(2.32221 - 1.34073i) q^{18} +(-4.35857 - 0.0538617i) q^{19} -3.35638i q^{20} +(1.54814 - 5.42589i) q^{21} +1.96179i q^{22} +(0.840390 - 1.45560i) q^{23} +(3.19896 - 1.84692i) q^{24} +(3.13264 + 5.42589i) q^{25} +(1.02117 + 0.589573i) q^{26} -3.09629 q^{27} +(-0.725929 + 2.54421i) q^{28} -4.64325i q^{29} +(6.19896 - 10.7369i) q^{30} +(-4.06632 - 7.04307i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(-1.20775 + 2.09189i) q^{33} +8.81342 q^{34} +(-2.15961 - 8.61354i) q^{35} -1.54814 q^{36} +(1.02117 + 0.589573i) q^{37} +(6.49120 + 3.85542i) q^{38} +(0.725929 + 1.25735i) q^{39} +(2.90671 - 5.03457i) q^{40} +11.6268 q^{41} +(-7.02117 + 6.79810i) q^{42} -5.94606 q^{43} +(0.566319 - 0.980893i) q^{44} +(4.50000 - 2.59808i) q^{45} +(-2.52117 + 1.45560i) q^{46} +(-2.70775 - 1.56332i) q^{47} -10.6632 q^{48} +(-0.225929 + 6.99635i) q^{49} -10.8518i q^{50} +(9.39791 + 5.42589i) q^{51} +(-0.340390 - 0.589573i) q^{52} +(-10.4191 + 6.01546i) q^{53} +(4.64443 + 2.68146i) q^{54} +3.80156i q^{55} +(-3.29225 + 3.18765i) q^{56} +(4.54814 + 8.10735i) q^{57} +(-4.02117 + 6.96487i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-6.19896 + 3.57897i) q^{60} +(0.0932912 + 0.0538617i) q^{61} +14.0861i q^{62} +(-3.97303 + 0.996129i) q^{63} -1.00000 q^{64} +(1.97883 + 1.14248i) q^{65} +(3.62326 - 2.09189i) q^{66} +(9.39791 - 5.42589i) q^{67} +(-4.40671 - 2.54421i) q^{68} -3.58449 q^{69} +(-4.22013 + 14.7906i) q^{70} +0.229735i q^{71} +(-2.32221 - 1.34073i) q^{72} +(7.89791 - 4.55986i) q^{73} +(-1.02117 - 1.76872i) q^{74} +(6.68078 - 11.5715i) q^{75} +(-2.13264 - 3.80156i) q^{76} +(0.822214 - 2.88167i) q^{77} -2.51469i q^{78} +(-12.5969 - 7.27281i) q^{79} +(-14.5335 + 8.39095i) q^{80} +(5.62384 + 9.74078i) q^{81} +(-17.4403 - 10.0691i) q^{82} -13.0290i q^{83} +(5.47303 - 1.37221i) q^{84} +17.0787 q^{85} +(8.91908 + 5.14943i) q^{86} +(-8.57570 + 4.95118i) q^{87} +(1.69896 - 0.980893i) q^{88} +(1.79225 - 3.10426i) q^{89} -9.00000 q^{90} +(-1.25290 - 1.29401i) q^{91} +1.68078 q^{92} +(-8.67198 + 15.0203i) q^{93} +(2.70775 + 4.68997i) q^{94} +(12.5787 + 7.47106i) q^{95} +(9.59687 + 5.54075i) q^{96} -2.90371 q^{97} +(6.39791 - 10.2989i) q^{98} +1.75348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{2} + 2 q^{3} + 3 q^{4} - 3 q^{5} + 5 q^{7} - 7 q^{9} + 3 q^{10} + 5 q^{11} - 2 q^{12} + 8 q^{13} - 3 q^{14} + 15 q^{16} - 12 q^{17} + 21 q^{18} - 7 q^{19} + 14 q^{21} - q^{23} - 6 q^{24} + 2 q^{25}+ \cdots - 54 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 + 2 * q^3 + 3 * q^4 - 3 * q^5 + 5 * q^7 - 7 * q^9 + 3 * q^10 + 5 * q^11 - 2 * q^12 + 8 * q^13 - 3 * q^14 + 15 * q^16 - 12 * q^17 + 21 * q^18 - 7 * q^19 + 14 * q^21 - q^23 - 6 * q^24 + 2 * q^25 - 12 * q^26 - 28 * q^27 - 2 * q^28 + 12 * q^30 - 16 * q^31 - 27 * q^32 - 18 * q^33 + 24 * q^34 - 19 * q^35 - 14 * q^36 - 12 * q^37 + 3 * q^38 + 2 * q^39 + 3 * q^40 + 12 * q^41 - 24 * q^42 + 10 * q^43 - 5 * q^44 + 27 * q^45 + 3 * q^46 - 27 * q^47 + 20 * q^48 + q^49 + 6 * q^51 + 4 * q^52 + 6 * q^53 + 42 * q^54 - 9 * q^56 + 32 * q^57 - 6 * q^58 - 18 * q^59 - 12 * q^60 + 15 * q^61 - q^63 - 6 * q^64 + 30 * q^65 + 54 * q^66 + 6 * q^67 - 12 * q^68 + 18 * q^70 - 21 * q^72 - 3 * q^73 + 12 * q^74 + 28 * q^75 + 4 * q^76 + 12 * q^77 - 15 * q^80 - 19 * q^81 - 18 * q^82 + 10 * q^84 + 40 * q^85 - 15 * q^86 + 6 * q^87 - 15 * q^88 - 54 * q^90 - 28 * q^91 - 2 * q^92 - 4 * q^93 + 27 * q^94 + 13 * q^95 - 18 * q^96 - 8 * q^97 - 12 * q^98 - 54 * q^99

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