LMFDB - Embedded newform 546.4.s.a.127.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(43,546)] 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("546.43"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1388 x^{18} + 806954 x^{16} + 255183238 x^{14} + 47714604791 x^{12} + 5370647791638 x^{10} + \cdots + 42\!\cdots\!84 $ x^20 + 1388x^18 + 806954x^16 + 255183238x^14 + 47714604791x^12 + 5370647791638x^10 + 354442825910071x^8 + 12732087350994070x^6 + 214746587484940741x^4 + 1171569470005573456*x^2 + 422518488802265284
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.8
Root			$0.622533i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.4.s.a.43.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} -0.377467i q^{5} +(-5.19615 - 3.00000i) q^{6} +(-6.06218 - 3.50000i) q^{7} -8.00000i q^{8} +(-4.50000 + 7.79423i) q^{9} +(-0.377467 - 0.653792i) q^{10} +(5.90128 - 3.40710i) q^{11} -12.0000 q^{12} +(-31.0923 + 35.0752i) q^{13} -14.0000 q^{14} +(-0.980688 + 0.566200i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-59.5501 + 103.144i) q^{17} +18.0000i q^{18} +(-71.1047 - 41.0523i) q^{19} +(-1.30758 - 0.754934i) q^{20} +21.0000i q^{21} +(6.81421 - 11.8026i) q^{22} +(69.0854 + 119.659i) q^{23} +(-20.7846 + 12.0000i) q^{24} +124.858 q^{25} +(-18.7783 + 91.8443i) q^{26} +27.0000 q^{27} +(-24.2487 + 14.0000i) q^{28} +(-131.333 - 227.476i) q^{29} +(-1.13240 + 1.96138i) q^{30} +52.5552i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-17.7038 - 10.2213i) q^{33} +238.200i q^{34} +(-1.32113 + 2.28827i) q^{35} +(18.0000 + 31.1769i) q^{36} +(26.1057 - 15.0722i) q^{37} -164.209 q^{38} +(137.766 + 28.1674i) q^{39} -3.01974 q^{40} +(49.5882 - 28.6297i) q^{41} +(21.0000 + 36.3731i) q^{42} +(-208.827 + 361.700i) q^{43} -27.2568i q^{44} +(2.94206 + 1.69860i) q^{45} +(239.319 + 138.171i) q^{46} +622.361i q^{47} +(-24.0000 + 41.5692i) q^{48} +(24.5000 + 42.4352i) q^{49} +(216.260 - 124.858i) q^{50} +357.301 q^{51} +(59.3193 + 177.857i) q^{52} -316.168 q^{53} +(46.7654 - 27.0000i) q^{54} +(-1.28607 - 2.22754i) q^{55} +(-28.0000 + 48.4974i) q^{56} +246.314i q^{57} +(-454.952 - 262.667i) q^{58} +(125.656 + 72.5477i) q^{59} +4.52960i q^{60} +(44.6132 - 77.2723i) q^{61} +(52.5552 + 91.0282i) q^{62} +(54.5596 - 31.5000i) q^{63} -64.0000 q^{64} +(13.2397 + 11.7363i) q^{65} -40.8853 q^{66} +(-380.584 + 219.730i) q^{67} +(238.200 + 412.575i) q^{68} +(207.256 - 358.978i) q^{69} +5.28454i q^{70} +(668.491 + 385.954i) q^{71} +(62.3538 + 36.0000i) q^{72} -147.441i q^{73} +(30.1443 - 52.2115i) q^{74} +(-187.286 - 324.389i) q^{75} +(-284.419 + 164.209i) q^{76} -47.6995 q^{77} +(266.786 - 88.9790i) q^{78} +245.601 q^{79} +(-5.23033 + 3.01974i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(57.2595 - 99.1764i) q^{82} +83.5159i q^{83} +(72.7461 + 42.0000i) q^{84} +(38.9334 + 22.4782i) q^{85} +835.310i q^{86} +(-394.000 + 682.428i) q^{87} +(-27.2568 - 47.2102i) q^{88} +(-164.388 + 94.9096i) q^{89} +6.79440 q^{90} +(311.250 - 103.809i) q^{91} +552.683 q^{92} +(136.542 - 78.8328i) q^{93} +(622.361 + 1077.96i) q^{94} +(-15.4959 + 26.8397i) q^{95} +96.0000i q^{96} +(1042.65 + 601.974i) q^{97} +(84.8705 + 49.0000i) q^{98} +61.3279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 40 q^{4} - 90 q^{9} - 24 q^{10} + 18 q^{11} - 240 q^{12} + 28 q^{13} - 280 q^{14} + 18 q^{15} - 160 q^{16} - 106 q^{17} - 60 q^{19} + 24 q^{20} - 24 q^{22} - 450 q^{23} - 304 q^{25} - 60 q^{26}+ \cdots - 1620 q^{97}+O(q^{100}) $ 20 * q - 30 * q^3 + 40 * q^4 - 90 * q^9 - 24 * q^10 + 18 * q^11 - 240 * q^12 + 28 * q^13 - 280 * q^14 + 18 * q^15 - 160 * q^16 - 106 * q^17 - 60 * q^19 + 24 * q^20 - 24 * q^22 - 450 * q^23 - 304 * q^25 - 60 * q^26 + 540 * q^27 + 290 * q^29 - 72 * q^30 - 54 * q^33 - 84 * q^35 + 360 * q^36 + 564 * q^37 + 160 * q^38 + 228 * q^39 - 192 * q^40 - 246 * q^41 + 420 * q^42 - 464 * q^43 - 54 * q^45 - 240 * q^46 - 480 * q^48 + 490 * q^49 + 720 * q^50 + 636 * q^51 + 416 * q^52 - 1528 * q^53 + 1384 * q^55 - 560 * q^56 - 480 * q^58 - 2496 * q^59 - 270 * q^61 - 60 * q^62 - 1280 * q^64 + 3042 * q^65 + 144 * q^66 + 1314 * q^67 + 424 * q^68 - 1350 * q^69 - 516 * q^71 - 540 * q^74 + 456 * q^75 - 240 * q^76 + 168 * q^77 + 1116 * q^78 - 4000 * q^79 + 96 * q^80 - 810 * q^81 - 476 * q^82 - 2730 * q^85 + 870 * q^87 + 96 * q^88 - 1266 * q^89 + 432 * q^90 + 1302 * q^91 - 3600 * q^92 + 1692 * q^93 + 1080 * q^94 - 3798 * q^95 - 1620 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		−	0.377467i		−	0.0337617i	−0.999858	−	0.0168808i	$-0.994626\pi$
$5$		−	0.377467i		−	0.0337617i	0.999858	−	0.0168808i	$-0.00537359\pi$
$6$	−5.19615	−	3.00000i	−0.353553	−	0.204124i
$7$	−6.06218	−	3.50000i	−0.327327	−	0.188982i
$7$	−6.06218	−	3.50000i	−0.327327	−	0.188982i
$8$		−	8.00000i		−	0.353553i
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−0.377467	−	0.653792i	−0.0119366	−	0.0206747i
$11$	5.90128	−	3.40710i	0.161755	−	0.0933892i	−0.416937	−	0.908935i	$-0.636897\pi$
$11$	5.90128	−	3.40710i	0.161755	−	0.0933892i	0.578692	+	0.815546i	$0.303563\pi$
$12$	−12.0000			−0.288675
$13$	−31.0923	+	35.0752i	−0.663343	+	0.748316i
$13$	−31.0923	+	35.0752i	−0.663343	+	0.748316i
$14$	−14.0000			−0.267261
$15$	−0.980688	+	0.566200i	−0.0168808	+	0.00974615i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−59.5501	+	103.144i	−0.849590	+	1.47153i	0.0319851	+	0.999488i	$0.489817\pi$
$17$	−59.5501	+	103.144i	−0.849590	+	1.47153i	−0.881575	+	0.472044i	$0.843516\pi$
$18$			18.0000i			0.235702i
$19$	−71.1047	−	41.0523i	−0.858555	−	0.495687i	0.00497346	−	0.999988i	$-0.498417\pi$
$19$	−71.1047	−	41.0523i	−0.858555	−	0.495687i	−0.863528	+	0.504301i	$0.831750\pi$
$20$	−1.30758	−	0.754934i	−0.0146192	−	0.00844042i
$21$			21.0000i			0.218218i
$22$	6.81421	−	11.8026i	0.0660361	−	0.114378i
$23$	69.0854	+	119.659i	0.626317	+	1.08481i	0.988285	+	0.152622i	$0.0487718\pi$
$23$	69.0854	+	119.659i	0.626317	+	1.08481i	−0.361967	+	0.932191i	$0.617895\pi$
$24$	−20.7846	+	12.0000i	−0.176777	+	0.102062i
$25$	124.858			0.998860
$26$	−18.7783	+	91.8443i	−0.141643	+	0.692775i
$27$	27.0000			0.192450
$28$	−24.2487	+	14.0000i	−0.163663	+	0.0944911i
$29$	−131.333	−	227.476i	−0.840965	−	1.45659i	−0.889080	−	0.457752i	$-0.848655\pi$
$29$	−131.333	−	227.476i	−0.840965	−	1.45659i	0.0481152	−	0.998842i	$-0.484679\pi$
$30$	−1.13240	+	1.96138i	−0.00689157	+	0.0119366i
$31$			52.5552i			0.304490i	0.988343	+	0.152245i	$0.0486503\pi$
$31$			52.5552i			0.304490i	−0.988343	+	0.152245i	$0.951350\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−17.7038	−	10.2213i	−0.0933892	−	0.0539183i
$34$			238.200i			1.20150i
$35$	−1.32113	+	2.28827i	−0.00638035	+	0.0110511i
$36$	18.0000	+	31.1769i	0.0833333	+	0.144338i
$37$	26.1057	−	15.0722i	0.115993	−	0.0669689i	−0.440881	−	0.897566i	$-0.645334\pi$
$37$	26.1057	−	15.0722i	0.115993	−	0.0669689i	0.556874	+	0.830597i	$0.312001\pi$
$38$	−164.209			−0.701007
$39$	137.766	+	28.1674i	0.565648	+	0.115651i
$40$	−3.01974			−0.0119366
$41$	49.5882	−	28.6297i	0.188887	−	0.109054i	−0.402574	−	0.915387i	$-0.631885\pi$
$41$	49.5882	−	28.6297i	0.188887	−	0.109054i	0.591461	+	0.806333i	$0.298551\pi$
$42$	21.0000	+	36.3731i	0.0771517	+	0.133631i
$43$	−208.827	+	361.700i	−0.740602	+	1.28276i	0.211620	+	0.977352i	$0.432126\pi$
$43$	−208.827	+	361.700i	−0.740602	+	1.28276i	−0.952222	+	0.305408i	$0.901207\pi$
$44$		−	27.2568i		−	0.0933892i
$45$	2.94206	+	1.69860i	0.00974615	+	0.00562694i
$46$	239.319	+	138.171i	0.767079	+	0.442873i
$47$			622.361i			1.93150i	0.259467	+	0.965752i	$0.416453\pi$
$47$			622.361i			1.93150i	−0.259467	+	0.965752i	$0.583547\pi$
$48$	−24.0000	+	41.5692i	−0.0721688	+	0.125000i
$49$	24.5000	+	42.4352i	0.0714286	+	0.123718i
$50$	216.260	−	124.858i	0.611674	−	0.353150i
$51$	357.301			0.981022
$52$	59.3193	+	177.857i	0.158194	+	0.474315i
$53$	−316.168			−0.819414			−0.409707	−	0.912217i	$-0.634369\pi$
$53$	−316.168			−0.819414			−0.409707	+	0.912217i	$0.634369\pi$
$54$	46.7654	−	27.0000i	0.117851	−	0.0680414i
$55$	−1.28607	−	2.22754i	−0.00315297	−	0.00546111i
$56$	−28.0000	+	48.4974i	−0.0668153	+	0.115728i
$57$			246.314i			0.572370i
$58$	−454.952	−	262.667i	−1.02997	−	0.594652i
$59$	125.656	+	72.5477i	0.277272	+	0.160083i	0.632188	−	0.774815i	$-0.282157\pi$
$59$	125.656	+	72.5477i	0.277272	+	0.160083i	−0.354916	+	0.934898i	$0.615490\pi$
$60$			4.52960i			0.00974615i
$61$	44.6132	−	77.2723i	0.0936416	−	0.162192i	−0.815399	−	0.578899i	$-0.803483\pi$
$61$	44.6132	−	77.2723i	0.0936416	−	0.162192i	0.909041	+	0.416707i	$0.136816\pi$
$62$	52.5552	+	91.0282i	0.107653	+	0.186461i
$63$	54.5596	−	31.5000i	0.109109	−	0.0629941i
$64$	−64.0000			−0.125000
$65$	13.2397	+	11.7363i	0.0252644	+	0.0223956i
$66$	−40.8853			−0.0762519
$67$	−380.584	+	219.730i	−0.693966	+	0.400661i	−0.805096	−	0.593145i	$-0.797886\pi$
$67$	−380.584	+	219.730i	−0.693966	+	0.400661i	0.111130	+	0.993806i	$0.464553\pi$
$68$	238.200	+	412.575i	0.424795	+	0.735766i
$69$	207.256	−	358.978i	0.361604	−	0.626317i
$70$			5.28454i			0.00902318i
$71$	668.491	+	385.954i	1.11740	+	0.645130i	0.940736	−	0.339141i	$-0.110136\pi$
$71$	668.491	+	385.954i	1.11740	+	0.645130i	0.176663	+	0.984271i	$0.443470\pi$
$72$	62.3538	+	36.0000i	0.102062	+	0.0589256i
$73$		−	147.441i		−	0.236393i	−0.992990	−	0.118196i	$-0.962289\pi$
$73$		−	147.441i		−	0.236393i	0.992990	−	0.118196i	$-0.0377113\pi$
$74$	30.1443	−	52.2115i	0.0473541	−	0.0820198i
$75$	−187.286	−	324.389i	−0.288346	−	0.499430i
$76$	−284.419	+	164.209i	−0.429277	+	0.247843i
$77$	−47.6995			−0.0705956
$78$	266.786	−	88.9790i	0.387276	−	0.129165i
$79$	245.601			0.349776			0.174888	−	0.984588i	$-0.444044\pi$
$79$	245.601			0.349776			0.174888	+	0.984588i	$0.444044\pi$
$80$	−5.23033	+	3.01974i	−0.00730961	+	0.00422021i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	57.2595	−	99.1764i	0.0771128	−	0.133563i
$83$			83.5159i			0.110446i	0.998474	+	0.0552232i	$0.0175871\pi$
$83$			83.5159i			0.110446i	−0.998474	+	0.0552232i	$0.982413\pi$
$84$	72.7461	+	42.0000i	0.0944911	+	0.0545545i
$85$	38.9334	+	22.4782i	0.0496814	+	0.0286836i
$86$			835.310i			1.04737i
$87$	−394.000	+	682.428i	−0.485531	+	0.840965i
$88$	−27.2568	−	47.2102i	−0.0330181	−	0.0571889i
$89$	−164.388	+	94.9096i	−0.195788	+	0.113038i	−0.594689	−	0.803956i	$-0.702725\pi$
$89$	−164.388	+	94.9096i	−0.195788	+	0.113038i	0.398901	+	0.916994i	$0.369392\pi$
$90$	6.79440			0.00795770
$91$	311.250	−	103.809i	0.358548	−	0.119584i
$92$	552.683			0.626317
$93$	136.542	−	78.8328i	0.152245	−	0.0878987i
$94$	622.361	+	1077.96i	0.682890	+	1.18280i
$95$	−15.4959	+	26.8397i	−0.0167352	+	0.0289862i
$96$			96.0000i			0.102062i
$97$	1042.65	+	601.974i	1.09139	+	0.630115i	0.933947	−	0.357412i	$-0.116341\pi$
$97$	1042.65	+	601.974i	1.09139	+	0.630115i	0.157445	+	0.987528i	$0.449674\pi$
$98$	84.8705	+	49.0000i	0.0874818	+	0.0505076i
$99$			61.3279i			0.0622594i
$100$	249.715	−	432.519i	0.249715	−	0.432519i
$101$	−206.799	−	358.187i	−0.203736	−	0.352881i	0.745993	−	0.665953i	$-0.231975\pi$
$101$	−206.799	−	358.187i	−0.203736	−	0.352881i	−0.949729	+	0.313073i	$0.898642\pi$
$102$	618.863	−	357.301i	0.600751	−	0.346844i
$103$	−1056.67			−1.01084			−0.505422	−	0.862872i	$-0.668663\pi$
$103$	−1056.67			−1.01084			−0.505422	+	0.862872i	$0.668663\pi$
$104$	280.601	+	248.739i	0.264570	+	0.234527i
$105$	7.92680			0.00736740
$106$	−547.618	+	316.168i	−0.501787	+	0.289707i
$107$	−904.150	−	1566.03i	−0.816892	−	1.41490i	−0.907961	−	0.419054i	$-0.862362\pi$
$107$	−904.150	−	1566.03i	−0.816892	−	1.41490i	0.0910689	−	0.995845i	$-0.470972\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$			852.869i			0.749450i	0.927136	+	0.374725i	$0.122263\pi$
$109$			852.869i			0.749450i	−0.927136	+	0.374725i	$0.877737\pi$
$110$	−4.45507	−	2.57214i	−0.00386159	−	0.00222949i
$111$	−78.3172	−	45.2165i	−0.0669689	−	0.0386645i
$112$			112.000i			0.0944911i
$113$	−43.8582	+	75.9646i	−0.0365118	+	0.0632402i	−0.883704	−	0.468046i	$-0.844958\pi$
$113$	−43.8582	+	75.9646i	−0.0365118	+	0.0632402i	0.847192	+	0.531287i	$0.178291\pi$
$114$	246.314	+	426.628i	0.202363	+	0.350503i
$115$	45.1674	−	26.0774i	0.0366251	−	0.0211455i
$116$	−1050.67			−0.840965
$117$	−133.468	−	400.179i	−0.105463	−	0.316210i
$118$	290.191			0.226392
$119$	722.007	−	416.851i	0.556187	−	0.321115i
$120$	4.52960	+	7.84550i	0.00344579	+	0.00596828i
$121$	−642.283	+	1112.47i	−0.482557	+	0.835813i
$122$		−	178.453i		−	0.132429i
$123$	−148.765	−	85.8892i	−0.109054	−	0.0629624i
$124$	182.056	+	105.110i	0.131848	+	0.0761225i
$125$		−	94.3129i		−	0.0674848i
$126$	63.0000	−	109.119i	0.0445435	−	0.0771517i
$127$	−78.7783	−	136.448i	−0.0550429	−	0.0953370i	0.837191	−	0.546911i	$-0.184196\pi$
$127$	−78.7783	−	136.448i	−0.0550429	−	0.0953370i	−0.892234	+	0.451573i	$0.850863\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	1252.96			0.855173
$130$	34.6682	+	7.08819i	0.0233892	+	0.00478212i
$131$	−363.525			−0.242453			−0.121227	−	0.992625i	$-0.538683\pi$
$131$	−363.525			−0.242453			−0.121227	+	0.992625i	$0.538683\pi$
$132$	−70.8153	+	40.8853i	−0.0466946	+	0.0269591i
$133$	287.366	+	497.733i	0.187352	+	0.324503i
$134$	−439.460	+	761.167i	−0.283310	+	0.490708i
$135$		−	10.1916i		−	0.00649744i
$136$	825.151	+	476.401i	0.520265	+	0.300375i
$137$	762.813	+	440.410i	0.475704	+	0.274648i	0.718625	−	0.695398i	$-0.244772\pi$
$137$	762.813	+	440.410i	0.475704	+	0.274648i	−0.242920	+	0.970046i	$0.578105\pi$
$138$		−	829.024i		−	0.511386i
$139$	−907.712	+	1572.20i	−0.553893	+	0.959371i	0.444096	+	0.895979i	$0.353525\pi$
$139$	−907.712	+	1572.20i	−0.553893	+	0.959371i	−0.997989	+	0.0633914i	$0.979808\pi$
$140$	5.28454	+	9.15309i	0.00319018	+	0.00552555i
$141$	1616.94	−	933.542i	0.965752	−	0.557577i
$142$	1543.81			0.912352
$143$	−63.9796	+	312.923i	−0.0374143	+	0.182993i
$144$	144.000			0.0833333
$145$	−85.8646	+	49.5740i	−0.0491770	+	0.0283924i
$146$	−147.441	−	255.376i	−0.0835775	−	0.144761i
$147$	73.5000	−	127.306i	0.0412393	−	0.0714286i
$148$		−	120.577i		−	0.0669689i
$149$	−1451.37	−	837.949i	−0.797993	−	0.460721i	0.0447761	−	0.998997i	$-0.485743\pi$
$149$	−1451.37	−	837.949i	−0.797993	−	0.460721i	−0.842769	+	0.538276i	$0.819076\pi$
$150$	−648.779	−	374.573i	−0.353150	−	0.203891i
$151$		−	1982.76i		−	1.06857i	−0.845303	−	0.534287i	$-0.820580\pi$
$151$		−	1982.76i		−	1.06857i	0.845303	−	0.534287i	$-0.179420\pi$
$152$	−328.419	+	568.838i	−0.175252	+	0.303545i
$153$	−535.951	−	928.295i	−0.283197	−	0.490511i
$154$	−82.6179	+	47.6995i	−0.0432308	+	0.0249593i
$155$	19.8378			0.0102801
$156$	373.108	−	420.902i	0.191491	−	0.216020i
$157$	−2398.98			−1.21949			−0.609744	−	0.792598i	$-0.708728\pi$
$157$	−2398.98			−1.21949			−0.609744	+	0.792598i	$0.708728\pi$
$158$	425.393	−	245.601i	0.214193	−	0.123664i
$159$	474.251	+	821.428i	0.236545	+	0.409707i
$160$	−6.03947	+	10.4607i	−0.00298414	+	0.00516868i
$161$		−	967.195i		−	0.473451i
$162$	−140.296	−	81.0000i	−0.0680414	−	0.0392837i
$163$	−3254.03	−	1878.72i	−1.56365	−	0.902775i	−0.996883	−	0.0788995i	$-0.974859\pi$
$163$	−3254.03	−	1878.72i	−1.56365	−	0.902775i	−0.566770	−	0.823876i	$-0.691807\pi$
$164$		−	229.038i		−	0.109054i
$165$	−3.85821	+	6.68261i	−0.00182037	+	0.00315297i
$166$	83.5159	+	144.654i	0.0390487	+	0.0676344i
$167$	−2967.27	+	1713.15i	−1.37494	+	0.793819i	−0.991545	−	0.129767i	$-0.958577\pi$
$167$	−2967.27	+	1713.15i	−1.37494	+	0.793819i	−0.383391	+	0.923586i	$0.625244\pi$
$168$	168.000			0.0771517
$169$	−263.536	−	2181.14i	−0.119952	−	0.992780i
$170$	89.9128			0.0405647
$171$	639.942	−	369.471i	0.286185	−	0.165229i
$172$	835.310	+	1446.80i	0.370301	+	0.641380i
$173$	501.441	−	868.521i	0.220369	−	0.381690i	−0.734551	−	0.678554i	$-0.762607\pi$
$173$	501.441	−	868.521i	0.220369	−	0.381690i	0.954920	+	0.296863i	$0.0959405\pi$
$174$			1576.00i			0.686645i
$175$	−756.908	−	437.001i	−0.326954	−	0.188767i
$176$	−94.4205	−	54.5137i	−0.0404387	−	0.0233473i
$177$		−	435.286i		−	0.184848i
$178$	−189.819	+	328.776i	−0.0799300	+	0.138443i
$179$	−2029.85	−	3515.80i	−0.847586	−	1.46806i	−0.883357	−	0.468701i	$-0.844722\pi$
$179$	−2029.85	−	3515.80i	−0.847586	−	1.46806i	0.0357711	−	0.999360i	$-0.488611\pi$
$180$	11.7683	−	6.79440i	0.00487308	−	0.00281347i
$181$	245.179			0.100685			0.0503426	−	0.998732i	$-0.483969\pi$
$181$	245.179			0.100685			0.0503426	+	0.998732i	$0.483969\pi$
$182$	435.292	−	491.052i	0.177286	−	0.199996i
$183$	−267.679			−0.108128
$184$	957.275	−	552.683i	0.383539	−	0.221437i
$185$	−5.68924	−	9.85406i	−0.00226098	−	0.00391613i
$186$	157.666	−	273.085i	0.0621538	−	0.107653i
$187$			811.574i			0.317370i
$188$	2155.92	+	1244.72i	0.836366	+	0.482876i
$189$	−163.679	−	94.5000i	−0.0629941	−	0.0363696i
$190$			61.9836i			0.0236672i
$191$	2013.74	−	3487.89i	0.762874	−	1.32134i	−0.178490	−	0.983942i	$-0.557121\pi$
$191$	2013.74	−	3487.89i	0.762874	−	1.32134i	0.941363	−	0.337394i	$-0.109546\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	443.433	−	256.016i	0.165383	−	0.0954842i	−0.415024	−	0.909811i	$-0.636227\pi$
$193$	443.433	−	256.016i	0.165383	−	0.0954842i	0.580407	+	0.814326i	$0.302893\pi$
$194$	2407.90			0.891118
$195$	10.6323	−	52.0023i	0.00390458	−	0.0190972i
$196$	196.000			0.0714286
$197$	649.944	−	375.245i	0.235059	−	0.135711i	−0.377845	−	0.925869i	$-0.623335\pi$
$197$	649.944	−	375.245i	0.235059	−	0.135711i	0.612904	+	0.790158i	$0.290001\pi$
$198$	61.3279	+	106.223i	0.0220120	+	0.0381260i
$199$	−233.170	+	403.863i	−0.0830604	+	0.143865i	−0.904563	−	0.426340i	$-0.859803\pi$
$199$	−233.170	+	403.863i	−0.0830604	+	0.143865i	0.821503	+	0.570205i	$0.193136\pi$
$200$		−	998.860i		−	0.353150i
$201$	1141.75	+	659.190i	0.400661	+	0.231322i
$202$	−716.374	−	413.599i	−0.249524	−	0.144063i
$203$			1838.67i			0.635710i
$204$	714.601	−	1237.73i	0.245255	−	0.424795i
$205$	−10.8068	−	18.7179i	−0.00368185	−	0.00637714i
$206$	−1830.21	+	1056.67i	−0.619013	+	0.357387i
$207$	−1243.54			−0.417545
$208$	734.754	+	150.226i	0.244933	+	0.0500785i
$209$	−559.478			−0.185167
$210$	13.7296	−	7.92680i	0.00451159	−	0.00260477i
$211$	2218.31	+	3842.22i	0.723766	+	1.25360i	0.959480	+	0.281776i	$0.0909236\pi$
$211$	2218.31	+	3842.22i	0.723766	+	1.25360i	−0.235715	+	0.971822i	$0.575743\pi$
$212$	−632.335	+	1095.24i	−0.204854	+	0.354817i
$213$		−	2315.72i		−	0.744933i
$214$	−3132.07	−	1808.30i	−1.00048	−	0.577630i
$215$	136.530	+	78.8254i	0.0433081	+	0.0250040i
$216$		−	216.000i		−	0.0680414i
$217$	183.943	−	318.599i	0.0575432	−	0.0996677i
$218$	852.869	+	1477.21i	0.264971	+	0.458942i
$219$	−383.063	+	221.162i	−0.118196	+	0.0682408i
$220$	−10.2886			−0.00315297
$221$	−1766.24	−	5295.71i	−0.537602	−	1.61189i
$222$	−180.866			−0.0546798
$223$	−3976.39	+	2295.77i	−1.19407	+	0.689399i	−0.959228	−	0.282633i	$-0.908792\pi$
$223$	−3976.39	+	2295.77i	−1.19407	+	0.689399i	−0.234847	+	0.972032i	$0.575459\pi$
$224$	112.000	+	193.990i	0.0334077	+	0.0578638i
$225$	−561.859	+	973.168i	−0.166477	+	0.288346i
$226$			175.433i			0.0516354i
$227$	−1344.26	−	776.110i	−0.393048	−	0.226926i	0.290432	−	0.956896i	$-0.406201\pi$
$227$	−1344.26	−	776.110i	−0.393048	−	0.226926i	−0.683480	+	0.729969i	$0.739534\pi$
$228$	853.256	+	492.628i	0.247843	+	0.143092i
$229$			2437.11i			0.703269i	0.936137	+	0.351634i	$0.114374\pi$
$229$			2437.11i			0.703269i	−0.936137	+	0.351634i	$0.885626\pi$
$230$	52.1549	−	90.3349i	0.0149521	−	0.0258979i
$231$	71.5492	+	123.927i	0.0203792	+	0.0352978i
$232$	−1819.81	+	1050.67i	−0.514984	+	0.297326i
$233$	6613.18			1.85942			0.929708	−	0.368297i	$-0.120059\pi$
$233$	6613.18			1.85942			0.929708	+	0.368297i	$0.120059\pi$
$234$	−631.353	−	559.662i	−0.176380	−	0.156351i
$235$	234.921			0.0652108
$236$	502.625	−	290.191i	0.138636	−	0.0800415i
$237$	−368.402	−	638.090i	−0.100972	−	0.174888i
$238$	833.702	−	1444.01i	0.227062	−	0.393284i
$239$		−	3845.30i		−	1.04072i	−0.853947	−	0.520360i	$-0.825798\pi$
$239$		−	3845.30i		−	1.04072i	0.853947	−	0.520360i	$-0.174202\pi$
$240$	15.6910	+	9.05921i	0.00422021	+	0.00243654i
$241$	−4015.72	−	2318.48i	−1.07334	−	0.619695i	−0.144250	−	0.989541i	$-0.546077\pi$
$241$	−4015.72	−	2318.48i	−1.07334	−	0.619695i	−0.929093	+	0.369847i	$0.879410\pi$
$242$			2569.13i			0.682439i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−178.453	−	309.089i	−0.0468208	−	0.0810960i
$245$	16.0179	−	9.24794i	0.00417692	−	0.00241155i
$246$	−343.557			−0.0890422
$247$	3650.73	−	1217.60i	0.940446	−	0.313660i
$248$	420.441			0.107653
$249$	216.981	−	125.274i	0.0552232	−	0.0318832i
$250$	−94.3129	−	163.355i	−0.0238595	−	0.0413259i
$251$	−1144.04	+	1981.54i	−0.287695	+	0.498302i	−0.973259	−	0.229710i	$-0.926222\pi$
$251$	−1144.04	+	1981.54i	−0.287695	+	0.498302i	0.685564	+	0.728012i	$0.259556\pi$
$252$		−	252.000i		−	0.0629941i
$253$	815.384	+	470.762i	0.202620	+	0.116982i
$254$	−272.896	−	157.557i	−0.0674135	−	0.0389212i
$255$		−	134.869i		−	0.0331209i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−3299.30	−	5714.56i	−0.800797	−	1.38702i	−0.919092	−	0.394043i	$-0.871076\pi$
$257$	−3299.30	−	5714.56i	−0.800797	−	1.38702i	0.118295	−	0.992978i	$-0.462257\pi$
$258$	2170.20	−	1252.96i	0.523685	−	0.302349i
$259$	−211.010			−0.0506237
$260$	67.1352	−	22.3911i	0.0160137	−	0.00534091i
$261$	2364.00			0.560643
$262$	−629.645	+	363.525i	−0.148472	+	0.0857201i
$263$	1071.28	+	1855.51i	0.251170	+	0.435040i	0.963848	−	0.266452i	$-0.0858512\pi$
$263$	1071.28	+	1855.51i	0.251170	+	0.435040i	−0.712678	+	0.701491i	$0.752518\pi$
$264$	−81.7705	+	141.631i	−0.0190630	+	0.0330181i
$265$			119.343i			0.0276648i
$266$	995.466	+	574.732i	0.229458	+	0.132478i
$267$	493.165	+	284.729i	0.113038	+	0.0652626i
$268$			1757.84i			0.400661i
$269$	2318.93	−	4016.50i	0.525605	−	0.910374i	−0.473951	−	0.880551i	$-0.657173\pi$
$269$	2318.93	−	4016.50i	0.525605	−	0.910374i	0.999555	−	0.0298224i	$-0.00949416\pi$
$270$	−10.1916	−	17.6524i	−0.00229719	−	0.00397885i
$271$	−5012.46	+	2893.94i	−1.12356	+	0.648688i	−0.942308	−	0.334748i	$-0.891349\pi$
$271$	−5012.46	+	2893.94i	−1.12356	+	0.648688i	−0.181253	+	0.983436i	$0.558015\pi$
$272$	1905.60			0.424795
$273$	−736.579	−	652.939i	−0.163296	−	0.144753i
$274$	1761.64			0.388411
$275$	736.819	−	425.403i	0.161570	−	0.0932827i
$276$	−829.024	−	1435.91i	−0.180802	−	0.313159i
$277$	−1813.31	+	3140.75i	−0.393327	+	0.681262i	−0.992886	−	0.119068i	$-0.962009\pi$
$277$	−1813.31	+	3140.75i	−0.393327	+	0.681262i	0.599559	+	0.800330i	$0.295343\pi$
$278$			3630.85i			0.783323i
$279$	−409.627	−	236.498i	−0.0878987	−	0.0507483i
$280$	18.3062	+	10.5691i	0.00390715	+	0.00225580i
$281$			4099.10i			0.870220i	0.900377	+	0.435110i	$0.143290\pi$
$281$			4099.10i			0.870220i	−0.900377	+	0.435110i	$0.856710\pi$
$282$	1867.08	−	3233.88i	0.394267	−	0.682890i
$283$	2943.68	+	5098.61i	0.618317	+	1.07096i	0.989793	+	0.142514i	$0.0455186\pi$
$283$	2943.68	+	5098.61i	0.618317	+	1.07096i	−0.371476	+	0.928443i	$0.621148\pi$
$284$	2673.96	−	1543.81i	0.558699	−	0.322565i
$285$	92.9753			0.0193242
$286$	202.107	+	605.978i	0.0417862	+	0.125288i
$287$	−400.816			−0.0824371
$288$	249.415	−	144.000i	0.0510310	−	0.0294628i
$289$	−4635.93	−	8029.67i	−0.943605	−	1.63437i
$290$	−99.1479	+	171.729i	−0.0200764	+	0.0347734i
$291$		−	3611.84i		−	0.727595i
$292$	−510.751	−	294.882i	−0.102361	−	0.0590982i
$293$	−338.207	−	195.264i	−0.0674343	−	0.0389332i	0.465904	−	0.884835i	$-0.345729\pi$
$293$	−338.207	−	195.264i	−0.0674343	−	0.0389332i	−0.533338	+	0.845902i	$0.679063\pi$
$294$		−	294.000i		−	0.0583212i
$295$	27.3843	−	47.4311i	0.00540467	−	0.00936116i
$296$	−120.577	−	208.846i	−0.0236771	−	0.0410099i
$297$	159.335	−	91.9918i	0.0311297	−	0.0179728i
$298$	−3351.80			−0.651558
$299$	−6345.10	−	1297.31i	−1.22725	−	0.250920i
$300$	−1498.29			−0.288346
$301$	2531.90	−	1461.79i	0.484838	−	0.279921i
$302$	−1982.76	−	3434.24i	−0.377798	−	0.654365i
$303$	−620.398	+	1074.56i	−0.117627	+	0.203736i
$304$			1313.67i			0.247843i
$305$	−29.1677	−	16.8400i	−0.00547587	−	0.00316150i
$306$	−1856.59	−	1071.90i	−0.346844	−	0.200250i
$307$			2492.28i			0.463329i	0.972796	+	0.231664i	$0.0744171\pi$
$307$			2492.28i			0.463329i	−0.972796	+	0.231664i	$0.925583\pi$
$308$	−95.3989	+	165.236i	−0.0176489	+	0.0305688i
$309$	1585.01	+	2745.31i	0.291805	+	0.505422i
$310$	34.3601	−	19.8378i	0.00629524	−	0.00363456i
$311$	6196.74			1.12986			0.564928	−	0.825140i	$-0.308904\pi$
$311$	6196.74			1.12986			0.564928	+	0.825140i	$0.308904\pi$
$312$	225.340	−	1102.13i	0.0408889	−	0.199987i
$313$	−93.5741			−0.0168981			−0.00844907	−	0.999964i	$-0.502689\pi$
$313$	−93.5741			−0.0168981			−0.00844907	+	0.999964i	$0.502689\pi$
$314$	−4155.16	+	2398.98i	−0.746781	+	0.431154i
$315$	−11.8902	−	20.5944i	−0.00212678	−	0.00368370i
$316$	491.202	−	850.787i	0.0874439	−	0.151457i
$317$			3937.88i			0.697707i	0.937177	+	0.348854i	$0.113429\pi$
$317$			3937.88i			0.697707i	−0.937177	+	0.348854i	$0.886571\pi$
$318$	1642.86	+	948.503i	0.289707	+	0.167262i
$319$	−1550.07	−	894.932i	−0.272060	−	0.157074i
$320$			24.1579i			0.00422021i
$321$	−2712.45	+	4698.10i	−0.471633	+	0.816892i
$322$	−967.195	−	1675.23i	−0.167390	−	0.289928i
$323$	8468.59	−	4889.34i	1.45884	−	0.842261i
$324$	−324.000			−0.0555556
$325$	−3882.11	+	4379.40i	−0.662587	+	0.747463i
$326$	−7514.86			−1.27672
$327$	2215.82	−	1279.30i	0.374725	−	0.216348i
$328$	−229.038	−	396.705i	−0.0385564	−	0.0667817i
$329$	2178.26	−	3772.86i	0.365020	−	0.632233i
$330$			15.4328i			0.00257439i
$331$	−3534.66	−	2040.74i	−0.586956	−	0.338879i	0.176937	−	0.984222i	$-0.443381\pi$
$331$	−3534.66	−	2040.74i	−0.586956	−	0.338879i	−0.763893	+	0.645343i	$0.776715\pi$
$332$	289.307	+	167.032i	0.0478247	+	0.0276116i
$333$			271.299i			0.0446459i
$334$	−3426.31	+	5934.54i	−0.561315	+	0.972226i
$335$	82.9408	+	143.658i	0.0135270	+	0.0234294i
$336$	290.985	−	168.000i	0.0472456	−	0.0272772i
$337$	991.003			0.160188			0.0800940	−	0.996787i	$-0.474478\pi$
$337$	991.003			0.160188			0.0800940	+	0.996787i	$0.474478\pi$
$338$	−2637.59	−	3514.30i	−0.424456	−	0.565541i
$339$	263.149			0.0421602
$340$	155.734	−	89.9128i	0.0248407	−	0.0143418i
$341$	179.061	+	310.143i	0.0284361	+	0.0492527i
$342$	738.942	−	1279.88i	0.116834	−	0.202363i
$343$		−	343.000i		−	0.0539949i
$344$	2893.60	+	1670.62i	0.453524	+	0.261842i
$345$	−135.502	−	78.2323i	−0.0211455	−	0.0122084i
$346$		−	2005.76i		−	0.311649i
$347$	2725.32	−	4720.39i	0.421622	−	0.730270i	−0.574477	−	0.818521i	$-0.694794\pi$
$347$	2725.32	−	4720.39i	0.421622	−	0.730270i	0.996098	+	0.0882509i	$0.0281277\pi$
$348$	1576.00	+	2729.71i	0.242766	+	0.420482i
$349$	3104.01	−	1792.10i	0.476086	−	0.274868i	−0.242698	−	0.970102i	$-0.578032\pi$
$349$	3104.01	−	1792.10i	0.476086	−	0.274868i	0.718784	+	0.695233i	$0.244699\pi$
$350$	−1748.01			−0.266957
$351$	−839.493	+	947.030i	−0.127660	+	0.144013i
$352$	−218.055			−0.0330181
$353$	8614.53	−	4973.60i	1.29888	−	0.749910i	0.318671	−	0.947866i	$-0.396764\pi$
$353$	8614.53	−	4973.60i	1.29888	−	0.749910i	0.980211	+	0.197956i	$0.0634303\pi$
$354$	−435.286	−	753.937i	−0.0653536	−	0.113196i
$355$	145.685	−	252.333i	0.0217807	−	0.0377252i
$356$			759.277i			0.113038i
$357$	−2166.02	−	1250.55i	−0.321115	−	0.185396i
$358$	−7031.59	−	4059.69i	−1.03808	−	0.599334i
$359$		−	4837.70i		−	0.711208i	−0.934637	−	0.355604i	$-0.884275\pi$
$359$		−	4837.70i		−	0.711208i	0.934637	−	0.355604i	$-0.115725\pi$
$360$	13.5888	−	23.5365i	0.00198943	−	0.00344579i
$361$	−58.9150	−	102.044i	−0.00858944	−	0.0148773i
$362$	424.663	−	245.179i	0.0616569	−	0.0355976i
$363$	3853.70			0.557209
$364$	262.896	−	1285.82i	0.0378558	−	0.185152i
$365$	−55.6542			−0.00798102
$366$	−463.634	+	267.679i	−0.0662146	+	0.0382290i
$367$	−2805.38	−	4859.06i	−0.399018	−	0.691119i	0.594587	−	0.804031i	$-0.297316\pi$
$367$	−2805.38	−	4859.06i	−0.399018	−	0.691119i	−0.993605	+	0.112912i	$0.963982\pi$
$368$	1105.37	−	1914.55i	0.156579	−	0.271203i
$369$			515.335i			0.0727027i
$370$	−19.7081	−	11.3785i	−0.00276912	−	0.00159875i
$371$	1916.66	+	1106.59i	0.268216	+	0.154855i
$372$		−	630.662i		−	0.0878987i
$373$	−2065.45	+	3577.47i	−0.286716	+	0.496607i	−0.973024	−	0.230704i	$-0.925897\pi$
$373$	−2065.45	+	3577.47i	−0.286716	+	0.496607i	0.686308	+	0.727311i	$0.259230\pi$
$374$	811.574	+	1405.69i	0.112207	+	0.194349i
$375$	−245.032	+	141.469i	−0.0337424	+	0.0194812i
$376$	4978.89			0.682890
$377$	12062.2	+	2466.22i	1.64784	+	0.336914i
$378$	−378.000			−0.0514344
$379$	−10291.6	+	5941.86i	−1.39484	+	0.805311i	−0.993846	−	0.110770i	$-0.964668\pi$
$379$	−10291.6	+	5941.86i	−1.39484	+	0.805311i	−0.400994	+	0.916081i	$0.631335\pi$
$380$	61.9836	+	107.359i	0.00836760	+	0.0144931i
$381$	−236.335	+	409.344i	−0.0317790	+	0.0550429i
$382$		−	8054.95i		−	1.07887i
$383$	−766.977	−	442.814i	−0.102326	−	0.0590777i	0.447964	−	0.894052i	$-0.352149\pi$
$383$	−766.977	−	442.814i	−0.102326	−	0.0590777i	−0.550289	+	0.834974i	$0.685483\pi$
$384$	332.554	+	192.000i	0.0441942	+	0.0255155i
$385$			18.0050i			0.00238342i
$386$	512.032	−	886.866i	0.0675175	−	0.116944i
$387$	−1879.45	−	3255.30i	−0.246867	−	0.427587i
$388$	4170.60	−	2407.90i	0.545696	−	0.315058i
$389$	8013.20			1.04444			0.522218	−	0.852812i	$-0.325105\pi$
$389$	8013.20			1.04444			0.522218	+	0.852812i	$0.325105\pi$
$390$	−33.5866	−	100.703i	−0.00436083	−	0.0130751i
$391$	−16456.2			−2.12845
$392$	339.482	−	196.000i	0.0437409	−	0.0252538i
$393$	545.288	+	944.467i	0.0699902	+	0.121227i
$394$	750.491	−	1299.89i	0.0959624	−	0.166212i
$395$		−	92.7063i		−	0.0118090i
$396$	212.446	+	122.656i	0.0269591	+	0.0155649i
$397$	12420.4	+	7170.92i	1.57018	+	0.906544i	0.996146	+	0.0877136i	$0.0279560\pi$
$397$	12420.4	+	7170.92i	1.57018	+	0.906544i	0.574035	+	0.818831i	$0.305377\pi$
$398$			932.682i			0.117465i
$399$	862.099	−	1493.20i	0.108168	−	0.187352i
$400$	−998.860	−	1730.08i	−0.124858	−	0.216260i
$401$	10169.2	−	5871.20i	1.26640	−	0.731156i	0.292095	−	0.956389i	$-0.405648\pi$
$401$	10169.2	−	5871.20i	1.26640	−	0.731156i	0.974305	+	0.225233i	$0.0723144\pi$
$402$	2636.76			0.327139
$403$	−1843.38	−	1634.06i	−0.227855	−	0.201981i
$404$	−1654.40			−0.203736
$405$	−26.4786	+	15.2874i	−0.00324872	+	0.00187565i
$406$	1838.67	+	3184.66i	0.224757	+	0.389291i
$407$	102.705	−	177.890i	0.0125083	−	0.0216651i
$408$		−	2858.41i		−	0.346844i
$409$	−6984.03	−	4032.23i	−0.844347	−	0.487484i	0.0143926	−	0.999896i	$-0.495419\pi$
$409$	−6984.03	−	4032.23i	−0.844347	−	0.487484i	−0.858739	+	0.512413i	$0.828752\pi$
$410$	−37.4358	−	21.6136i	−0.00450932	−	0.00260346i
$411$		−	2642.46i		−	0.317136i
$412$	−2113.34	+	3660.42i	−0.252711	+	0.437708i
$413$	−507.834	−	879.594i	−0.0605057	−	0.104799i
$414$	−2153.87	+	1243.54i	−0.255693	+	0.147624i
$415$	31.5245			0.00372886
$416$	1422.86	−	474.555i	0.167696	−	0.0559302i
$417$	5446.27			0.639580
$418$	−969.045	+	559.478i	−0.113391	+	0.0654664i
$419$	6903.75	+	11957.7i	0.804941	+	1.39420i	0.916331	+	0.400423i	$0.131137\pi$
$419$	6903.75	+	11957.7i	0.804941	+	1.39420i	−0.111389	+	0.993777i	$0.535530\pi$
$420$	15.8536	−	27.4593i	0.00184185	−	0.00319018i
$421$			10101.5i			1.16940i	0.811249	+	0.584701i	$0.198788\pi$
$421$			10101.5i			1.16940i	−0.811249	+	0.584701i	$0.801212\pi$
$422$	7684.44	+	4436.61i	0.886428	+	0.511779i
$423$	−4850.82	−	2800.62i	−0.557577	−	0.321917i
$424$			2529.34i			0.289707i
$425$	−7435.28	+	12878.3i	−0.848621	+	1.46986i
$426$	−2315.72	−	4010.95i	−0.263373	−	0.456176i
$427$	−540.906	+	312.292i	−0.0613028	+	0.0353932i
$428$	−7233.20			−0.816892
$429$	908.968	−	303.161i	0.102297	−	0.0341183i
$430$	315.302			0.0353609
$431$	−8397.87	+	4848.52i	−0.938542	+	0.541867i	−0.889503	−	0.456930i	$-0.848949\pi$
$431$	−8397.87	+	4848.52i	−0.938542	+	0.541867i	−0.0490387	+	0.998797i	$0.515616\pi$
$432$	−216.000	−	374.123i	−0.0240563	−	0.0416667i
$433$	−3640.18	+	6304.98i	−0.404009	+	0.699765i	−0.994206	−	0.107495i	$-0.965717\pi$
$433$	−3640.18	+	6304.98i	−0.404009	+	0.699765i	0.590196	+	0.807260i	$0.299050\pi$
$434$		−	735.773i		−	0.0813784i
$435$	257.594	+	148.722i	0.0283924	+	0.0163923i
$436$	2954.42	+	1705.74i	0.324521	+	0.187362i
$437$		−	11344.5i		−	1.24183i
$438$	−442.324	+	766.127i	−0.0482535	+	0.0835775i
$439$	6060.21	+	10496.6i	0.658857	+	1.14117i	0.980912	+	0.194453i	$0.0622931\pi$
$439$	6060.21	+	10496.6i	0.658857	+	1.14117i	−0.322055	+	0.946721i	$0.604374\pi$
$440$	−17.8203	+	10.2886i	−0.00193079	+	0.00111474i
$441$	−441.000			−0.0476190
$442$	−8354.92	−	7406.20i	−0.899102	−	0.797007i
$443$	−889.789			−0.0954292			−0.0477146	−	0.998861i	$-0.515194\pi$
$443$	−889.789			−0.0954292			−0.0477146	+	0.998861i	$0.515194\pi$
$444$	−313.269	+	180.866i	−0.0334844	+	0.0193322i
$445$	35.8252	+	62.0511i	0.00381636	+	0.00661012i
$446$	−4591.54	+	7952.78i	−0.487479	+	0.844338i
$447$			5027.69i			0.531995i
$448$	387.979	+	224.000i	0.0409159	+	0.0236228i
$449$	−4271.88	−	2466.37i	−0.449003	−	0.259232i	0.258406	−	0.966036i	$-0.416803\pi$
$449$	−4271.88	−	2466.37i	−0.449003	−	0.259232i	−0.707409	+	0.706804i	$0.750136\pi$
$450$			2247.44i			0.235434i
$451$	195.089	−	337.904i	0.0203689	−	0.0352800i
$452$	175.433	+	303.858i	0.0182559	+	0.0316201i
$453$	−5151.36	+	2974.14i	−0.534287	+	0.308471i
$454$	−3104.44			−0.320922
$455$	−39.1844	−	117.487i	−0.00403735	−	0.0121052i
$456$	1970.51			0.202363
$457$	16447.2	−	9495.77i	1.68351	−	0.971977i	0.724218	−	0.689572i	$-0.242201\pi$
$457$	16447.2	−	9495.77i	1.68351	−	0.971977i	0.959295	−	0.282405i	$-0.0911322\pi$
$458$	2437.11	+	4221.19i	0.248643	+	0.430662i
$459$	−1607.85	+	2784.88i	−0.163504	+	0.283197i
$460$		−	208.619i		−	0.0211455i
$461$	−12816.2	−	7399.41i	−1.29481	−	0.747560i	−0.315309	−	0.948989i	$-0.602108\pi$
$461$	−12816.2	−	7399.41i	−1.29481	−	0.747560i	−0.979503	+	0.201429i	$0.935441\pi$
$462$	247.854	+	143.098i	0.0249593	+	0.0144103i
$463$			16651.4i			1.67140i	0.549186	+	0.835700i	$0.314938\pi$
$463$			16651.4i			1.67140i	−0.549186	+	0.835700i	$0.685062\pi$
$464$	−2101.33	+	3639.61i	−0.210241	+	0.364148i
$465$	−29.7568	−	51.5402i	−0.00296761	−	0.00514004i
$466$	11454.4	−	6613.18i	1.13866	−	0.657403i
$467$	4402.63			0.436251			0.218126	−	0.975921i	$-0.430006\pi$
$467$	4402.63			0.436251			0.218126	+	0.975921i	$0.430006\pi$
$468$	−1653.20	−	338.009i	−0.163289	−	0.0333857i
$469$	3076.22			0.302871
$470$	406.895	−	234.921i	0.0399333	−	0.0230555i
$471$	3598.48	+	6232.74i	0.352036	+	0.609744i
$472$	580.381	−	1005.25i	0.0565979	−	0.0980304i
$473$			2845.99i			0.276657i
$474$	−1276.18	−	736.803i	−0.123664	−	0.0713976i
$475$	−8877.96	−	5125.69i	−0.857576	−	0.495122i
$476$		−	3334.81i		−	0.321115i
$477$	1422.75	−	2464.28i	0.136569	−	0.236545i
$478$	−3845.30	−	6660.26i	−0.367950	−	0.637308i
$479$	−808.928	+	467.035i	−0.0771626	+	0.0445498i	−0.538085	−	0.842891i	$-0.680852\pi$
$479$	−808.928	+	467.035i	−0.0771626	+	0.0445498i	0.460922	+	0.887441i	$0.347519\pi$
$480$	36.2368			0.00344579
$481$	−283.030	+	1384.29i	−0.0268296	+	0.131223i
$482$	−9273.92			−0.876380
$483$	−2512.85	+	1450.79i	−0.236726	+	0.136674i
$484$	2569.13	+	4449.87i	0.241278	+	0.417907i
$485$	227.225	−	393.566i	0.0212737	−	0.0368472i
$486$			486.000i			0.0453609i
$487$	16095.1	+	9292.53i	1.49762	+	0.864650i	0.999996	−	0.00274352i	$-0.000873290\pi$
$487$	16095.1	+	9292.53i	1.49762	+	0.864650i	0.497622	+	0.867394i	$0.334207\pi$
$488$	−618.179	−	356.906i	−0.0573435	−	0.0331073i
$489$			11272.3i			1.04244i
$490$	18.4959	−	32.0358i	0.00170522	−	0.00295353i
$491$	6768.62	+	11723.6i	0.622125	+	1.07755i	0.989089	+	0.147318i	$0.0470640\pi$
$491$	6768.62	+	11723.6i	0.622125	+	1.07755i	−0.366964	+	0.930235i	$0.619603\pi$
$492$	−595.058	+	343.557i	−0.0545270	+	0.0314812i
$493$	31283.7			2.85790
$494$	5105.65	−	5759.67i	0.465008	−	0.524574i
$495$	23.1492			0.00210198
$496$	728.226	−	420.441i	0.0659240	−	0.0380612i
$497$	−2701.68	−	4679.44i	−0.243836	−	0.422337i
$498$	250.548	−	433.961i	0.0225448	−	0.0390487i
$499$			123.810i			0.0111072i	0.999985	+	0.00555360i	$0.00176777\pi$
$499$			123.810i			0.0111072i	−0.999985	+	0.00555360i	$0.998232\pi$
$500$	−326.710	−	188.626i	−0.0292218	−	0.0168712i
$501$	8901.81	+	5139.46i	0.793819	+	0.458312i
$502$			4576.17i			0.406862i
$503$	2601.41	−	4505.77i	0.230599	−	0.399408i	−0.727386	−	0.686229i	$-0.759265\pi$
$503$	2601.41	−	4505.77i	0.230599	−	0.399408i	0.957984	+	0.286820i	$0.0925982\pi$
$504$	−252.000	−	436.477i	−0.0222718	−	0.0385758i
$505$	−135.204	+	78.0600i	−0.0119138	+	0.00687846i
$506$	1883.05			0.165438
$507$	−5271.46	+	3956.39i	−0.461763	+	0.346567i
$508$	−630.226			−0.0550429
$509$	1991.85	−	1149.99i	0.173452	−	0.100142i	−0.410761	−	0.911743i	$-0.634737\pi$
$509$	1991.85	−	1149.99i	0.173452	−	0.100142i	0.584212	+	0.811601i	$0.301403\pi$
$510$	−134.869	−	233.600i	−0.0117100	−	0.0202823i
$511$	−516.044	+	893.815i	−0.0446741	+	0.0773778i
$512$			512.000i			0.0441942i
$513$	−1919.83	−	1108.41i	−0.165229	−	0.0953949i
$514$	−11429.1	−	6598.61i	−0.980772	−	0.566249i
$515$			398.858i			0.0341278i
$516$	2505.93	−	4340.40i	0.213793	−	0.370301i
$517$	2120.45	+	3672.73i	0.180382	+	0.312430i
$518$	−365.480	+	211.010i	−0.0310006	+	0.0178982i
$519$	−3008.65			−0.254460
$520$	93.8906	−	105.918i	0.00791803	−	0.00893231i
$521$	7461.28			0.627418			0.313709	−	0.949519i	$-0.398428\pi$
$521$	7461.28			0.627418			0.313709	+	0.949519i	$0.398428\pi$
$522$	4094.57	−	2364.00i	0.343322	−	0.198217i
$523$	3076.05	+	5327.87i	0.257182	+	0.445452i	0.965486	−	0.260455i	$-0.0838727\pi$
$523$	3076.05	+	5327.87i	0.257182	+	0.445452i	−0.708304	+	0.705908i	$0.750539\pi$
$524$	−727.051	+	1259.29i	−0.0606133	+	0.104985i
$525$			2622.01i			0.217969i
$526$	3711.01	+	2142.56i	0.307620	+	0.177604i
$527$	−5420.74	−	3129.67i	−0.448067	−	0.258692i
$528$			327.082i			0.0269591i
$529$	−3462.07	+	5996.49i	−0.284546	+	0.492849i
$530$	119.343	+	206.708i	0.00978098	+	0.0169412i
$531$	−1130.91	+	652.929i	−0.0924240	+	0.0533610i
$532$	2298.93			0.187352
$533$	−537.618	+	2629.48i	−0.0436901	+	0.213687i
$534$	1138.92			0.0922953
$535$	−591.126	+	341.287i	−0.0477693	+	0.0275796i
$536$	1757.84	+	3044.67i	0.141655	+	0.245354i
$537$	−6089.54	+	10547.4i	−0.489354	+	0.847586i
$538$		−	9275.72i		−	0.743317i
$539$	289.163	+	166.948i	0.0231078	+	0.0133413i
$540$	−35.3048	−	20.3832i	−0.00281347	−	0.00162436i
$541$			3738.39i			0.297091i	0.988906	+	0.148545i	$0.0474591\pi$
$541$			3738.39i			0.297091i	−0.988906	+	0.148545i	$0.952541\pi$
$542$	−5787.89	+	10024.9i	−0.458692	+	0.794478i
$543$	−367.769	−	636.994i	−0.0290653	−	0.0503426i
$544$	3300.60	−	1905.60i	0.260133	−	0.150188i
$545$	321.930			0.0253027
$546$	−1928.73	−	394.344i	−0.151176	−	0.0309091i
$547$	−15484.8			−1.21039			−0.605193	−	0.796079i	$-0.706904\pi$
$547$	−15484.8			−1.21039			−0.605193	+	0.796079i	$0.706904\pi$
$548$	3051.25	−	1761.64i	0.237852	−	0.137324i
$549$	401.519	+	695.451i	0.0312139	+	0.0540640i
$550$	850.805	−	1473.64i	0.0659608	−	0.114248i
$551$			21566.1i			1.66742i
$552$	−2871.82	−	1658.05i	−0.221437	−	0.127846i
$553$	−1488.88	−	859.604i	−0.114491	−	0.0661014i
$554$			7253.26i			0.556248i
$555$	−17.0677	+	29.5622i	−0.00130538	+	0.00226098i
$556$	3630.85	+	6288.81i	0.276946	+	0.479685i
$557$	−10454.1	+	6035.67i	−0.795249	+	0.459137i	−0.841807	−	0.539778i	$-0.818508\pi$
$557$	−10454.1	+	6035.67i	−0.795249	+	0.459137i	0.0465581	+	0.998916i	$0.485175\pi$
$558$	−945.993			−0.0717690
$559$	−6193.75	−	18570.7i	−0.468636	−	1.40511i
$560$	42.2763			0.00319018
$561$	2108.53	−	1217.36i	0.158685	−	0.0916168i
$562$	4099.10	+	7099.85i	0.307669	+	0.532899i
$563$	−6628.13	+	11480.3i	−0.496168	+	0.859388i	−0.999990	−	0.00441930i	$-0.998593\pi$
$563$	−6628.13	+	11480.3i	−0.496168	+	0.859388i	0.503822	+	0.863807i	$0.331927\pi$
$564$		−	7468.33i		−	0.557577i
$565$	28.6741	+	16.5550i	0.00213510	+	0.00123270i
$566$	10197.2	+	5887.36i	0.757281	+	0.437216i
$567$			567.000i			0.0419961i
$568$	3087.63	−	5347.93i	0.228088	−	0.395060i
$569$	3157.44	+	5468.84i	0.232630	+	0.402928i	0.958581	−	0.284819i	$-0.0919334\pi$
$569$	3157.44	+	5468.84i	0.232630	+	0.402928i	−0.725951	+	0.687746i	$0.758600\pi$
$570$	161.038	−	92.9753i	0.0118336	−	0.00683212i
$571$	4761.88			0.348999			0.174500	−	0.984657i	$-0.444169\pi$
$571$	4761.88			0.348999			0.174500	+	0.984657i	$0.444169\pi$
$572$	956.038	+	847.478i	0.0698846	+	0.0619490i
$573$	−12082.4			−0.880891
$574$	−694.235	+	400.816i	−0.0504822	+	0.0291459i
$575$	8625.83	+	14940.4i	0.625603	+	1.08358i
$576$	288.000	−	498.831i	0.0208333	−	0.0360844i
$577$			6750.69i			0.487062i	0.969893	+	0.243531i	$0.0783058\pi$
$577$			6750.69i			0.487062i	−0.969893	+	0.243531i	$0.921694\pi$
$578$	−16059.3	−	9271.87i	−1.15568	−	0.667230i
$579$	−1330.30	−	768.048i	−0.0954842	−	0.0551278i
$580$			396.592i			0.0283924i
$581$	292.306	−	506.288i	0.0208724	−	0.0361521i
$582$	−3611.84	−	6255.90i	−0.257244	−	0.445559i
$583$	−1865.79	+	1077.22i	−0.132544	+	0.0765244i
$584$	−1179.53			−0.0835775
$585$	−151.054	+	50.3799i	−0.0106758	+	0.00356061i
$586$	−781.055			−0.0550598
$587$	7317.45	−	4224.73i	0.514520	−	0.297058i	−0.220170	−	0.975462i	$-0.570661\pi$
$587$	7317.45	−	4224.73i	0.514520	−	0.297058i	0.734690	+	0.678403i	$0.237328\pi$
$588$	−294.000	−	509.223i	−0.0206197	−	0.0357143i
$589$	2157.51	−	3736.92i	0.150932	−	0.261421i
$590$		−	109.537i		−	0.00764336i
$591$	−1949.83	−	1125.74i	−0.135711	−	0.0783530i
$592$	−417.692	−	241.155i	−0.0289984	−	0.0167422i
$593$			18850.8i			1.30541i	0.757611	+	0.652707i	$0.226367\pi$
$593$			18850.8i			1.30541i	−0.757611	+	0.652707i	$0.773633\pi$
$594$	183.984	−	318.669i	0.0127087	−	0.0220120i
$595$	−157.347	−	272.534i	−0.0108414	−	0.0187778i
$596$	−5805.48	+	3351.80i	−0.398996	+	0.230361i
$597$	1399.02			0.0959099
$598$	−12287.3	+	4098.10i	−0.840245	+	0.280240i
$599$	−5871.99			−0.400539			−0.200270	−	0.979741i	$-0.564182\pi$
$599$	−5871.99			−0.400539			−0.200270	+	0.979741i	$0.564182\pi$
$600$	−2595.11	+	1498.29i	−0.176575	+	0.101946i
$601$	10591.4	+	18344.8i	0.718852	+	1.24509i	0.961455	+	0.274963i	$0.0886656\pi$
$601$	10591.4	+	18344.8i	0.718852	+	1.24509i	−0.242602	+	0.970126i	$0.578001\pi$
$602$	2923.58	−	5063.80i	0.197934	−	0.342832i
$603$		−	3955.14i		−	0.267108i
$604$	−6868.48	−	3965.52i	−0.462706	−	0.267144i
$605$	419.920	+	242.441i	0.0282184	+	0.0162919i
$606$			2481.59i			0.166350i
$607$	−4259.97	+	7378.48i	−0.284855	+	0.493383i	−0.972574	−	0.232594i	$-0.925279\pi$
$607$	−4259.97	+	7378.48i	−0.284855	+	0.493383i	0.687719	+	0.725977i	$0.258612\pi$
$608$	1313.67	+	2275.35i	0.0876259	+	0.151772i
$609$	4776.99	−	2758.00i	0.317855	−	0.183514i
$610$	−67.3600			−0.00447103
$611$	−21829.4	−	19350.6i	−1.44537	−	1.28125i
$612$	−4287.61			−0.283197
$613$	3539.07	−	2043.28i	0.233184	−	0.134629i	−0.378856	−	0.925456i	$-0.623682\pi$
$613$	3539.07	−	2043.28i	0.233184	−	0.134629i	0.612040	+	0.790827i	$0.290349\pi$
$614$	2492.28	+	4316.76i	0.163812	+	0.283730i
$615$	−32.4203	+	56.1537i	−0.00212571	+	0.00368185i
$616$			381.596i			0.0249593i
$617$	16844.7	+	9725.30i	1.09910	+	0.634564i	0.935984	−	0.352044i	$-0.114513\pi$
$617$	16844.7	+	9725.30i	1.09910	+	0.634564i	0.163113	+	0.986607i	$0.447846\pi$
$618$	5490.63	+	3170.01i	0.357387	+	0.206338i
$619$		−	20431.4i		−	1.32667i	−0.748324	−	0.663334i	$-0.769141\pi$
$619$		−	20431.4i		−	1.32667i	0.748324	−	0.663334i	$-0.230859\pi$
$620$	39.6757	−	68.7203i	0.00257002	−	0.00445141i
$621$	1865.30	+	3230.80i	0.120535	+	0.208772i
$622$	10733.1	−	6196.74i	0.691892	−	0.399464i
$623$	1328.73			0.0854488
$624$	−711.832	−	2134.29i	−0.0456668	−	0.136923i
$625$	15571.6			0.996582
$626$	−162.075	+	93.5741i	−0.0103480	+	0.00597440i
$627$	839.217	+	1453.57i	0.0534531	+	0.0925835i
$628$	−4797.97	+	8310.32i	−0.304872	+	0.528054i
$629$			3590.20i			0.227584i
$630$	−41.1889	−	23.7804i	−0.00260477	−	0.00150386i
$631$	7232.60	+	4175.74i	0.456300	+	0.263445i	0.710487	−	0.703710i	$-0.248475\pi$
$631$	7232.60	+	4175.74i	0.456300	+	0.263445i	−0.254187	+	0.967155i	$0.581808\pi$
$632$		−	1964.81i		−	0.123664i
$633$	6654.92	−	11526.7i	0.417866	−	0.723766i
$634$	3937.88	+	6820.60i	0.246677	+	0.427257i
$635$	−51.5046	+	29.7362i	−0.00321874	+	0.00185834i
$636$	3794.01			0.236545
$637$	−2250.19	−	460.068i	−0.139962	−	0.0286163i
$638$	−3579.73			−0.222136
$639$	−6016.42	+	3473.58i	−0.372466	+	0.215043i
$640$	24.1579	+	41.8427i	0.00149207	+	0.00258434i
$641$	14833.4	−	25692.2i	0.914016	−	1.58312i	0.105680	−	0.994400i	$-0.466298\pi$
$641$	14833.4	−	25692.2i	0.914016	−	1.58312i	0.808336	−	0.588722i	$-0.200369\pi$
$642$			10849.8i			0.666990i
$643$	15635.0	+	9026.89i	0.958920	+	0.553632i	0.895840	−	0.444376i	$-0.146575\pi$
$643$	15635.0	+	9026.89i	0.958920	+	0.553632i	0.0630792	+	0.998009i	$0.479908\pi$
$644$	−3350.46	−	1934.39i	−0.205010	−	0.118363i
$645$		−	472.953i		−	0.0288721i
$646$	9778.68	−	16937.2i	0.595568	−	1.03155i
$647$	−10522.4	−	18225.2i	−0.639376	−	1.10743i	−0.985570	−	0.169269i	$-0.945859\pi$
$647$	−10522.4	−	18225.2i	−0.639376	−	1.10743i	0.346194	−	0.938163i	$-0.387474\pi$
$648$	−561.184	+	324.000i	−0.0340207	+	0.0196419i
$649$	988.710			0.0598001
$650$	−2344.61	+	11467.5i	−0.141482	+	0.691985i
$651$	−1103.66			−0.0664452
$652$	−13016.1	+	7514.86i	−0.781826	+	0.451388i
$653$	−12118.2	−	20989.4i	−0.726222	−	1.25785i	−0.958469	−	0.285196i	$-0.907941\pi$
$653$	−12118.2	−	20989.4i	−0.726222	−	1.25785i	0.232247	−	0.972657i	$-0.425392\pi$
$654$	2558.61	−	4431.64i	0.152981	−	0.264971i
$655$			137.219i			0.00818562i
$656$	−793.411	−	458.076i	−0.0472218	−	0.0272635i
$657$	1149.19	+	663.485i	0.0682408	+	0.0393988i
$658$		−	8713.06i		−	0.516216i
$659$	−11155.3	+	19321.6i	−0.659408	+	1.14213i	0.321361	+	0.946957i	$0.395860\pi$
$659$	−11155.3	+	19321.6i	−0.659408	+	1.14213i	−0.980769	+	0.195172i	$0.937474\pi$
$660$	15.4328	+	26.7304i	0.000910185	+	0.00157649i
$661$	7919.98	−	4572.60i	0.466038	−	0.269067i	−0.248541	−	0.968621i	$-0.579951\pi$
$661$	7919.98	−	4572.60i	0.466038	−	0.269067i	0.714580	+	0.699554i	$0.246618\pi$
$662$	−8162.95			−0.479248
$663$	−11109.3	+	12532.4i	−0.650754	+	0.734114i
$664$	668.127			0.0390487
$665$	187.878	−	108.471i	0.0109558	−	0.00632531i
$666$	271.299	+	469.903i	0.0157847	+	0.0273399i
$667$	18146.4	−	31430.5i	1.05342	−	1.82458i
$668$			13705.2i			0.793819i
$669$	11929.2	+	6887.31i	0.689399	+	0.398025i
$670$	287.316	+	165.882i	0.0165671	+	0.00956503i
$671$		−	608.007i		−	0.0349804i
$672$	336.000	−	581.969i	0.0192879	−	0.0334077i
$673$	−14947.3	−	25889.5i	−0.856130	−	1.48286i	−0.875593	−	0.483050i	$-0.839529\pi$
$673$	−14947.3	−	25889.5i	−0.856130	−	1.48286i	0.0194623	−	0.999811i	$-0.493805\pi$
$674$	1716.47	−	991.003i	0.0980947	−	0.0566350i
$675$	3371.15			0.192231
$676$	−8082.75	−	3449.36i	−0.459874	−	0.196254i
$677$	−27154.7			−1.54157			−0.770783	−	0.637097i	$-0.780135\pi$
$677$	−27154.7			−1.54157			−0.770783	+	0.637097i	$0.780135\pi$
$678$	455.787	−	263.149i	0.0258177	−	0.0149059i
$679$	−4213.82	−	7298.55i	−0.238161	−	0.412507i
$680$	179.826	−	311.467i	0.0101412	−	0.0175650i
$681$			4656.66i			0.262032i
$682$	620.285	+	358.122i	0.0348269	+	0.0201073i
$683$	−4793.84	−	2767.72i	−0.268567	−	0.155057i	0.359669	−	0.933080i	$-0.382889\pi$
$683$	−4793.84	−	2767.72i	−0.268567	−	0.155057i	−0.628236	+	0.778023i	$0.716223\pi$
$684$		−	2955.77i		−	0.165229i
$685$	166.240	−	287.937i	0.00927257	−	0.0160606i
$686$	−343.000	−	594.093i	−0.0190901	−	0.0330650i
$687$	6331.79	−	3655.66i	0.351634	−	0.203016i
$688$	6682.48			0.370301
$689$	9830.38	−	11089.6i	0.543553	−	0.613181i
$690$	−312.929			−0.0172652
$691$	−12844.0	+	7415.47i	−0.707102	+	0.408246i	−0.809987	−	0.586448i	$-0.800526\pi$
$691$	−12844.0	+	7415.47i	−0.707102	+	0.408246i	0.102885	+	0.994693i	$0.467193\pi$
$692$	−2005.76	−	3474.08i	−0.110185	−	0.190845i
$693$	214.648	−	371.781i	0.0117659	−	0.0203792i
$694$		−	10901.3i		−	0.596263i
$695$	593.455	+	342.631i	0.0323900	+	0.0187003i
$696$	5459.42	+	3152.00i	0.297326	+	0.171661i
$697$			6819.62i			0.370605i
$698$	3584.21	−	6208.03i	0.194361	−	0.336644i
$699$	−9919.77	−	17181.6i	−0.536767	−	0.929708i
$700$	−3027.63	+	1748.01i	−0.163477	+	0.0943834i
$701$	17024.5			0.917271			0.458635	−	0.888625i	$-0.348338\pi$
$701$	17024.5			0.917271			0.458635	+	0.888625i	$0.348338\pi$
$702$	−507.014	+	2479.80i	−0.0272593	+	0.133325i
$703$	−2474.99			−0.132782
$704$	−377.682	+	218.055i	−0.0202193	+	0.0116736i
$705$	−352.381	−	610.342i	−0.0188247	−	0.0326054i
$706$	9947.20	−	17229.1i	0.530266	−	0.918448i
$707$			2895.19i			0.154010i
$708$	−1507.87	−	870.572i	−0.0800415	−	0.0462120i
$709$	−7497.26	−	4328.55i	−0.397131	−	0.229283i	0.288115	−	0.957596i	$-0.406972\pi$
$709$	−7497.26	−	4328.55i	−0.397131	−	0.229283i	−0.685245	+	0.728313i	$0.740305\pi$
$710$		−	582.739i		−	0.0308025i
$711$	−1105.20	+	1914.27i	−0.0582959	+	0.100972i
$712$	759.277	+	1315.11i	0.0399650	+	0.0692215i
$713$	−6288.72	+	3630.79i	−0.330315	+	0.190707i
$714$	−5002.21			−0.262189
$715$	118.118	+	24.1502i	0.00617814	+	0.00126317i
$716$	−16238.8			−0.847586
$717$	−9990.39	+	5767.95i	−0.520360	+	0.300430i
$718$	−4837.70	−	8379.14i	−0.251450	−	0.435524i
$719$	−2320.65	+	4019.49i	−0.120370	+	0.208486i	−0.919913	−	0.392121i	$-0.871741\pi$
$719$	−2320.65	+	4019.49i	−0.120370	+	0.208486i	0.799544	+	0.600608i	$0.205075\pi$
$720$		−	54.3552i		−	0.00281347i
$721$	6405.73	+	3698.35i	0.330876	+	0.191032i
$722$	−204.087	−	117.830i	−0.0105199	−	0.00607365i
$723$			13910.9i			0.715562i
$724$	490.358	−	849.326i	0.0251713	−	0.0435980i
$725$	−16397.9	−	28402.1i	−0.840006	−	1.45493i
$726$	6674.80	−	3853.70i	0.341219	−	0.197003i
$727$	28569.6			1.45748			0.728739	−	0.684791i	$-0.240107\pi$
$727$	28569.6			1.45748			0.728739	+	0.684791i	$0.240107\pi$
$728$	−830.471	−	2490.00i	−0.0422792	−	0.126766i
$729$	729.000			0.0370370
$730$	−96.3959	+	55.6542i	−0.00488736	+	0.00282172i
$731$	−24871.4	−	43078.5i	−1.25842	−	2.17964i
$732$	−535.358	+	927.268i	−0.0270320	+	0.0468208i
$733$			5807.38i			0.292634i	0.989238	+	0.146317i	$0.0467419\pi$
$733$			5807.38i			0.292634i	−0.989238	+	0.146317i	$0.953258\pi$
$734$	−9718.12	−	5610.76i	−0.488695	−	0.282148i
$735$	−48.0537	−	27.7438i	−0.00241155	−	0.00139231i
$736$		−	4421.46i		−	0.221437i
$737$	−1497.29	+	2593.38i	−0.0748348	+	0.129618i
$738$	515.335	+	892.587i	0.0257043	+	0.0445211i
$739$	29836.8	−	17226.3i	1.48520	−	0.857483i	0.485346	−	0.874322i	$-0.338693\pi$
$739$	29836.8	−	17226.3i	1.48520	−	0.857483i	0.999858	+	0.0168386i	$0.00536015\pi$
$740$	−45.5139			−0.00226098
$741$	−8639.50	−	7658.47i	−0.428313	−	0.379677i
$742$	4426.35			0.218998
$743$	6977.71	−	4028.58i	0.344532	−	0.198916i	−0.317742	−	0.948177i	$-0.602925\pi$
$743$	6977.71	−	4028.58i	0.344532	−	0.198916i	0.662274	+	0.749261i	$0.269591\pi$
$744$	−630.662	−	1092.34i	−0.0310769	−	0.0538267i
$745$	−316.298	+	547.844i	−0.0155547	+	0.0269416i
$746$			8261.81i			0.405478i
$747$	−650.942	−	375.821i	−0.0318832	−	0.0184077i
$748$	2811.37	+	1623.15i	0.137425	+	0.0793425i
$749$			12658.1i			0.617513i
$750$	−282.939	+	490.064i	−0.0137753	+	0.0238595i
$751$	1440.81	+	2495.56i	0.0700081	+	0.121258i	0.898905	−	0.438144i	$-0.144364\pi$
$751$	1440.81	+	2495.56i	0.0700081	+	0.121258i	−0.828897	+	0.559402i	$0.811031\pi$
$752$	8623.69	−	4978.89i	0.418183	−	0.241438i
$753$	6864.26			0.332201
$754$	23358.6	−	7790.60i	1.12821	−	0.376283i
$755$	−748.426			−0.0360768
$756$	−654.715	+	378.000i	−0.0314970	+	0.0181848i
$757$	7833.65	+	13568.3i	0.376115	+	0.651450i	0.990493	−	0.137562i	$-0.0439265\pi$
$757$	7833.65	+	13568.3i	0.376115	+	0.651450i	−0.614378	+	0.789012i	$0.710593\pi$
$758$	−11883.7	+	20583.2i	−0.569441	+	0.986301i
$759$		−	2824.57i		−	0.135080i
$760$	214.717	+	123.967i	0.0102482	+	0.00591679i
$761$	−10326.4	−	5961.96i	−0.491895	−	0.283996i	0.233465	−	0.972365i	$-0.424994\pi$
$761$	−10326.4	−	5961.96i	−0.491895	−	0.283996i	−0.725360	+	0.688369i	$0.758327\pi$
$762$			945.340i			0.0449423i
$763$	2985.04	−	5170.24i	0.141633	−	0.245315i
$764$	−8054.95	−	13951.6i	−0.381437	−	0.660668i
$765$	−350.400	+	202.304i	−0.0165605	+	0.00956119i
$766$	−1771.26			−0.0835485
$767$	−6451.56	+	2151.74i	−0.303719	+	0.101297i
$768$	768.000			0.0360844
$769$	5989.70	−	3458.15i	0.280877	−	0.162164i	−0.352944	−	0.935645i	$-0.614819\pi$
$769$	5989.70	−	3458.15i	0.280877	−	0.162164i	0.633820	+	0.773480i	$0.281486\pi$
$770$	18.0050	+	31.1855i	0.000842668	+	0.00145954i
$771$	−9897.91	+	17143.7i	−0.462340	+	0.800797i
$772$		−	2048.13i		−	0.0954842i
$773$	4236.03	+	2445.67i	0.197101	+	0.113797i	0.595303	−	0.803502i	$-0.297032\pi$
$773$	4236.03	+	2445.67i	0.197101	+	0.113797i	−0.398201	+	0.917298i	$0.630365\pi$
$774$	−6510.59	−	3758.89i	−0.302349	−	0.174562i
$775$			6561.91i			0.304143i
$776$	4815.79	−	8341.20i	0.222779	−	0.385865i
$777$	316.515	+	548.221i	0.0146138	+	0.0253119i
$778$	13879.3	−	8013.20i	0.639583	−	0.369264i
$779$	−4701.27			−0.216227
$780$	−158.877	−	140.836i	−0.00729320	−	0.00646504i
$781$	5259.94			0.240993
$782$	−28502.9	+	16456.2i	−1.30340	+	0.752521i
$783$	−3546.00	−	6141.85i	−0.161844	−	0.280322i
$784$	392.000	−	678.964i	0.0178571	−	0.0309295i
$785$			905.537i			0.0411720i
$786$	1888.93	+	1090.58i	0.0857201	+	0.0494905i
$787$	−27093.7	−	15642.6i	−1.22718	−	0.708510i	−0.260737	−	0.965410i	$-0.583966\pi$
$787$	−27093.7	−	15642.6i	−1.22718	−	0.708510i	−0.966438	+	0.256900i	$0.917299\pi$
$788$		−	3001.96i		−	0.135711i
$789$	3213.83	−	5566.52i	0.145013	−	0.251170i
$790$	−92.7063	−	160.572i	−0.00417511	−	0.00723151i
$791$	531.752	−	307.007i	0.0239026	−	0.0138002i
$792$	490.623			0.0220120
$793$	1323.21	+	3967.39i	0.0592543	+	0.177662i
$794$	28683.7			1.28205
$795$	310.062	−	179.014i	0.0138324	−	0.00798614i
$796$	932.682	+	1615.45i	0.0415302	+	0.0719324i
$797$	12709.3	−	22013.2i	0.564852	−	0.978352i	−0.432211	−	0.901772i	$-0.642267\pi$
$797$	12709.3	−	22013.2i	0.564852	−	0.978352i	0.997063	−	0.0765800i	$-0.0244001\pi$
$798$		−	3448.39i		−	0.152972i
$799$	−64192.7	−	37061.7i	−2.84227	−	1.64099i
$800$	−3460.15	−	1997.72i	−0.152919	−	0.0882876i
$801$		−	1708.37i		−	0.0753588i
$802$	11742.4	−	20338.4i	0.517006	−	0.895480i
$803$	−502.348	−	870.092i	−0.0220765	−	0.0382377i
$804$	4567.00	−	2636.76i	0.200331	−	0.115661i
$805$	−365.084			−0.0159845
$806$	−4826.89	−	986.897i	−0.210943	−	0.0431290i
$807$	−13913.6			−0.606916
$808$	−2865.50	+	1654.40i	−0.124762	+	0.0720315i
$809$	3966.39	+	6869.99i	0.172374	+	0.298561i	0.939249	−	0.343235i	$-0.111523\pi$
$809$	3966.39	+	6869.99i	0.172374	+	0.298561i	−0.766875	+	0.641796i	$0.778189\pi$
$810$	−30.5748	+	52.9571i	−0.00132628	+	0.00229719i
$811$			3650.65i			0.158066i	0.996872	+	0.0790331i	$0.0251833\pi$
$811$			3650.65i			0.158066i	−0.996872	+	0.0790331i	$0.974817\pi$
$812$	6369.33	+	3677.33i	0.275270	+	0.158927i
$813$	15037.4	+	8681.83i	0.648688	+	0.374520i
$814$		−	410.819i		−	0.0176895i
$815$	−709.153	+	1228.29i	−0.0304792	+	0.0527915i
$816$	−2858.41	−	4950.90i	−0.122628	−	0.212397i
$817$	29697.2	−	17145.7i	1.27169	−	0.734213i
$818$	−16128.9			−0.689406
$819$	−591.516	+	2893.10i	−0.0252372	+	0.123435i
$820$	−86.4543			−0.00368185
$821$	9939.46	−	5738.55i	0.422521	−	0.243943i	−0.273634	−	0.961834i	$-0.588226\pi$
$821$	9939.46	−	5738.55i	0.422521	−	0.243943i	0.696155	+	0.717891i	$0.254892\pi$
$822$	−2642.46	−	4576.88i	−0.112125	−	0.194205i
$823$	22809.2	−	39506.7i	0.966075	−	1.67329i	0.259376	−	0.965776i	$-0.416483\pi$
$823$	22809.2	−	39506.7i	0.966075	−	1.67329i	0.706699	−	0.707514i	$-0.250184\pi$
$824$			8453.37i			0.357387i
$825$	−2210.46	−	1276.21i	−0.0932827	−	0.0538568i
$826$	−1759.19	−	1015.67i	−0.0741040	−	0.0427840i
$827$		−	4492.42i		−	0.188896i	−0.995530	−	0.0944478i	$-0.969891\pi$
$827$		−	4492.42i		−	0.188896i	0.995530	−	0.0944478i	$-0.0301085\pi$
$828$	−2487.07	+	4307.74i	−0.104386	+	0.180802i
$829$	−22979.5	−	39801.6i	−0.962738	−	1.66751i	−0.715574	−	0.698537i	$-0.753835\pi$
$829$	−22979.5	−	39801.6i	−0.962738	−	1.66751i	−0.247164	−	0.968974i	$-0.579499\pi$
$830$	54.6020	−	31.5245i	0.00228345	−	0.00131835i
$831$	10879.9			0.454175
$832$	1989.91	−	2244.81i	0.0829179	−	0.0935395i
$833$	−5835.91			−0.242740
$834$	9433.22	−	5446.27i	0.391661	−	0.226126i
$835$	646.659	+	1120.05i	0.0268007	+	0.0464201i
$836$	−1118.96	+	1938.09i	−0.0462918	+	0.0801797i
$837$			1418.99i			0.0585991i
$838$	23915.3	+	13807.5i	0.985848	+	0.569180i
$839$	−8152.41	−	4706.79i	−0.335462	−	0.193679i	0.322802	−	0.946467i	$-0.395375\pi$
$839$	−8152.41	−	4706.79i	−0.335462	−	0.193679i	−0.658263	+	0.752788i	$0.728709\pi$
$840$		−	63.4144i		−	0.00260477i
$841$	−22302.4	+	38628.8i	−0.914443	+	1.58386i
$842$	10101.5	+	17496.3i	0.413446	+	0.716109i
$843$	10649.8	−	6148.65i	0.435110	−	0.251211i
$844$	17746.5			0.723766
$845$	−823.307	+	99.4760i	−0.0335179	+	0.00404980i
$846$	−11202.5			−0.455260
$847$	7787.27	−	4495.98i	0.315908	−	0.182389i
$848$	2529.34	+	4380.95i	0.102427	+	0.177408i
$849$	8831.05	−	15295.8i	0.356986	−	0.618317i
$850$			29741.1i			1.20013i
$851$	3607.05	+	2082.53i	0.145297	+	0.0838875i
$852$	−8021.89	−	4631.44i	−0.322565	−	0.186233i
$853$		−	27990.3i		−	1.12353i	−0.827297	−	0.561765i	$-0.810123\pi$
$853$		−	27990.3i		−	1.12353i	0.827297	−	0.561765i	$-0.189877\pi$
$854$	−624.585	+	1081.81i	−0.0250268	+	0.0433476i
$855$	−139.463	−	241.557i	−0.00557840	−	0.00966208i
$856$	−12528.3	+	7233.20i	−0.500242	+	0.288815i
$857$	−2954.76			−0.117774			−0.0588872	−	0.998265i	$-0.518755\pi$
$857$	−2954.76			−0.117774			−0.0588872	+	0.998265i	$0.518755\pi$
$858$	1271.22	−	1434.06i	0.0505812	−	0.0570605i
$859$	−5266.19			−0.209173			−0.104587	−	0.994516i	$-0.533352\pi$
$859$	−5266.19			−0.209173			−0.104587	+	0.994516i	$0.533352\pi$
$860$	546.119	−	315.302i	0.0216541	−	0.0125020i
$861$	601.225	+	1041.35i	0.0237975	+	0.0412186i
$862$	−9697.03	+	16795.7i	−0.383158	+	0.663649i
$863$			6993.17i			0.275840i	0.990443	+	0.137920i	$0.0440418\pi$
$863$			6993.17i			0.275840i	−0.990443	+	0.137920i	$0.955958\pi$
$864$	−748.246	−	432.000i	−0.0294628	−	0.0170103i
$865$	−327.838	−	189.277i	−0.0128865	−	0.00744003i
$866$			14560.7i			0.571356i
$867$	−13907.8	+	24089.0i	−0.544791	+	0.943605i
$868$	−735.773	−	1274.40i	−0.0287716	−	0.0498339i
$869$	1449.36	−	836.788i	0.0565779	−	0.0326652i
$870$	594.888			0.0231823
$871$	4126.16	−	20181.0i	0.160516	−	0.785081i
$872$	6822.95			0.264971
$873$	−9383.85	+	5417.77i	−0.363797	+	0.210038i
$874$	−11344.5	−	19649.2i	−0.439053	−	0.760461i
$875$	−330.095	+	571.742i	−0.0127534	+	0.0220896i
$876$			1769.29i			0.0682408i
$877$	−39053.0	−	22547.2i	−1.50368	−	0.868149i	−0.999991	−	0.00426259i	$-0.998643\pi$
$877$	−39053.0	−	22547.2i	−1.50368	−	0.868149i	−0.503687	−	0.863886i	$-0.668023\pi$
$878$	20993.2	+	12120.4i	0.806932	+	0.465882i
$879$			1171.58i			0.0449562i
$880$	−20.5771	+	35.6406i	−0.000788243	+	0.00136528i
$881$	22726.6	+	39363.7i	0.869102	+	1.50533i	0.862915	+	0.505349i	$0.168636\pi$
$881$	22726.6	+	39363.7i	0.869102	+	1.50533i	0.00618730	+	0.999981i	$0.498031\pi$
$882$	−763.834	+	441.000i	−0.0291606	+	0.0168359i
$883$	18404.7			0.701435			0.350717	−	0.936481i	$-0.385938\pi$
$883$	18404.7			0.701435			0.350717	+	0.936481i	$0.385938\pi$
$884$	−21877.4	−	4473.00i	−0.832370	−	0.170185i
$885$	−164.306			−0.00624078
$886$	−1541.16	+	889.789i	−0.0584382	+	0.0337393i
$887$	−10636.6	−	18423.1i	−0.402640	−	0.697392i	0.591404	−	0.806375i	$-0.298574\pi$
$887$	−10636.6	−	18423.1i	−0.402640	−	0.697392i	−0.994044	+	0.108983i	$0.965241\pi$
$888$	−361.732	+	626.538i	−0.0136700	+	0.0236771i
$889$			1102.90i			0.0416085i
$890$	124.102	+	71.6505i	0.00467406	+	0.00269857i
$891$	−478.004	−	275.975i	−0.0179728	−	0.0103766i
$892$			18366.2i			0.689399i
$893$	25549.4	−	44252.8i	0.957421	−	1.65830i
$894$	5027.69	+	8708.22i	0.188089	+	0.325779i
$895$	−1327.10	+	766.200i	−0.0495642	+	0.0286159i
$896$	896.000			0.0334077
$897$	6147.15	+	18431.0i	0.228815	+	0.686057i
$898$	−9865.48			−0.366610
$899$	11955.0	−	6902.24i	0.443518	−	0.256065i
$900$	2247.44	+	3892.67i	0.0832383	+	0.144173i
$901$	18827.8	−	32610.7i	0.696166	−	1.20579i
$902$		−	780.356i		−	0.0288060i
$903$	−7595.69	−	4385.38i	−0.279921	−	0.161613i
$904$	607.717	+	350.865i	0.0223588	+	0.0129089i
$905$		−	92.5470i		−	0.00339930i
$906$	−5948.28	+	10302.7i	−0.218122	+	0.377798i
$907$	2467.16	+	4273.24i	0.0903204	+	0.156440i	0.907646	−	0.419737i	$-0.137878\pi$
$907$	2467.16	+	4273.24i	0.0903204	+	0.156440i	−0.817326	+	0.576176i	$0.804544\pi$
$908$	−5377.05	+	3104.44i	−0.196524	+	0.113463i
$909$	3722.39			0.135824
$910$	−185.356	−	164.308i	−0.00675219	−	0.00598547i
$911$	−21871.2			−0.795418			−0.397709	−	0.917512i	$-0.630195\pi$
$911$	−21871.2			−0.795418			−0.397709	+	0.917512i	$0.630195\pi$
$912$	3413.03	−	1970.51i	0.123922	−	0.0715462i
$913$	284.547	+	492.850i	0.0103145	+	0.0178652i
$914$	18991.5	−	32894.3i	0.687291	−	1.19042i
$915$			101.040i			0.00365058i
$916$	8442.38	+	4874.21i	0.304524	+	0.175817i
$917$	2203.76	+	1272.34i	0.0793614	+	0.0458193i
$918$			6431.41i			0.231229i
$919$	−9949.33	+	17232.7i	−0.357125	+	0.618559i	−0.987479	−	0.157749i	$-0.949576\pi$
$919$	−9949.33	+	17232.7i	−0.357125	+	0.618559i	0.630354	+	0.776308i	$0.282910\pi$
$920$	−208.619	−	361.340i	−0.00747607	−	0.0129489i
$921$	6475.14	−	3738.42i	0.231664	−	0.133752i
$922$	−29597.7			−1.05721
$923$	−34322.3	+	11447.3i	−1.22398	+	0.408224i
$924$	572.394			0.0203792
$925$	3259.50	−	1881.87i	0.115861	−	0.0668925i
$926$	16651.4	+	28841.1i	0.590929	+	1.02352i
$927$	4755.02	−	8235.94i	0.168474	−	0.291805i
$928$			8405.33i			0.297326i
$929$	−31176.3	−	17999.6i	−1.10103	−	0.635683i	−0.164542	−	0.986370i	$-0.552615\pi$
$929$	−31176.3	−	17999.6i	−1.10103	−	0.635683i	−0.936493	+	0.350688i	$0.885948\pi$
$930$	−103.080	−	59.5135i	−0.00363456	−	0.00209841i
$931$		−	4023.13i		−	0.141625i
$932$	13226.4	−	22908.7i	0.464854	−	0.805151i
$933$	−9295.11	−	16099.6i	−0.326161	−	0.564928i
$934$	7625.58	−	4402.63i	0.267148	−	0.154238i
$935$	306.342			0.0107149
$936$	−3201.43	+	1067.75i	−0.111797	+	0.0372868i
$937$	52302.0			1.82351			0.911757	−	0.410729i	$-0.134726\pi$
$937$	52302.0			1.82351			0.911757	+	0.410729i	$0.134726\pi$
$938$	5328.17	−	3076.22i	0.185470	−	0.107081i
$939$	140.361	+	243.113i	0.00487807	+	0.00844907i
$940$	469.841	−	813.789i	0.0163027	−	0.0282371i
$941$			43058.7i			1.49168i	0.666123	+	0.745842i	$0.267952\pi$
$941$			43058.7i			1.49168i	−0.666123	+	0.745842i	$0.732048\pi$
$942$	12465.5	+	7196.95i	0.431154	+	0.248927i
$943$	6851.63	+	3955.79i	0.236606	+	0.136605i
$944$		−	2321.52i		−	0.0800415i
$945$	−35.6706	+	61.7833i	−0.00122790	+	0.00212678i
$946$	2845.99	+	4929.39i	0.0978129	+	0.169417i
$947$	36551.3	−	21102.9i	1.25423	−	0.724131i	0.282285	−	0.959331i	$-0.408908\pi$
$947$	36551.3	−	21102.9i	1.25423	−	0.724131i	0.971947	+	0.235200i	$0.0755744\pi$
$948$	−2947.21			−0.100972
$949$	5171.53	+	4584.29i	0.176897	+	0.156810i
$950$	−20502.8			−0.700208
$951$	10230.9	−	5906.82i	0.348854	−	0.201411i
$952$	−3334.81	−	5776.05i	−0.113531	−	0.196642i
$953$	−7599.48	+	13162.7i	−0.258312	+	0.447409i	−0.965790	−	0.259326i	$-0.916500\pi$
$953$	−7599.48	+	13162.7i	−0.258312	+	0.447409i	0.707478	+	0.706735i	$0.249833\pi$
$954$		−	5691.02i		−	0.193138i
$955$	−1316.56	−	760.119i	−0.0446105	−	0.0257559i
$956$	−13320.5	−	7690.60i	−0.450645	−	0.260180i
$957$			5369.59i			0.181373i
$958$	−934.070	+	1617.86i	−0.0315015	+	0.0545622i
$959$	−3082.87	−	5339.69i	−0.103807	−	0.179799i
$960$	62.7640	−	36.2368i	0.00211010	−	0.00121827i
$961$	27029.0			0.907286
$962$	894.070	+	2680.69i	0.0299646	+	0.0898431i
$963$	16274.7			0.544595
$964$	−16062.9	+	9273.92i	−0.536671	+	0.309847i
$965$	−96.6376	−	167.381i	−0.00322370	−	0.00558362i
$966$	−2901.59	+	5025.69i	−0.0966428	+	0.167390i
$967$			55495.1i			1.84550i	0.385394	+	0.922752i	$0.374066\pi$
$967$			55495.1i			1.84550i	−0.385394	+	0.922752i	$0.625934\pi$
$968$	8899.74	+	5138.27i	0.295505	+	0.170610i
$969$	−25405.8	−	14668.0i	−0.842261	−	0.486279i
$970$		−	908.901i		−	0.0300856i
$971$	−5544.89	+	9604.03i	−0.183259	+	0.317413i	−0.942988	−	0.332826i	$-0.891998\pi$
$971$	−5544.89	+	9604.03i	−0.183259	+	0.317413i	0.759730	+	0.650239i	$0.225331\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	11005.4	−	6353.98i	0.362608	−	0.209352i
$974$	37170.1			1.22280
$975$	17201.2	+	3516.92i	0.565004	+	0.115519i
$976$	−1427.62			−0.0468208
$977$	−38008.1	+	21944.0i	−1.24461	+	0.718578i	−0.970030	−	0.242985i	$-0.921873\pi$
$977$	−38008.1	+	21944.0i	−1.24461	+	0.718578i	−0.274584	+	0.961563i	$0.588540\pi$
$978$	11272.3	+	19524.2i	0.368557	+	0.638359i
$979$	−646.734	+	1120.18i	−0.0211131	+	0.0365689i
$980$		−	73.9835i		−	0.00241155i
$981$	−6647.46	−	3837.91i	−0.216348	−	0.124908i
$982$	23447.2	+	13537.2i	0.761945	+	0.439909i
$983$			38690.1i			1.25536i	0.778470	+	0.627682i	$0.215996\pi$
$983$			38690.1i			1.25536i	−0.778470	+	0.627682i	$0.784004\pi$
$984$	−687.114	+	1190.12i	−0.0222606	+	0.0385564i
$985$	−141.643	−	245.332i	−0.00458184	−	0.00793598i
$986$	54184.9	−	31283.7i	1.75010	−	1.01042i
$987$	−13069.6			−0.421489
$988$	3083.57	−	15081.7i	0.0992930	−	0.485640i
$989$	−57707.7			−1.85541
$990$	40.0957	−	23.1492i	0.00128720	−	0.000743163i
$991$	−10126.5	−	17539.6i	−0.324601	−	0.562225i	0.656831	−	0.754038i	$-0.271897\pi$
$991$	−10126.5	−	17539.6i	−0.324601	−	0.562225i	−0.981431	+	0.191813i	$0.938563\pi$
$992$	840.883	−	1456.45i	0.0269134	−	0.0466153i
$993$			12244.4i			0.391304i
$994$	−9358.88	−	5403.35i	−0.298637	−	0.172418i
$995$	152.445	+	88.0141i	0.00485712	+	0.00280426i
$996$		−	1002.19i		−	0.0318832i
$997$	16059.9	−	27816.6i	0.510153	−	0.883612i	−0.489777	−	0.871847i	$-0.662922\pi$
$997$	16059.9	−	27816.6i	0.510153	−	0.883612i	0.999931	−	0.0117640i	$-0.00374469\pi$
$998$	123.810	+	214.445i	0.00392699	+	0.00680174i
$999$	704.855	−	406.948i	0.0223230	−	0.0128882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.s.a.127.8	yes	20
13.4	even	6	inner	546.4.s.a.43.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.s.a.43.8	✓	20	13.4	even	6	inner
546.4.s.a.127.8	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} -0.377467i q^{5} +(-5.19615 - 3.00000i) q^{6} +(-6.06218 - 3.50000i) q^{7} -8.00000i q^{8} +(-4.50000 + 7.79423i) q^{9} +(-0.377467 - 0.653792i) q^{10} +(5.90128 - 3.40710i) q^{11} -12.0000 q^{12} +(-31.0923 + 35.0752i) q^{13} -14.0000 q^{14} +(-0.980688 + 0.566200i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-59.5501 + 103.144i) q^{17} +18.0000i q^{18} +(-71.1047 - 41.0523i) q^{19} +(-1.30758 - 0.754934i) q^{20} +21.0000i q^{21} +(6.81421 - 11.8026i) q^{22} +(69.0854 + 119.659i) q^{23} +(-20.7846 + 12.0000i) q^{24} +124.858 q^{25} +(-18.7783 + 91.8443i) q^{26} +27.0000 q^{27} +(-24.2487 + 14.0000i) q^{28} +(-131.333 - 227.476i) q^{29} +(-1.13240 + 1.96138i) q^{30} +52.5552i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-17.7038 - 10.2213i) q^{33} +238.200i q^{34} +(-1.32113 + 2.28827i) q^{35} +(18.0000 + 31.1769i) q^{36} +(26.1057 - 15.0722i) q^{37} -164.209 q^{38} +(137.766 + 28.1674i) q^{39} -3.01974 q^{40} +(49.5882 - 28.6297i) q^{41} +(21.0000 + 36.3731i) q^{42} +(-208.827 + 361.700i) q^{43} -27.2568i q^{44} +(2.94206 + 1.69860i) q^{45} +(239.319 + 138.171i) q^{46} +622.361i q^{47} +(-24.0000 + 41.5692i) q^{48} +(24.5000 + 42.4352i) q^{49} +(216.260 - 124.858i) q^{50} +357.301 q^{51} +(59.3193 + 177.857i) q^{52} -316.168 q^{53} +(46.7654 - 27.0000i) q^{54} +(-1.28607 - 2.22754i) q^{55} +(-28.0000 + 48.4974i) q^{56} +246.314i q^{57} +(-454.952 - 262.667i) q^{58} +(125.656 + 72.5477i) q^{59} +4.52960i q^{60} +(44.6132 - 77.2723i) q^{61} +(52.5552 + 91.0282i) q^{62} +(54.5596 - 31.5000i) q^{63} -64.0000 q^{64} +(13.2397 + 11.7363i) q^{65} -40.8853 q^{66} +(-380.584 + 219.730i) q^{67} +(238.200 + 412.575i) q^{68} +(207.256 - 358.978i) q^{69} +5.28454i q^{70} +(668.491 + 385.954i) q^{71} +(62.3538 + 36.0000i) q^{72} -147.441i q^{73} +(30.1443 - 52.2115i) q^{74} +(-187.286 - 324.389i) q^{75} +(-284.419 + 164.209i) q^{76} -47.6995 q^{77} +(266.786 - 88.9790i) q^{78} +245.601 q^{79} +(-5.23033 + 3.01974i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(57.2595 - 99.1764i) q^{82} +83.5159i q^{83} +(72.7461 + 42.0000i) q^{84} +(38.9334 + 22.4782i) q^{85} +835.310i q^{86} +(-394.000 + 682.428i) q^{87} +(-27.2568 - 47.2102i) q^{88} +(-164.388 + 94.9096i) q^{89} +6.79440 q^{90} +(311.250 - 103.809i) q^{91} +552.683 q^{92} +(136.542 - 78.8328i) q^{93} +(622.361 + 1077.96i) q^{94} +(-15.4959 + 26.8397i) q^{95} +96.0000i q^{96} +(1042.65 + 601.974i) q^{97} +(84.8705 + 49.0000i) q^{98} +61.3279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 40 q^{4} - 90 q^{9} - 24 q^{10} + 18 q^{11} - 240 q^{12} + 28 q^{13} - 280 q^{14} + 18 q^{15} - 160 q^{16} - 106 q^{17} - 60 q^{19} + 24 q^{20} - 24 q^{22} - 450 q^{23} - 304 q^{25} - 60 q^{26}+ \cdots - 1620 q^{97}+O(q^{100}) \) 20 * q - 30 * q^3 + 40 * q^4 - 90 * q^9 - 24 * q^10 + 18 * q^11 - 240 * q^12 + 28 * q^13 - 280 * q^14 + 18 * q^15 - 160 * q^16 - 106 * q^17 - 60 * q^19 + 24 * q^20 - 24 * q^22 - 450 * q^23 - 304 * q^25 - 60 * q^26 + 540 * q^27 + 290 * q^29 - 72 * q^30 - 54 * q^33 - 84 * q^35 + 360 * q^36 + 564 * q^37 + 160 * q^38 + 228 * q^39 - 192 * q^40 - 246 * q^41 + 420 * q^42 - 464 * q^43 - 54 * q^45 - 240 * q^46 - 480 * q^48 + 490 * q^49 + 720 * q^50 + 636 * q^51 + 416 * q^52 - 1528 * q^53 + 1384 * q^55 - 560 * q^56 - 480 * q^58 - 2496 * q^59 - 270 * q^61 - 60 * q^62 - 1280 * q^64 + 3042 * q^65 + 144 * q^66 + 1314 * q^67 + 424 * q^68 - 1350 * q^69 - 516 * q^71 - 540 * q^74 + 456 * q^75 - 240 * q^76 + 168 * q^77 + 1116 * q^78 - 4000 * q^79 + 96 * q^80 - 810 * q^81 - 476 * q^82 - 2730 * q^85 + 870 * q^87 + 96 * q^88 - 1266 * q^89 + 432 * q^90 + 1302 * q^91 - 3600 * q^92 + 1692 * q^93 + 1080 * q^94 - 3798 * q^95 - 1620 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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