LMFDB - Embedded newform 546.4.l.a.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(211,546)] 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("546.211"); 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, 2])) N = Newforms(chi, 4, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,-2,-3,-4,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.4.l.a.295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +7.00000 q^{5} +(-3.00000 + 5.19615i) q^{6} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-7.00000 - 12.1244i) q^{10} +(8.00000 + 13.8564i) q^{11} +12.0000 q^{12} +(45.5000 - 11.2583i) q^{13} -14.0000 q^{14} +(-10.5000 - 18.1865i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(16.5000 - 28.5788i) q^{17} +18.0000 q^{18} +(-72.0000 + 124.708i) q^{19} +(-14.0000 + 24.2487i) q^{20} -21.0000 q^{21} +(16.0000 - 27.7128i) q^{22} +(22.0000 + 38.1051i) q^{23} +(-12.0000 - 20.7846i) q^{24} -76.0000 q^{25} +(-65.0000 - 67.5500i) q^{26} +27.0000 q^{27} +(14.0000 + 24.2487i) q^{28} +(92.5000 + 160.215i) q^{29} +(-21.0000 + 36.3731i) q^{30} +184.000 q^{31} +(-16.0000 + 27.7128i) q^{32} +(24.0000 - 41.5692i) q^{33} -66.0000 q^{34} +(24.5000 - 42.4352i) q^{35} +(-18.0000 - 31.1769i) q^{36} +(112.500 + 194.856i) q^{37} +288.000 q^{38} +(-97.5000 - 101.325i) q^{39} +56.0000 q^{40} +(82.5000 + 142.894i) q^{41} +(21.0000 + 36.3731i) q^{42} +(10.0000 - 17.3205i) q^{43} -64.0000 q^{44} +(-31.5000 + 54.5596i) q^{45} +(44.0000 - 76.2102i) q^{46} -88.0000 q^{47} +(-24.0000 + 41.5692i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(76.0000 + 131.636i) q^{50} -99.0000 q^{51} +(-52.0000 + 180.133i) q^{52} +111.000 q^{53} +(-27.0000 - 46.7654i) q^{54} +(56.0000 + 96.9948i) q^{55} +(28.0000 - 48.4974i) q^{56} +432.000 q^{57} +(185.000 - 320.429i) q^{58} +(-110.000 + 190.526i) q^{59} +84.0000 q^{60} +(134.500 - 232.961i) q^{61} +(-184.000 - 318.697i) q^{62} +(31.5000 + 54.5596i) q^{63} +64.0000 q^{64} +(318.500 - 78.8083i) q^{65} -96.0000 q^{66} +(-350.000 - 606.218i) q^{67} +(66.0000 + 114.315i) q^{68} +(66.0000 - 114.315i) q^{69} -98.0000 q^{70} +(-508.000 + 879.882i) q^{71} +(-36.0000 + 62.3538i) q^{72} +947.000 q^{73} +(225.000 - 389.711i) q^{74} +(114.000 + 197.454i) q^{75} +(-288.000 - 498.831i) q^{76} +112.000 q^{77} +(-78.0000 + 270.200i) q^{78} +1244.00 q^{79} +(-56.0000 - 96.9948i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(165.000 - 285.788i) q^{82} +1140.00 q^{83} +(42.0000 - 72.7461i) q^{84} +(115.500 - 200.052i) q^{85} -40.0000 q^{86} +(277.500 - 480.644i) q^{87} +(64.0000 + 110.851i) q^{88} +(-429.000 - 743.050i) q^{89} +126.000 q^{90} +(91.0000 - 315.233i) q^{91} -176.000 q^{92} +(-276.000 - 478.046i) q^{93} +(88.0000 + 152.420i) q^{94} +(-504.000 + 872.954i) q^{95} +96.0000 q^{96} +(431.000 - 746.514i) q^{97} +(-49.0000 + 84.8705i) q^{98} -144.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} + 14 q^{5} - 6 q^{6} + 7 q^{7} + 16 q^{8} - 9 q^{9} - 14 q^{10} + 16 q^{11} + 24 q^{12} + 91 q^{13} - 28 q^{14} - 21 q^{15} - 16 q^{16} + 33 q^{17} + 36 q^{18} - 144 q^{19}+ \cdots - 288 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 + 14 * q^5 - 6 * q^6 + 7 * q^7 + 16 * q^8 - 9 * q^9 - 14 * q^10 + 16 * q^11 + 24 * q^12 + 91 * q^13 - 28 * q^14 - 21 * q^15 - 16 * q^16 + 33 * q^17 + 36 * q^18 - 144 * q^19 - 28 * q^20 - 42 * q^21 + 32 * q^22 + 44 * q^23 - 24 * q^24 - 152 * q^25 - 130 * q^26 + 54 * q^27 + 28 * q^28 + 185 * q^29 - 42 * q^30 + 368 * q^31 - 32 * q^32 + 48 * q^33 - 132 * q^34 + 49 * q^35 - 36 * q^36 + 225 * q^37 + 576 * q^38 - 195 * q^39 + 112 * q^40 + 165 * q^41 + 42 * q^42 + 20 * q^43 - 128 * q^44 - 63 * q^45 + 88 * q^46 - 176 * q^47 - 48 * q^48 - 49 * q^49 + 152 * q^50 - 198 * q^51 - 104 * q^52 + 222 * q^53 - 54 * q^54 + 112 * q^55 + 56 * q^56 + 864 * q^57 + 370 * q^58 - 220 * q^59 + 168 * q^60 + 269 * q^61 - 368 * q^62 + 63 * q^63 + 128 * q^64 + 637 * q^65 - 192 * q^66 - 700 * q^67 + 132 * q^68 + 132 * q^69 - 196 * q^70 - 1016 * q^71 - 72 * q^72 + 1894 * q^73 + 450 * q^74 + 228 * q^75 - 576 * q^76 + 224 * q^77 - 156 * q^78 + 2488 * q^79 - 112 * q^80 - 81 * q^81 + 330 * q^82 + 2280 * q^83 + 84 * q^84 + 231 * q^85 - 80 * q^86 + 555 * q^87 + 128 * q^88 - 858 * q^89 + 252 * q^90 + 182 * q^91 - 352 * q^92 - 552 * q^93 + 176 * q^94 - 1008 * q^95 + 192 * q^96 + 862 * q^97 - 98 * q^98 - 288 * q^99

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−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
$5$	7.00000			0.626099			0.313050	−	0.949737i	$-0.398649\pi$
$5$	7.00000			0.626099			0.313050	+	0.949737i	$0.398649\pi$
$6$	−3.00000	+	5.19615i	−0.204124	+	0.353553i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−7.00000	−	12.1244i	−0.221359	−	0.383406i
$11$	8.00000	+	13.8564i	0.219281	+	0.379806i	0.954588	−	0.297928i	$-0.0962955\pi$
$11$	8.00000	+	13.8564i	0.219281	+	0.379806i	−0.735307	+	0.677734i	$0.762962\pi$
$12$	12.0000			0.288675
$13$	45.5000	−	11.2583i	0.970725	−	0.240192i
$13$	45.5000	−	11.2583i	0.970725	−	0.240192i
$14$	−14.0000			−0.267261
$15$	−10.5000	−	18.1865i	−0.180739	−	0.313050i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	16.5000	−	28.5788i	0.235402	−	0.407729i	−0.723987	−	0.689813i	$-0.757693\pi$
$17$	16.5000	−	28.5788i	0.235402	−	0.407729i	0.959390	+	0.282085i	$0.0910259\pi$
$18$	18.0000			0.235702
$19$	−72.0000	+	124.708i	−0.869365	+	1.50578i	−0.00671805	+	0.999977i	$0.502138\pi$
$19$	−72.0000	+	124.708i	−0.869365	+	1.50578i	−0.862647	+	0.505807i	$0.831195\pi$
$20$	−14.0000	+	24.2487i	−0.156525	+	0.271109i
$21$	−21.0000			−0.218218
$22$	16.0000	−	27.7128i	0.155055	−	0.268563i
$23$	22.0000	+	38.1051i	0.199449	+	0.345455i	0.948350	−	0.317227i	$-0.102752\pi$
$23$	22.0000	+	38.1051i	0.199449	+	0.345455i	−0.748901	+	0.662682i	$0.769418\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−76.0000			−0.608000
$26$	−65.0000	−	67.5500i	−0.490290	−	0.509525i
$27$	27.0000			0.192450
$28$	14.0000	+	24.2487i	0.0944911	+	0.163663i
$29$	92.5000	+	160.215i	0.592304	+	1.02590i	0.993921	+	0.110093i	$0.0351149\pi$
$29$	92.5000	+	160.215i	0.592304	+	1.02590i	−0.401617	+	0.915808i	$0.631552\pi$
$30$	−21.0000	+	36.3731i	−0.127802	+	0.221359i
$31$	184.000			1.06604			0.533022	−	0.846101i	$-0.321056\pi$
$31$	184.000			1.06604			0.533022	+	0.846101i	$0.321056\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	24.0000	−	41.5692i	0.126602	−	0.219281i
$34$	−66.0000			−0.332909
$35$	24.5000	−	42.4352i	0.118322	−	0.204939i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	112.500	+	194.856i	0.499862	+	0.865786i	1.00000		0.000159589i	$-5.07987e-5\pi$
$37$	112.500	+	194.856i	0.499862	+	0.865786i	−0.500138	+	0.865946i	$0.666717\pi$
$38$	288.000			1.22947
$39$	−97.5000	−	101.325i	−0.400320	−	0.416025i
$40$	56.0000			0.221359
$41$	82.5000	+	142.894i	0.314252	+	0.544301i	0.979278	−	0.202520i	$-0.0649130\pi$
$41$	82.5000	+	142.894i	0.314252	+	0.544301i	−0.665026	+	0.746820i	$0.731580\pi$
$42$	21.0000	+	36.3731i	0.0771517	+	0.133631i
$43$	10.0000	−	17.3205i	0.0354648	−	0.0614268i	−0.847748	−	0.530399i	$-0.822042\pi$
$43$	10.0000	−	17.3205i	0.0354648	−	0.0614268i	0.883213	+	0.468972i	$0.155376\pi$
$44$	−64.0000			−0.219281
$45$	−31.5000	+	54.5596i	−0.104350	+	0.180739i
$46$	44.0000	−	76.2102i	0.141031	−	0.244274i
$47$	−88.0000			−0.273109			−0.136554	−	0.990633i	$-0.543603\pi$
$47$	−88.0000			−0.273109			−0.136554	+	0.990633i	$0.543603\pi$
$48$	−24.0000	+	41.5692i	−0.0721688	+	0.125000i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	76.0000	+	131.636i	0.214960	+	0.372322i
$51$	−99.0000			−0.271819
$52$	−52.0000	+	180.133i	−0.138675	+	0.480384i
$53$	111.000			0.287680			0.143840	−	0.989601i	$-0.454055\pi$
$53$	111.000			0.287680			0.143840	+	0.989601i	$0.454055\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	56.0000	+	96.9948i	0.137292	+	0.237796i
$56$	28.0000	−	48.4974i	0.0668153	−	0.115728i
$57$	432.000			1.00386
$58$	185.000	−	320.429i	0.418822	−	0.725421i
$59$	−110.000	+	190.526i	−0.242725	+	0.420412i	−0.961490	−	0.274841i	$-0.911375\pi$
$59$	−110.000	+	190.526i	−0.242725	+	0.420412i	0.718764	+	0.695254i	$0.244708\pi$
$60$	84.0000			0.180739
$61$	134.500	−	232.961i	0.282311	−	0.488977i	−0.689643	−	0.724150i	$-0.742232\pi$
$61$	134.500	−	232.961i	0.282311	−	0.488977i	0.971953	+	0.235173i	$0.0755657\pi$
$62$	−184.000	−	318.697i	−0.376904	−	0.652816i
$63$	31.5000	+	54.5596i	0.0629941	+	0.109109i
$64$	64.0000			0.125000
$65$	318.500	−	78.8083i	0.607770	−	0.150384i
$66$	−96.0000			−0.179042
$67$	−350.000	−	606.218i	−0.638199	−	1.10539i	−0.985828	−	0.167760i	$-0.946347\pi$
$67$	−350.000	−	606.218i	−0.638199	−	1.10539i	0.347629	−	0.937632i	$-0.386987\pi$
$68$	66.0000	+	114.315i	0.117701	+	0.203864i
$69$	66.0000	−	114.315i	0.115152	−	0.199449i
$70$	−98.0000			−0.167332
$71$	−508.000	+	879.882i	−0.849134	+	1.47074i	0.0328483	+	0.999460i	$0.489542\pi$
$71$	−508.000	+	879.882i	−0.849134	+	1.47074i	−0.881982	+	0.471283i	$0.843791\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	947.000			1.51833			0.759164	−	0.650899i	$-0.225608\pi$
$73$	947.000			1.51833			0.759164	+	0.650899i	$0.225608\pi$
$74$	225.000	−	389.711i	0.353456	−	0.612203i
$75$	114.000	+	197.454i	0.175514	+	0.304000i
$76$	−288.000	−	498.831i	−0.434682	−	0.752892i
$77$	112.000			0.165761
$78$	−78.0000	+	270.200i	−0.113228	+	0.392232i
$79$	1244.00			1.77166			0.885829	−	0.464012i	$-0.153591\pi$
$79$	1244.00			1.77166			0.885829	+	0.464012i	$0.153591\pi$
$80$	−56.0000	−	96.9948i	−0.0782624	−	0.135554i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	165.000	−	285.788i	0.222210	−	0.384879i
$83$	1140.00			1.50761			0.753803	−	0.657101i	$-0.228217\pi$
$83$	1140.00			1.50761			0.753803	+	0.657101i	$0.228217\pi$
$84$	42.0000	−	72.7461i	0.0545545	−	0.0944911i
$85$	115.500	−	200.052i	0.147385	−	0.255278i
$86$	−40.0000			−0.0501548
$87$	277.500	−	480.644i	0.341967	−	0.592304i
$88$	64.0000	+	110.851i	0.0775275	+	0.134282i
$89$	−429.000	−	743.050i	−0.510943	−	0.884979i	−0.999920	−	0.0126821i	$-0.995963\pi$
$89$	−429.000	−	743.050i	−0.510943	−	0.884979i	0.488977	−	0.872297i	$-0.337370\pi$
$90$	126.000			0.147573
$91$	91.0000	−	315.233i	0.104828	−	0.363137i
$92$	−176.000			−0.199449
$93$	−276.000	−	478.046i	−0.307741	−	0.533022i
$94$	88.0000	+	152.420i	0.0965586	+	0.167244i
$95$	−504.000	+	872.954i	−0.544309	+	0.942770i
$96$	96.0000			0.102062
$97$	431.000	−	746.514i	0.451149	−	0.781412i	−0.547309	−	0.836931i	$-0.684348\pi$
$97$	431.000	−	746.514i	0.451149	−	0.781412i	0.998458	+	0.0555182i	$0.0176811\pi$
$98$	−49.0000	+	84.8705i	−0.0505076	+	0.0874818i
$99$	−144.000			−0.146187
$100$	152.000	−	263.272i	0.152000	−	0.263272i
$101$	−635.500	−	1100.72i	−0.626085	−	1.08441i	−0.988330	−	0.152328i	$-0.951323\pi$
$101$	−635.500	−	1100.72i	−0.626085	−	1.08441i	0.362245	−	0.932083i	$-0.382010\pi$
$102$	99.0000	+	171.473i	0.0961026	+	0.166455i
$103$	1552.00			1.48469			0.742345	−	0.670018i	$-0.233713\pi$
$103$	1552.00			1.48469			0.742345	+	0.670018i	$0.233713\pi$
$104$	364.000	−	90.0666i	0.343203	−	0.0849208i
$105$	−147.000			−0.136626
$106$	−111.000	−	192.258i	−0.101710	−	0.176167i
$107$	−722.000	−	1250.54i	−0.652321	−	1.12985i	−0.982558	−	0.185955i	$-0.940462\pi$
$107$	−722.000	−	1250.54i	−0.652321	−	1.12985i	0.330237	−	0.943898i	$-0.392871\pi$
$108$	−54.0000	+	93.5307i	−0.0481125	+	0.0833333i
$109$	−362.000			−0.318104			−0.159052	−	0.987270i	$-0.550844\pi$
$109$	−362.000			−0.318104			−0.159052	+	0.987270i	$0.550844\pi$
$110$	112.000	−	193.990i	0.0970798	−	0.168147i
$111$	337.500	−	584.567i	0.288595	−	0.499862i
$112$	−112.000			−0.0944911
$113$	506.500	−	877.284i	0.421659	−	0.730336i	−0.574443	−	0.818545i	$-0.694781\pi$
$113$	506.500	−	877.284i	0.421659	−	0.730336i	0.996102	+	0.0882094i	$0.0281145\pi$
$114$	−432.000	−	748.246i	−0.354917	−	0.614734i
$115$	154.000	+	266.736i	0.124875	+	0.216289i
$116$	−740.000			−0.592304
$117$	−117.000	+	405.300i	−0.0924500	+	0.320256i
$118$	440.000			0.343265
$119$	−115.500	−	200.052i	−0.0889737	−	0.154107i
$120$	−84.0000	−	145.492i	−0.0639010	−	0.110680i
$121$	537.500	−	930.977i	0.403832	−	0.699457i
$122$	−538.000			−0.399248
$123$	247.500	−	428.683i	0.181434	−	0.314252i
$124$	−368.000	+	637.395i	−0.266511	+	0.461611i
$125$	−1407.00			−1.00677
$126$	63.0000	−	109.119i	0.0445435	−	0.0771517i
$127$	1102.00	+	1908.72i	0.769974	+	1.33363i	0.937576	+	0.347779i	$0.113064\pi$
$127$	1102.00	+	1908.72i	0.769974	+	1.33363i	−0.167603	+	0.985855i	$0.553603\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−60.0000			−0.0409512
$130$	−455.000	−	472.850i	−0.306970	−	0.319013i
$131$	616.000			0.410841			0.205420	−	0.978674i	$-0.434144\pi$
$131$	616.000			0.410841			0.205420	+	0.978674i	$0.434144\pi$
$132$	96.0000	+	166.277i	0.0633010	+	0.109640i
$133$	504.000	+	872.954i	0.328589	+	0.569133i
$134$	−700.000	+	1212.44i	−0.451275	+	0.781630i
$135$	189.000			0.120493
$136$	132.000	−	228.631i	0.0832273	−	0.144154i
$137$	466.500	−	808.002i	0.290918	−	0.503885i	−0.683109	−	0.730316i	$-0.739373\pi$
$137$	466.500	−	808.002i	0.290918	−	0.503885i	0.974027	+	0.226431i	$0.0727059\pi$
$138$	−264.000			−0.162849
$139$	−1088.00	+	1884.47i	−0.663906	+	1.14992i	0.315674	+	0.948868i	$0.397769\pi$
$139$	−1088.00	+	1884.47i	−0.663906	+	1.14992i	−0.979581	+	0.201052i	$0.935564\pi$
$140$	98.0000	+	169.741i	0.0591608	+	0.102470i
$141$	132.000	+	228.631i	0.0788398	+	0.136554i
$142$	2032.00			1.20086
$143$	520.000	+	540.400i	0.304088	+	0.316018i
$144$	144.000			0.0833333
$145$	647.500	+	1121.50i	0.370841	+	0.642315i
$146$	−947.000	−	1640.25i	−0.536810	−	0.929782i
$147$	−73.5000	+	127.306i	−0.0412393	+	0.0714286i
$148$	−900.000			−0.499862
$149$	−79.5000	+	137.698i	−0.0437107	+	0.0757091i	−0.887053	−	0.461668i	$-0.847251\pi$
$149$	−79.5000	+	137.698i	−0.0437107	+	0.0757091i	0.843342	+	0.537377i	$0.180585\pi$
$150$	228.000	−	394.908i	0.124107	−	0.214960i
$151$	−1500.00			−0.808399			−0.404200	−	0.914671i	$-0.632450\pi$
$151$	−1500.00			−0.808399			−0.404200	+	0.914671i	$0.632450\pi$
$152$	−576.000	+	997.661i	−0.307367	+	0.532375i
$153$	148.500	+	257.210i	0.0784674	+	0.135910i
$154$	−112.000	−	193.990i	−0.0586053	−	0.101507i
$155$	1288.00			0.667449
$156$	546.000	−	135.100i	0.280224	−	0.0693375i
$157$	1943.00			0.987696			0.493848	−	0.869548i	$-0.335590\pi$
$157$	1943.00			0.987696			0.493848	+	0.869548i	$0.335590\pi$
$158$	−1244.00	−	2154.67i	−0.626375	−	1.08491i
$159$	−166.500	−	288.386i	−0.0830460	−	0.143840i
$160$	−112.000	+	193.990i	−0.0553399	+	0.0958514i
$161$	308.000			0.150769
$162$	−81.0000	+	140.296i	−0.0392837	+	0.0680414i
$163$	380.000	−	658.179i	0.182601	−	0.316274i	−0.760165	−	0.649730i	$-0.774882\pi$
$163$	380.000	−	658.179i	0.182601	−	0.316274i	0.942765	+	0.333457i	$0.108215\pi$
$164$	−660.000			−0.314252
$165$	168.000	−	290.985i	0.0792653	−	0.137292i
$166$	−1140.00	−	1974.54i	−0.533019	−	0.923216i
$167$	714.000	+	1236.68i	0.330844	+	0.573039i	0.982678	−	0.185323i	$-0.0593332\pi$
$167$	714.000	+	1236.68i	0.330844	+	0.573039i	−0.651833	+	0.758362i	$0.726000\pi$
$168$	−168.000			−0.0771517
$169$	1943.50	−	1024.51i	0.884615	−	0.466321i
$170$	−462.000			−0.208434
$171$	−648.000	−	1122.37i	−0.289788	−	0.501928i
$172$	40.0000	+	69.2820i	0.0177324	+	0.0307134i
$173$	−1403.00	+	2430.07i	−0.616579	+	1.06795i	0.373527	+	0.927619i	$0.378148\pi$
$173$	−1403.00	+	2430.07i	−0.616579	+	1.06795i	−0.990105	+	0.140326i	$0.955185\pi$
$174$	−1110.00			−0.483614
$175$	−266.000	+	460.726i	−0.114901	+	0.199015i
$176$	128.000	−	221.703i	0.0548202	−	0.0949514i
$177$	660.000			0.280275
$178$	−858.000	+	1486.10i	−0.361291	+	0.625775i
$179$	−90.0000	−	155.885i	−0.0375805	−	0.0650914i	0.846623	−	0.532192i	$-0.178632\pi$
$179$	−90.0000	−	155.885i	−0.0375805	−	0.0650914i	−0.884204	+	0.467101i	$0.845298\pi$
$180$	−126.000	−	218.238i	−0.0521749	−	0.0903696i
$181$	−633.000			−0.259948			−0.129974	−	0.991517i	$-0.541489\pi$
$181$	−633.000			−0.259948			−0.129974	+	0.991517i	$0.541489\pi$
$182$	−637.000	+	157.617i	−0.259437	+	0.0641941i
$183$	−807.000			−0.325984
$184$	176.000	+	304.841i	0.0705157	+	0.122137i
$185$	787.500	+	1363.99i	0.312963	+	0.542068i
$186$	−552.000	+	956.092i	−0.217605	+	0.376904i
$187$	528.000			0.206477
$188$	176.000	−	304.841i	0.0682772	−	0.118260i
$189$	94.5000	−	163.679i	0.0363696	−	0.0629941i
$190$	2016.00			0.769768
$191$	−1852.00	+	3207.76i	−0.701602	+	1.21521i	0.266302	+	0.963890i	$0.414198\pi$
$191$	−1852.00	+	3207.76i	−0.701602	+	1.21521i	−0.967904	+	0.251321i	$0.919135\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	1266.50	+	2193.64i	0.472356	+	0.818144i	0.999500	−	0.0316319i	$-0.0100704\pi$
$193$	1266.50	+	2193.64i	0.472356	+	0.818144i	−0.527144	+	0.849776i	$0.676737\pi$
$194$	−1724.00			−0.638021
$195$	−682.500	−	709.275i	−0.250640	−	0.260473i
$196$	196.000			0.0714286
$197$	−111.000	−	192.258i	−0.0401443	−	0.0695319i	0.845255	−	0.534363i	$-0.179448\pi$
$197$	−111.000	−	192.258i	−0.0401443	−	0.0695319i	−0.885399	+	0.464831i	$0.846115\pi$
$198$	144.000	+	249.415i	0.0516850	+	0.0895211i
$199$	−142.000	+	245.951i	−0.0505835	+	0.0876132i	−0.890208	−	0.455553i	$-0.849441\pi$
$199$	−142.000	+	245.951i	−0.0505835	+	0.0876132i	0.839625	+	0.543166i	$0.182775\pi$
$200$	−608.000			−0.214960
$201$	−1050.00	+	1818.65i	−0.368464	+	0.638199i
$202$	−1271.00	+	2201.44i	−0.442709	+	0.766795i
$203$	1295.00			0.447740
$204$	198.000	−	342.946i	0.0679548	−	0.117701i
$205$	577.500	+	1000.26i	0.196753	+	0.340786i
$206$	−1552.00	−	2688.14i	−0.524917	−	0.909183i
$207$	−396.000			−0.132966
$208$	−520.000	−	540.400i	−0.173344	−	0.180144i
$209$	−2304.00			−0.762541
$210$	147.000	+	254.611i	0.0483046	+	0.0836660i
$211$	2588.00	+	4482.55i	0.844385	+	1.46252i	0.886154	+	0.463391i	$0.153367\pi$
$211$	2588.00	+	4482.55i	0.844385	+	1.46252i	−0.0417689	+	0.999127i	$0.513299\pi$
$212$	−222.000	+	384.515i	−0.0719199	+	0.124569i
$213$	3048.00			0.980495
$214$	−1444.00	+	2501.08i	−0.461261	+	0.798927i
$215$	70.0000	−	121.244i	0.0222045	−	0.0384593i
$216$	216.000			0.0680414
$217$	644.000	−	1115.44i	0.201463	−	0.348945i
$218$	362.000	+	627.002i	0.112467	+	0.194798i
$219$	−1420.50	−	2460.38i	−0.438304	−	0.759164i
$220$	−448.000			−0.137292
$221$	429.000	−	1486.10i	0.130578	−	0.452334i
$222$	−1350.00			−0.408135
$223$	−1032.00	−	1787.48i	−0.309901	−	0.536764i	0.668440	−	0.743766i	$-0.266962\pi$
$223$	−1032.00	−	1787.48i	−0.309901	−	0.536764i	−0.978340	+	0.207003i	$0.933629\pi$
$224$	112.000	+	193.990i	0.0334077	+	0.0578638i
$225$	342.000	−	592.361i	0.101333	−	0.175514i
$226$	−2026.00			−0.596316
$227$	−1632.00	+	2826.71i	−0.477179	+	0.826498i	−0.999658	−	0.0261539i	$-0.991674\pi$
$227$	−1632.00	+	2826.71i	−0.477179	+	0.826498i	0.522479	+	0.852652i	$0.325007\pi$
$228$	−864.000	+	1496.49i	−0.250964	+	0.434682i
$229$	2766.00			0.798177			0.399088	−	0.916913i	$-0.369327\pi$
$229$	2766.00			0.798177			0.399088	+	0.916913i	$0.369327\pi$
$230$	308.000	−	533.472i	0.0882996	−	0.152939i
$231$	−168.000	−	290.985i	−0.0478510	−	0.0828804i
$232$	740.000	+	1281.72i	0.209411	+	0.362711i
$233$	2762.00			0.776586			0.388293	−	0.921536i	$-0.373065\pi$
$233$	2762.00			0.776586			0.388293	+	0.921536i	$0.373065\pi$
$234$	819.000	−	202.650i	0.228802	−	0.0566139i
$235$	−616.000			−0.170993
$236$	−440.000	−	762.102i	−0.121363	−	0.210206i
$237$	−1866.00	−	3232.01i	−0.511433	−	0.885829i
$238$	−231.000	+	400.104i	−0.0629139	+	0.108970i
$239$	−6168.00			−1.66935			−0.834675	−	0.550742i	$-0.814345\pi$
$239$	−6168.00			−1.66935			−0.834675	+	0.550742i	$0.814345\pi$
$240$	−168.000	+	290.985i	−0.0451848	+	0.0782624i
$241$	1174.50	−	2034.29i	0.313926	−	0.543736i	−0.665283	−	0.746592i	$-0.731689\pi$
$241$	1174.50	−	2034.29i	0.313926	−	0.543736i	0.979209	+	0.202856i	$0.0650222\pi$
$242$	−2150.00			−0.571104
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	538.000	+	931.843i	0.141155	+	0.244488i
$245$	−171.500	−	297.047i	−0.0447214	−	0.0774597i
$246$	−990.000			−0.256586
$247$	−1872.00	+	6484.80i	−0.482237	+	1.67052i
$248$	1472.00			0.376904
$249$	−1710.00	−	2961.81i	−0.435208	−	0.753803i
$250$	1407.00	+	2437.00i	0.355946	+	0.616517i
$251$	−2652.00	+	4593.40i	−0.666903	+	1.15511i	0.311862	+	0.950127i	$0.399047\pi$
$251$	−2652.00	+	4593.40i	−0.666903	+	1.15511i	−0.978765	+	0.204983i	$0.934286\pi$
$252$	−252.000			−0.0629941
$253$	−352.000	+	609.682i	−0.0874706	+	0.151503i
$254$	2204.00	−	3817.44i	0.544454	−	0.943022i
$255$	−693.000			−0.170186
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	634.500	+	1098.99i	0.154004	+	0.266743i	0.932696	−	0.360664i	$-0.117450\pi$
$257$	634.500	+	1098.99i	0.154004	+	0.266743i	−0.778692	+	0.627406i	$0.784116\pi$
$258$	60.0000	+	103.923i	0.0144784	+	0.0250774i
$259$	1575.00			0.377860
$260$	−364.000	+	1260.93i	−0.0868243	+	0.300768i
$261$	−1665.00			−0.394869
$262$	−616.000	−	1066.94i	−0.145254	−	0.251588i
$263$	−3102.00	−	5372.82i	−0.727291	−	1.25970i	−0.958024	−	0.286688i	$-0.907446\pi$
$263$	−3102.00	−	5372.82i	−0.727291	−	1.25970i	0.230733	−	0.973017i	$-0.425888\pi$
$264$	192.000	−	332.554i	0.0447605	−	0.0775275i
$265$	777.000			0.180116
$266$	1008.00	−	1745.91i	0.232348	−	0.402438i
$267$	−1287.00	+	2229.15i	−0.294993	+	0.510943i
$268$	2800.00			0.638199
$269$	−1275.00	+	2208.36i	−0.288989	+	0.500544i	−0.973569	−	0.228394i	$-0.926653\pi$
$269$	−1275.00	+	2208.36i	−0.288989	+	0.500544i	0.684579	+	0.728938i	$0.259986\pi$
$270$	−189.000	−	327.358i	−0.0426006	−	0.0737865i
$271$	2338.00	+	4049.53i	0.524072	+	0.907719i	0.999607	+	0.0280221i	$0.00892089\pi$
$271$	2338.00	+	4049.53i	0.524072	+	0.907719i	−0.475536	+	0.879696i	$0.657746\pi$
$272$	−528.000			−0.117701
$273$	−955.500	+	236.425i	−0.211830	+	0.0524142i
$274$	−1866.00			−0.411420
$275$	−608.000	−	1053.09i	−0.133323	−	0.230922i
$276$	264.000	+	457.261i	0.0575758	+	0.0997243i
$277$	1714.50	−	2969.60i	0.371893	−	0.644137i	−0.617964	−	0.786206i	$-0.712042\pi$
$277$	1714.50	−	2969.60i	0.371893	−	0.644137i	0.989857	+	0.142069i	$0.0453755\pi$
$278$	4352.00			0.938905
$279$	−828.000	+	1434.14i	−0.177674	+	0.307741i
$280$	196.000	−	339.482i	0.0418330	−	0.0724569i
$281$	3023.00			0.641769			0.320884	−	0.947118i	$-0.396020\pi$
$281$	3023.00			0.641769			0.320884	+	0.947118i	$0.396020\pi$
$282$	264.000	−	457.261i	0.0557481	−	0.0965586i
$283$	−3536.00	−	6124.53i	−0.742733	−	1.28645i	−0.951247	−	0.308432i	$-0.900196\pi$
$283$	−3536.00	−	6124.53i	−0.742733	−	1.28645i	0.208514	−	0.978019i	$-0.433137\pi$
$284$	−2032.00	−	3519.53i	−0.424567	−	0.735372i
$285$	3024.00			0.628513
$286$	416.000	−	1441.07i	0.0860091	−	0.297944i
$287$	1155.00			0.237552
$288$	−144.000	−	249.415i	−0.0294628	−	0.0510310i
$289$	1912.00	+	3311.68i	0.389172	+	0.674065i
$290$	1295.00	−	2243.01i	0.262224	−	0.454186i
$291$	−2586.00			−0.520942
$292$	−1894.00	+	3280.50i	−0.379582	+	0.657455i
$293$	−2201.50	+	3813.11i	−0.438952	+	0.760288i	−0.997609	−	0.0691114i	$-0.977984\pi$
$293$	−2201.50	+	3813.11i	−0.438952	+	0.760288i	0.558657	+	0.829399i	$0.311317\pi$
$294$	294.000			0.0583212
$295$	−770.000	+	1333.68i	−0.151970	+	0.263220i
$296$	900.000	+	1558.85i	0.176728	+	0.306102i
$297$	216.000	+	374.123i	0.0422006	+	0.0730937i
$298$	318.000			0.0618163
$299$	1430.00	+	1486.10i	0.276585	+	0.287436i
$300$	−912.000			−0.175514
$301$	−70.0000	−	121.244i	−0.0134044	−	0.0232172i
$302$	1500.00	+	2598.08i	0.285812	+	0.495041i
$303$	−1906.50	+	3302.15i	−0.361471	+	0.626085i
$304$	2304.00			0.434682
$305$	941.500	−	1630.73i	0.176755	−	0.306148i
$306$	297.000	−	514.419i	0.0554848	−	0.0961026i
$307$	4364.00			0.811292			0.405646	−	0.914030i	$-0.367047\pi$
$307$	4364.00			0.811292			0.405646	+	0.914030i	$0.367047\pi$
$308$	−224.000	+	387.979i	−0.0414402	+	0.0717765i
$309$	−2328.00	−	4032.21i	−0.428593	−	0.742345i
$310$	−1288.00	−	2230.88i	−0.235979	−	0.408728i
$311$	−1536.00			−0.280060			−0.140030	−	0.990147i	$-0.544720\pi$
$311$	−1536.00			−0.280060			−0.140030	+	0.990147i	$0.544720\pi$
$312$	−780.000	−	810.600i	−0.141535	−	0.147087i
$313$	−6886.00			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−6886.00			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−1943.00	−	3365.37i	−0.349203	−	0.604838i
$315$	220.500	+	381.917i	0.0394405	+	0.0683130i
$316$	−2488.00	+	4309.34i	−0.442914	+	0.767150i
$317$	−7677.00			−1.36020			−0.680100	−	0.733120i	$-0.738064\pi$
$317$	−7677.00			−1.36020			−0.680100	+	0.733120i	$0.738064\pi$
$318$	−333.000	+	576.773i	−0.0587224	+	0.101710i
$319$	−1480.00	+	2563.44i	−0.259762	+	0.449921i
$320$	448.000			0.0782624
$321$	−2166.00	+	3751.62i	−0.376618	+	0.652321i
$322$	−308.000	−	533.472i	−0.0533049	−	0.0923267i
$323$	2376.00	+	4115.35i	0.409301	+	0.708930i
$324$	324.000			0.0555556
$325$	−3458.00	+	855.633i	−0.590201	+	0.146037i
$326$	−1520.00			−0.258236
$327$	543.000	+	940.504i	0.0918287	+	0.159052i
$328$	660.000	+	1143.15i	0.111105	+	0.192439i
$329$	−308.000	+	533.472i	−0.0516127	+	0.0893959i
$330$	−672.000			−0.112098
$331$	−4.00000	+	6.92820i	−0.000664229	+	0.00115048i	−0.866357	−	0.499425i	$-0.833545\pi$
$331$	−4.00000	+	6.92820i	−0.000664229	+	0.00115048i	0.865693	+	0.500575i	$0.166878\pi$
$332$	−2280.00	+	3949.08i	−0.376901	+	0.652812i
$333$	−2025.00			−0.333241
$334$	1428.00	−	2473.37i	0.233942	−	0.405200i
$335$	−2450.00	−	4243.52i	−0.399576	−	0.692085i
$336$	168.000	+	290.985i	0.0272772	+	0.0472456i
$337$	−1201.00			−0.194132			−0.0970662	−	0.995278i	$-0.530946\pi$
$337$	−1201.00			−0.194132			−0.0970662	+	0.995278i	$0.530946\pi$
$338$	−3718.00	−	2341.73i	−0.598321	−	0.376845i
$339$	−3039.00			−0.486890
$340$	462.000	+	800.207i	0.0736926	+	0.127639i
$341$	1472.00	+	2549.58i	0.233763	+	0.404890i
$342$	−1296.00	+	2244.74i	−0.204911	+	0.354917i
$343$	−343.000			−0.0539949
$344$	80.0000	−	138.564i	0.0125387	−	0.0217177i
$345$	462.000	−	800.207i	0.0720964	−	0.124875i
$346$	5612.00			0.871974
$347$	3750.00	−	6495.19i	0.580146	−	1.00484i	−0.415316	−	0.909677i	$-0.636329\pi$
$347$	3750.00	−	6495.19i	0.580146	−	1.00484i	0.995462	−	0.0951645i	$-0.0303377\pi$
$348$	1110.00	+	1922.58i	0.170983	+	0.296152i
$349$	925.000	+	1602.15i	0.141874	+	0.245733i	0.928202	−	0.372076i	$-0.121354\pi$
$349$	925.000	+	1602.15i	0.141874	+	0.245733i	−0.786328	+	0.617809i	$0.788020\pi$
$350$	1064.00			0.162495
$351$	1228.50	−	303.975i	0.186816	−	0.0462250i
$352$	−512.000			−0.0775275
$353$	−1061.50	−	1838.57i	−0.160051	−	0.277216i	0.774836	−	0.632162i	$-0.217832\pi$
$353$	−1061.50	−	1838.57i	−0.160051	−	0.277216i	−0.934887	+	0.354946i	$0.884499\pi$
$354$	−660.000	−	1143.15i	−0.0990921	−	0.171633i
$355$	−3556.00	+	6159.17i	−0.531642	+	0.920831i
$356$	3432.00			0.510943
$357$	−346.500	+	600.156i	−0.0513690	+	0.0889737i
$358$	−180.000	+	311.769i	−0.0265735	+	0.0460266i
$359$	5268.00			0.774469			0.387235	−	0.921981i	$-0.373430\pi$
$359$	5268.00			0.774469			0.387235	+	0.921981i	$0.373430\pi$
$360$	−252.000	+	436.477i	−0.0368932	+	0.0639010i
$361$	−6938.50	−	12017.8i	−1.01159	−	1.75213i
$362$	633.000	+	1096.39i	0.0919054	+	0.159185i
$363$	−3225.00			−0.466305
$364$	910.000	+	945.700i	0.131036	+	0.136176i
$365$	6629.00			0.950624
$366$	807.000	+	1397.77i	0.115253	+	0.199624i
$367$	−5890.00	−	10201.8i	−0.837753	−	1.45103i	−0.891769	−	0.452491i	$-0.850535\pi$
$367$	−5890.00	−	10201.8i	−0.837753	−	1.45103i	0.0540154	−	0.998540i	$-0.482798\pi$
$368$	352.000	−	609.682i	0.0498621	−	0.0863638i
$369$	−1485.00			−0.209501
$370$	1575.00	−	2727.98i	0.221298	−	0.383300i
$371$	388.500	−	672.902i	0.0543663	−	0.0941653i
$372$	2208.00			0.307741
$373$	7080.50	−	12263.8i	0.982880	−	1.70240i	0.331880	−	0.943322i	$-0.392317\pi$
$373$	7080.50	−	12263.8i	0.982880	−	1.70240i	0.651001	−	0.759077i	$-0.274349\pi$
$374$	−528.000	−	914.523i	−0.0730006	−	0.126441i
$375$	2110.50	+	3655.49i	0.290629	+	0.503384i
$376$	−704.000			−0.0965586
$377$	6012.50	+	6248.37i	0.821378	+	0.853601i
$378$	−378.000			−0.0514344
$379$	−2930.00	−	5074.91i	−0.397108	−	0.687811i	0.596260	−	0.802792i	$-0.296653\pi$
$379$	−2930.00	−	5074.91i	−0.397108	−	0.687811i	−0.993368	+	0.114980i	$0.963320\pi$
$380$	−2016.00	−	3491.81i	−0.272154	−	0.471385i
$381$	3306.00	−	5726.16i	0.444545	−	0.769974i
$382$	7408.00			0.992215
$383$	−4968.00	+	8604.83i	−0.662801	+	1.14801i	0.317075	+	0.948400i	$0.397299\pi$
$383$	−4968.00	+	8604.83i	−0.662801	+	1.14801i	−0.979876	+	0.199605i	$0.936034\pi$
$384$	−192.000	+	332.554i	−0.0255155	+	0.0441942i
$385$	784.000			0.103783
$386$	2533.00	−	4387.28i	0.334006	−	0.578515i
$387$	90.0000	+	155.885i	0.0118216	+	0.0204756i
$388$	1724.00	+	2986.06i	0.225574	+	0.390706i
$389$	3735.00			0.486818			0.243409	−	0.969924i	$-0.421734\pi$
$389$	3735.00			0.486818			0.243409	+	0.969924i	$0.421734\pi$
$390$	−546.000	+	1891.40i	−0.0708918	+	0.245576i
$391$	1452.00			0.187803
$392$	−196.000	−	339.482i	−0.0252538	−	0.0437409i
$393$	−924.000	−	1600.41i	−0.118600	−	0.205420i
$394$	−222.000	+	384.515i	−0.0283863	+	0.0491665i
$395$	8708.00			1.10923
$396$	288.000	−	498.831i	0.0365468	−	0.0633010i
$397$	−3859.00	+	6683.98i	−0.487853	+	0.844986i	−0.999902	−	0.0139698i	$-0.995553\pi$
$397$	−3859.00	+	6683.98i	−0.487853	+	0.844986i	0.512049	+	0.858956i	$0.328886\pi$
$398$	568.000			0.0715358
$399$	1512.00	−	2618.86i	0.189711	−	0.328589i
$400$	608.000	+	1053.09i	0.0760000	+	0.131636i
$401$	1576.50	+	2730.58i	0.196326	+	0.340046i	0.947334	−	0.320246i	$-0.103766\pi$
$401$	1576.50	+	2730.58i	0.196326	+	0.340046i	−0.751009	+	0.660293i	$0.770432\pi$
$402$	4200.00			0.521087
$403$	8372.00	−	2071.53i	1.03484	−	0.256056i
$404$	5084.00			0.626085
$405$	−283.500	−	491.036i	−0.0347833	−	0.0602464i
$406$	−1295.00	−	2243.01i	−0.158300	−	0.274184i
$407$	−1800.00	+	3117.69i	−0.219220	+	0.379701i
$408$	−792.000			−0.0961026
$409$	−1179.50	+	2042.95i	−0.142598	+	0.246987i	−0.928474	−	0.371397i	$-0.878879\pi$
$409$	−1179.50	+	2042.95i	−0.142598	+	0.246987i	0.785876	+	0.618384i	$0.212212\pi$
$410$	1155.00	−	2000.52i	0.139125	−	0.240972i
$411$	−2799.00			−0.335923
$412$	−3104.00	+	5376.29i	−0.371173	+	0.642890i
$413$	770.000	+	1333.68i	0.0917415	+	0.158901i
$414$	396.000	+	685.892i	0.0470105	+	0.0814245i
$415$	7980.00			0.943910
$416$	−416.000	+	1441.07i	−0.0490290	+	0.169842i
$417$	6528.00			0.766613
$418$	2304.00	+	3990.65i	0.269599	+	0.466959i
$419$	−5436.00	−	9415.43i	−0.633809	−	1.09779i	−0.986766	−	0.162150i	$-0.948157\pi$
$419$	−5436.00	−	9415.43i	−0.633809	−	1.09779i	0.352957	−	0.935639i	$-0.385176\pi$
$420$	294.000	−	509.223i	0.0341565	−	0.0591608i
$421$	7711.00			0.892663			0.446332	−	0.894868i	$-0.352730\pi$
$421$	7711.00			0.892663			0.446332	+	0.894868i	$0.352730\pi$
$422$	5176.00	−	8965.09i	0.597070	−	1.03416i
$423$	396.000	−	685.892i	0.0455182	−	0.0788398i
$424$	888.000			0.101710
$425$	−1254.00	+	2171.99i	−0.143125	+	0.247899i
$426$	−3048.00	−	5279.29i	−0.346657	−	0.600428i
$427$	−941.500	−	1630.73i	−0.106703	−	0.184816i
$428$	5776.00			0.652321
$429$	624.000	−	2161.60i	0.0702261	−	0.243270i
$430$	−280.000			−0.0314019
$431$	−4518.00	−	7825.41i	−0.504929	−	0.874563i	−0.999984	−	0.00570091i	$-0.998185\pi$
$431$	−4518.00	−	7825.41i	−0.504929	−	0.874563i	0.495055	−	0.868862i	$-0.335148\pi$
$432$	−216.000	−	374.123i	−0.0240563	−	0.0416667i
$433$	−1497.50	+	2593.75i	−0.166202	+	0.287869i	−0.937081	−	0.349111i	$-0.886484\pi$
$433$	−1497.50	+	2593.75i	−0.166202	+	0.287869i	0.770880	+	0.636981i	$0.219817\pi$
$434$	−2576.00			−0.284912
$435$	1942.50	−	3364.51i	0.214105	−	0.370841i
$436$	724.000	−	1254.00i	0.0795259	−	0.137743i
$437$	−6336.00			−0.693574
$438$	−2841.00	+	4920.76i	−0.309927	+	0.536810i
$439$	6002.00	+	10395.8i	0.652528	+	1.13021i	0.982507	+	0.186224i	$0.0596249\pi$
$439$	6002.00	+	10395.8i	0.652528	+	1.13021i	−0.329979	+	0.943988i	$0.607042\pi$
$440$	448.000	+	775.959i	0.0485399	+	0.0840736i
$441$	441.000			0.0476190
$442$	−3003.00	+	743.050i	−0.323163	+	0.0799622i
$443$	−11400.0			−1.22264			−0.611321	−	0.791383i	$-0.709362\pi$
$443$	−11400.0			−1.22264			−0.611321	+	0.791383i	$0.709362\pi$
$444$	1350.00	+	2338.27i	0.144298	+	0.249931i
$445$	−3003.00	−	5201.35i	−0.319901	−	0.554084i
$446$	−2064.00	+	3574.95i	−0.219133	+	0.379549i
$447$	477.000			0.0504728
$448$	224.000	−	387.979i	0.0236228	−	0.0409159i
$449$	7295.00	−	12635.3i	0.766754	−	1.32806i	−0.172561	−	0.984999i	$-0.555204\pi$
$449$	7295.00	−	12635.3i	0.766754	−	1.32806i	0.939315	−	0.343057i	$-0.111462\pi$
$450$	−1368.00			−0.143307
$451$	−1320.00	+	2286.31i	−0.137819	+	0.238710i
$452$	2026.00	+	3509.13i	0.210830	+	0.365168i
$453$	2250.00	+	3897.11i	0.233365	+	0.404200i
$454$	6528.00			0.674833
$455$	637.000	−	2206.63i	0.0656330	−	0.227359i
$456$	3456.00			0.354917
$457$	−2583.50	−	4474.75i	−0.264444	−	0.458031i	0.702974	−	0.711216i	$-0.251855\pi$
$457$	−2583.50	−	4474.75i	−0.264444	−	0.458031i	−0.967418	+	0.253185i	$0.918522\pi$
$458$	−2766.00	−	4790.85i	−0.282198	−	0.488781i
$459$	445.500	−	771.629i	0.0453032	−	0.0784674i
$460$	−1232.00			−0.124875
$461$	6724.50	−	11647.2i	0.679374	−	1.17671i	−0.295796	−	0.955251i	$-0.595585\pi$
$461$	6724.50	−	11647.2i	0.679374	−	1.17671i	0.975170	−	0.221458i	$-0.0710817\pi$
$462$	−336.000	+	581.969i	−0.0338358	+	0.0586053i
$463$	10540.0			1.05796			0.528980	−	0.848634i	$-0.322575\pi$
$463$	10540.0			1.05796			0.528980	+	0.848634i	$0.322575\pi$
$464$	1480.00	−	2563.44i	0.148076	−	0.256475i
$465$	−1932.00	−	3346.32i	−0.192676	−	0.333725i
$466$	−2762.00	−	4783.92i	−0.274565	−	0.475560i
$467$	3976.00			0.393977			0.196989	−	0.980406i	$-0.436884\pi$
$467$	3976.00			0.393977			0.196989	+	0.980406i	$0.436884\pi$
$468$	−1170.00	−	1215.90i	−0.115563	−	0.120096i
$469$	−4900.00			−0.482433
$470$	616.000	+	1066.94i	0.0604552	+	0.104712i
$471$	−2914.50	−	5048.06i	−0.285123	−	0.493848i
$472$	−880.000	+	1524.20i	−0.0858163	+	0.148638i
$473$	320.000			0.0311070
$474$	−3732.00	+	6464.01i	−0.361638	+	0.626375i
$475$	5472.00	−	9477.78i	0.528574	−	0.915517i
$476$	924.000			0.0889737
$477$	−499.500	+	865.159i	−0.0479466	+	0.0830460i
$478$	6168.00	+	10683.3i	0.590205	+	1.02226i
$479$	−2634.00	−	4562.22i	−0.251254	−	0.435184i	0.712618	−	0.701553i	$-0.247510\pi$
$479$	−2634.00	−	4562.22i	−0.251254	−	0.435184i	−0.963871	+	0.266369i	$0.914176\pi$
$480$	672.000			0.0639010
$481$	7312.50	+	7599.37i	0.693184	+	0.720378i
$482$	−4698.00			−0.443959
$483$	−462.000	−	800.207i	−0.0435232	−	0.0753845i
$484$	2150.00	+	3723.91i	0.201916	+	0.349729i
$485$	3017.00	−	5225.60i	0.282464	−	0.489242i
$486$	486.000			0.0453609
$487$	−1810.00	+	3135.01i	−0.168417	+	0.291706i	−0.937863	−	0.347005i	$-0.887199\pi$
$487$	−1810.00	+	3135.01i	−0.168417	+	0.291706i	0.769447	+	0.638711i	$0.220532\pi$
$488$	1076.00	−	1863.69i	0.0998119	−	0.172879i
$489$	−2280.00			−0.210849
$490$	−343.000	+	594.093i	−0.0316228	+	0.0547723i
$491$	1382.00	+	2393.69i	0.127024	+	0.220012i	0.922522	−	0.385944i	$-0.126124\pi$
$491$	1382.00	+	2393.69i	0.127024	+	0.220012i	−0.795498	+	0.605956i	$0.792791\pi$
$492$	990.000	+	1714.73i	0.0907168	+	0.157126i
$493$	6105.00			0.557719
$494$	13104.0	−	3242.40i	1.19348	−	0.295309i
$495$	−1008.00			−0.0915277
$496$	−1472.00	−	2549.58i	−0.133256	−	0.230805i
$497$	3556.00	+	6159.17i	0.320942	+	0.555889i
$498$	−3420.00	+	5923.61i	−0.307739	+	0.533019i
$499$	−5708.00			−0.512074			−0.256037	−	0.966667i	$-0.582417\pi$
$499$	−5708.00			−0.512074			−0.256037	+	0.966667i	$0.582417\pi$
$500$	2814.00	−	4873.99i	0.251692	−	0.435943i
$501$	2142.00	−	3710.05i	0.191013	−	0.330844i
$502$	10608.0			0.943144
$503$	−7282.00	+	12612.8i	−0.645504	+	1.11805i	0.338681	+	0.940901i	$0.390019\pi$
$503$	−7282.00	+	12612.8i	−0.645504	+	1.11805i	−0.984185	+	0.177144i	$0.943314\pi$
$504$	252.000	+	436.477i	0.0222718	+	0.0385758i
$505$	−4448.50	−	7705.03i	−0.391991	−	0.678949i
$506$	1408.00			0.123702
$507$	−5577.00	−	3512.60i	−0.488527	−	0.307692i
$508$	−8816.00			−0.769974
$509$	9966.50	+	17262.5i	0.867893	+	1.50323i	0.864146	+	0.503241i	$0.167859\pi$
$509$	9966.50	+	17262.5i	0.867893	+	1.50323i	0.00374660	+	0.999993i	$0.498807\pi$
$510$	693.000	+	1200.31i	0.0601697	+	0.104217i
$511$	3314.50	−	5740.88i	0.286937	−	0.496990i
$512$	512.000			0.0441942
$513$	−1944.00	+	3367.11i	−0.167309	+	0.289788i
$514$	1269.00	−	2197.97i	0.108897	−	0.188616i
$515$	10864.0			0.929563
$516$	120.000	−	207.846i	0.0102378	−	0.0177324i
$517$	−704.000	−	1219.36i	−0.0598876	−	0.103728i
$518$	−1575.00	−	2727.98i	−0.133594	−	0.231391i
$519$	8418.00			0.711964
$520$	2548.00	−	630.466i	0.214879	−	0.0531688i
$521$	−15669.0			−1.31760			−0.658802	−	0.752317i	$-0.728936\pi$
$521$	−15669.0			−1.31760			−0.658802	+	0.752317i	$0.728936\pi$
$522$	1665.00	+	2883.86i	0.139607	+	0.241807i
$523$	−1308.00	−	2265.52i	−0.109359	−	0.189416i	0.806152	−	0.591709i	$-0.201547\pi$
$523$	−1308.00	−	2265.52i	−0.109359	−	0.189416i	−0.915511	+	0.402293i	$0.868213\pi$
$524$	−1232.00	+	2133.89i	−0.102710	+	0.177899i
$525$	1596.00			0.132676
$526$	−6204.00	+	10745.6i	−0.514272	+	0.890746i
$527$	3036.00	−	5258.51i	0.250949	−	0.434657i
$528$	−768.000			−0.0633010
$529$	5115.50	−	8860.31i	0.420441	−	0.728224i
$530$	−777.000	−	1345.80i	−0.0636806	−	0.110298i
$531$	−990.000	−	1714.73i	−0.0809084	−	0.140137i
$532$	−4032.00			−0.328589
$533$	5362.50	+	5572.87i	0.435789	+	0.452885i
$534$	5148.00			0.417183
$535$	−5054.00	−	8753.78i	−0.408418	−	0.707400i
$536$	−2800.00	−	4849.74i	−0.225637	−	0.390815i
$537$	−270.000	+	467.654i	−0.0216971	+	0.0375805i
$538$	5100.00			0.408693
$539$	392.000	−	678.964i	0.0313259	−	0.0542580i
$540$	−378.000	+	654.715i	−0.0301232	+	0.0521749i
$541$	12419.0			0.986940			0.493470	−	0.869763i	$-0.335728\pi$
$541$	12419.0			0.986940			0.493470	+	0.869763i	$0.335728\pi$
$542$	4676.00	−	8099.07i	0.370575	−	0.641854i
$543$	949.500	+	1644.58i	0.0750404	+	0.129974i
$544$	528.000	+	914.523i	0.0416136	+	0.0720769i
$545$	−2534.00			−0.199164
$546$	1365.00	+	1418.55i	0.106990	+	0.111187i
$547$	−19328.0			−1.51080			−0.755398	−	0.655266i	$-0.772557\pi$
$547$	−19328.0			−1.51080			−0.755398	+	0.655266i	$0.772557\pi$
$548$	1866.00	+	3232.01i	0.145459	+	0.251942i
$549$	1210.50	+	2096.65i	0.0941036	+	0.162992i
$550$	−1216.00	+	2106.17i	−0.0942735	+	0.163286i
$551$	−26640.0			−2.05971
$552$	528.000	−	914.523i	0.0407123	−	0.0705157i
$553$	4354.00	−	7541.35i	0.334812	−	0.579911i
$554$	−6858.00			−0.525936
$555$	2362.50	−	4091.97i	0.180689	−	0.312963i
$556$	−4352.00	−	7537.89i	−0.331953	−	0.574960i
$557$	−3403.50	−	5895.03i	−0.258907	−	0.448439i	0.707043	−	0.707171i	$-0.250029\pi$
$557$	−3403.50	−	5895.03i	−0.258907	−	0.448439i	−0.965949	+	0.258732i	$0.916695\pi$
$558$	3312.00			0.251269
$559$	260.000	−	900.666i	0.0196723	−	0.0681469i
$560$	−784.000			−0.0591608
$561$	−792.000	−	1371.78i	−0.0596048	−	0.103238i
$562$	−3023.00	−	5235.99i	−0.226900	−	0.393002i
$563$	−10802.0	+	18709.6i	−0.808615	+	1.40056i	0.105209	+	0.994450i	$0.466449\pi$
$563$	−10802.0	+	18709.6i	−0.808615	+	1.40056i	−0.913824	+	0.406111i	$0.866884\pi$
$564$	−1056.00			−0.0788398
$565$	3545.50	−	6140.99i	0.264001	−	0.457262i
$566$	−7072.00	+	12249.1i	−0.525191	+	0.909658i
$567$	−567.000			−0.0419961
$568$	−4064.00	+	7039.05i	−0.300214	+	0.519986i
$569$	−9157.00	−	15860.4i	−0.674660	−	1.16855i	−0.976568	−	0.215208i	$-0.930957\pi$
$569$	−9157.00	−	15860.4i	−0.674660	−	1.16855i	0.301908	−	0.953337i	$-0.402376\pi$
$570$	−3024.00	−	5237.72i	−0.222213	−	0.384884i
$571$	−18192.0			−1.33330			−0.666648	−	0.745373i	$-0.732271\pi$
$571$	−18192.0			−1.33330			−0.666648	+	0.745373i	$0.732271\pi$
$572$	−2912.00	+	720.533i	−0.212862	+	0.0526696i
$573$	11112.0			0.810140
$574$	−1155.00	−	2000.52i	−0.0839874	−	0.145470i
$575$	−1672.00	−	2895.99i	−0.121265	−	0.210037i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−11313.0			−0.816233			−0.408116	−	0.912930i	$-0.633814\pi$
$577$	−11313.0			−0.816233			−0.408116	+	0.912930i	$0.633814\pi$
$578$	3824.00	−	6623.36i	0.275186	−	0.476636i
$579$	3799.50	−	6580.93i	0.272715	−	0.472356i
$580$	−5180.00			−0.370841
$581$	3990.00	−	6910.88i	0.284911	−	0.493480i
$582$	2586.00	+	4479.08i	0.184181	+	0.319010i
$583$	888.000	+	1538.06i	0.0630827	+	0.109262i
$584$	7576.00			0.536810
$585$	−819.000	+	2837.10i	−0.0578829	+	0.200512i
$586$	8806.00			0.620772
$587$	12208.0	+	21144.9i	0.858395	+	1.48678i	0.873459	+	0.486898i	$0.161872\pi$
$587$	12208.0	+	21144.9i	0.858395	+	1.48678i	−0.0150635	+	0.999887i	$0.504795\pi$
$588$	−294.000	−	509.223i	−0.0206197	−	0.0357143i
$589$	−13248.0	+	22946.2i	−0.926782	+	1.60523i
$590$	3080.00			0.214918
$591$	−333.000	+	576.773i	−0.0231773	+	0.0401443i
$592$	1800.00	−	3117.69i	0.124965	−	0.216447i
$593$	13267.0			0.918736			0.459368	−	0.888246i	$-0.348076\pi$
$593$	13267.0			0.918736			0.459368	+	0.888246i	$0.348076\pi$
$594$	432.000	−	748.246i	0.0298404	−	0.0516850i
$595$	−808.500	−	1400.36i	−0.0557063	−	0.0964862i
$596$	−318.000	−	550.792i	−0.0218553	−	0.0378546i
$597$	852.000			0.0584088
$598$	1144.00	−	3962.93i	0.0782302	−	0.270997i
$599$	22088.0			1.50666			0.753332	−	0.657641i	$-0.228446\pi$
$599$	22088.0			1.50666			0.753332	+	0.657641i	$0.228446\pi$
$600$	912.000	+	1579.63i	0.0620537	+	0.107480i
$601$	−8913.50	−	15438.6i	−0.604974	−	1.04785i	−0.992056	−	0.125800i	$-0.959850\pi$
$601$	−8913.50	−	15438.6i	−0.604974	−	1.04785i	0.387082	−	0.922045i	$-0.373483\pi$
$602$	−140.000	+	242.487i	−0.00947836	+	0.0164170i
$603$	6300.00			0.425466
$604$	3000.00	−	5196.15i	0.202100	−	0.350047i
$605$	3762.50	−	6516.84i	0.252839	−	0.437929i
$606$	7626.00			0.511196
$607$	−2718.00	+	4707.71i	−0.181747	+	0.314794i	−0.942475	−	0.334275i	$-0.891508\pi$
$607$	−2718.00	+	4707.71i	−0.181747	+	0.314794i	0.760729	+	0.649070i	$0.224842\pi$
$608$	−2304.00	−	3990.65i	−0.153683	−	0.266188i
$609$	−1942.50	−	3364.51i	−0.129251	−	0.223870i
$610$	−3766.00			−0.249969
$611$	−4004.00	+	990.733i	−0.265114	+	0.0655986i
$612$	−1188.00			−0.0784674
$613$	5580.50	+	9665.71i	0.367690	+	0.636859i	0.989204	−	0.146545i	$-0.0468153\pi$
$613$	5580.50	+	9665.71i	0.367690	+	0.636859i	−0.621514	+	0.783403i	$0.713482\pi$
$614$	−4364.00	−	7558.67i	−0.286835	−	0.496813i
$615$	1732.50	−	3000.78i	0.113595	−	0.196753i
$616$	896.000			0.0586053
$617$	−407.500	+	705.811i	−0.0265889	+	0.0460533i	−0.879014	−	0.476797i	$-0.841798\pi$
$617$	−407.500	+	705.811i	−0.0265889	+	0.0460533i	0.852425	+	0.522850i	$0.175131\pi$
$618$	−4656.00	+	8064.43i	−0.303061	+	0.524917i
$619$	−1916.00			−0.124411			−0.0622056	−	0.998063i	$-0.519813\pi$
$619$	−1916.00			−0.124411			−0.0622056	+	0.998063i	$0.519813\pi$
$620$	−2576.00	+	4461.76i	−0.166862	+	0.289014i
$621$	594.000	+	1028.84i	0.0383839	+	0.0664829i
$622$	1536.00	+	2660.43i	0.0990161	+	0.171501i
$623$	−6006.00			−0.386236
$624$	−624.000	+	2161.60i	−0.0400320	+	0.138675i
$625$	−349.000			−0.0223360
$626$	6886.00	+	11926.9i	0.439648	+	0.761493i
$627$	3456.00	+	5985.97i	0.220127	+	0.381270i
$628$	−3886.00	+	6730.75i	−0.246924	+	0.427685i
$629$	7425.00			0.470674
$630$	441.000	−	763.834i	0.0278887	−	0.0483046i
$631$	−428.000	+	741.318i	−0.0270022	+	0.0467692i	−0.879211	−	0.476433i	$-0.841929\pi$
$631$	−428.000	+	741.318i	−0.0270022	+	0.0467692i	0.852209	+	0.523202i	$0.175263\pi$
$632$	9952.00			0.626375
$633$	7764.00	−	13447.6i	0.487506	−	0.844385i
$634$	7677.00	+	13297.0i	0.480903	+	0.832949i
$635$	7714.00	+	13361.0i	0.482080	+	0.834987i
$636$	1332.00			0.0830460
$637$	−1592.50	−	1654.97i	−0.0990536	−	0.102940i
$638$	5920.00			0.367359
$639$	−4572.00	−	7918.94i	−0.283045	−	0.490248i
$640$	−448.000	−	775.959i	−0.0276699	−	0.0479257i
$641$	−3263.50	+	5652.55i	−0.201093	+	0.348303i	−0.948881	−	0.315635i	$-0.897783\pi$
$641$	−3263.50	+	5652.55i	−0.201093	+	0.348303i	0.747788	+	0.663938i	$0.231116\pi$
$642$	8664.00			0.532618
$643$	−6274.00	+	10866.9i	−0.384794	+	0.666482i	−0.991741	−	0.128260i	$-0.959061\pi$
$643$	−6274.00	+	10866.9i	−0.384794	+	0.666482i	0.606947	+	0.794742i	$0.292394\pi$
$644$	−616.000	+	1066.94i	−0.0376922	+	0.0652849i
$645$	−420.000			−0.0256395
$646$	4752.00	−	8230.71i	0.289419	−	0.501289i
$647$	7988.00	+	13835.6i	0.485380	+	0.840702i	0.999859	−	0.0168005i	$-0.00534803\pi$
$647$	7988.00	+	13835.6i	0.485380	+	0.840702i	−0.514479	+	0.857503i	$0.672015\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−3520.00			−0.212900
$650$	4940.00	+	5133.80i	0.298097	+	0.309791i
$651$	−3864.00			−0.232630
$652$	1520.00	+	2632.72i	0.0913003	+	0.158137i
$653$	−555.000	−	961.288i	−0.0332601	−	0.0576081i	0.848916	−	0.528527i	$-0.177256\pi$
$653$	−555.000	−	961.288i	−0.0332601	−	0.0576081i	−0.882176	+	0.470919i	$0.843922\pi$
$654$	1086.00	−	1881.01i	0.0649327	−	0.112467i
$655$	4312.00			0.257227
$656$	1320.00	−	2286.31i	0.0785630	−	0.136075i
$657$	−4261.50	+	7381.13i	−0.253055	+	0.438304i
$658$	1232.00			0.0729914
$659$	−9852.00	+	17064.2i	−0.582366	+	1.00869i	0.412832	+	0.910807i	$0.364540\pi$
$659$	−9852.00	+	17064.2i	−0.582366	+	1.00869i	−0.995198	+	0.0978808i	$0.968794\pi$
$660$	672.000	+	1163.94i	0.0396327	+	0.0686458i
$661$	5286.50	+	9156.49i	0.311076	+	0.538799i	0.978596	−	0.205793i	$-0.0659774\pi$
$661$	5286.50	+	9156.49i	0.311076	+	0.538799i	−0.667520	+	0.744592i	$0.732644\pi$
$662$	16.0000			0.000939362
$663$	−4504.50	+	1114.57i	−0.263862	+	0.0652888i
$664$	9120.00			0.533019
$665$	3528.00	+	6110.68i	0.205729	+	0.356334i
$666$	2025.00	+	3507.40i	0.117819	+	0.204068i
$667$	−4070.00	+	7049.45i	−0.236268	+	0.409229i
$668$	−5712.00			−0.330844
$669$	−3096.00	+	5362.43i	−0.178921	+	0.309901i
$670$	−4900.00	+	8487.05i	−0.282543	+	0.489378i
$671$	4304.00			0.247622
$672$	336.000	−	581.969i	0.0192879	−	0.0334077i
$673$	−3009.50	−	5212.61i	−0.172374	−	0.298561i	0.766875	−	0.641796i	$-0.221810\pi$
$673$	−3009.50	−	5212.61i	−0.172374	−	0.298561i	−0.939249	+	0.343236i	$0.888477\pi$
$674$	1201.00	+	2080.19i	0.0686362	+	0.118881i
$675$	−2052.00			−0.117010
$676$	−338.000	+	8781.50i	−0.0192308	+	0.499630i
$677$	−20130.0			−1.14278			−0.571388	−	0.820680i	$-0.693595\pi$
$677$	−20130.0			−1.14278			−0.571388	+	0.820680i	$0.693595\pi$
$678$	3039.00	+	5263.70i	0.172142	+	0.298158i
$679$	−3017.00	−	5225.60i	−0.170518	−	0.295346i
$680$	924.000	−	1600.41i	0.0521085	−	0.0902546i
$681$	9792.00			0.550999
$682$	2944.00	−	5099.16i	0.165296	−	0.286300i
$683$	16496.0	−	28571.9i	0.924161	−	1.60069i	0.131256	−	0.991349i	$-0.458099\pi$
$683$	16496.0	−	28571.9i	0.924161	−	1.60069i	0.792905	−	0.609345i	$-0.208568\pi$
$684$	5184.00			0.289788
$685$	3265.50	−	5656.01i	0.182144	−	0.315482i
$686$	343.000	+	594.093i	0.0190901	+	0.0330650i
$687$	−4149.00	−	7186.28i	−0.230414	−	0.399088i
$688$	−320.000			−0.0177324
$689$	5050.50	−	1249.67i	0.279258	−	0.0690984i
$690$	−1848.00			−0.101960
$691$	904.000	+	1565.77i	0.0497681	+	0.0862009i	0.889836	−	0.456280i	$-0.150818\pi$
$691$	904.000	+	1565.77i	0.0497681	+	0.0862009i	−0.840068	+	0.542481i	$0.817485\pi$
$692$	−5612.00	−	9720.27i	−0.308289	−	0.533973i
$693$	−504.000	+	872.954i	−0.0276268	+	0.0478510i
$694$	−15000.0			−0.820450
$695$	−7616.00	+	13191.3i	−0.415671	+	0.719963i
$696$	2220.00	−	3845.15i	0.120904	−	0.209411i
$697$	5445.00			0.295903
$698$	1850.00	−	3204.29i	0.100320	−	0.173760i
$699$	−4143.00	−	7175.89i	−0.224181	−	0.388293i
$700$	−1064.00	−	1842.90i	−0.0574506	−	0.0995074i
$701$	6390.00			0.344290			0.172145	−	0.985072i	$-0.444930\pi$
$701$	6390.00			0.344290			0.172145	+	0.985072i	$0.444930\pi$
$702$	−1755.00	−	1823.85i	−0.0943564	−	0.0980581i
$703$	−32400.0			−1.73825
$704$	512.000	+	886.810i	0.0274101	+	0.0474757i
$705$	924.000	+	1600.41i	0.0493615	+	0.0854966i
$706$	−2123.00	+	3677.14i	−0.113173	+	0.196021i
$707$	−8897.00			−0.473276
$708$	−1320.00	+	2286.31i	−0.0700687	+	0.121363i
$709$	2892.50	−	5009.96i	0.153216	−	0.265378i	−0.779192	−	0.626785i	$-0.784370\pi$
$709$	2892.50	−	5009.96i	0.153216	−	0.265378i	0.932408	+	0.361407i	$0.117704\pi$
$710$	14224.0			0.751855
$711$	−5598.00	+	9696.02i	−0.295276	+	0.511433i
$712$	−3432.00	−	5944.40i	−0.180646	−	0.312887i
$713$	4048.00	+	7011.34i	0.212621	+	0.368270i
$714$	1386.00			0.0726467
$715$	3640.00	+	3782.80i	0.190389	+	0.197858i
$716$	720.000			0.0375805
$717$	9252.00	+	16024.9i	0.481900	+	0.834675i
$718$	−5268.00	−	9124.44i	−0.273816	−	0.474264i
$719$	−9038.00	+	15654.3i	−0.468791	+	0.811969i	−0.999364	−	0.0356700i	$-0.988643\pi$
$719$	−9038.00	+	15654.3i	−0.468791	+	0.811969i	0.530573	+	0.847639i	$0.321977\pi$
$720$	1008.00			0.0521749
$721$	5432.00	−	9408.50i	0.280580	−	0.485979i
$722$	−13877.0	+	24035.7i	−0.715303	+	1.23894i
$723$	−7047.00			−0.362491
$724$	1266.00	−	2192.78i	0.0649869	−	0.112561i
$725$	−7030.00	−	12176.3i	−0.360121	−	0.623748i
$726$	3225.00	+	5585.86i	0.164864	+	0.285552i
$727$	−12656.0			−0.645647			−0.322823	−	0.946459i	$-0.604632\pi$
$727$	−12656.0			−0.645647			−0.322823	+	0.946459i	$0.604632\pi$
$728$	728.000	−	2521.87i	0.0370625	−	0.128388i
$729$	729.000			0.0370370
$730$	−6629.00	−	11481.8i	−0.336096	−	0.582136i
$731$	−330.000	−	571.577i	−0.0166970	−	0.0289200i
$732$	1614.00	−	2795.53i	0.0814961	−	0.141155i
$733$	11459.0			0.577419			0.288709	−	0.957417i	$-0.406774\pi$
$733$	11459.0			0.577419			0.288709	+	0.957417i	$0.406774\pi$
$734$	−11780.0	+	20403.6i	−0.592381	+	1.02603i
$735$	−514.500	+	891.140i	−0.0258199	+	0.0447214i
$736$	−1408.00			−0.0705157
$737$	5600.00	−	9699.48i	0.279890	−	0.484783i
$738$	1485.00	+	2572.10i	0.0740699	+	0.128293i
$739$	−7512.00	−	13011.2i	−0.373929	−	0.647664i	0.616237	−	0.787561i	$-0.288656\pi$
$739$	−7512.00	−	13011.2i	−0.373929	−	0.647664i	−0.990166	+	0.139897i	$0.955323\pi$
$740$	−6300.00			−0.312963
$741$	19656.0	−	4863.60i	0.974469	−	0.241118i
$742$	−1554.00			−0.0768856
$743$	12920.0	+	22378.1i	0.637939	+	1.10494i	0.985884	+	0.167428i	$0.0535462\pi$
$743$	12920.0	+	22378.1i	0.637939	+	1.10494i	−0.347945	+	0.937515i	$0.613120\pi$
$744$	−2208.00	−	3824.37i	−0.108803	−	0.188452i
$745$	−556.500	+	963.886i	−0.0273672	+	0.0474014i
$746$	−28322.0			−1.39000
$747$	−5130.00	+	8885.42i	−0.251268	+	0.435208i
$748$	−1056.00	+	1829.05i	−0.0516192	+	0.0894071i
$749$	−10108.0			−0.493109
$750$	4221.00	−	7310.99i	0.205506	−	0.355946i
$751$	−20010.0	−	34658.3i	−0.972271	−	1.68402i	−0.688663	−	0.725082i	$-0.741802\pi$
$751$	−20010.0	−	34658.3i	−0.972271	−	1.68402i	−0.283608	−	0.958940i	$-0.591531\pi$
$752$	704.000	+	1219.36i	0.0341386	+	0.0591298i
$753$	15912.0			0.770074
$754$	4810.00	−	16662.3i	0.232321	−	0.804783i
$755$	−10500.0			−0.506138
$756$	378.000	+	654.715i	0.0181848	+	0.0314970i
$757$	−519.000	−	898.934i	−0.0249186	−	0.0431603i	0.853297	−	0.521425i	$-0.174599\pi$
$757$	−519.000	−	898.934i	−0.0249186	−	0.0431603i	−0.878216	+	0.478265i	$0.841266\pi$
$758$	−5860.00	+	10149.8i	−0.280798	+	0.486356i
$759$	2112.00			0.101002
$760$	−4032.00	+	6983.63i	−0.192442	+	0.333320i
$761$	−10437.0	+	18077.4i	−0.497163	+	0.861111i	−0.999995	−	0.00327293i	$-0.998958\pi$
$761$	−10437.0	+	18077.4i	−0.497163	+	0.861111i	0.502832	+	0.864384i	$0.332292\pi$
$762$	−13224.0			−0.628681
$763$	−1267.00	+	2194.51i	−0.0601160	+	0.104124i
$764$	−7408.00	−	12831.0i	−0.350801	−	0.607605i
$765$	1039.50	+	1800.47i	0.0491284	+	0.0850928i
$766$	19872.0			0.937343
$767$	−2860.00	+	9907.33i	−0.134640	+	0.466405i
$768$	768.000			0.0360844
$769$	1527.00	+	2644.84i	0.0716060	+	0.124025i	0.899605	−	0.436704i	$-0.143854\pi$
$769$	1527.00	+	2644.84i	0.0716060	+	0.124025i	−0.827999	+	0.560729i	$0.810521\pi$
$770$	−784.000	−	1357.93i	−0.0366927	−	0.0635537i
$771$	1903.50	−	3296.96i	0.0889142	−	0.154004i
$772$	−10132.0			−0.472356
$773$	−3863.00	+	6690.91i	−0.179744	+	0.311327i	−0.941793	−	0.336193i	$-0.890860\pi$
$773$	−3863.00	+	6690.91i	−0.179744	+	0.311327i	0.762049	+	0.647520i	$0.224194\pi$
$774$	180.000	−	311.769i	0.00835913	−	0.0144784i
$775$	−13984.0			−0.648155
$776$	3448.00	−	5972.11i	0.159505	−	0.276271i
$777$	−2362.50	−	4091.97i	−0.109079	−	0.188930i
$778$	−3735.00	−	6469.21i	−0.172116	−	0.298114i
$779$	−23760.0			−1.09280
$780$	3822.00	−	945.700i	0.175448	−	0.0434122i
$781$	−16256.0			−0.744796
$782$	−1452.00	−	2514.94i	−0.0663982	−	0.115005i
$783$	2497.50	+	4325.80i	0.113989	+	0.197435i
$784$	−392.000	+	678.964i	−0.0178571	+	0.0309295i
$785$	13601.0			0.618396
$786$	−1848.00	+	3200.83i	−0.0838626	+	0.145254i
$787$	−8392.00	+	14535.4i	−0.380105	+	0.658361i	−0.991077	−	0.133291i	$-0.957445\pi$
$787$	−8392.00	+	14535.4i	−0.380105	+	0.658361i	0.610972	+	0.791652i	$0.290779\pi$
$788$	888.000			0.0401443
$789$	−9306.00	+	16118.5i	−0.419902	+	0.727291i
$790$	−8708.00	−	15082.7i	−0.392173	−	0.679264i
$791$	−3545.50	−	6140.99i	−0.159372	−	0.276041i
$792$	−1152.00			−0.0516850
$793$	3497.00	−	12114.0i	0.156598	−	0.542471i
$794$	15436.0			0.689928
$795$	−1165.50	−	2018.71i	−0.0519950	−	0.0900580i
$796$	−568.000	−	983.805i	−0.0252917	−	0.0438066i
$797$	−19659.0	+	34050.4i	−0.873723	+	1.51333i	−0.0156068	+	0.999878i	$0.504968\pi$
$797$	−19659.0	+	34050.4i	−0.873723	+	1.51333i	−0.858117	+	0.513455i	$0.828365\pi$
$798$	−6048.00			−0.268292
$799$	−1452.00	+	2514.94i	−0.0642904	+	0.111354i
$800$	1216.00	−	2106.17i	0.0537401	−	0.0930806i
$801$	7722.00			0.340629
$802$	3153.00	−	5461.16i	0.138823	−	0.240449i
$803$	7576.00	+	13122.0i	0.332941	+	0.576670i
$804$	−4200.00	−	7274.61i	−0.184232	−	0.319099i
$805$	2156.00			0.0943963
$806$	−11960.0	−	12429.2i	−0.522671	−	0.543176i
$807$	7650.00			0.333696
$808$	−5084.00	−	8805.75i	−0.221355	−	0.383397i
$809$	−6205.50	−	10748.2i	−0.269683	−	0.467105i	0.699097	−	0.715027i	$-0.253586\pi$
$809$	−6205.50	−	10748.2i	−0.269683	−	0.467105i	−0.968780	+	0.247922i	$0.920252\pi$
$810$	−567.000	+	982.073i	−0.0245955	+	0.0426006i
$811$	−8920.00			−0.386219			−0.193109	−	0.981177i	$-0.561857\pi$
$811$	−8920.00			−0.386219			−0.193109	+	0.981177i	$0.561857\pi$
$812$	−2590.00	+	4486.01i	−0.111935	+	0.193877i
$813$	7014.00	−	12148.6i	0.302573	−	0.524072i
$814$	7200.00			0.310024
$815$	2660.00	−	4607.26i	0.114326	−	0.198019i
$816$	792.000	+	1371.78i	0.0339774	+	0.0588506i
$817$	1440.00	+	2494.15i	0.0616637	+	0.106805i
$818$	4718.00			0.201664
$819$	2047.50	+	2127.82i	0.0873571	+	0.0907841i
$820$	−4620.00			−0.196753
$821$	−2951.00	−	5111.28i	−0.125445	−	0.217278i	0.796462	−	0.604689i	$-0.206703\pi$
$821$	−2951.00	−	5111.28i	−0.125445	−	0.217278i	−0.921907	+	0.387411i	$0.873369\pi$
$822$	2799.00	+	4848.01i	0.118767	+	0.205710i
$823$	4374.00	−	7575.99i	0.185259	−	0.320878i	−0.758405	−	0.651784i	$-0.774021\pi$
$823$	4374.00	−	7575.99i	0.185259	−	0.320878i	0.943664	+	0.330906i	$0.107354\pi$
$824$	12416.0			0.524917
$825$	−1824.00	+	3159.26i	−0.0769740	+	0.133323i
$826$	1540.00	−	2667.36i	0.0648710	−	0.112360i
$827$	−3540.00			−0.148849			−0.0744243	−	0.997227i	$-0.523712\pi$
$827$	−3540.00			−0.148849			−0.0744243	+	0.997227i	$0.523712\pi$
$828$	792.000	−	1371.78i	0.0332414	−	0.0575758i
$829$	−20661.5	−	35786.8i	−0.865626	−	1.49931i	−0.866425	−	0.499308i	$-0.833588\pi$
$829$	−20661.5	−	35786.8i	−0.865626	−	1.49931i	0.000799214	−	1.00000i	$-0.499746\pi$
$830$	−7980.00	−	13821.8i	−0.333723	−	0.578025i
$831$	−10287.0			−0.429425
$832$	2912.00	−	720.533i	0.121341	−	0.0300240i
$833$	−1617.00			−0.0672578
$834$	−6528.00	−	11306.8i	−0.271039	−	0.469453i
$835$	4998.00	+	8656.79i	0.207141	+	0.358779i
$836$	4608.00	−	7981.29i	0.190635	−	0.330190i
$837$	4968.00			0.205160
$838$	−10872.0	+	18830.9i	−0.448171	+	0.776254i
$839$	22306.0	−	38635.1i	0.917865	−	1.58979i	0.115213	−	0.993341i	$-0.463245\pi$
$839$	22306.0	−	38635.1i	0.917865	−	1.58979i	0.802652	−	0.596448i	$-0.203422\pi$
$840$	−1176.00			−0.0483046
$841$	−4918.00	+	8518.23i	−0.201648	+	0.349265i
$842$	−7711.00	−	13355.8i	−0.315604	−	0.546642i
$843$	−4534.50	−	7853.98i	−0.185263	−	0.320884i
$844$	−20704.0			−0.844385
$845$	13604.5	−	7171.56i	0.553857	−	0.291963i
$846$	−1584.00			−0.0643724
$847$	−3762.50	−	6516.84i	−0.152634	−	0.264370i
$848$	−888.000	−	1538.06i	−0.0359600	−	0.0622845i
$849$	−10608.0	+	18373.6i	−0.428817	+	0.742733i
$850$	5016.00			0.202409
$851$	−4950.00	+	8573.65i	−0.199393	+	0.345360i
$852$	−6096.00	+	10558.6i	−0.245124	+	0.424567i
$853$	32587.0			1.30804			0.654020	−	0.756478i	$-0.273081\pi$
$853$	32587.0			1.30804			0.654020	+	0.756478i	$0.273081\pi$
$854$	−1883.00	+	3261.45i	−0.0754507	+	0.130685i
$855$	−4536.00	−	7856.58i	−0.181436	−	0.314257i
$856$	−5776.00	−	10004.3i	−0.230630	−	0.399464i
$857$	−24061.0			−0.959053			−0.479526	−	0.877528i	$-0.659191\pi$
$857$	−24061.0			−0.959053			−0.479526	+	0.877528i	$0.659191\pi$
$858$	−4368.00	+	1080.80i	−0.173801	+	0.0430045i
$859$	−13324.0			−0.529231			−0.264615	−	0.964354i	$-0.585245\pi$
$859$	−13324.0			−0.529231			−0.264615	+	0.964354i	$0.585245\pi$
$860$	280.000	+	484.974i	0.0111022	+	0.0192296i
$861$	−1732.50	−	3000.78i	−0.0685754	−	0.118776i
$862$	−9036.00	+	15650.8i	−0.357039	+	0.618409i
$863$	7640.00			0.301354			0.150677	−	0.988583i	$-0.451855\pi$
$863$	7640.00			0.301354			0.150677	+	0.988583i	$0.451855\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−9821.00	+	17010.5i	−0.386039	+	0.668640i
$866$	5990.00			0.235044
$867$	5736.00	−	9935.04i	0.224688	−	0.389172i
$868$	2576.00	+	4461.76i	0.100732	+	0.174472i
$869$	9952.00	+	17237.4i	0.388491	+	0.672886i
$870$	−7770.00			−0.302790
$871$	−22750.0	−	23642.5i	−0.885022	−	0.919742i
$872$	−2896.00			−0.112467
$873$	3879.00	+	6718.63i	0.150383	+	0.260471i
$874$	6336.00	+	10974.3i	0.245216	+	0.424726i
$875$	−4924.50	+	8529.48i	−0.190261	+	0.329542i
$876$	11364.0			0.438304
$877$	−12385.5	+	21452.3i	−0.476886	+	0.825990i	−0.999649	−	0.0264877i	$-0.991568\pi$
$877$	−12385.5	+	21452.3i	−0.476886	+	0.825990i	0.522764	+	0.852478i	$0.324901\pi$
$878$	12004.0	−	20791.5i	0.461407	−	0.799180i
$879$	13209.0			0.506858
$880$	896.000	−	1551.92i	0.0343229	−	0.0594490i
$881$	11938.5	+	20678.1i	0.456547	+	0.790763i	0.998776	−	0.0494679i	$-0.0157525\pi$
$881$	11938.5	+	20678.1i	0.456547	+	0.790763i	−0.542228	+	0.840231i	$0.682419\pi$
$882$	−441.000	−	763.834i	−0.0168359	−	0.0291606i
$883$	−1172.00			−0.0446670			−0.0223335	−	0.999751i	$-0.507110\pi$
$883$	−1172.00			−0.0446670			−0.0223335	+	0.999751i	$0.507110\pi$
$884$	4290.00	+	4458.30i	0.163222	+	0.169625i
$885$	4620.00			0.175480
$886$	11400.0	+	19745.4i	0.432269	+	0.748712i
$887$	962.000	+	1666.23i	0.0364158	+	0.0630740i	0.883659	−	0.468131i	$-0.155073\pi$
$887$	962.000	+	1666.23i	0.0364158	+	0.0630740i	−0.847243	+	0.531205i	$0.821739\pi$
$888$	2700.00	−	4676.54i	0.102034	−	0.176728i
$889$	15428.0			0.582046
$890$	−6006.00	+	10402.7i	−0.226204	+	0.391797i
$891$	648.000	−	1122.37i	0.0243646	−	0.0422006i
$892$	8256.00			0.309901
$893$	6336.00	−	10974.3i	0.237431	−	0.411243i
$894$	−477.000	−	826.188i	−0.0178448	−	0.0309081i
$895$	−630.000	−	1091.19i	−0.0235291	−	0.0407537i
$896$	−896.000			−0.0334077
$897$	1716.00	−	5944.40i	0.0638747	−	0.221268i
$898$	−29180.0			−1.08435
$899$	17020.0	+	29479.5i	0.631422	+	1.09366i
$900$	1368.00	+	2369.45i	0.0506667	+	0.0877572i
$901$	1831.50	−	3172.25i	0.0677204	−	0.117295i
$902$	5280.00			0.194906
$903$	−210.000	+	363.731i	−0.00773905	+	0.0134044i
$904$	4052.00	−	7018.27i	0.149079	−	0.258213i
$905$	−4431.00			−0.162753
$906$	4500.00	−	7794.23i	0.165014	−	0.285812i
$907$	−11916.0	−	20639.1i	−0.436234	−	0.755580i	0.561161	−	0.827706i	$-0.310355\pi$
$907$	−11916.0	−	20639.1i	−0.436234	−	0.755580i	−0.997395	+	0.0721268i	$0.977021\pi$
$908$	−6528.00	−	11306.8i	−0.238590	−	0.413249i
$909$	11439.0			0.417390
$910$	−4459.00	+	1103.32i	−0.162433	+	0.0401918i
$911$	−27084.0			−0.984998			−0.492499	−	0.870313i	$-0.663916\pi$
$911$	−27084.0			−0.984998			−0.492499	+	0.870313i	$0.663916\pi$
$912$	−3456.00	−	5985.97i	−0.125482	−	0.217341i
$913$	9120.00	+	15796.3i	0.330589	+	0.572597i
$914$	−5167.00	+	8949.51i	−0.186990	+	0.323877i
$915$	−5649.00			−0.204099
$916$	−5532.00	+	9581.71i	−0.199544	+	0.345621i
$917$	2156.00	−	3734.30i	0.0776416	−	0.134479i
$918$	−1782.00			−0.0640684
$919$	21630.0	−	37464.3i	0.776396	−	1.34476i	−0.157611	−	0.987501i	$-0.550379\pi$
$919$	21630.0	−	37464.3i	0.776396	−	1.34476i	0.934007	−	0.357256i	$-0.116288\pi$
$920$	1232.00	+	2133.89i	0.0441498	+	0.0764697i
$921$	−6546.00	−	11338.0i	−0.234200	−	0.405646i
$922$	−26898.0			−0.960779
$923$	−13208.0	+	45753.9i	−0.471015	+	1.63164i
$924$	1344.00			0.0478510
$925$	−8550.00	−	14809.0i	−0.303916	−	0.526398i
$926$	−10540.0	−	18255.8i	−0.374045	−	0.647865i
$927$	−6984.00	+	12096.6i	−0.247448	+	0.428593i
$928$	−5920.00			−0.209411
$929$	23680.5	−	41015.8i	0.836310	−	1.44853i	−0.0566493	−	0.998394i	$-0.518042\pi$
$929$	23680.5	−	41015.8i	0.836310	−	1.44853i	0.892959	−	0.450137i	$-0.148625\pi$
$930$	−3864.00	+	6692.64i	−0.136243	+	0.235979i
$931$	7056.00			0.248390
$932$	−5524.00	+	9567.85i	−0.194147	+	0.336272i
$933$	2304.00	+	3990.65i	0.0808463	+	0.140030i
$934$	−3976.00	−	6886.63i	−0.139292	−	0.241261i
$935$	3696.00			0.129275
$936$	−936.000	+	3242.40i	−0.0326860	+	0.113228i
$937$	43179.0			1.50544			0.752720	−	0.658341i	$-0.228742\pi$
$937$	43179.0			1.50544			0.752720	+	0.658341i	$0.228742\pi$
$938$	4900.00	+	8487.05i	0.170566	+	0.295429i
$939$	10329.0	+	17890.4i	0.358971	+	0.621757i
$940$	1232.00	−	2133.89i	0.0427483	−	0.0740422i
$941$	33398.0			1.15701			0.578504	−	0.815680i	$-0.303637\pi$
$941$	33398.0			1.15701			0.578504	+	0.815680i	$0.303637\pi$
$942$	−5829.00	+	10096.1i	−0.201613	+	0.349203i
$943$	−3630.00	+	6287.34i	−0.125354	+	0.217120i
$944$	3520.00			0.121363
$945$	661.500	−	1145.75i	0.0227710	−	0.0394405i
$946$	−320.000	−	554.256i	−0.0109980	−	0.0190491i
$947$	−9318.00	−	16139.2i	−0.319741	−	0.553807i	0.660693	−	0.750656i	$-0.270262\pi$
$947$	−9318.00	−	16139.2i	−0.319741	−	0.553807i	−0.980434	+	0.196849i	$0.936929\pi$
$948$	14928.0			0.511433
$949$	43088.5	−	10661.6i	1.47388	−	0.364691i
$950$	−21888.0			−0.747516
$951$	11515.5	+	19945.4i	0.392656	+	0.680100i
$952$	−924.000	−	1600.41i	−0.0314569	−	0.0544850i
$953$	2251.00	−	3898.85i	0.0765132	−	0.132525i	−0.825230	−	0.564797i	$-0.808955\pi$
$953$	2251.00	−	3898.85i	0.0765132	−	0.132525i	0.901743	+	0.432272i	$0.142288\pi$
$954$	1998.00			0.0678067
$955$	−12964.0	+	22454.3i	−0.439272	+	0.760842i
$956$	12336.0	−	21366.6i	0.417338	−	0.722850i
$957$	8880.00			0.299947
$958$	−5268.00	+	9124.44i	−0.177663	+	0.307722i
$959$	−3265.50	−	5656.01i	−0.109957	−	0.190451i
$960$	−672.000	−	1163.94i	−0.0225924	−	0.0391312i
$961$	4065.00			0.136451
$962$	5850.00	−	20265.0i	0.196062	−	0.679178i
$963$	12996.0			0.434881
$964$	4698.00	+	8137.17i	0.156963	+	0.271868i
$965$	8865.50	+	15355.5i	0.295741	+	0.512239i
$966$	−924.000	+	1600.41i	−0.0307756	+	0.0533049i
$967$	−48184.0			−1.60237			−0.801186	−	0.598416i	$-0.795797\pi$
$967$	−48184.0			−1.60237			−0.801186	+	0.598416i	$0.795797\pi$
$968$	4300.00	−	7447.82i	0.142776	−	0.247295i
$969$	7128.00	−	12346.1i	0.236310	−	0.409301i
$970$	−12068.0			−0.399464
$971$	−546.000	+	945.700i	−0.0180453	+	0.0312554i	−0.874907	−	0.484291i	$-0.839078\pi$
$971$	−546.000	+	945.700i	−0.0180453	+	0.0312554i	0.856862	+	0.515546i	$0.172411\pi$
$972$	−486.000	−	841.777i	−0.0160375	−	0.0277778i
$973$	7616.00	+	13191.3i	0.250933	+	0.434629i
$974$	7240.00			0.238177
$975$	7410.00	+	7700.70i	0.243395	+	0.252943i
$976$	−4304.00			−0.141155
$977$	−13759.5	−	23832.2i	−0.450568	−	0.780407i	0.547853	−	0.836575i	$-0.315445\pi$
$977$	−13759.5	−	23832.2i	−0.450568	−	0.780407i	−0.998421	+	0.0561672i	$0.982112\pi$
$978$	2280.00	+	3949.08i	0.0745464	+	0.129118i
$979$	6864.00	−	11888.8i	0.224080	−	0.388118i
$980$	1372.00			0.0447214
$981$	1629.00	−	2821.51i	0.0530173	−	0.0918287i
$982$	2764.00	−	4787.39i	0.0898195	−	0.155572i
$983$	47176.0			1.53070			0.765351	−	0.643613i	$-0.222565\pi$
$983$	47176.0			1.53070			0.765351	+	0.643613i	$0.222565\pi$
$984$	1980.00	−	3429.46i	0.0641464	−	0.111105i
$985$	−777.000	−	1345.80i	−0.0251343	−	0.0435339i
$986$	−6105.00	−	10574.2i	−0.197183	−	0.341532i
$987$	1848.00			0.0595973
$988$	−18720.0	−	19454.4i	−0.602796	−	0.626444i
$989$	880.000			0.0282936
$990$	1008.00	+	1745.91i	0.0323599	+	0.0560491i
$991$	27372.0	+	47409.7i	0.877397	+	1.51970i	0.854187	+	0.519965i	$0.174055\pi$
$991$	27372.0	+	47409.7i	0.877397	+	1.51970i	0.0232094	+	0.999731i	$0.492612\pi$
$992$	−2944.00	+	5099.16i	−0.0942259	+	0.163204i
$993$	24.0000			0.000766986
$994$	7112.00	−	12318.3i	0.226941	−	0.393073i
$995$	−994.000	+	1721.66i	−0.0316703	+	0.0548545i
$996$	13680.0			0.435208
$997$	−30005.5	+	51971.1i	−0.953143	+	1.65089i	−0.214582	+	0.976706i	$0.568839\pi$
$997$	−30005.5	+	51971.1i	−0.953143	+	1.65089i	−0.738561	+	0.674186i	$0.764494\pi$
$998$	5708.00	+	9886.55i	0.181046	+	0.313580i
$999$	3037.50	+	5261.10i	0.0961984	+	0.166621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.l.a.211.1	✓	2
13.9	even	3	inner	546.4.l.a.295.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.l.a.211.1	✓	2	1.1	even	1	trivial
546.4.l.a.295.1	yes	2	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +7.00000 q^{5} +(-3.00000 + 5.19615i) q^{6} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-7.00000 - 12.1244i) q^{10} +(8.00000 + 13.8564i) q^{11} +12.0000 q^{12} +(45.5000 - 11.2583i) q^{13} -14.0000 q^{14} +(-10.5000 - 18.1865i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(16.5000 - 28.5788i) q^{17} +18.0000 q^{18} +(-72.0000 + 124.708i) q^{19} +(-14.0000 + 24.2487i) q^{20} -21.0000 q^{21} +(16.0000 - 27.7128i) q^{22} +(22.0000 + 38.1051i) q^{23} +(-12.0000 - 20.7846i) q^{24} -76.0000 q^{25} +(-65.0000 - 67.5500i) q^{26} +27.0000 q^{27} +(14.0000 + 24.2487i) q^{28} +(92.5000 + 160.215i) q^{29} +(-21.0000 + 36.3731i) q^{30} +184.000 q^{31} +(-16.0000 + 27.7128i) q^{32} +(24.0000 - 41.5692i) q^{33} -66.0000 q^{34} +(24.5000 - 42.4352i) q^{35} +(-18.0000 - 31.1769i) q^{36} +(112.500 + 194.856i) q^{37} +288.000 q^{38} +(-97.5000 - 101.325i) q^{39} +56.0000 q^{40} +(82.5000 + 142.894i) q^{41} +(21.0000 + 36.3731i) q^{42} +(10.0000 - 17.3205i) q^{43} -64.0000 q^{44} +(-31.5000 + 54.5596i) q^{45} +(44.0000 - 76.2102i) q^{46} -88.0000 q^{47} +(-24.0000 + 41.5692i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(76.0000 + 131.636i) q^{50} -99.0000 q^{51} +(-52.0000 + 180.133i) q^{52} +111.000 q^{53} +(-27.0000 - 46.7654i) q^{54} +(56.0000 + 96.9948i) q^{55} +(28.0000 - 48.4974i) q^{56} +432.000 q^{57} +(185.000 - 320.429i) q^{58} +(-110.000 + 190.526i) q^{59} +84.0000 q^{60} +(134.500 - 232.961i) q^{61} +(-184.000 - 318.697i) q^{62} +(31.5000 + 54.5596i) q^{63} +64.0000 q^{64} +(318.500 - 78.8083i) q^{65} -96.0000 q^{66} +(-350.000 - 606.218i) q^{67} +(66.0000 + 114.315i) q^{68} +(66.0000 - 114.315i) q^{69} -98.0000 q^{70} +(-508.000 + 879.882i) q^{71} +(-36.0000 + 62.3538i) q^{72} +947.000 q^{73} +(225.000 - 389.711i) q^{74} +(114.000 + 197.454i) q^{75} +(-288.000 - 498.831i) q^{76} +112.000 q^{77} +(-78.0000 + 270.200i) q^{78} +1244.00 q^{79} +(-56.0000 - 96.9948i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(165.000 - 285.788i) q^{82} +1140.00 q^{83} +(42.0000 - 72.7461i) q^{84} +(115.500 - 200.052i) q^{85} -40.0000 q^{86} +(277.500 - 480.644i) q^{87} +(64.0000 + 110.851i) q^{88} +(-429.000 - 743.050i) q^{89} +126.000 q^{90} +(91.0000 - 315.233i) q^{91} -176.000 q^{92} +(-276.000 - 478.046i) q^{93} +(88.0000 + 152.420i) q^{94} +(-504.000 + 872.954i) q^{95} +96.0000 q^{96} +(431.000 - 746.514i) q^{97} +(-49.0000 + 84.8705i) q^{98} -144.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} + 14 q^{5} - 6 q^{6} + 7 q^{7} + 16 q^{8} - 9 q^{9} - 14 q^{10} + 16 q^{11} + 24 q^{12} + 91 q^{13} - 28 q^{14} - 21 q^{15} - 16 q^{16} + 33 q^{17} + 36 q^{18} - 144 q^{19}+ \cdots - 288 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 + 14 * q^5 - 6 * q^6 + 7 * q^7 + 16 * q^8 - 9 * q^9 - 14 * q^10 + 16 * q^11 + 24 * q^12 + 91 * q^13 - 28 * q^14 - 21 * q^15 - 16 * q^16 + 33 * q^17 + 36 * q^18 - 144 * q^19 - 28 * q^20 - 42 * q^21 + 32 * q^22 + 44 * q^23 - 24 * q^24 - 152 * q^25 - 130 * q^26 + 54 * q^27 + 28 * q^28 + 185 * q^29 - 42 * q^30 + 368 * q^31 - 32 * q^32 + 48 * q^33 - 132 * q^34 + 49 * q^35 - 36 * q^36 + 225 * q^37 + 576 * q^38 - 195 * q^39 + 112 * q^40 + 165 * q^41 + 42 * q^42 + 20 * q^43 - 128 * q^44 - 63 * q^45 + 88 * q^46 - 176 * q^47 - 48 * q^48 - 49 * q^49 + 152 * q^50 - 198 * q^51 - 104 * q^52 + 222 * q^53 - 54 * q^54 + 112 * q^55 + 56 * q^56 + 864 * q^57 + 370 * q^58 - 220 * q^59 + 168 * q^60 + 269 * q^61 - 368 * q^62 + 63 * q^63 + 128 * q^64 + 637 * q^65 - 192 * q^66 - 700 * q^67 + 132 * q^68 + 132 * q^69 - 196 * q^70 - 1016 * q^71 - 72 * q^72 + 1894 * q^73 + 450 * q^74 + 228 * q^75 - 576 * q^76 + 224 * q^77 - 156 * q^78 + 2488 * q^79 - 112 * q^80 - 81 * q^81 + 330 * q^82 + 2280 * q^83 + 84 * q^84 + 231 * q^85 - 80 * q^86 + 555 * q^87 + 128 * q^88 - 858 * q^89 + 252 * q^90 + 182 * q^91 - 352 * q^92 - 552 * q^93 + 176 * q^94 - 1008 * q^95 + 192 * q^96 + 862 * q^97 - 98 * q^98 - 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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