LMFDB - Embedded newform 91.4.f.a.29.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [91,4,Mod(22,91)] 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("91.22"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(91, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.36917381052$
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			29.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	91.29
Dual form			91.4.f.a.22.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.50000 + 4.33013i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-8.50000 + 14.7224i) q^{4} -19.0000 q^{5} +(5.00000 - 8.66025i) q^{6} +(-3.50000 + 6.06218i) q^{7} -45.0000 q^{8} +(11.5000 - 19.9186i) q^{9} +(-47.5000 - 82.2724i) q^{10} +(25.0000 + 43.3013i) q^{11} +34.0000 q^{12} +(-45.5000 + 11.2583i) q^{13} -35.0000 q^{14} +(19.0000 + 32.9090i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(-38.5000 + 66.6840i) q^{17} +115.000 q^{18} +(-6.00000 + 10.3923i) q^{19} +(161.500 - 279.726i) q^{20} +14.0000 q^{21} +(-125.000 + 216.506i) q^{22} +(69.0000 + 119.512i) q^{23} +(45.0000 + 77.9423i) q^{24} +236.000 q^{25} +(-162.500 - 168.875i) q^{26} -100.000 q^{27} +(-59.5000 - 103.057i) q^{28} +(-125.500 - 217.372i) q^{29} +(-95.0000 + 164.545i) q^{30} +250.000 q^{31} +(42.5000 - 73.6122i) q^{32} +(50.0000 - 86.6025i) q^{33} -385.000 q^{34} +(66.5000 - 115.181i) q^{35} +(195.500 + 338.616i) q^{36} +(-39.5000 - 68.4160i) q^{37} -60.0000 q^{38} +(65.0000 + 67.5500i) q^{39} +855.000 q^{40} +(109.500 + 189.660i) q^{41} +(35.0000 + 60.6218i) q^{42} +(-129.000 + 223.435i) q^{43} -850.000 q^{44} +(-218.500 + 378.453i) q^{45} +(-345.000 + 597.558i) q^{46} +72.0000 q^{47} +(-89.0000 + 154.153i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(590.000 + 1021.91i) q^{50} +154.000 q^{51} +(221.000 - 765.566i) q^{52} +111.000 q^{53} +(-250.000 - 433.013i) q^{54} +(-475.000 - 822.724i) q^{55} +(157.500 - 272.798i) q^{56} +24.0000 q^{57} +(627.500 - 1086.86i) q^{58} +(-63.0000 + 109.119i) q^{59} -646.000 q^{60} +(179.500 - 310.903i) q^{61} +(625.000 + 1082.53i) q^{62} +(80.5000 + 139.430i) q^{63} -287.000 q^{64} +(864.500 - 213.908i) q^{65} +500.000 q^{66} +(-143.000 - 247.683i) q^{67} +(-654.500 - 1133.63i) q^{68} +(138.000 - 239.023i) q^{69} +665.000 q^{70} +(60.0000 - 103.923i) q^{71} +(-517.500 + 896.336i) q^{72} +89.0000 q^{73} +(197.500 - 342.080i) q^{74} +(-236.000 - 408.764i) q^{75} +(-102.000 - 176.669i) q^{76} -350.000 q^{77} +(-130.000 + 450.333i) q^{78} -1030.00 q^{79} +(845.500 + 1464.45i) q^{80} +(-210.500 - 364.597i) q^{81} +(-547.500 + 948.298i) q^{82} +826.000 q^{83} +(-119.000 + 206.114i) q^{84} +(731.500 - 1267.00i) q^{85} -1290.00 q^{86} +(-251.000 + 434.745i) q^{87} +(-1125.00 - 1948.56i) q^{88} +(763.000 + 1321.55i) q^{89} -2185.00 q^{90} +(91.0000 - 315.233i) q^{91} -2346.00 q^{92} +(-250.000 - 433.013i) q^{93} +(180.000 + 311.769i) q^{94} +(114.000 - 197.454i) q^{95} -170.000 q^{96} +(-281.000 + 486.706i) q^{97} +(122.500 - 212.176i) q^{98} +1150.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} - 2 q^{3} - 17 q^{4} - 38 q^{5} + 10 q^{6} - 7 q^{7} - 90 q^{8} + 23 q^{9} - 95 q^{10} + 50 q^{11} + 68 q^{12} - 91 q^{13} - 70 q^{14} + 38 q^{15} - 89 q^{16} - 77 q^{17} + 230 q^{18} - 12 q^{19}+ \cdots + 2300 q^{99}+O(q^{100}) $ 2 * q + 5 * q^2 - 2 * q^3 - 17 * q^4 - 38 * q^5 + 10 * q^6 - 7 * q^7 - 90 * q^8 + 23 * q^9 - 95 * q^10 + 50 * q^11 + 68 * q^12 - 91 * q^13 - 70 * q^14 + 38 * q^15 - 89 * q^16 - 77 * q^17 + 230 * q^18 - 12 * q^19 + 323 * q^20 + 28 * q^21 - 250 * q^22 + 138 * q^23 + 90 * q^24 + 472 * q^25 - 325 * q^26 - 200 * q^27 - 119 * q^28 - 251 * q^29 - 190 * q^30 + 500 * q^31 + 85 * q^32 + 100 * q^33 - 770 * q^34 + 133 * q^35 + 391 * q^36 - 79 * q^37 - 120 * q^38 + 130 * q^39 + 1710 * q^40 + 219 * q^41 + 70 * q^42 - 258 * q^43 - 1700 * q^44 - 437 * q^45 - 690 * q^46 + 144 * q^47 - 178 * q^48 - 49 * q^49 + 1180 * q^50 + 308 * q^51 + 442 * q^52 + 222 * q^53 - 500 * q^54 - 950 * q^55 + 315 * q^56 + 48 * q^57 + 1255 * q^58 - 126 * q^59 - 1292 * q^60 + 359 * q^61 + 1250 * q^62 + 161 * q^63 - 574 * q^64 + 1729 * q^65 + 1000 * q^66 - 286 * q^67 - 1309 * q^68 + 276 * q^69 + 1330 * q^70 + 120 * q^71 - 1035 * q^72 + 178 * q^73 + 395 * q^74 - 472 * q^75 - 204 * q^76 - 700 * q^77 - 260 * q^78 - 2060 * q^79 + 1691 * q^80 - 421 * q^81 - 1095 * q^82 + 1652 * q^83 - 238 * q^84 + 1463 * q^85 - 2580 * q^86 - 502 * q^87 - 2250 * q^88 + 1526 * q^89 - 4370 * q^90 + 182 * q^91 - 4692 * q^92 - 500 * q^93 + 360 * q^94 + 228 * q^95 - 340 * q^96 - 562 * q^97 + 245 * q^98 + 2300 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.50000	+	4.33013i	0.883883	+	1.53093i	0.846988	+	0.531612i	$0.178414\pi$
$2$	2.50000	+	4.33013i	0.883883	+	1.53093i	0.0368954	+	0.999319i	$0.488253\pi$
$3$	−1.00000	−	1.73205i	−0.192450	−	0.333333i	0.753612	−	0.657320i	$-0.228310\pi$
$3$	−1.00000	−	1.73205i	−0.192450	−	0.333333i	−0.946062	+	0.323987i	$0.894977\pi$
$4$	−8.50000	+	14.7224i	−1.06250	+	1.84030i
$5$	−19.0000			−1.69941			−0.849706	−	0.527257i	$-0.823220\pi$
$5$	−19.0000			−1.69941			−0.849706	+	0.527257i	$0.823220\pi$
$6$	5.00000	−	8.66025i	0.340207	−	0.589256i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$	−45.0000			−1.98874
$9$	11.5000	−	19.9186i	0.425926	−	0.737725i
$10$	−47.5000	−	82.2724i	−1.50208	−	2.60168i
$11$	25.0000	+	43.3013i	0.685253	+	1.18689i	0.973357	+	0.229294i	$0.0736417\pi$
$11$	25.0000	+	43.3013i	0.685253	+	1.18689i	−0.288104	+	0.957599i	$0.593025\pi$
$12$	34.0000			0.817913
$13$	−45.5000	+	11.2583i	−0.970725	+	0.240192i
$13$	−45.5000	+	11.2583i	−0.970725	+	0.240192i
$14$	−35.0000			−0.668153
$15$	19.0000	+	32.9090i	0.327052	+	0.566471i
$16$	−44.5000	−	77.0763i	−0.695312	−	1.20432i
$17$	−38.5000	+	66.6840i	−0.549272	+	0.951367i	0.449053	+	0.893505i	$0.351762\pi$
$17$	−38.5000	+	66.6840i	−0.549272	+	0.951367i	−0.998325	+	0.0578615i	$0.981572\pi$
$18$	115.000			1.50588
$19$	−6.00000	+	10.3923i	−0.0724471	+	0.125482i	−0.899973	−	0.435945i	$-0.856414\pi$
$19$	−6.00000	+	10.3923i	−0.0724471	+	0.125482i	0.827526	+	0.561427i	$0.189748\pi$
$20$	161.500	−	279.726i	1.80562	−	3.12743i
$21$	14.0000			0.145479
$22$	−125.000	+	216.506i	−1.21137	+	2.09815i
$23$	69.0000	+	119.512i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	69.0000	+	119.512i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	45.0000	+	77.9423i	0.382733	+	0.662913i
$25$	236.000			1.88800
$26$	−162.500	−	168.875i	−1.22573	−	1.27381i
$27$	−100.000			−0.712778
$28$	−59.5000	−	103.057i	−0.401587	−	0.695570i
$29$	−125.500	−	217.372i	−0.803613	−	1.39190i	−0.917224	−	0.398373i	$-0.869575\pi$
$29$	−125.500	−	217.372i	−0.803613	−	1.39190i	0.113611	−	0.993525i	$-0.463758\pi$
$30$	−95.0000	+	164.545i	−0.578152	+	1.00139i
$31$	250.000			1.44843			0.724215	−	0.689574i	$-0.242202\pi$
$31$	250.000			1.44843			0.724215	+	0.689574i	$0.242202\pi$
$32$	42.5000	−	73.6122i	0.234782	−	0.406654i
$33$	50.0000	−	86.6025i	0.263754	−	0.456835i
$34$	−385.000			−1.94197
$35$	66.5000	−	115.181i	0.321159	−	0.556263i
$36$	195.500	+	338.616i	0.905093	+	1.56767i
$37$	−39.5000	−	68.4160i	−0.175507	−	0.303987i	0.764830	−	0.644233i	$-0.222823\pi$
$37$	−39.5000	−	68.4160i	−0.175507	−	0.303987i	−0.940337	+	0.340246i	$0.889490\pi$
$38$	−60.0000			−0.256139
$39$	65.0000	+	67.5500i	0.266880	+	0.277350i
$40$	855.000			3.37968
$41$	109.500	+	189.660i	0.417098	+	0.722435i	0.995646	−	0.0932131i	$-0.0297138\pi$
$41$	109.500	+	189.660i	0.417098	+	0.722435i	−0.578548	+	0.815648i	$0.696380\pi$
$42$	35.0000	+	60.6218i	0.128586	+	0.222718i
$43$	−129.000	+	223.435i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−129.000	+	223.435i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	−850.000			−2.91233
$45$	−218.500	+	378.453i	−0.723823	+	1.25370i
$46$	−345.000	+	597.558i	−1.10581	+	1.91533i
$47$	72.0000			0.223453			0.111726	−	0.993739i	$-0.464362\pi$
$47$	72.0000			0.223453			0.111726	+	0.993739i	$0.464362\pi$
$48$	−89.0000	+	154.153i	−0.267626	+	0.463542i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	590.000	+	1021.91i	1.66877	+	2.89040i
$51$	154.000			0.422830
$52$	221.000	−	765.566i	0.589369	−	2.04163i
$53$	111.000			0.287680			0.143840	−	0.989601i	$-0.454055\pi$
$53$	111.000			0.287680			0.143840	+	0.989601i	$0.454055\pi$
$54$	−250.000	−	433.013i	−0.630013	−	1.09121i
$55$	−475.000	−	822.724i	−1.16453	−	2.01702i
$56$	157.500	−	272.798i	0.375836	−	0.650967i
$57$	24.0000			0.0557698
$58$	627.500	−	1086.86i	1.42060	−	2.46055i
$59$	−63.0000	+	109.119i	−0.139015	+	0.240782i	−0.927124	−	0.374754i	$-0.877727\pi$
$59$	−63.0000	+	109.119i	−0.139015	+	0.240782i	0.788109	+	0.615536i	$0.211060\pi$
$60$	−646.000			−1.38997
$61$	179.500	−	310.903i	0.376764	−	0.652575i	−0.613825	−	0.789442i	$-0.710370\pi$
$61$	179.500	−	310.903i	0.376764	−	0.652575i	0.990589	+	0.136867i	$0.0437033\pi$
$62$	625.000	+	1082.53i	1.28024	+	2.21745i
$63$	80.5000	+	139.430i	0.160985	+	0.278834i
$64$	−287.000			−0.560547
$65$	864.500	−	213.908i	1.64966	−	0.408185i
$66$	500.000			0.932511
$67$	−143.000	−	247.683i	−0.260750	−	0.451632i	0.705692	−	0.708519i	$-0.250636\pi$
$67$	−143.000	−	247.683i	−0.260750	−	0.451632i	−0.966441	+	0.256887i	$0.917303\pi$
$68$	−654.500	−	1133.63i	−1.16720	−	2.02165i
$69$	138.000	−	239.023i	0.240772	−	0.417029i
$70$	665.000			1.13547
$71$	60.0000	−	103.923i	0.100291	−	0.173710i	−0.811513	−	0.584334i	$-0.801356\pi$
$71$	60.0000	−	103.923i	0.100291	−	0.173710i	0.911805	+	0.410624i	$0.134689\pi$
$72$	−517.500	+	896.336i	−0.847055	+	1.46714i
$73$	89.0000			0.142694			0.0713470	−	0.997452i	$-0.477270\pi$
$73$	89.0000			0.142694			0.0713470	+	0.997452i	$0.477270\pi$
$74$	197.500	−	342.080i	0.310256	−	0.537378i
$75$	−236.000	−	408.764i	−0.363346	−	0.629333i
$76$	−102.000	−	176.669i	−0.153950	−	0.266649i
$77$	−350.000			−0.518003
$78$	−130.000	+	450.333i	−0.188713	+	0.653720i
$79$	−1030.00			−1.46689			−0.733443	−	0.679751i	$-0.762088\pi$
$79$	−1030.00			−1.46689			−0.733443	+	0.679751i	$0.762088\pi$
$80$	845.500	+	1464.45i	1.18162	+	2.04663i
$81$	−210.500	−	364.597i	−0.288752	−	0.500133i
$82$	−547.500	+	948.298i	−0.737332	+	1.27710i
$83$	826.000			1.09235			0.546176	−	0.837670i	$-0.316083\pi$
$83$	826.000			1.09235			0.546176	+	0.837670i	$0.316083\pi$
$84$	−119.000	+	206.114i	−0.154571	+	0.267725i
$85$	731.500	−	1267.00i	0.933439	−	1.61676i
$86$	−1290.00			−1.61749
$87$	−251.000	+	434.745i	−0.309311	+	0.535742i
$88$	−1125.00	−	1948.56i	−1.36279	−	2.36042i
$89$	763.000	+	1321.55i	0.908740	+	1.57398i	0.815817	+	0.578310i	$0.196288\pi$
$89$	763.000	+	1321.55i	0.908740	+	1.57398i	0.0929227	+	0.995673i	$0.470379\pi$
$90$	−2185.00			−2.55910
$91$	91.0000	−	315.233i	0.104828	−	0.363137i
$92$	−2346.00			−2.65856
$93$	−250.000	−	433.013i	−0.278750	−	0.482810i
$94$	180.000	+	311.769i	0.197506	+	0.342091i
$95$	114.000	−	197.454i	0.123117	−	0.213246i
$96$	−170.000			−0.180735
$97$	−281.000	+	486.706i	−0.294136	+	0.509459i	−0.974784	−	0.223152i	$-0.928365\pi$
$97$	−281.000	+	486.706i	−0.294136	+	0.509459i	0.680647	+	0.732611i	$0.261699\pi$
$98$	122.500	−	212.176i	0.126269	−	0.218704i
$99$	1150.00			1.16747
$100$	−2006.00	+	3474.49i	−2.00600	+	3.47449i
$101$	121.500	+	210.444i	0.119700	+	0.207327i	0.919649	−	0.392742i	$-0.128473\pi$
$101$	121.500	+	210.444i	0.119700	+	0.207327i	−0.799949	+	0.600068i	$0.795140\pi$
$102$	385.000	+	666.840i	0.373732	+	0.647323i
$103$	−180.000			−0.172193			−0.0860967	−	0.996287i	$-0.527439\pi$
$103$	−180.000			−0.172193			−0.0860967	+	0.996287i	$0.527439\pi$
$104$	2047.50	−	506.625i	1.93052	−	0.477679i
$105$	−266.000			−0.247228
$106$	277.500	+	480.644i	0.254275	+	0.440418i
$107$	468.000	+	810.600i	0.422834	+	0.732370i	0.996215	−	0.0869183i	$-0.0277019\pi$
$107$	468.000	+	810.600i	0.422834	+	0.732370i	−0.573381	+	0.819289i	$0.694369\pi$
$108$	850.000	−	1472.24i	0.757327	−	1.31173i
$109$	202.000			0.177505			0.0887527	−	0.996054i	$-0.471712\pi$
$109$	202.000			0.177505			0.0887527	+	0.996054i	$0.471712\pi$
$110$	2375.00	−	4113.62i	2.05861	−	3.56562i
$111$	−79.0000	+	136.832i	−0.0675527	+	0.117005i
$112$	623.000			0.525607
$113$	−433.500	+	750.844i	−0.360887	+	0.625075i	−0.988107	−	0.153767i	$-0.950859\pi$
$113$	−433.500	+	750.844i	−0.360887	+	0.625075i	0.627220	+	0.778842i	$0.284193\pi$
$114$	60.0000	+	103.923i	0.0492940	+	0.0853797i
$115$	−1311.00	−	2270.72i	−1.06306	−	1.84127i
$116$	4267.00			3.41535
$117$	−299.000	+	1035.77i	−0.236261	+	0.818433i
$118$	−630.000			−0.491493
$119$	−269.500	−	466.788i	−0.207605	−	0.359583i
$120$	−855.000	−	1480.90i	−0.650421	−	1.12656i
$121$	−584.500	+	1012.38i	−0.439144	+	0.760619i
$122$	1795.00			1.33206
$123$	219.000	−	379.319i	0.160541	−	0.278065i
$124$	−2125.00	+	3680.61i	−1.53896	+	2.66555i
$125$	−2109.00			−1.50908
$126$	−402.500	+	697.150i	−0.284584	+	0.492913i
$127$	−1018.00	−	1763.23i	−0.711283	−	1.23198i	−0.964376	−	0.264536i	$-0.914781\pi$
$127$	−1018.00	−	1763.23i	−0.711283	−	1.23198i	0.253093	−	0.967442i	$-0.418552\pi$
$128$	−1057.50	−	1831.64i	−0.730240	−	1.26481i
$129$	516.000			0.352180
$130$	3087.50	+	3208.62i	2.08301	+	2.16473i
$131$	1864.00			1.24319			0.621597	−	0.783337i	$-0.286484\pi$
$131$	1864.00			1.24319			0.621597	+	0.783337i	$0.286484\pi$
$132$	850.000	+	1472.24i	0.560477	+	0.970775i
$133$	−42.0000	−	72.7461i	−0.0273824	−	0.0474277i
$134$	715.000	−	1238.42i	0.460945	−	0.798380i
$135$	1900.00			1.21130
$136$	1732.50	−	3000.78i	1.09236	−	1.89202i
$137$	−529.500	+	917.121i	−0.330206	+	0.571934i	−0.982552	−	0.185988i	$-0.940452\pi$
$137$	−529.500	+	917.121i	−0.330206	+	0.571934i	0.652346	+	0.757921i	$0.273785\pi$
$138$	1380.00			0.851257
$139$	237.000	−	410.496i	0.144619	−	0.250488i	−0.784612	−	0.619988i	$-0.787138\pi$
$139$	237.000	−	410.496i	0.144619	−	0.250488i	0.929231	+	0.369500i	$0.120471\pi$
$140$	1130.50	+	1958.08i	0.682462	+	1.18206i
$141$	−72.0000	−	124.708i	−0.0430035	−	0.0744843i
$142$	600.000			0.354584
$143$	−1625.00	−	1688.75i	−0.950275	−	0.987555i
$144$	−2047.00			−1.18461
$145$	2384.50	+	4130.08i	1.36567	+	2.36541i
$146$	222.500	+	385.381i	0.126125	+	0.218455i
$147$	−49.0000	+	84.8705i	−0.0274929	+	0.0476190i
$148$	1343.00			0.745905
$149$	−1273.50	+	2205.77i	−0.700196	+	1.21277i	0.268202	+	0.963363i	$0.413571\pi$
$149$	−1273.50	+	2205.77i	−0.700196	+	1.21277i	−0.968397	+	0.249412i	$0.919763\pi$
$150$	1180.00	−	2043.82i	0.642311	−	1.11251i
$151$	2512.00			1.35380			0.676900	−	0.736075i	$-0.263323\pi$
$151$	2512.00			1.35380			0.676900	+	0.736075i	$0.263323\pi$
$152$	270.000	−	467.654i	0.144078	−	0.249551i
$153$	885.500	+	1533.73i	0.467898	+	0.810424i
$154$	−875.000	−	1515.54i	−0.457854	−	0.793026i
$155$	−4750.00			−2.46148
$156$	−1547.00	+	382.783i	−0.793969	+	0.196456i
$157$	−2319.00			−1.17883			−0.589415	−	0.807830i	$-0.700642\pi$
$157$	−2319.00			−1.17883			−0.589415	+	0.807830i	$0.700642\pi$
$158$	−2575.00	−	4460.03i	−1.29656	−	2.24570i
$159$	−111.000	−	192.258i	−0.0553640	−	0.0958932i
$160$	−807.500	+	1398.63i	−0.398991	+	0.691072i
$161$	−966.000			−0.472866
$162$	1052.50	−	1822.98i	0.510446	−	0.884118i
$163$	−451.000	+	781.155i	−0.216718	+	0.375367i	−0.953803	−	0.300434i	$-0.902869\pi$
$163$	−451.000	+	781.155i	−0.216718	+	0.375367i	0.737085	+	0.675800i	$0.236202\pi$
$164$	−3723.00			−1.77267
$165$	−950.000	+	1645.45i	−0.448227	+	0.776351i
$166$	2065.00	+	3576.68i	0.965513	+	1.67232i
$167$	337.000	+	583.701i	0.156155	+	0.270468i	0.933479	−	0.358632i	$-0.116757\pi$
$167$	337.000	+	583.701i	0.156155	+	0.270468i	−0.777324	+	0.629100i	$0.783423\pi$
$168$	−630.000			−0.289319
$169$	1943.50	−	1024.51i	0.884615	−	0.466321i
$170$	7315.00			3.30021
$171$	138.000	+	239.023i	0.0617142	+	0.106892i
$172$	−2193.00	−	3798.39i	−0.972178	−	1.68386i
$173$	57.0000	−	98.7269i	0.0250499	−	0.0433877i	−0.853229	−	0.521537i	$-0.825359\pi$
$173$	57.0000	−	98.7269i	0.0250499	−	0.0433877i	0.878279	+	0.478149i	$0.158692\pi$
$174$	−2510.00			−1.09358
$175$	−826.000	+	1430.67i	−0.356798	+	0.617993i
$176$	2225.00	−	3853.81i	0.952930	−	1.65052i
$177$	252.000			0.107014
$178$	−3815.00	+	6607.77i	−1.60644	+	2.78244i
$179$	1432.00	+	2480.30i	0.597948	+	1.03568i	0.993124	+	0.117071i	$0.0373504\pi$
$179$	1432.00	+	2480.30i	0.597948	+	1.03568i	−0.395175	+	0.918606i	$0.629316\pi$
$180$	−3714.50	−	6433.70i	−1.53812	−	2.66411i
$181$	−2275.00			−0.934251			−0.467125	−	0.884191i	$-0.654710\pi$
$181$	−2275.00			−0.934251			−0.467125	+	0.884191i	$0.654710\pi$
$182$	1592.50	−	394.042i	0.648593	−	0.160485i
$183$	−718.000			−0.290033
$184$	−3105.00	−	5378.02i	−1.24404	−	2.15474i
$185$	750.500	+	1299.90i	0.298259	+	0.516599i
$186$	1250.00	−	2165.06i	0.492766	−	0.853495i
$187$	−3850.00			−1.50556
$188$	−612.000	+	1060.02i	−0.237419	+	0.411221i
$189$	350.000	−	606.218i	0.134702	−	0.233311i
$190$	1140.00			0.435286
$191$	1145.00	−	1983.20i	0.433766	−	0.751305i	−0.563428	−	0.826165i	$-0.690518\pi$
$191$	1145.00	−	1983.20i	0.433766	−	0.751305i	0.997194	+	0.0748605i	$0.0238511\pi$
$192$	287.000	+	497.099i	0.107877	+	0.186849i
$193$	1792.50	+	3104.70i	0.668534	+	1.15793i	0.978314	+	0.207126i	$0.0664110\pi$
$193$	1792.50	+	3104.70i	0.668534	+	1.15793i	−0.309781	+	0.950808i	$0.600256\pi$
$194$	−2810.00			−1.03993
$195$	−1235.00	−	1283.45i	−0.453539	−	0.471332i
$196$	833.000			0.303571
$197$	963.000	+	1667.96i	0.348279	+	0.603236i	0.985944	−	0.167077i	$-0.0534329\pi$
$197$	963.000	+	1667.96i	0.348279	+	0.603236i	−0.637665	+	0.770314i	$0.720100\pi$
$198$	2875.00	+	4979.65i	1.03191	+	1.78731i
$199$	−238.000	+	412.228i	−0.0847808	+	0.146845i	−0.905298	−	0.424778i	$-0.860352\pi$
$199$	−238.000	+	412.228i	−0.0847808	+	0.146845i	0.820517	+	0.571622i	$0.193686\pi$
$200$	−10620.0			−3.75474
$201$	−286.000	+	495.367i	−0.100363	+	0.173833i
$202$	−607.500	+	1052.22i	−0.211602	+	0.366505i
$203$	1757.00			0.607474
$204$	−1309.00	+	2267.25i	−0.449257	+	0.778135i
$205$	−2080.50	−	3603.53i	−0.708822	−	1.22771i
$206$	−450.000	−	779.423i	−0.152199	−	0.263616i
$207$	3174.00			1.06574
$208$	2892.50	+	3005.97i	0.964225	+	1.00205i
$209$	−600.000			−0.198578
$210$	−665.000	−	1151.81i	−0.218521	−	0.378489i
$211$	−1067.00	−	1848.10i	−0.348129	−	0.602978i	0.637788	−	0.770212i	$-0.279850\pi$
$211$	−1067.00	−	1848.10i	−0.348129	−	0.602978i	−0.985917	+	0.167234i	$0.946516\pi$
$212$	−943.500	+	1634.19i	−0.305660	+	0.529418i
$213$	−240.000			−0.0772044
$214$	−2340.00	+	4053.00i	−0.747472	+	1.29466i
$215$	2451.00	−	4245.26i	0.777474	−	1.34662i
$216$	4500.00			1.41753
$217$	−875.000	+	1515.54i	−0.273728	+	0.474110i
$218$	505.000	+	874.686i	0.156894	+	0.271749i
$219$	−89.0000	−	154.153i	−0.0274615	−	0.0475647i
$220$	16150.0			4.94924
$221$	1001.00	−	3467.57i	0.304681	−	1.05545i
$222$	−790.000			−0.238835
$223$	−146.000	−	252.879i	−0.0438425	−	0.0759375i	0.843271	−	0.537488i	$-0.180627\pi$
$223$	−146.000	−	252.879i	−0.0438425	−	0.0759375i	−0.887114	+	0.461550i	$0.847293\pi$
$224$	297.500	+	515.285i	0.0887391	+	0.153701i
$225$	2714.00	−	4700.79i	0.804148	−	1.39283i
$226$	−4335.00			−1.27593
$227$	2653.00	−	4595.13i	0.775708	−	1.34357i	−0.158687	−	0.987329i	$-0.550726\pi$
$227$	2653.00	−	4595.13i	0.775708	−	1.34357i	0.934395	−	0.356237i	$-0.115941\pi$
$228$	−204.000	+	353.338i	−0.0592554	+	0.102633i
$229$	−250.000			−0.0721418			−0.0360709	−	0.999349i	$-0.511484\pi$
$229$	−250.000			−0.0721418			−0.0360709	+	0.999349i	$0.511484\pi$
$230$	6555.00	−	11353.6i	1.87923	−	3.25493i
$231$	350.000	+	606.218i	0.0996897	+	0.172668i
$232$	5647.50	+	9781.76i	1.59817	+	2.76812i
$233$	1294.00			0.363832			0.181916	−	0.983314i	$-0.441770\pi$
$233$	1294.00			0.363832			0.181916	+	0.983314i	$0.441770\pi$
$234$	−5232.50	+	1294.71i	−1.46179	+	0.361700i
$235$	−1368.00			−0.379738
$236$	−1071.00	−	1855.03i	−0.295407	−	0.511661i
$237$	1030.00	+	1784.01i	0.282302	+	0.488962i
$238$	1347.50	−	2333.94i	0.366998	−	0.635659i
$239$	−2658.00			−0.719380			−0.359690	−	0.933072i	$-0.617117\pi$
$239$	−2658.00			−0.719380			−0.359690	+	0.933072i	$0.617117\pi$
$240$	1691.00	−	2928.90i	0.454807	−	0.787748i
$241$	2327.50	−	4031.35i	0.622106	−	1.07752i	−0.366987	−	0.930226i	$-0.619611\pi$
$241$	2327.50	−	4031.35i	0.622106	−	1.07752i	0.989093	−	0.147293i	$-0.0470559\pi$
$242$	−5845.00			−1.55261
$243$	−1771.00	+	3067.46i	−0.467530	+	0.809785i
$244$	3051.50	+	5285.35i	0.800624	+	1.38672i
$245$	465.500	+	806.270i	0.121387	+	0.210248i
$246$	2190.00			0.567599
$247$	156.000	−	540.400i	0.0401864	−	0.139210i
$248$	−11250.0			−2.88055
$249$	−826.000	−	1430.67i	−0.210223	−	0.364118i
$250$	−5272.50	−	9132.24i	−1.33385	−	2.31029i
$251$	−1506.00	+	2608.47i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−1506.00	+	2608.47i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	−2737.00			−0.684186
$253$	−3450.00	+	5975.58i	−0.857311	+	1.48491i
$254$	5090.00	−	8816.14i	1.25738	−	2.17785i
$255$	−2926.00			−0.718562
$256$	4139.50	−	7169.82i	1.01062	−	1.75045i
$257$	−38.5000	−	66.6840i	−0.00934461	−	0.0161853i	0.861315	−	0.508071i	$-0.169641\pi$
$257$	−38.5000	−	66.6840i	−0.00934461	−	0.0161853i	−0.870660	+	0.491886i	$0.836308\pi$
$258$	1290.00	+	2234.35i	0.311286	+	0.539164i
$259$	553.000			0.132671
$260$	−4199.00	+	14545.8i	−1.00158	+	3.46958i
$261$	−5773.00			−1.36912
$262$	4660.00	+	8071.36i	1.09884	+	1.90324i
$263$	3609.00	+	6250.97i	0.846161	+	1.46559i	0.884609	+	0.466334i	$0.154426\pi$
$263$	3609.00	+	6250.97i	0.846161	+	1.46559i	−0.0384472	+	0.999261i	$0.512241\pi$
$264$	−2250.00	+	3897.11i	−0.524538	+	0.908526i
$265$	−2109.00			−0.488886
$266$	210.000	−	363.731i	0.0484057	−	0.0838412i
$267$	1526.00	−	2643.11i	0.349774	−	0.605827i
$268$	4862.00			1.10819
$269$	1435.00	−	2485.49i	0.325255	−	0.563358i	−0.656309	−	0.754492i	$-0.727883\pi$
$269$	1435.00	−	2485.49i	0.325255	−	0.563358i	0.981564	+	0.191134i	$0.0612167\pi$
$270$	4750.00	+	8227.24i	1.07065	+	1.85442i
$271$	−651.000	−	1127.57i	−0.145924	−	0.252748i	0.783793	−	0.621022i	$-0.213282\pi$
$271$	−651.000	−	1127.57i	−0.145924	−	0.252748i	−0.929717	+	0.368274i	$0.879949\pi$
$272$	6853.00			1.52766
$273$	−637.000	+	157.617i	−0.141220	+	0.0349428i
$274$	−5295.00			−1.16745
$275$	5900.00	+	10219.1i	1.29376	+	2.24085i
$276$	2346.00	+	4063.39i	0.511640	+	0.886186i
$277$	2676.50	−	4635.83i	0.580561	−	1.00556i	−0.414852	−	0.909889i	$-0.636167\pi$
$277$	2676.50	−	4635.83i	0.580561	−	1.00556i	0.995413	−	0.0956718i	$-0.0304999\pi$
$278$	2370.00			0.511306
$279$	2875.00	−	4979.65i	0.616924	−	1.06854i
$280$	−2992.50	+	5183.16i	−0.638700	+	1.10626i
$281$	−733.000			−0.155613			−0.0778063	−	0.996968i	$-0.524792\pi$
$281$	−733.000			−0.155613			−0.0778063	+	0.996968i	$0.524792\pi$
$282$	360.000	−	623.538i	0.0760202	−	0.131671i
$283$	825.000	+	1428.94i	0.173290	+	0.300148i	0.939568	−	0.342362i	$-0.111227\pi$
$283$	825.000	+	1428.94i	0.173290	+	0.300148i	−0.766278	+	0.642509i	$0.777893\pi$
$284$	1020.00	+	1766.69i	0.213119	+	0.369133i
$285$	−456.000			−0.0947758
$286$	3250.00	−	11258.3i	0.671946	−	2.32769i
$287$	−1533.00			−0.315297
$288$	−977.500	−	1693.08i	−0.199999	−	0.346409i
$289$	−508.000	−	879.882i	−0.103399	−	0.179093i
$290$	−11922.5	+	20650.4i	−2.41418	+	4.18149i
$291$	1124.00			0.226426
$292$	−756.500	+	1310.30i	−0.151612	+	0.262600i
$293$	2221.50	−	3847.75i	0.442940	−	0.767195i	−0.554966	−	0.831873i	$-0.687269\pi$
$293$	2221.50	−	3847.75i	0.442940	−	0.767195i	0.997906	+	0.0646784i	$0.0206021\pi$
$294$	−490.000			−0.0972020
$295$	1197.00	−	2073.26i	0.236244	−	0.409187i
$296$	1777.50	+	3078.72i	0.349037	+	0.604551i
$297$	−2500.00	−	4330.13i	−0.488433	−	0.845991i
$298$	−12735.0			−2.47557
$299$	−4485.00	−	4660.95i	−0.867472	−	0.901504i
$300$	8024.00			1.54422
$301$	−903.000	−	1564.04i	−0.172917	−	0.299501i
$302$	6280.00	+	10877.3i	1.19660	+	2.07257i
$303$	243.000	−	420.888i	0.0460726	−	0.0798000i
$304$	1068.00			0.201493
$305$	−3410.50	+	5907.16i	−0.640278	+	1.10899i
$306$	−4427.50	+	7668.65i	−0.827135	+	1.43264i
$307$	−9898.00			−1.84009			−0.920047	−	0.391809i	$-0.871850\pi$
$307$	−9898.00			−1.84009			−0.920047	+	0.391809i	$0.871850\pi$
$308$	2975.00	−	5152.85i	0.550378	−	0.953282i
$309$	180.000	+	311.769i	0.0331386	+	0.0573978i
$310$	−11875.0	−	20568.1i	−2.17566	−	3.76835i
$311$	1314.00			0.239582			0.119791	−	0.992799i	$-0.461777\pi$
$311$	1314.00			0.239582			0.119791	+	0.992799i	$0.461777\pi$
$312$	−2925.00	−	3039.75i	−0.530755	−	0.551577i
$313$	10950.0			1.97741			0.988707	−	0.149861i	$-0.0478827\pi$
$313$	10950.0			1.97741			0.988707	+	0.149861i	$0.0478827\pi$
$314$	−5797.50	−	10041.6i	−1.04195	−	1.80471i
$315$	−1529.50	−	2649.17i	−0.273580	−	0.473854i
$316$	8755.00	−	15164.1i	1.55857	−	2.69952i
$317$	11255.0			1.99414			0.997072	−	0.0764658i	$-0.0243636\pi$
$317$	11255.0			1.99414			0.997072	+	0.0764658i	$0.0243636\pi$
$318$	555.000	−	961.288i	0.0978706	−	0.169517i
$319$	6275.00	−	10868.6i	1.10136	−	1.90760i
$320$	5453.00			0.952600
$321$	936.000	−	1621.20i	0.162749	−	0.281890i
$322$	−2415.00	−	4182.90i	−0.417959	−	0.723926i
$323$	−462.000	−	800.207i	−0.0795863	−	0.137847i
$324$	7157.00			1.22719
$325$	−10738.0	+	2656.97i	−1.83273	+	0.453483i
$326$	−4510.00			−0.766214
$327$	−202.000	−	349.874i	−0.0341609	−	0.0591685i
$328$	−4927.50	−	8534.68i	−0.829499	−	1.43673i
$329$	−252.000	+	436.477i	−0.0422286	+	0.0731421i
$330$	−9500.00			−1.58472
$331$	4295.00	−	7439.16i	0.713216	−	1.23533i	−0.250427	−	0.968135i	$-0.580571\pi$
$331$	4295.00	−	7439.16i	0.713216	−	1.23533i	0.963644	−	0.267191i	$-0.0860955\pi$
$332$	−7021.00	+	12160.7i	−1.16062	+	2.01026i
$333$	−1817.00			−0.299012
$334$	−1685.00	+	2918.51i	−0.276045	+	0.478124i
$335$	2717.00	+	4705.98i	0.443121	+	0.767508i
$336$	−623.000	−	1079.07i	−0.101153	−	0.175202i
$337$	1731.00			0.279803			0.139901	−	0.990165i	$-0.455321\pi$
$337$	1731.00			0.279803			0.139901	+	0.990165i	$0.455321\pi$
$338$	9295.00	+	5854.33i	1.49580	+	0.942111i
$339$	1734.00			0.277811
$340$	12435.5	+	21538.9i	1.98356	+	3.43562i
$341$	6250.00	+	10825.3i	0.992541	+	1.71913i
$342$	−690.000	+	1195.12i	−0.109096	+	0.188960i
$343$	343.000			0.0539949
$344$	5805.00	−	10054.6i	0.909839	−	1.57589i
$345$	−2622.00	+	4541.44i	−0.409170	+	0.708704i
$346$	570.000			0.0885647
$347$	1245.00	−	2156.40i	0.192608	−	0.333607i	−0.753506	−	0.657442i	$-0.771639\pi$
$347$	1245.00	−	2156.40i	0.192608	−	0.333607i	0.946114	+	0.323834i	$0.104972\pi$
$348$	−4267.00	−	7390.66i	−0.657285	−	1.13845i
$349$	2899.00	+	5021.22i	0.444642	+	0.770142i	0.998027	−	0.0627834i	$-0.0199977\pi$
$349$	2899.00	+	5021.22i	0.444642	+	0.770142i	−0.553386	+	0.832925i	$0.686664\pi$
$350$	−8260.00			−1.26147
$351$	4550.00	−	1125.83i	0.691912	−	0.171204i
$352$	4250.00			0.643539
$353$	−3210.50	−	5560.75i	−0.484073	−	0.838439i	0.515760	−	0.856733i	$-0.327510\pi$
$353$	−3210.50	−	5560.75i	−0.484073	−	0.838439i	−0.999833	+	0.0182946i	$0.994176\pi$
$354$	630.000	+	1091.19i	0.0945879	+	0.163831i
$355$	−1140.00	+	1974.54i	−0.170436	+	0.295204i
$356$	−25942.0			−3.86214
$357$	−539.000	+	933.575i	−0.0799073	+	0.138403i
$358$	−7160.00	+	12401.5i	−1.05703	+	1.83083i
$359$	−2220.00			−0.326371			−0.163185	−	0.986595i	$-0.552177\pi$
$359$	−2220.00			−0.326371			−0.163185	+	0.986595i	$0.552177\pi$
$360$	9832.50	−	17030.4i	1.43950	−	2.49328i
$361$	3357.50	+	5815.36i	0.489503	+	0.847844i
$362$	−5687.50	−	9851.04i	−0.825769	−	1.43027i
$363$	2338.00			0.338053
$364$	3867.50	+	4019.22i	0.556901	+	0.578749i
$365$	−1691.00			−0.242496
$366$	−1795.00	−	3109.03i	−0.256356	−	0.444021i
$367$	−1037.00	−	1796.14i	−0.147496	−	0.255470i	0.782806	−	0.622266i	$-0.213788\pi$
$367$	−1037.00	−	1796.14i	−0.147496	−	0.255470i	−0.930301	+	0.366796i	$0.880455\pi$
$368$	6141.00	−	10636.5i	0.869896	−	1.50670i
$369$	5037.00			0.710612
$370$	−3752.50	+	6499.52i	−0.527252	+	0.913227i
$371$	−388.500	+	672.902i	−0.0543663	+	0.0941653i
$372$	8500.00			1.18469
$373$	−1161.50	+	2011.78i	−0.161234	+	0.279265i	−0.935311	−	0.353826i	$-0.884881\pi$
$373$	−1161.50	+	2011.78i	−0.161234	+	0.279265i	0.774078	+	0.633091i	$0.218214\pi$
$374$	−9625.00	−	16671.0i	−1.33074	−	2.30491i
$375$	2109.00	+	3652.90i	0.290422	+	0.503026i
$376$	−3240.00			−0.444389
$377$	8157.50	+	8477.52i	1.11441	+	1.15813i
$378$	3500.00			0.476245
$379$	−5715.00	−	9898.67i	−0.774564	−	1.34158i	−0.935039	−	0.354545i	$-0.884636\pi$
$379$	−5715.00	−	9898.67i	−0.774564	−	1.34158i	0.160475	−	0.987040i	$-0.448697\pi$
$380$	1938.00	+	3356.71i	0.261624	+	0.453147i
$381$	−2036.00	+	3526.46i	−0.273773	+	0.474188i
$382$	11450.0			1.53359
$383$	−2869.00	+	4969.25i	−0.382765	+	0.662969i	−0.991456	−	0.130438i	$-0.958361\pi$
$383$	−2869.00	+	4969.25i	−0.382765	+	0.662969i	0.608691	+	0.793407i	$0.291695\pi$
$384$	−2115.00	+	3663.29i	−0.281069	+	0.486826i
$385$	6650.00			0.880300
$386$	−8962.50	+	15523.5i	−1.18181	+	2.04696i
$387$	2967.00	+	5138.99i	0.389719	+	0.675012i
$388$	−4777.00	−	8274.01i	−0.625040	−	1.08260i
$389$	−11369.0			−1.48183			−0.740914	−	0.671600i	$-0.765607\pi$
$389$	−11369.0			−1.48183			−0.740914	+	0.671600i	$0.765607\pi$
$390$	2470.00	−	8556.33i	0.320701	−	1.11094i
$391$	−10626.0			−1.37437
$392$	1102.50	+	1909.59i	0.142053	+	0.246042i
$393$	−1864.00	−	3228.54i	−0.239253	−	0.414398i
$394$	−4815.00	+	8339.82i	−0.615676	+	1.06638i
$395$	19570.0			2.49284
$396$	−9775.00	+	16930.8i	−1.24043	+	2.14850i
$397$	1877.00	−	3251.06i	0.237289	−	0.410997i	−0.722646	−	0.691218i	$-0.757074\pi$
$397$	1877.00	−	3251.06i	0.237289	−	0.410997i	0.959936	+	0.280221i	$0.0904077\pi$
$398$	−2380.00			−0.299745
$399$	−84.0000	+	145.492i	−0.0105395	+	0.0182549i
$400$	−10502.0	−	18190.0i	−1.31275	−	2.27375i
$401$	−6171.50	−	10689.4i	−0.768554	−	1.33117i	−0.938347	−	0.345694i	$-0.887643\pi$
$401$	−6171.50	−	10689.4i	−0.768554	−	1.33117i	0.169794	−	0.985480i	$-0.445690\pi$
$402$	−2860.00			−0.354835
$403$	−11375.0	+	2814.58i	−1.40603	+	0.347902i
$404$	−4131.00			−0.508725
$405$	3999.50	+	6927.34i	0.490708	+	0.849931i
$406$	4392.50	+	7608.03i	0.536936	+	0.930001i
$407$	1975.00	−	3420.80i	0.240533	−	0.416616i
$408$	−6930.00			−0.840897
$409$	−3174.50	+	5498.40i	−0.383787	+	0.664739i	−0.991600	−	0.129341i	$-0.958714\pi$
$409$	−3174.50	+	5498.40i	−0.383787	+	0.664739i	0.607813	+	0.794080i	$0.292047\pi$
$410$	10402.5	−	18017.7i	1.25303	−	2.17031i
$411$	2118.00			0.254193
$412$	1530.00	−	2650.04i	0.182956	−	0.316888i
$413$	−441.000	−	763.834i	−0.0525428	−	0.0910069i
$414$	7935.00	+	13743.8i	0.941990	+	1.63158i
$415$	−15694.0			−1.85636
$416$	−1105.00	+	3827.83i	−0.130233	+	0.451142i
$417$	−948.000			−0.111328
$418$	−1500.00	−	2598.08i	−0.175520	−	0.304010i
$419$	−1469.00	−	2544.38i	−0.171278	−	0.296662i	0.767589	−	0.640942i	$-0.221456\pi$
$419$	−1469.00	−	2544.38i	−0.171278	−	0.296662i	−0.938867	+	0.344281i	$0.888123\pi$
$420$	2261.00	−	3916.17i	0.262680	−	0.454975i
$421$	11699.0			1.35433			0.677167	−	0.735830i	$-0.263208\pi$
$421$	11699.0			1.35433			0.677167	+	0.735830i	$0.263208\pi$
$422$	5335.00	−	9240.49i	0.615412	−	1.06592i
$423$	828.000	−	1434.14i	0.0951743	−	0.164847i
$424$	−4995.00			−0.572119
$425$	−9086.00	+	15737.4i	−1.03703	+	1.79618i
$426$	−600.000	−	1039.23i	−0.0682397	−	0.118195i
$427$	1256.50	+	2176.32i	0.142404	+	0.246650i
$428$	−15912.0			−1.79705
$429$	−1300.00	+	4503.33i	−0.146304	+	0.506813i
$430$	24510.0			2.74878
$431$	1530.00	+	2650.04i	0.170992	+	0.296167i	0.938767	−	0.344553i	$-0.111969\pi$
$431$	1530.00	+	2650.04i	0.170992	+	0.296167i	−0.767775	+	0.640720i	$0.778636\pi$
$432$	4450.00	+	7707.63i	0.495604	+	0.858410i
$433$	4013.50	−	6951.59i	0.445442	−	0.771529i	−0.552641	−	0.833420i	$-0.686380\pi$
$433$	4013.50	−	6951.59i	0.445442	−	0.771529i	0.998083	+	0.0618910i	$0.0197131\pi$
$434$	−8750.00			−0.967773
$435$	4769.00	−	8260.15i	0.525646	−	0.910446i
$436$	−1717.00	+	2973.93i	−0.188600	+	0.326664i
$437$	−1656.00			−0.181275
$438$	445.000	−	770.763i	0.0485455	−	0.0840832i
$439$	2009.00	+	3479.69i	0.218415	+	0.378306i	0.954324	−	0.298775i	$-0.0965779\pi$
$439$	2009.00	+	3479.69i	0.218415	+	0.378306i	−0.735908	+	0.677081i	$0.763245\pi$
$440$	21375.0	+	37022.6i	2.31594	+	4.01132i
$441$	−1127.00			−0.121693
$442$	17517.5	−	4334.46i	1.88512	−	0.466446i
$443$	−7624.00			−0.817669			−0.408834	−	0.912609i	$-0.634065\pi$
$443$	−7624.00			−0.817669			−0.408834	+	0.912609i	$0.634065\pi$
$444$	−1343.00	−	2326.14i	−0.143549	−	0.248635i
$445$	−14497.0	−	25109.5i	−1.54432	−	2.67485i
$446$	730.000	−	1264.40i	0.0775034	−	0.134240i
$447$	5094.00			0.539011
$448$	1004.50	−	1739.85i	0.105933	−	0.183482i
$449$	3721.00	−	6444.96i	0.391102	−	0.677409i	−0.601493	−	0.798878i	$-0.705427\pi$
$449$	3721.00	−	6444.96i	0.391102	−	0.677409i	0.992595	+	0.121469i	$0.0387606\pi$
$450$	27140.0			2.84309
$451$	−5475.00	+	9482.98i	−0.571636	+	0.990102i
$452$	−7369.50	−	12764.3i	−0.766885	−	1.32828i
$453$	−2512.00	−	4350.91i	−0.260539	−	0.451266i
$454$	26530.0			2.74254
$455$	−1729.00	+	5989.43i	−0.178147	+	0.617118i
$456$	−1080.00			−0.110911
$457$	9732.50	+	16857.2i	0.996208	+	1.72548i	0.573449	+	0.819241i	$0.305605\pi$
$457$	9732.50	+	16857.2i	0.996208	+	1.72548i	0.422759	+	0.906242i	$0.361062\pi$
$458$	−625.000	−	1082.53i	−0.0637649	−	0.110444i
$459$	3850.00	−	6668.40i	0.391509	−	0.678113i
$460$	44574.0			4.51799
$461$	−8712.50	+	15090.5i	−0.880220	+	1.52459i	−0.0291246	+	0.999576i	$0.509272\pi$
$461$	−8712.50	+	15090.5i	−0.880220	+	1.52459i	−0.851096	+	0.525011i	$0.824061\pi$
$462$	−1750.00	+	3031.09i	−0.176228	+	0.305236i
$463$	814.000			0.0817058			0.0408529	−	0.999165i	$-0.486992\pi$
$463$	814.000			0.0817058			0.0408529	+	0.999165i	$0.486992\pi$
$464$	−11169.5	+	19346.1i	−1.11752	+	1.93561i
$465$	4750.00	+	8227.24i	0.473712	+	0.820493i
$466$	3235.00	+	5603.18i	0.321585	+	0.557001i
$467$	−10806.0			−1.07075			−0.535377	−	0.844613i	$-0.679830\pi$
$467$	−10806.0			−1.07075			−0.535377	+	0.844613i	$0.679830\pi$
$468$	−12707.5	−	13206.0i	−1.25514	−	1.30438i
$469$	2002.00			0.197108
$470$	−3420.00	−	5923.61i	−0.335644	−	0.581353i
$471$	2319.00	+	4016.63i	0.226866	+	0.392943i
$472$	2835.00	−	4910.36i	0.276465	−	0.478851i
$473$	−12900.0			−1.25400
$474$	−5150.00	+	8920.06i	−0.499045	+	0.864371i
$475$	−1416.00	+	2452.58i	−0.136780	+	0.236910i
$476$	9163.00			0.882322
$477$	1276.50	−	2210.96i	0.122530	−	0.212229i
$478$	−6645.00	−	11509.5i	−0.635848	−	1.10132i
$479$	5277.00	+	9140.03i	0.503366	+	0.871855i	0.999992	+	0.00389102i	$0.00123855\pi$
$479$	5277.00	+	9140.03i	0.503366	+	0.871855i	−0.496626	+	0.867964i	$0.665428\pi$
$480$	3230.00			0.307143
$481$	2567.50	+	2668.22i	0.243384	+	0.252933i
$482$	23275.0			2.19948
$483$	966.000	+	1673.16i	0.0910032	+	0.157622i
$484$	−9936.50	−	17210.5i	−0.933180	−	1.61632i
$485$	5339.00	−	9247.42i	0.499859	−	0.865781i
$486$	−17710.0			−1.65297
$487$	3072.00	−	5320.86i	0.285843	−	0.495095i	−0.686970	−	0.726686i	$-0.741060\pi$
$487$	3072.00	−	5320.86i	0.285843	−	0.495095i	0.972813	+	0.231591i	$0.0743930\pi$
$488$	−8077.50	+	13990.6i	−0.749285	+	1.29780i
$489$	1804.00			0.166830
$490$	−2327.50	+	4031.35i	−0.214583	+	0.371669i
$491$	−6912.00	−	11971.9i	−0.635304	−	1.10038i	−0.986451	−	0.164058i	$-0.947542\pi$
$491$	−6912.00	−	11971.9i	−0.635304	−	1.10038i	0.351147	−	0.936320i	$-0.385792\pi$
$492$	3723.00	+	6448.43i	0.341150	+	0.590889i
$493$	19327.0			1.76561
$494$	2730.00	−	675.500i	0.248641	−	0.0615226i
$495$	−21850.0			−1.98401
$496$	−11125.0	−	19269.1i	−1.00711	−	1.74437i
$497$	420.000	+	727.461i	0.0379066	+	0.0656561i
$498$	4130.00	−	7153.37i	0.371626	−	0.643675i
$499$	16470.0			1.47755			0.738776	−	0.673951i	$-0.235404\pi$
$499$	16470.0			1.47755			0.738776	+	0.673951i	$0.235404\pi$
$500$	17926.5	−	31049.6i	1.60339	−	2.77716i
$501$	674.000	−	1167.40i	0.0601040	−	0.104103i
$502$	−15060.0			−1.33897
$503$	6019.00	−	10425.2i	0.533547	−	0.924130i	−0.465686	−	0.884950i	$-0.654192\pi$
$503$	6019.00	−	10425.2i	0.533547	−	0.924130i	0.999232	−	0.0391796i	$-0.0124744\pi$
$504$	−3622.50	−	6274.35i	−0.320157	−	0.554528i
$505$	−2308.50	−	3998.44i	−0.203420	−	0.352333i
$506$	−34500.0			−3.03105
$507$	−3718.00	−	2341.73i	−0.325685	−	0.205128i
$508$	34612.0			3.02295
$509$	−10734.5	−	18592.7i	−0.934771	−	1.61907i	−0.775042	−	0.631910i	$-0.782271\pi$
$509$	−10734.5	−	18592.7i	−0.934771	−	1.61907i	−0.159729	−	0.987161i	$-0.551062\pi$
$510$	−7315.00	−	12670.0i	−0.635125	−	1.10007i
$511$	−311.500	+	539.534i	−0.0269666	+	0.0467076i
$512$	24475.0			2.11260
$513$	600.000	−	1039.23i	0.0516387	−	0.0894408i
$514$	192.500	−	333.420i	0.0165191	−	0.0286119i
$515$	3420.00			0.292628
$516$	−4386.00	+	7596.77i	−0.374192	+	0.648119i
$517$	1800.00	+	3117.69i	0.153122	+	0.265215i
$518$	1382.50	+	2394.56i	0.117266	+	0.203110i
$519$	−228.000			−0.0192834
$520$	−38902.5	+	9625.87i	−3.28075	+	0.811774i
$521$	10113.0			0.850400			0.425200	−	0.905099i	$-0.360204\pi$
$521$	10113.0			0.850400			0.425200	+	0.905099i	$0.360204\pi$
$522$	−14432.5	−	24997.8i	−1.21014	−	2.09602i
$523$	5474.00	+	9481.25i	0.457670	+	0.792707i	0.998837	−	0.0482074i	$-0.0153509\pi$
$523$	5474.00	+	9481.25i	0.457670	+	0.792707i	−0.541168	+	0.840915i	$0.682018\pi$
$524$	−15844.0	+	27442.6i	−1.32089	+	2.28786i
$525$	3304.00			0.274664
$526$	−18045.0	+	31254.9i	−1.49582	+	2.59083i
$527$	−9625.00	+	16671.0i	−0.795582	+	1.37799i
$528$	−8900.00			−0.733566
$529$	−3438.50	+	5955.66i	−0.282609	+	0.489493i
$530$	−5272.50	−	9132.24i	−0.432118	−	0.748451i
$531$	1449.00	+	2509.74i	0.118420	+	0.205110i
$532$	1428.00			0.116375
$533$	−7117.50	−	7396.72i	−0.578411	−	0.601103i
$534$	15260.0			1.23664
$535$	−8892.00	−	15401.4i	−0.718570	−	1.24460i
$536$	6435.00	+	11145.7i	0.518563	+	0.898177i
$537$	2864.00	−	4960.59i	0.230150	−	0.398632i
$538$	14350.0			1.14995
$539$	1225.00	−	2121.76i	0.0978933	−	0.169556i
$540$	−16150.0	+	27972.6i	−1.28701	+	2.22917i
$541$	−17025.0			−1.35298			−0.676490	−	0.736452i	$-0.736500\pi$
$541$	−17025.0			−1.35298			−0.676490	+	0.736452i	$0.736500\pi$
$542$	3255.00	−	5637.83i	0.257960	−	0.446800i
$543$	2275.00	+	3940.42i	0.179797	+	0.311417i
$544$	3272.50	+	5668.14i	0.257918	+	0.446727i
$545$	−3838.00			−0.301655
$546$	−2275.00	−	2364.25i	−0.178317	−	0.185312i
$547$	−22622.0			−1.76828			−0.884138	−	0.467226i	$-0.845253\pi$
$547$	−22622.0			−1.76828			−0.884138	+	0.467226i	$0.845253\pi$
$548$	−9001.50	−	15591.1i	−0.701688	−	1.21536i
$549$	−4128.50	−	7150.77i	−0.320947	−	0.555897i
$550$	−29500.0	+	51095.5i	−2.28706	+	3.96131i
$551$	3012.00			0.232878
$552$	−6210.00	+	10756.0i	−0.478832	+	0.829361i
$553$	3605.00	−	6244.04i	0.277216	−	0.480151i
$554$	26765.0			2.05259
$555$	1501.00	−	2599.81i	0.114800	−	0.198839i
$556$	4029.00	+	6978.43i	0.307316	+	0.532287i
$557$	−3583.50	−	6206.80i	−0.272599	−	0.472156i	0.696927	−	0.717142i	$-0.254550\pi$
$557$	−3583.50	−	6206.80i	−0.272599	−	0.472156i	−0.969527	+	0.244986i	$0.921217\pi$
$558$	28750.0			2.18116
$559$	3354.00	−	11618.6i	0.253773	−	0.879095i
$560$	−11837.0			−0.893222
$561$	3850.00	+	6668.40i	0.289745	+	0.501854i
$562$	−1832.50	−	3173.98i	−0.137543	−	0.238232i
$563$	−7581.00	+	13130.7i	−0.567497	+	0.982934i	0.429315	+	0.903155i	$0.358755\pi$
$563$	−7581.00	+	13130.7i	−0.567497	+	0.982934i	−0.996813	+	0.0797796i	$0.974578\pi$
$564$	2448.00			0.182765
$565$	8236.50	−	14266.0i	0.613296	−	1.06226i
$566$	−4125.00	+	7144.71i	−0.306337	+	0.530591i
$567$	2947.00			0.218276
$568$	−2700.00	+	4676.54i	−0.199453	+	0.345463i
$569$	−9815.00	−	17000.1i	−0.723139	−	1.25251i	−0.959735	−	0.280906i	$-0.909365\pi$
$569$	−9815.00	−	17000.1i	−0.723139	−	1.25251i	0.236596	−	0.971608i	$-0.423968\pi$
$570$	−1140.00	−	1974.54i	−0.0837708	−	0.145095i
$571$	11864.0			0.869515			0.434757	−	0.900548i	$-0.356834\pi$
$571$	11864.0			0.869515			0.434757	+	0.900548i	$0.356834\pi$
$572$	38675.0	−	9569.58i	2.82707	−	0.699518i
$573$	−4580.00			−0.333913
$574$	−3832.50	−	6638.08i	−0.278685	−	0.482697i
$575$	16284.0	+	28204.7i	1.18103	+	2.04560i
$576$	−3300.50	+	5716.63i	−0.238751	+	0.413530i
$577$	−8395.00			−0.605699			−0.302850	−	0.953038i	$-0.597938\pi$
$577$	−8395.00			−0.605699			−0.302850	+	0.953038i	$0.597938\pi$
$578$	2540.00	−	4399.41i	0.182786	−	0.316594i
$579$	3585.00	−	6209.40i	0.257319	−	0.445689i
$580$	−81073.0			−5.80409
$581$	−2891.00	+	5007.36i	−0.206435	+	0.357556i
$582$	2810.00	+	4867.06i	0.200134	+	0.346643i
$583$	2775.00	+	4806.44i	0.197133	+	0.341445i
$584$	−4005.00			−0.283781
$585$	5681.00	−	19679.6i	0.401505	−	1.39085i
$586$	22215.0			1.56603
$587$	10942.0	+	18952.1i	0.769378	+	1.33260i	0.937901	+	0.346903i	$0.112767\pi$
$587$	10942.0	+	18952.1i	0.769378	+	1.33260i	−0.168523	+	0.985698i	$0.553900\pi$
$588$	−833.000	−	1442.80i	−0.0584223	−	0.101190i
$589$	−1500.00	+	2598.08i	−0.104935	+	0.181752i
$590$	11970.0			0.835249
$591$	1926.00	−	3335.93i	0.134053	−	0.232186i
$592$	−3515.50	+	6089.02i	−0.244064	+	0.422732i
$593$	−24407.0			−1.69018			−0.845089	−	0.534626i	$-0.820453\pi$
$593$	−24407.0			−1.69018			−0.845089	+	0.534626i	$0.820453\pi$
$594$	12500.0	−	21650.6i	0.863436	−	1.49552i
$595$	5120.50	+	8868.97i	0.352807	+	0.611079i
$596$	−21649.5	−	37498.0i	−1.48792	−	2.57715i
$597$	952.000			0.0652643
$598$	8970.00	−	31073.0i	0.613396	−	2.12486i
$599$	1700.00			0.115960			0.0579801	−	0.998318i	$-0.481534\pi$
$599$	1700.00			0.115960			0.0579801	+	0.998318i	$0.481534\pi$
$600$	10620.0	+	18394.4i	0.722599	+	1.25158i
$601$	−7086.50	−	12274.2i	−0.480972	−	0.833068i	0.518789	−	0.854902i	$-0.326383\pi$
$601$	−7086.50	−	12274.2i	−0.480972	−	0.833068i	−0.999762	+	0.0218336i	$0.993050\pi$
$602$	4515.00	−	7820.21i	0.305677	−	0.529448i
$603$	−6578.00			−0.444240
$604$	−21352.0	+	36982.7i	−1.43841	+	2.49140i
$605$	11105.5	−	19235.3i	0.746286	−	1.29260i
$606$	2430.00			0.162891
$607$	−3982.00	+	6897.03i	−0.266268	+	0.461189i	−0.967895	−	0.251355i	$-0.919124\pi$
$607$	−3982.00	+	6897.03i	−0.266268	+	0.461189i	0.701627	+	0.712544i	$0.252457\pi$
$608$	510.000	+	883.346i	0.0340185	+	0.0589217i
$609$	−1757.00	−	3043.21i	−0.116908	−	0.202491i
$610$	−34105.0			−2.26372
$611$	−3276.00	+	810.600i	−0.216911	+	0.0536716i
$612$	−30107.0			−1.98857
$613$	8582.50	+	14865.3i	0.565488	+	0.979453i	0.997004	+	0.0773483i	$0.0246453\pi$
$613$	8582.50	+	14865.3i	0.565488	+	0.979453i	−0.431517	+	0.902105i	$0.642021\pi$
$614$	−24745.0	−	42859.6i	−1.62643	−	2.81706i
$615$	−4161.00	+	7207.06i	−0.272826	+	0.472548i
$616$	15750.0			1.03017
$617$	3626.50	−	6281.28i	0.236625	−	0.409846i	−0.723119	−	0.690724i	$-0.757292\pi$
$617$	3626.50	−	6281.28i	0.236625	−	0.409846i	0.959744	+	0.280878i	$0.0906255\pi$
$618$	−900.000	+	1558.85i	−0.0585814	+	0.101466i
$619$	4590.00			0.298041			0.149021	−	0.988834i	$-0.452388\pi$
$619$	4590.00			0.298041			0.149021	+	0.988834i	$0.452388\pi$
$620$	40375.0	−	69931.6i	2.61532	−	4.52987i
$621$	−6900.00	−	11951.2i	−0.445874	−	0.772276i
$622$	3285.00	+	5689.79i	0.211763	+	0.366784i
$623$	−10682.0			−0.686943
$624$	2314.00	−	8015.93i	0.148452	−	0.514253i
$625$	10571.0			0.676544
$626$	27375.0	+	47414.9i	1.74780	+	3.02728i
$627$	600.000	+	1039.23i	0.0382164	+	0.0661928i
$628$	19711.5	−	34141.3i	1.25251	−	2.16941i
$629$	6083.00			0.385604
$630$	7647.50	−	13245.9i	0.483625	−	0.837663i
$631$	998.000	−	1728.59i	0.0629632	−	0.109055i	−0.832826	−	0.553536i	$-0.813278\pi$
$631$	998.000	−	1728.59i	0.0629632	−	0.109055i	0.895789	+	0.444480i	$0.146612\pi$
$632$	46350.0			2.91725
$633$	−2134.00	+	3696.20i	−0.133995	+	0.232086i
$634$	28137.5	+	48735.6i	1.76259	+	3.05290i
$635$	19342.0	+	33501.3i	1.20876	+	2.09364i
$636$	3774.00			0.235297
$637$	1592.50	+	1654.97i	0.0990536	+	0.102940i
$638$	62750.0			3.89388
$639$	−1380.00	−	2390.23i	−0.0854334	−	0.147975i
$640$	20092.5	+	34801.2i	1.24098	+	2.14944i
$641$	2928.50	−	5072.31i	0.180451	−	0.312550i	−0.761584	−	0.648067i	$-0.775578\pi$
$641$	2928.50	−	5072.31i	0.180451	−	0.312550i	0.942034	+	0.335517i	$0.108911\pi$
$642$	9360.00			0.575405
$643$	−1996.00	+	3457.17i	−0.122418	+	0.212034i	−0.920721	−	0.390223i	$-0.872398\pi$
$643$	−1996.00	+	3457.17i	−0.122418	+	0.212034i	0.798303	+	0.602256i	$0.205731\pi$
$644$	8211.00	−	14221.9i	0.502420	−	0.870218i
$645$	−9804.00			−0.598499
$646$	2310.00	−	4001.04i	0.140690	−	0.243682i
$647$	832.000	+	1441.07i	0.0505553	+	0.0875644i	0.890196	−	0.455578i	$-0.150568\pi$
$647$	832.000	+	1441.07i	0.0505553	+	0.0875644i	−0.839640	+	0.543143i	$0.817234\pi$
$648$	9472.50	+	16406.9i	0.574251	+	0.994633i
$649$	−6300.00			−0.381043
$650$	−38350.0	−	39854.5i	−2.31417	−	2.40496i
$651$	3500.00			0.210716
$652$	−7667.00	−	13279.6i	−0.460526	−	0.797654i
$653$	9015.00	+	15614.4i	0.540251	+	0.935743i	0.998889	+	0.0471197i	$0.0150042\pi$
$653$	9015.00	+	15614.4i	0.540251	+	0.935743i	−0.458638	+	0.888623i	$0.651662\pi$
$654$	1010.00	−	1749.37i	0.0603886	−	0.104596i
$655$	−35416.0			−2.11270
$656$	9745.50	−	16879.7i	0.580027	−	1.00464i
$657$	1023.50	−	1772.75i	0.0607771	−	0.105269i
$658$	−2520.00			−0.149301
$659$	−3608.00	+	6249.24i	−0.213274	+	0.369402i	−0.952737	−	0.303795i	$-0.901746\pi$
$659$	−3608.00	+	6249.24i	−0.213274	+	0.369402i	0.739463	+	0.673197i	$0.235079\pi$
$660$	−16150.0	−	27972.6i	−0.952482	−	1.64975i
$661$	14149.5	+	24507.7i	0.832605	+	1.44211i	0.895966	+	0.444123i	$0.146485\pi$
$661$	14149.5	+	24507.7i	0.832605	+	1.44211i	−0.0633610	+	0.997991i	$0.520182\pi$
$662$	42950.0			2.52160
$663$	−7007.00	+	1733.78i	−0.410451	+	0.101560i
$664$	−37170.0			−2.17240
$665$	798.000	+	1382.18i	0.0465340	+	0.0805993i
$666$	−4542.50	−	7867.84i	−0.264292	−	0.457767i
$667$	17319.0	−	29997.4i	1.00539	−	1.74138i
$668$	−11458.0			−0.663658
$669$	−292.000	+	505.759i	−0.0168750	+	0.0292284i
$670$	−13585.0	+	23529.9i	−0.783335	+	1.35678i
$671$	17950.0			1.03272
$672$	595.000	−	1030.57i	0.0341557	−	0.0591594i
$673$	5306.50	+	9191.13i	0.303938	+	0.526437i	0.977024	−	0.213127i	$-0.0683650\pi$
$673$	5306.50	+	9191.13i	0.303938	+	0.526437i	−0.673086	+	0.739564i	$0.735032\pi$
$674$	4327.50	+	7495.45i	0.247313	+	0.428359i
$675$	−23600.0			−1.34573
$676$	−1436.50	+	37321.4i	−0.0817308	+	2.12343i
$677$	17614.0			0.999942			0.499971	−	0.866042i	$-0.333344\pi$
$677$	17614.0			0.999942			0.499971	+	0.866042i	$0.333344\pi$
$678$	4335.00	+	7508.44i	0.245553	+	0.425310i
$679$	−1967.00	−	3406.94i	−0.111173	−	0.192557i
$680$	−32917.5	+	57014.8i	−1.85637	+	3.21532i
$681$	−10612.0			−0.597141
$682$	−31250.0	+	54126.6i	−1.75458	+	3.03902i
$683$	−8520.00	+	14757.1i	−0.477319	+	0.826740i	−0.999662	−	0.0259949i	$-0.991725\pi$
$683$	−8520.00	+	14757.1i	−0.477319	+	0.826740i	0.522343	+	0.852735i	$0.325058\pi$
$684$	−4692.00			−0.262285
$685$	10060.5	−	17425.3i	0.561156	−	0.971951i
$686$	857.500	+	1485.23i	0.0477252	+	0.0826625i
$687$	250.000	+	433.013i	0.0138837	+	0.0240473i
$688$	22962.0			1.27241
$689$	−5050.50	+	1249.67i	−0.279258	+	0.0690984i
$690$	−26220.0			−1.44664
$691$	1260.00	+	2182.38i	0.0693671	+	0.120147i	0.898623	−	0.438722i	$-0.144569\pi$
$691$	1260.00	+	2182.38i	0.0693671	+	0.120147i	−0.829256	+	0.558869i	$0.811235\pi$
$692$	969.000	+	1678.36i	0.0532310	+	0.0921988i
$693$	−4025.00	+	6971.50i	−0.220631	+	0.382144i
$694$	12450.0			0.680973
$695$	−4503.00	+	7799.42i	−0.245768	+	0.425682i
$696$	11295.0	−	19563.5i	0.615138	−	1.06545i
$697$	−16863.0			−0.916401
$698$	−14495.0	+	25106.1i	−0.786023	+	1.36143i
$699$	−1294.00	−	2241.27i	−0.0700194	−	0.121277i
$700$	−14042.0	−	24321.5i	−0.758197	−	1.31324i
$701$	19322.0			1.04106			0.520529	−	0.853844i	$-0.325735\pi$
$701$	19322.0			1.04106			0.520529	+	0.853844i	$0.325735\pi$
$702$	16250.0	+	16887.5i	0.873671	+	0.907945i
$703$	948.000			0.0508599
$704$	−7175.00	−	12427.5i	−0.384116	−	0.665309i
$705$	1368.00	+	2369.45i	0.0730807	+	0.126579i
$706$	16052.5	−	27803.7i	0.855728	−	1.48216i
$707$	−1701.00			−0.0904847
$708$	−2142.00	+	3710.05i	−0.113702	+	0.196938i
$709$	−1119.50	+	1939.03i	−0.0593000	+	0.102711i	−0.894151	−	0.447765i	$-0.852220\pi$
$709$	−1119.50	+	1939.03i	−0.0593000	+	0.102711i	0.834851	+	0.550475i	$0.185554\pi$
$710$	−11400.0			−0.602584
$711$	−11845.0	+	20516.1i	−0.624785	+	1.08216i
$712$	−34335.0	−	59470.0i	−1.80725	−	3.13024i
$713$	17250.0	+	29877.9i	0.906056	+	1.56933i
$714$	−5390.00			−0.282515
$715$	30875.0	+	32086.2i	1.61491	+	1.67826i
$716$	−48688.0			−2.54128
$717$	2658.00	+	4603.79i	0.138445	+	0.239793i
$718$	−5550.00	−	9612.88i	−0.288474	−	0.499651i
$719$	1401.00	−	2426.60i	0.0726683	−	0.125865i	−0.827402	−	0.561611i	$-0.810182\pi$
$719$	1401.00	−	2426.60i	0.0726683	−	0.125865i	0.900070	+	0.435746i	$0.143515\pi$
$720$	38893.0			2.01313
$721$	630.000	−	1091.19i	0.0325415	−	0.0563635i
$722$	−16787.5	+	29076.8i	−0.865327	+	1.49879i
$723$	−9310.00			−0.478897
$724$	19337.5	−	33493.5i	0.992642	−	1.71931i
$725$	−29618.0	−	51299.9i	−1.51722	−	2.62790i
$726$	5845.00	+	10123.8i	0.298799	+	0.517536i
$727$	37184.0			1.89694			0.948472	−	0.316861i	$-0.102629\pi$
$727$	37184.0			1.89694			0.948472	+	0.316861i	$0.102629\pi$
$728$	−4095.00	+	14185.5i	−0.208476	+	0.722183i
$729$	−4283.00			−0.217599
$730$	−4227.50	−	7322.24i	−0.214338	−	0.371244i
$731$	−9933.00	−	17204.5i	−0.502579	−	0.870492i
$732$	6103.00	−	10570.7i	0.308160	−	0.533749i
$733$	−26703.0			−1.34556			−0.672782	−	0.739841i	$-0.734901\pi$
$733$	−26703.0			−1.34556			−0.672782	+	0.739841i	$0.734901\pi$
$734$	5185.00	−	8980.68i	0.260738	−	0.451612i
$735$	931.000	−	1612.54i	0.0467217	−	0.0809244i
$736$	11730.0			0.587464
$737$	7150.00	−	12384.2i	0.357359	−	0.618964i
$738$	12592.5	+	21810.8i	0.628098	+	1.08790i
$739$	7088.00	+	12276.8i	0.352823	+	0.611108i	0.986743	−	0.162291i	$-0.0518884\pi$
$739$	7088.00	+	12276.8i	0.352823	+	0.611108i	−0.633920	+	0.773399i	$0.718555\pi$
$740$	−25517.0			−1.26760
$741$	−1092.00	+	270.200i	−0.0541371	+	0.0133955i
$742$	−3885.00			−0.192214
$743$	5688.00	+	9851.90i	0.280851	+	0.486449i	0.971595	−	0.236651i	$-0.0760499\pi$
$743$	5688.00	+	9851.90i	0.280851	+	0.486449i	−0.690743	+	0.723100i	$0.742717\pi$
$744$	11250.0	+	19485.6i	0.554362	+	0.960182i
$745$	24196.5	−	41909.6i	1.18992	−	2.06100i
$746$	−11615.0			−0.570047
$747$	9499.00	−	16452.8i	0.465261	−	0.805856i
$748$	32725.0	−	56681.4i	1.59966	−	2.77069i
$749$	−6552.00			−0.319633
$750$	−10545.0	+	18264.5i	−0.513399	+	0.889232i
$751$	−2563.00	−	4439.25i	−0.124534	−	0.215700i	0.797017	−	0.603957i	$-0.206410\pi$
$751$	−2563.00	−	4439.25i	−0.124534	−	0.215700i	−0.921551	+	0.388258i	$0.873077\pi$
$752$	−3204.00	−	5549.49i	−0.155369	−	0.269108i
$753$	6024.00			0.291536
$754$	−16315.0	+	56516.8i	−0.788007	+	2.72974i
$755$	−47728.0			−2.30066
$756$	5950.00	+	10305.7i	0.286243	+	0.495787i
$757$	−5813.00	−	10068.4i	−0.279098	−	0.483412i	0.692063	−	0.721837i	$-0.256702\pi$
$757$	−5813.00	−	10068.4i	−0.279098	−	0.483412i	−0.971161	+	0.238425i	$0.923369\pi$
$758$	28575.0	−	49493.4i	1.36925	−	2.37161i
$759$	13800.0			0.659958
$760$	−5130.00	+	8885.42i	−0.244848	+	0.424090i
$761$	12503.0	−	21655.8i	0.595576	−	1.03157i	−0.397889	−	0.917433i	$-0.630257\pi$
$761$	12503.0	−	21655.8i	0.595576	−	1.03157i	0.993465	−	0.114135i	$-0.0364095\pi$
$762$	−20360.0			−0.967933
$763$	−707.000	+	1224.56i	−0.0335454	+	0.0581023i
$764$	19465.0	+	33714.4i	0.921753	+	1.59652i
$765$	−16824.5	−	29140.9i	−0.795152	−	1.37724i
$766$	−28690.0			−1.35328
$767$	1638.00	−	5674.20i	0.0771118	−	0.267123i
$768$	−16558.0			−0.777976
$769$	1023.00	+	1771.89i	0.0479718	+	0.0830896i	0.889014	−	0.457880i	$-0.151391\pi$
$769$	1023.00	+	1771.89i	0.0479718	+	0.0830896i	−0.841042	+	0.540969i	$0.818058\pi$
$770$	16625.0	+	28795.3i	0.778082	+	1.34768i
$771$	−77.0000	+	133.368i	−0.00359674	+	0.00622974i
$772$	−60945.0			−2.84127
$773$	−15911.0	+	27558.7i	−0.740335	+	1.28230i	0.212008	+	0.977268i	$0.432000\pi$
$773$	−15911.0	+	27558.7i	−0.740335	+	1.28230i	−0.952343	+	0.305030i	$0.901334\pi$
$774$	−14835.0	+	25695.0i	−0.688932	+	1.19326i
$775$	59000.0			2.73464
$776$	12645.0	−	21901.8i	0.584960	−	1.01318i
$777$	−553.000	−	957.824i	−0.0255325	−	0.0442236i
$778$	−28422.5	−	49229.2i	−1.30976	−	2.26858i
$779$	−2628.00			−0.120870
$780$	29393.0	−	7272.88i	1.34928	−	0.333860i
$781$	6000.00			0.274900
$782$	−26565.0	−	46011.9i	−1.21479	−	2.10407i
$783$	12550.0	+	21737.2i	0.572797	+	0.992114i
$784$	−2180.50	+	3776.74i	−0.0993304	+	0.172045i
$785$	44061.0			2.00332
$786$	9320.00	−	16142.7i	0.422943	−	0.732559i
$787$	−6125.00	+	10608.8i	−0.277424	+	0.480512i	−0.970744	−	0.240118i	$-0.922814\pi$
$787$	−6125.00	+	10608.8i	−0.277424	+	0.480512i	0.693320	+	0.720630i	$0.256147\pi$
$788$	−32742.0			−1.48018
$789$	7218.00	−	12501.9i	0.325688	−	0.564108i
$790$	48925.0	+	84740.6i	2.20338	+	3.81637i
$791$	−3034.50	−	5255.91i	−0.136403	−	0.236256i
$792$	−51750.0			−2.32179
$793$	−4667.00	+	16167.0i	−0.208991	+	0.723967i
$794$	18770.0			0.838945
$795$	2109.00	+	3652.90i	0.0940862	+	0.162962i
$796$	−4046.00	−	7007.88i	−0.180159	−	0.312045i
$797$	−21575.0	+	37369.0i	−0.958878	+	1.66083i	−0.233645	+	0.972322i	$0.575065\pi$
$797$	−21575.0	+	37369.0i	−0.958878	+	1.66083i	−0.725233	+	0.688503i	$0.758268\pi$
$798$	−840.000			−0.0372628
$799$	−2772.00	+	4801.24i	−0.122736	+	0.212586i
$800$	10030.0	−	17372.5i	0.443268	−	0.767762i
$801$	35098.0			1.54822
$802$	30857.5	−	53446.8i	1.35862	−	2.35321i
$803$	2225.00	+	3853.81i	0.0977815	+	0.169363i
$804$	−4862.00	−	8421.23i	−0.213271	−	0.369395i
$805$	18354.0			0.803594
$806$	−40625.0	−	42218.7i	−1.77538	−	1.84503i
$807$	−5740.00			−0.250381
$808$	−5467.50	−	9469.99i	−0.238052	−	0.412318i
$809$	16702.5	+	28929.6i	0.725870	+	1.25724i	0.958615	+	0.284706i	$0.0918958\pi$
$809$	16702.5	+	28929.6i	0.725870	+	1.25724i	−0.232745	+	0.972538i	$0.574771\pi$
$810$	−19997.5	+	34636.7i	−0.867457	+	1.50248i
$811$	2870.00			0.124266			0.0621328	−	0.998068i	$-0.480210\pi$
$811$	2870.00			0.124266			0.0621328	+	0.998068i	$0.480210\pi$
$812$	−14934.5	+	25867.3i	−0.645441	+	1.11794i
$813$	−1302.00	+	2255.13i	−0.0561662	+	0.0972827i
$814$	19750.0			0.850414
$815$	8569.00	−	14841.9i	0.368293	−	0.637903i
$816$	−6853.00	−	11869.7i	−0.293999	−	0.509221i
$817$	−1548.00	−	2681.21i	−0.0662885	−	0.114815i
$818$	−31745.0			−1.35689
$819$	−5232.50	−	5437.77i	−0.223246	−	0.232004i
$820$	70737.0			3.01249
$821$	2393.00	+	4144.80i	0.101725	+	0.176193i	0.912395	−	0.409310i	$-0.134230\pi$
$821$	2393.00	+	4144.80i	0.101725	+	0.176193i	−0.810670	+	0.585503i	$0.800897\pi$
$822$	5295.00	+	9171.21i	0.224677	+	0.389152i
$823$	4038.00	−	6994.02i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$823$	4038.00	−	6994.02i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$824$	8100.00			0.342448
$825$	11800.0	−	20438.2i	0.497968	−	0.862505i
$826$	2205.00	−	3819.17i	0.0928835	−	0.160879i
$827$	18286.0			0.768883			0.384442	−	0.923149i	$-0.374394\pi$
$827$	18286.0			0.768883			0.384442	+	0.923149i	$0.374394\pi$
$828$	−26979.0	+	46729.0i	−1.13235	+	1.96129i
$829$	−14900.5	−	25808.4i	−0.624265	−	1.08126i	−0.988682	−	0.150023i	$-0.952065\pi$
$829$	−14900.5	−	25808.4i	−0.624265	−	1.08126i	0.364417	−	0.931236i	$-0.381268\pi$
$830$	−39235.0	−	67957.0i	−1.64080	−	2.84195i
$831$	−10706.0			−0.446916
$832$	13058.5	−	3231.14i	0.544137	−	0.134639i
$833$	3773.00			0.156935
$834$	−2370.00	−	4104.96i	−0.0984009	−	0.170435i
$835$	−6403.00	−	11090.3i	−0.265371	−	0.459636i
$836$	5100.00	−	8833.46i	0.210989	−	0.365444i
$837$	−25000.0			−1.03241
$838$	7345.00	−	12721.9i	0.302779	−	0.524429i
$839$	15546.0	−	26926.5i	0.639699	−	1.10799i	−0.345800	−	0.938308i	$-0.612392\pi$
$839$	15546.0	−	26926.5i	0.639699	−	1.10799i	0.985499	−	0.169683i	$-0.0542744\pi$
$840$	11970.0			0.491672
$841$	−19306.0	+	33439.0i	−0.791586	+	1.37107i
$842$	29247.5	+	50658.2i	1.19707	+	2.07339i
$843$	733.000	+	1269.59i	0.0299476	+	0.0518708i
$844$	36278.0			1.47955
$845$	−36926.5	+	19465.7i	−1.50333	+	0.792472i
$846$	8280.00			0.336492
$847$	−4091.50	−	7086.69i	−0.165981	−	0.287487i
$848$	−4939.50	−	8555.46i	−0.200027	−	0.346457i
$849$	1650.00	−	2857.88i	0.0666995	−	0.115527i
$850$	−90860.0			−3.66644
$851$	5451.00	−	9441.41i	0.219574	−	0.380314i
$852$	2040.00	−	3533.38i	0.0820296	−	0.142079i
$853$	−9555.00			−0.383537			−0.191768	−	0.981440i	$-0.561422\pi$
$853$	−9555.00			−0.383537			−0.191768	+	0.981440i	$0.561422\pi$
$854$	−6282.50	+	10881.6i	−0.251736	+	0.436020i
$855$	−2622.00	−	4541.44i	−0.104878	−	0.181654i
$856$	−21060.0	−	36477.0i	−0.840907	−	1.45649i
$857$	−16711.0			−0.666087			−0.333044	−	0.942911i	$-0.608076\pi$
$857$	−16711.0			−0.666087			−0.333044	+	0.942911i	$0.608076\pi$
$858$	−22750.0	+	5629.17i	−0.905212	+	0.223982i
$859$	27442.0			1.09000			0.544999	−	0.838436i	$-0.316530\pi$
$859$	27442.0			1.09000			0.544999	+	0.838436i	$0.316530\pi$
$860$	41667.0	+	72169.4i	1.65213	+	2.86158i
$861$	1533.00	+	2655.23i	0.0606789	+	0.105099i
$862$	−7650.00	+	13250.2i	−0.302274	+	0.523554i
$863$	−27518.0			−1.08543			−0.542714	−	0.839918i	$-0.682603\pi$
$863$	−27518.0			−1.08543			−0.542714	+	0.839918i	$0.682603\pi$
$864$	−4250.00	+	7361.22i	−0.167347	+	0.289854i
$865$	−1083.00	+	1875.81i	−0.0425701	+	0.0737335i
$866$	40135.0			1.57488
$867$	−1016.00	+	1759.76i	−0.0397983	+	0.0689328i
$868$	−14875.0	−	25764.3i	−0.581671	−	1.00748i
$869$	−25750.0	−	44600.3i	−1.00519	−	1.74104i
$870$	47690.0			1.85844
$871$	9295.00	+	9659.65i	0.361595	+	0.375780i
$872$	−9090.00			−0.353012
$873$	6463.00	+	11194.2i	0.250561	+	0.433984i
$874$	−4140.00	−	7170.69i	−0.160226	−	0.277520i
$875$	7381.50	−	12785.1i	0.285189	−	0.493962i
$876$	3026.00			0.116711
$877$	4116.50	−	7129.99i	0.158500	−	0.274530i	−0.775828	−	0.630944i	$-0.782668\pi$
$877$	4116.50	−	7129.99i	0.158500	−	0.274530i	0.934328	+	0.356415i	$0.116001\pi$
$878$	−10045.0	+	17398.5i	−0.386107	+	0.668758i
$879$	−8886.00			−0.340975
$880$	−42275.0	+	73222.4i	−1.61942	+	2.80492i
$881$	−8178.50	−	14165.6i	−0.312759	−	0.541714i	0.666200	−	0.745773i	$-0.267920\pi$
$881$	−8178.50	−	14165.6i	−0.312759	−	0.541714i	−0.978959	+	0.204059i	$0.934587\pi$
$882$	−2817.50	−	4880.05i	−0.107563	−	0.186304i
$883$	−1958.00			−0.0746228			−0.0373114	−	0.999304i	$-0.511879\pi$
$883$	−1958.00			−0.0746228			−0.0373114	+	0.999304i	$0.511879\pi$
$884$	42542.5	+	44211.5i	1.61862	+	1.68212i
$885$	−4788.00			−0.181861
$886$	−19060.0	−	33012.9i	−0.722724	−	1.25179i
$887$	−16548.0	−	28662.0i	−0.626412	−	1.08498i	−0.988266	−	0.152743i	$-0.951189\pi$
$887$	−16548.0	−	28662.0i	−0.626412	−	1.08498i	0.361854	−	0.932235i	$-0.382144\pi$
$888$	3555.00	−	6157.44i	0.134345	−	0.232692i
$889$	14252.0			0.537679
$890$	72485.0	−	125548.i	2.73000	−	4.72850i
$891$	10525.0	−	18229.8i	0.395736	−	0.685435i
$892$	4964.00			0.186331
$893$	−432.000	+	748.246i	−0.0161885	+	0.0280393i
$894$	12735.0	+	22057.7i	0.476423	+	0.825189i
$895$	−27208.0	−	47125.6i	−1.01616	−	1.76004i
$896$	14805.0			0.552009
$897$	−3588.00	+	12429.2i	−0.133556	+	0.462652i
$898$	37210.0			1.38275
$899$	−31375.0	−	54343.1i	−1.16398	−	2.01607i
$900$	46138.0	+	79913.4i	1.70881	+	2.95975i
$901$	−4273.50	+	7401.92i	−0.158014	+	0.273689i
$902$	−54750.0			−2.02104
$903$	−1806.00	+	3128.08i	−0.0665558	+	0.115278i
$904$	19507.5	−	33788.0i	0.717710	−	1.24311i
$905$	43225.0			1.58768
$906$	12560.0	−	21754.6i	0.460572	−	0.797734i
$907$	−5925.00	−	10262.4i	−0.216909	−	0.375697i	0.736952	−	0.675945i	$-0.236264\pi$
$907$	−5925.00	−	10262.4i	−0.216909	−	0.375697i	−0.953861	+	0.300247i	$0.902931\pi$
$908$	45101.0	+	78117.2i	1.64838	+	2.85508i
$909$	5589.00			0.203933
$910$	−30257.5	+	7486.79i	−1.10223	+	0.272730i
$911$	−36076.0			−1.31202			−0.656011	−	0.754752i	$-0.727757\pi$
$911$	−36076.0			−1.31202			−0.656011	+	0.754752i	$0.727757\pi$
$912$	−1068.00	−	1849.83i	−0.0387774	−	0.0671645i
$913$	20650.0	+	35766.8i	0.748538	+	1.29651i
$914$	−48662.5	+	84285.9i	−1.76106	+	3.05025i
$915$	13642.0			0.492886
$916$	2125.00	−	3680.61i	0.0766506	−	0.132763i
$917$	−6524.00	+	11299.9i	−0.234942	+	0.406931i
$918$	38500.0			1.38419
$919$	−4140.00	+	7170.69i	−0.148603	+	0.257388i	−0.930711	−	0.365755i	$-0.880811\pi$
$919$	−4140.00	+	7170.69i	−0.148603	+	0.257388i	0.782108	+	0.623142i	$0.214144\pi$
$920$	58995.0	+	102182.i	2.11414	+	3.66180i
$921$	9898.00	+	17143.8i	0.354126	+	0.613364i
$922$	−87125.0			−3.11205
$923$	−1560.00	+	5404.00i	−0.0556317	+	0.192714i
$924$	−11900.0			−0.423681
$925$	−9322.00	−	16146.2i	−0.331357	−	0.573928i
$926$	2035.00	+	3524.72i	0.0722184	+	0.125086i
$927$	−2070.00	+	3585.35i	−0.0733417	+	0.127031i
$928$	−21335.0			−0.754694
$929$	−10600.5	+	18360.6i	−0.374371	+	0.648430i	−0.990233	−	0.139424i	$-0.955475\pi$
$929$	−10600.5	+	18360.6i	−0.374371	+	0.648430i	0.615861	+	0.787855i	$0.288808\pi$
$930$	−23750.0	+	41136.2i	−0.837412	+	1.45044i
$931$	588.000			0.0206992
$932$	−10999.0	+	19050.8i	−0.386571	+	0.669561i
$933$	−1314.00	−	2275.91i	−0.0461076	−	0.0798608i
$934$	−27015.0	−	46791.4i	−0.946422	−	1.63925i
$935$	73150.0			2.55857
$936$	13455.0	−	46609.5i	0.469862	−	1.62765i
$937$	33677.0			1.17415			0.587076	−	0.809532i	$-0.300279\pi$
$937$	33677.0			1.17415			0.587076	+	0.809532i	$0.300279\pi$
$938$	5005.00	+	8668.91i	0.174221	+	0.301759i
$939$	−10950.0	−	18966.0i	−0.380554	−	0.659138i
$940$	11628.0	−	20140.3i	0.403472	−	0.698834i
$941$	5878.00			0.203632			0.101816	−	0.994803i	$-0.467535\pi$
$941$	5878.00			0.203632			0.101816	+	0.994803i	$0.467535\pi$
$942$	−11595.0	+	20083.1i	−0.401046	+	0.694632i
$943$	−15111.0	+	26173.0i	−0.521826	+	0.903829i
$944$	11214.0			0.386636
$945$	−6650.00	+	11518.1i	−0.228915	+	0.396492i
$946$	−32250.0	−	55858.6i	−1.10839	−	1.91979i
$947$	16323.0	+	28272.3i	0.560112	+	0.970143i	0.997486	+	0.0708630i	$0.0225753\pi$
$947$	16323.0	+	28272.3i	0.560112	+	0.970143i	−0.437374	+	0.899280i	$0.644091\pi$
$948$	−35020.0			−1.19979
$949$	−4049.50	+	1001.99i	−0.138517	+	0.0342740i
$950$	−14160.0			−0.483591
$951$	−11255.0	−	19494.2i	−0.383773	−	0.664715i
$952$	12127.5	+	21005.4i	0.412872	+	0.715116i
$953$	3525.00	−	6105.48i	0.119817	−	0.207530i	−0.799878	−	0.600163i	$-0.795102\pi$
$953$	3525.00	−	6105.48i	0.119817	−	0.207530i	0.919695	+	0.392633i	$0.128436\pi$
$954$	12765.0			0.433210
$955$	−21755.0	+	37680.8i	−0.737147	+	1.27678i
$956$	22593.0	−	39132.2i	0.764341	−	1.32388i
$957$	−25100.0			−0.847824
$958$	−26385.0	+	45700.2i	−0.889834	+	1.54124i
$959$	−3706.50	−	6419.85i	−0.124806	−	0.216171i
$960$	−5453.00	−	9444.87i	−0.183328	−	0.317533i
$961$	32709.0			1.09795
$962$	−5135.00	+	17788.2i	−0.172099	+	0.596168i
$963$	21528.0			0.720384
$964$	39567.5	+	68532.9i	1.32197	+	2.28973i
$965$	−34057.5	−	58989.3i	−1.13611	−	1.96781i
$966$	−4830.00	+	8365.81i	−0.160872	+	0.278639i
$967$	−37294.0			−1.24022			−0.620111	−	0.784514i	$-0.712912\pi$
$967$	−37294.0			−1.24022			−0.620111	+	0.784514i	$0.712912\pi$
$968$	26302.5	−	45557.3i	0.873341	−	1.51267i
$969$	−924.000	+	1600.41i	−0.0306328	+	0.0530575i
$970$	53390.0			1.76727
$971$	12804.0	−	22177.2i	0.423172	−	0.732955i	−0.573076	−	0.819502i	$-0.694250\pi$
$971$	12804.0	−	22177.2i	0.423172	−	0.732955i	0.996248	+	0.0865471i	$0.0275833\pi$
$972$	−30107.0	−	52146.9i	−0.993500	−	1.72079i
$973$	1659.00	+	2873.47i	0.0546609	+	0.0946755i
$974$	30720.0			1.01061
$975$	15340.0	+	15941.8i	0.503870	+	0.523637i
$976$	−31951.0			−1.04788
$977$	13930.5	+	24128.3i	0.456168	+	0.790106i	0.998755	−	0.0498937i	$-0.0158883\pi$
$977$	13930.5	+	24128.3i	0.456168	+	0.790106i	−0.542586	+	0.840000i	$0.682555\pi$
$978$	4510.00	+	7811.55i	0.147458	+	0.255405i
$979$	−38150.0	+	66077.7i	−1.24543	+	2.15715i
$980$	−15827.0			−0.515893
$981$	2323.00	−	4023.55i	0.0756042	−	0.130950i
$982$	34560.0	−	59859.7i	1.12307	−	1.94521i
$983$	−20288.0			−0.658277			−0.329139	−	0.944282i	$-0.606758\pi$
$983$	−20288.0			−0.658277			−0.329139	+	0.944282i	$0.606758\pi$
$984$	−9855.00	+	17069.4i	−0.319274	+	0.552999i
$985$	−18297.0	−	31691.3i	−0.591869	−	1.02515i
$986$	48317.5	+	83688.4i	1.56059	+	2.70302i
$987$	1008.00			0.0325076
$988$	6630.00	+	6890.10i	0.213490	+	0.221866i
$989$	−35604.0			−1.14473
$990$	−54625.0	−	94613.3i	−1.75363	−	3.03738i
$991$	12667.0	+	21939.9i	0.406035	+	0.703273i	0.994441	−	0.105292i	$-0.0335778\pi$
$991$	12667.0	+	21939.9i	0.406035	+	0.703273i	−0.588406	+	0.808565i	$0.700244\pi$
$992$	10625.0	−	18403.0i	0.340065	−	0.589009i
$993$	−17180.0			−0.549034
$994$	−2100.00	+	3637.31i	−0.0670100	+	0.116065i
$995$	4522.00	−	7832.33i	0.144077	−	0.249549i
$996$	28084.0			0.893449
$997$	6653.50	−	11524.2i	0.211353	−	0.366073i	−0.740786	−	0.671742i	$-0.765547\pi$
$997$	6653.50	−	11524.2i	0.211353	−	0.366073i	0.952138	+	0.305668i	$0.0988799\pi$
$998$	41175.0	+	71317.2i	1.30598	+	2.26203i
$999$	3950.00	+	6841.60i	0.125098	+	0.216675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.4.f.a.29.1	yes	2
13.3	even	3		1183.4.a.a.1.1		1
13.9	even	3	inner	91.4.f.a.22.1	✓	2
13.10	even	6		1183.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.4.f.a.22.1	✓	2	13.9	even	3	inner
91.4.f.a.29.1	yes	2	1.1	even	1	trivial
1183.4.a.a.1.1		1	13.3	even	3
1183.4.a.c.1.1		1	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.50000 + 4.33013i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-8.50000 + 14.7224i) q^{4} -19.0000 q^{5} +(5.00000 - 8.66025i) q^{6} +(-3.50000 + 6.06218i) q^{7} -45.0000 q^{8} +(11.5000 - 19.9186i) q^{9} +(-47.5000 - 82.2724i) q^{10} +(25.0000 + 43.3013i) q^{11} +34.0000 q^{12} +(-45.5000 + 11.2583i) q^{13} -35.0000 q^{14} +(19.0000 + 32.9090i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(-38.5000 + 66.6840i) q^{17} +115.000 q^{18} +(-6.00000 + 10.3923i) q^{19} +(161.500 - 279.726i) q^{20} +14.0000 q^{21} +(-125.000 + 216.506i) q^{22} +(69.0000 + 119.512i) q^{23} +(45.0000 + 77.9423i) q^{24} +236.000 q^{25} +(-162.500 - 168.875i) q^{26} -100.000 q^{27} +(-59.5000 - 103.057i) q^{28} +(-125.500 - 217.372i) q^{29} +(-95.0000 + 164.545i) q^{30} +250.000 q^{31} +(42.5000 - 73.6122i) q^{32} +(50.0000 - 86.6025i) q^{33} -385.000 q^{34} +(66.5000 - 115.181i) q^{35} +(195.500 + 338.616i) q^{36} +(-39.5000 - 68.4160i) q^{37} -60.0000 q^{38} +(65.0000 + 67.5500i) q^{39} +855.000 q^{40} +(109.500 + 189.660i) q^{41} +(35.0000 + 60.6218i) q^{42} +(-129.000 + 223.435i) q^{43} -850.000 q^{44} +(-218.500 + 378.453i) q^{45} +(-345.000 + 597.558i) q^{46} +72.0000 q^{47} +(-89.0000 + 154.153i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(590.000 + 1021.91i) q^{50} +154.000 q^{51} +(221.000 - 765.566i) q^{52} +111.000 q^{53} +(-250.000 - 433.013i) q^{54} +(-475.000 - 822.724i) q^{55} +(157.500 - 272.798i) q^{56} +24.0000 q^{57} +(627.500 - 1086.86i) q^{58} +(-63.0000 + 109.119i) q^{59} -646.000 q^{60} +(179.500 - 310.903i) q^{61} +(625.000 + 1082.53i) q^{62} +(80.5000 + 139.430i) q^{63} -287.000 q^{64} +(864.500 - 213.908i) q^{65} +500.000 q^{66} +(-143.000 - 247.683i) q^{67} +(-654.500 - 1133.63i) q^{68} +(138.000 - 239.023i) q^{69} +665.000 q^{70} +(60.0000 - 103.923i) q^{71} +(-517.500 + 896.336i) q^{72} +89.0000 q^{73} +(197.500 - 342.080i) q^{74} +(-236.000 - 408.764i) q^{75} +(-102.000 - 176.669i) q^{76} -350.000 q^{77} +(-130.000 + 450.333i) q^{78} -1030.00 q^{79} +(845.500 + 1464.45i) q^{80} +(-210.500 - 364.597i) q^{81} +(-547.500 + 948.298i) q^{82} +826.000 q^{83} +(-119.000 + 206.114i) q^{84} +(731.500 - 1267.00i) q^{85} -1290.00 q^{86} +(-251.000 + 434.745i) q^{87} +(-1125.00 - 1948.56i) q^{88} +(763.000 + 1321.55i) q^{89} -2185.00 q^{90} +(91.0000 - 315.233i) q^{91} -2346.00 q^{92} +(-250.000 - 433.013i) q^{93} +(180.000 + 311.769i) q^{94} +(114.000 - 197.454i) q^{95} -170.000 q^{96} +(-281.000 + 486.706i) q^{97} +(122.500 - 212.176i) q^{98} +1150.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} - 2 q^{3} - 17 q^{4} - 38 q^{5} + 10 q^{6} - 7 q^{7} - 90 q^{8} + 23 q^{9} - 95 q^{10} + 50 q^{11} + 68 q^{12} - 91 q^{13} - 70 q^{14} + 38 q^{15} - 89 q^{16} - 77 q^{17} + 230 q^{18} - 12 q^{19}+ \cdots + 2300 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 - 2 * q^3 - 17 * q^4 - 38 * q^5 + 10 * q^6 - 7 * q^7 - 90 * q^8 + 23 * q^9 - 95 * q^10 + 50 * q^11 + 68 * q^12 - 91 * q^13 - 70 * q^14 + 38 * q^15 - 89 * q^16 - 77 * q^17 + 230 * q^18 - 12 * q^19 + 323 * q^20 + 28 * q^21 - 250 * q^22 + 138 * q^23 + 90 * q^24 + 472 * q^25 - 325 * q^26 - 200 * q^27 - 119 * q^28 - 251 * q^29 - 190 * q^30 + 500 * q^31 + 85 * q^32 + 100 * q^33 - 770 * q^34 + 133 * q^35 + 391 * q^36 - 79 * q^37 - 120 * q^38 + 130 * q^39 + 1710 * q^40 + 219 * q^41 + 70 * q^42 - 258 * q^43 - 1700 * q^44 - 437 * q^45 - 690 * q^46 + 144 * q^47 - 178 * q^48 - 49 * q^49 + 1180 * q^50 + 308 * q^51 + 442 * q^52 + 222 * q^53 - 500 * q^54 - 950 * q^55 + 315 * q^56 + 48 * q^57 + 1255 * q^58 - 126 * q^59 - 1292 * q^60 + 359 * q^61 + 1250 * q^62 + 161 * q^63 - 574 * q^64 + 1729 * q^65 + 1000 * q^66 - 286 * q^67 - 1309 * q^68 + 276 * q^69 + 1330 * q^70 + 120 * q^71 - 1035 * q^72 + 178 * q^73 + 395 * q^74 - 472 * q^75 - 204 * q^76 - 700 * q^77 - 260 * q^78 - 2060 * q^79 + 1691 * q^80 - 421 * q^81 - 1095 * q^82 + 1652 * q^83 - 238 * q^84 + 1463 * q^85 - 2580 * q^86 - 502 * q^87 - 2250 * q^88 + 1526 * q^89 - 4370 * q^90 + 182 * q^91 - 4692 * q^92 - 500 * q^93 + 360 * q^94 + 228 * q^95 - 340 * q^96 - 562 * q^97 + 245 * q^98 + 2300 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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