LMFDB - Embedded newform 39.4.e.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(16,39)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("39.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.30107449022$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	39.16
Dual form			39.4.e.b.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +7.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(5.00000 - 8.66025i) q^{7} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +7.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(5.00000 - 8.66025i) q^{7} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(3.50000 + 6.06218i) q^{10} +(11.0000 + 19.0526i) q^{11} -21.0000 q^{12} +(-45.5000 + 11.2583i) q^{13} +10.0000 q^{14} +(-10.5000 - 18.1865i) q^{15} +(-20.5000 - 35.5070i) q^{16} +(-18.5000 + 32.0429i) q^{17} -9.00000 q^{18} +(-15.0000 + 25.9808i) q^{19} +(24.5000 - 42.4352i) q^{20} -30.0000 q^{21} +(-11.0000 + 19.0526i) q^{22} +(81.0000 + 140.296i) q^{23} +(-22.5000 - 38.9711i) q^{24} -76.0000 q^{25} +(-32.5000 - 33.7750i) q^{26} +27.0000 q^{27} +(-35.0000 - 60.6218i) q^{28} +(56.5000 + 97.8609i) q^{29} +(10.5000 - 18.1865i) q^{30} +196.000 q^{31} +(80.5000 - 139.430i) q^{32} +(33.0000 - 57.1577i) q^{33} -37.0000 q^{34} +(35.0000 - 60.6218i) q^{35} +(31.5000 + 54.5596i) q^{36} +(-6.50000 - 11.2583i) q^{37} -30.0000 q^{38} +(97.5000 + 101.325i) q^{39} +105.000 q^{40} +(-142.500 - 246.817i) q^{41} +(-15.0000 - 25.9808i) q^{42} +(123.000 - 213.042i) q^{43} +154.000 q^{44} +(-31.5000 + 54.5596i) q^{45} +(-81.0000 + 140.296i) q^{46} -462.000 q^{47} +(-61.5000 + 106.521i) q^{48} +(121.500 + 210.444i) q^{49} +(-38.0000 - 65.8179i) q^{50} +111.000 q^{51} +(-91.0000 + 315.233i) q^{52} -537.000 q^{53} +(13.5000 + 23.3827i) q^{54} +(77.0000 + 133.368i) q^{55} +(75.0000 - 129.904i) q^{56} +90.0000 q^{57} +(-56.5000 + 97.8609i) q^{58} +(-288.000 + 498.831i) q^{59} -147.000 q^{60} +(317.500 - 549.926i) q^{61} +(98.0000 + 169.741i) q^{62} +(45.0000 + 77.9423i) q^{63} -167.000 q^{64} +(-318.500 + 78.8083i) q^{65} +66.0000 q^{66} +(-101.000 - 174.937i) q^{67} +(129.500 + 224.301i) q^{68} +(243.000 - 420.888i) q^{69} +70.0000 q^{70} +(543.000 - 940.504i) q^{71} +(-67.5000 + 116.913i) q^{72} -805.000 q^{73} +(6.50000 - 11.2583i) q^{74} +(114.000 + 197.454i) q^{75} +(105.000 + 181.865i) q^{76} +220.000 q^{77} +(-39.0000 + 135.100i) q^{78} +884.000 q^{79} +(-143.500 - 248.549i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(142.500 - 246.817i) q^{82} +518.000 q^{83} +(-105.000 + 181.865i) q^{84} +(-129.500 + 224.301i) q^{85} +246.000 q^{86} +(169.500 - 293.583i) q^{87} +(165.000 + 285.788i) q^{88} +(-97.0000 - 168.009i) q^{89} -63.0000 q^{90} +(-130.000 + 450.333i) q^{91} +1134.00 q^{92} +(-294.000 - 509.223i) q^{93} +(-231.000 - 400.104i) q^{94} +(-105.000 + 181.865i) q^{95} -483.000 q^{96} +(601.000 - 1040.96i) q^{97} +(-121.500 + 210.444i) q^{98} -198.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} + 7 q^{4} + 14 q^{5} + 3 q^{6} + 10 q^{7} + 30 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 + 7 * q^4 + 14 * q^5 + 3 * q^6 + 10 * q^7 + 30 * q^8 - 9 * q^9	\( 2 q + q^{2} - 3 q^{3} + 7 q^{4} + 14 q^{5} + 3 q^{6} + 10 q^{7} + 30 q^{8} - 9 q^{9} + 7 q^{10} + 22 q^{11} - 42 q^{12} - 91 q^{13} + 20 q^{14} - 21 q^{15} - 41 q^{16} - 37 q^{17} - 18 q^{18} - 30 q^{19} + 49 q^{20} - 60 q^{21} - 22 q^{22} + 162 q^{23} - 45 q^{24} - 152 q^{25} - 65 q^{26} + 54 q^{27} - 70 q^{28} + 113 q^{29} + 21 q^{30} + 392 q^{31} + 161 q^{32} + 66 q^{33} - 74 q^{34} + 70 q^{35} + 63 q^{36} - 13 q^{37} - 60 q^{38} + 195 q^{39} + 210 q^{40} - 285 q^{41} - 30 q^{42} + 246 q^{43} + 308 q^{44} - 63 q^{45} - 162 q^{46} - 924 q^{47} - 123 q^{48} + 243 q^{49} - 76 q^{50} + 222 q^{51} - 182 q^{52} - 1074 q^{53} + 27 q^{54} + 154 q^{55} + 150 q^{56} + 180 q^{57} - 113 q^{58} - 576 q^{59} - 294 q^{60} + 635 q^{61} + 196 q^{62} + 90 q^{63} - 334 q^{64} - 637 q^{65} + 132 q^{66} - 202 q^{67} + 259 q^{68} + 486 q^{69} + 140 q^{70} + 1086 q^{71} - 135 q^{72} - 1610 q^{73} + 13 q^{74} + 228 q^{75} + 210 q^{76} + 440 q^{77} - 78 q^{78} + 1768 q^{79} - 287 q^{80} - 81 q^{81} + 285 q^{82} + 1036 q^{83} - 210 q^{84} - 259 q^{85} + 492 q^{86} + 339 q^{87} + 330 q^{88} - 194 q^{89} - 126 q^{90} - 260 q^{91} + 2268 q^{92} - 588 q^{93} - 462 q^{94} - 210 q^{95} - 966 q^{96} + 1202 q^{97} - 243 q^{98} - 396 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 + 7 * q^4 + 14 * q^5 + 3 * q^6 + 10 * q^7 + 30 * q^8 - 9 * q^9 + 7 * q^10 + 22 * q^11 - 42 * q^12 - 91 * q^13 + 20 * q^14 - 21 * q^15 - 41 * q^16 - 37 * q^17 - 18 * q^18 - 30 * q^19 + 49 * q^20 - 60 * q^21 - 22 * q^22 + 162 * q^23 - 45 * q^24 - 152 * q^25 - 65 * q^26 + 54 * q^27 - 70 * q^28 + 113 * q^29 + 21 * q^30 + 392 * q^31 + 161 * q^32 + 66 * q^33 - 74 * q^34 + 70 * q^35 + 63 * q^36 - 13 * q^37 - 60 * q^38 + 195 * q^39 + 210 * q^40 - 285 * q^41 - 30 * q^42 + 246 * q^43 + 308 * q^44 - 63 * q^45 - 162 * q^46 - 924 * q^47 - 123 * q^48 + 243 * q^49 - 76 * q^50 + 222 * q^51 - 182 * q^52 - 1074 * q^53 + 27 * q^54 + 154 * q^55 + 150 * q^56 + 180 * q^57 - 113 * q^58 - 576 * q^59 - 294 * q^60 + 635 * q^61 + 196 * q^62 + 90 * q^63 - 334 * q^64 - 637 * q^65 + 132 * q^66 - 202 * q^67 + 259 * q^68 + 486 * q^69 + 140 * q^70 + 1086 * q^71 - 135 * q^72 - 1610 * q^73 + 13 * q^74 + 228 * q^75 + 210 * q^76 + 440 * q^77 - 78 * q^78 + 1768 * q^79 - 287 * q^80 - 81 * q^81 + 285 * q^82 + 1036 * q^83 - 210 * q^84 - 259 * q^85 + 492 * q^86 + 339 * q^87 + 330 * q^88 - 194 * q^89 - 126 * q^90 - 260 * q^91 + 2268 * q^92 - 588 * q^93 - 462 * q^94 - 210 * q^95 - 966 * q^96 + 1202 * q^97 - 243 * q^98 - 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	0.940775	−	0.339032i	$-0.110100\pi$
$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	3.50000	−	6.06218i	0.437500	−	0.757772i
$5$	7.00000			0.626099			0.313050	−	0.949737i	$-0.398649\pi$
$5$	7.00000			0.626099			0.313050	+	0.949737i	$0.398649\pi$
$6$	1.50000	−	2.59808i	0.102062	−	0.176777i
$7$	5.00000	−	8.66025i	0.269975	−	0.467610i	−0.698880	−	0.715239i	$-0.746318\pi$
$7$	5.00000	−	8.66025i	0.269975	−	0.467610i	0.968855	+	0.247629i	$0.0796514\pi$
$8$	15.0000			0.662913
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	3.50000	+	6.06218i	0.110680	+	0.191703i
$11$	11.0000	+	19.0526i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	11.0000	+	19.0526i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−21.0000			−0.505181
$13$	−45.5000	+	11.2583i	−0.970725	+	0.240192i
$13$	−45.5000	+	11.2583i	−0.970725	+	0.240192i
$14$	10.0000			0.190901
$15$	−10.5000	−	18.1865i	−0.180739	−	0.313050i
$16$	−20.5000	−	35.5070i	−0.320312	−	0.554798i
$17$	−18.5000	+	32.0429i	−0.263936	+	0.457150i	−0.967284	−	0.253695i	$-0.918354\pi$
$17$	−18.5000	+	32.0429i	−0.263936	+	0.457150i	0.703348	+	0.710845i	$0.251687\pi$
$18$	−9.00000			−0.117851
$19$	−15.0000	+	25.9808i	−0.181118	+	0.313705i	−0.942261	−	0.334878i	$-0.891305\pi$
$19$	−15.0000	+	25.9808i	−0.181118	+	0.313705i	0.761144	+	0.648583i	$0.224638\pi$
$20$	24.5000	−	42.4352i	0.273918	−	0.474440i
$21$	−30.0000			−0.311740
$22$	−11.0000	+	19.0526i	−0.106600	+	0.184637i
$23$	81.0000	+	140.296i	0.734333	+	1.27190i	0.955015	+	0.296557i	$0.0958384\pi$
$23$	81.0000	+	140.296i	0.734333	+	1.27190i	−0.220682	+	0.975346i	$0.570828\pi$
$24$	−22.5000	−	38.9711i	−0.191366	−	0.331456i
$25$	−76.0000			−0.608000
$26$	−32.5000	−	33.7750i	−0.245145	−	0.254762i
$27$	27.0000			0.192450
$28$	−35.0000	−	60.6218i	−0.236228	−	0.409159i
$29$	56.5000	+	97.8609i	0.361786	+	0.626631i	0.988255	−	0.152815i	$-0.0488339\pi$
$29$	56.5000	+	97.8609i	0.361786	+	0.626631i	−0.626469	+	0.779446i	$0.715501\pi$
$30$	10.5000	−	18.1865i	0.0639010	−	0.110680i
$31$	196.000			1.13557			0.567785	−	0.823177i	$-0.307801\pi$
$31$	196.000			1.13557			0.567785	+	0.823177i	$0.307801\pi$
$32$	80.5000	−	139.430i	0.444704	−	0.770250i
$33$	33.0000	−	57.1577i	0.174078	−	0.301511i
$34$	−37.0000			−0.186631
$35$	35.0000	−	60.6218i	0.169031	−	0.292770i
$36$	31.5000	+	54.5596i	0.145833	+	0.252591i
$37$	−6.50000	−	11.2583i	−0.0288809	−	0.0500232i	0.851224	−	0.524803i	$-0.175861\pi$
$37$	−6.50000	−	11.2583i	−0.0288809	−	0.0500232i	−0.880105	+	0.474780i	$0.842528\pi$
$38$	−30.0000			−0.128070
$39$	97.5000	+	101.325i	0.400320	+	0.416025i
$40$	105.000			0.415049
$41$	−142.500	−	246.817i	−0.542799	−	0.940156i	−0.998742	−	0.0501465i	$-0.984031\pi$
$41$	−142.500	−	246.817i	−0.542799	−	0.940156i	0.455943	−	0.890009i	$-0.349302\pi$
$42$	−15.0000	−	25.9808i	−0.0551083	−	0.0954504i
$43$	123.000	−	213.042i	0.436217	−	0.755550i	−0.561177	−	0.827696i	$-0.689651\pi$
$43$	123.000	−	213.042i	0.436217	−	0.755550i	0.997394	+	0.0721459i	$0.0229847\pi$
$44$	154.000			0.527645
$45$	−31.5000	+	54.5596i	−0.104350	+	0.180739i
$46$	−81.0000	+	140.296i	−0.259626	+	0.449686i
$47$	−462.000			−1.43382			−0.716911	−	0.697165i	$-0.754445\pi$
$47$	−462.000			−1.43382			−0.716911	+	0.697165i	$0.754445\pi$
$48$	−61.5000	+	106.521i	−0.184933	+	0.320312i
$49$	121.500	+	210.444i	0.354227	+	0.613540i
$50$	−38.0000	−	65.8179i	−0.107480	−	0.186161i
$51$	111.000			0.304767
$52$	−91.0000	+	315.233i	−0.242681	+	0.840673i
$53$	−537.000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$53$	−537.000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$54$	13.5000	+	23.3827i	0.0340207	+	0.0589256i
$55$	77.0000	+	133.368i	0.188776	+	0.326970i
$56$	75.0000	−	129.904i	0.178970	−	0.309984i
$57$	90.0000			0.209137
$58$	−56.5000	+	97.8609i	−0.127911	+	0.221548i
$59$	−288.000	+	498.831i	−0.635498	+	1.10072i	0.350911	+	0.936409i	$0.385872\pi$
$59$	−288.000	+	498.831i	−0.635498	+	1.10072i	−0.986409	+	0.164307i	$0.947461\pi$
$60$	−147.000			−0.316294
$61$	317.500	−	549.926i	0.666421	−	1.15428i	−0.312476	−	0.949926i	$-0.601159\pi$
$61$	317.500	−	549.926i	0.666421	−	1.15428i	0.978898	−	0.204350i	$-0.0655082\pi$
$62$	98.0000	+	169.741i	0.200742	+	0.347696i
$63$	45.0000	+	77.9423i	0.0899915	+	0.155870i
$64$	−167.000			−0.326172
$65$	−318.500	+	78.8083i	−0.607770	+	0.150384i
$66$	66.0000			0.123091
$67$	−101.000	−	174.937i	−0.184166	−	0.318985i	0.759129	−	0.650940i	$-0.225625\pi$
$67$	−101.000	−	174.937i	−0.184166	−	0.318985i	−0.943295	+	0.331955i	$0.892292\pi$
$68$	129.500	+	224.301i	0.230944	+	0.400006i
$69$	243.000	−	420.888i	0.423968	−	0.734333i
$70$	70.0000			0.119523
$71$	543.000	−	940.504i	0.907637	−	1.57207i	0.0902997	−	0.995915i	$-0.471217\pi$
$71$	543.000	−	940.504i	0.907637	−	1.57207i	0.817338	−	0.576159i	$-0.195449\pi$
$72$	−67.5000	+	116.913i	−0.110485	+	0.191366i
$73$	−805.000			−1.29066			−0.645330	−	0.763904i	$-0.723280\pi$
$73$	−805.000			−1.29066			−0.645330	+	0.763904i	$0.723280\pi$
$74$	6.50000	−	11.2583i	0.0102109	−	0.0176859i
$75$	114.000	+	197.454i	0.175514	+	0.304000i
$76$	105.000	+	181.865i	0.158478	+	0.274492i
$77$	220.000			0.325602
$78$	−39.0000	+	135.100i	−0.0566139	+	0.196116i
$79$	884.000			1.25896			0.629480	−	0.777017i	$-0.283268\pi$
$79$	884.000			1.25896			0.629480	+	0.777017i	$0.283268\pi$
$80$	−143.500	−	248.549i	−0.200547	−	0.347358i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	142.500	−	246.817i	0.191908	−	0.332395i
$83$	518.000			0.685035			0.342517	−	0.939511i	$-0.388720\pi$
$83$	518.000			0.685035			0.342517	+	0.939511i	$0.388720\pi$
$84$	−105.000	+	181.865i	−0.136386	+	0.236228i
$85$	−129.500	+	224.301i	−0.165250	+	0.286221i
$86$	246.000			0.308452
$87$	169.500	−	293.583i	0.208877	−	0.361786i
$88$	165.000	+	285.788i	0.199876	+	0.346195i
$89$	−97.0000	−	168.009i	−0.115528	−	0.200100i	0.802463	−	0.596702i	$-0.203523\pi$
$89$	−97.0000	−	168.009i	−0.115528	−	0.200100i	−0.917991	+	0.396602i	$0.870189\pi$
$90$	−63.0000			−0.0737865
$91$	−130.000	+	450.333i	−0.149755	+	0.518766i
$92$	1134.00			1.28508
$93$	−294.000	−	509.223i	−0.327811	−	0.567785i
$94$	−231.000	−	400.104i	−0.253466	−	0.439016i
$95$	−105.000	+	181.865i	−0.113398	+	0.196410i
$96$	−483.000			−0.513500
$97$	601.000	−	1040.96i	0.629096	−	1.08963i	−0.358638	−	0.933477i	$-0.616759\pi$
$97$	601.000	−	1040.96i	0.629096	−	1.08963i	0.987733	−	0.156149i	$-0.0499081\pi$
$98$	−121.500	+	210.444i	−0.125238	+	0.216919i
$99$	−198.000			−0.201008
$100$	−266.000	+	460.726i	−0.266000	+	0.460726i
$101$	214.500	+	371.525i	0.211322	+	0.366021i	0.952129	−	0.305698i	$-0.0988897\pi$
$101$	214.500	+	371.525i	0.211322	+	0.366021i	−0.740806	+	0.671719i	$0.765556\pi$
$102$	55.5000	+	96.1288i	0.0538757	+	0.0933154i
$103$	−1302.00			−1.24553			−0.622766	−	0.782408i	$-0.713991\pi$
$103$	−1302.00			−1.24553			−0.622766	+	0.782408i	$0.713991\pi$
$104$	−682.500	+	168.875i	−0.643506	+	0.159226i
$105$	−210.000			−0.195180
$106$	−268.500	−	465.056i	−0.246029	−	0.426134i
$107$	669.000	+	1158.74i	0.604436	+	1.04691i	0.992140	+	0.125130i	$0.0399349\pi$
$107$	669.000	+	1158.74i	0.604436	+	1.04691i	−0.387704	+	0.921784i	$0.626732\pi$
$108$	94.5000	−	163.679i	0.0841969	−	0.145833i
$109$	−1034.00			−0.908617			−0.454308	−	0.890844i	$-0.650114\pi$
$109$	−1034.00			−0.908617			−0.454308	+	0.890844i	$0.650114\pi$
$110$	−77.0000	+	133.368i	−0.0667424	+	0.115601i
$111$	−19.5000	+	33.7750i	−0.0166744	+	0.0288809i
$112$	−410.000			−0.345905
$113$	−538.500	+	932.709i	−0.448299	+	0.776477i	−0.998275	−	0.0587032i	$-0.981303\pi$
$113$	−538.500	+	932.709i	−0.448299	+	0.776477i	0.549976	+	0.835180i	$0.314637\pi$
$114$	45.0000	+	77.9423i	0.0369705	+	0.0640348i
$115$	567.000	+	982.073i	0.459765	+	0.796337i
$116$	791.000			0.633125
$117$	117.000	−	405.300i	0.0924500	−	0.320256i
$118$	−576.000			−0.449365
$119$	185.000	+	320.429i	0.142512	+	0.246838i
$120$	−157.500	−	272.798i	−0.119814	−	0.207524i
$121$	423.500	−	733.524i	0.318182	−	0.551107i
$122$	635.000			0.471231
$123$	−427.500	+	740.452i	−0.313385	+	0.542799i
$124$	686.000	−	1188.19i	0.496811	−	0.860503i
$125$	−1407.00			−1.00677
$126$	−45.0000	+	77.9423i	−0.0318168	+	0.0551083i
$127$	494.000	+	855.633i	0.345161	+	0.597836i	0.985383	−	0.170354i	$-0.0544911\pi$
$127$	494.000	+	855.633i	0.345161	+	0.597836i	−0.640222	+	0.768190i	$0.721158\pi$
$128$	−727.500	−	1260.07i	−0.502363	−	0.870119i
$129$	−738.000			−0.503700
$130$	−227.500	−	236.425i	−0.153485	−	0.159506i
$131$	560.000			0.373492			0.186746	−	0.982408i	$-0.440206\pi$
$131$	560.000			0.373492			0.186746	+	0.982408i	$0.440206\pi$
$132$	−231.000	−	400.104i	−0.152318	−	0.263822i
$133$	150.000	+	259.808i	0.0977944	+	0.169385i
$134$	101.000	−	174.937i	0.0651125	−	0.112778i
$135$	189.000			0.120493
$136$	−277.500	+	480.644i	−0.174966	+	0.303051i
$137$	259.500	−	449.467i	0.161829	−	0.280296i	−0.773696	−	0.633557i	$-0.781594\pi$
$137$	259.500	−	449.467i	0.161829	−	0.280296i	0.935525	+	0.353261i	$0.114927\pi$
$138$	486.000			0.299790
$139$	174.000	−	301.377i	0.106176	−	0.183903i	−0.808042	−	0.589125i	$-0.799473\pi$
$139$	174.000	−	301.377i	0.106176	−	0.183903i	0.914218	+	0.405222i	$0.132806\pi$
$140$	−245.000	−	424.352i	−0.147902	−	0.256174i
$141$	693.000	+	1200.31i	0.413909	+	0.716911i
$142$	1086.00			0.641796
$143$	−715.000	−	743.050i	−0.418121	−	0.434524i
$144$	369.000			0.213542
$145$	395.500	+	685.026i	0.226514	+	0.392333i
$146$	−402.500	−	697.150i	−0.228158	−	0.395182i
$147$	364.500	−	631.333i	0.204513	−	0.354227i
$148$	−91.0000			−0.0505416
$149$	322.500	−	558.586i	0.177317	−	0.307122i	−0.763644	−	0.645638i	$-0.776592\pi$
$149$	322.500	−	558.586i	0.177317	−	0.307122i	0.940961	+	0.338516i	$0.109925\pi$
$150$	−114.000	+	197.454i	−0.0620537	+	0.107480i
$151$	2914.00			1.57045			0.785225	−	0.619211i	$-0.212547\pi$
$151$	2914.00			1.57045			0.785225	+	0.619211i	$0.212547\pi$
$152$	−225.000	+	389.711i	−0.120065	+	0.207959i
$153$	−166.500	−	288.386i	−0.0879786	−	0.152383i
$154$	110.000	+	190.526i	0.0575588	+	0.0996947i
$155$	1372.00			0.710979
$156$	955.500	−	236.425i	0.490392	−	0.121341i
$157$	−2079.00			−1.05683			−0.528415	−	0.848986i	$-0.677213\pi$
$157$	−2079.00			−1.05683			−0.528415	+	0.848986i	$0.677213\pi$
$158$	442.000	+	765.566i	0.222555	+	0.385476i
$159$	805.500	+	1395.17i	0.401763	+	0.695874i
$160$	563.500	−	976.011i	0.278429	−	0.482253i
$161$	1620.00			0.793006
$162$	40.5000	−	70.1481i	0.0196419	−	0.0340207i
$163$	−850.000	+	1472.24i	−0.408449	+	0.707454i	−0.994716	−	0.102664i	$-0.967263\pi$
$163$	−850.000	+	1472.24i	−0.408449	+	0.707454i	0.586267	+	0.810118i	$0.300597\pi$
$164$	−1995.00			−0.949898
$165$	231.000	−	400.104i	0.108990	−	0.188776i
$166$	259.000	+	448.601i	0.121098	+	0.209748i
$167$	−1840.00	−	3186.97i	−0.852596	−	1.47674i	−0.878858	−	0.477084i	$-0.841694\pi$
$167$	−1840.00	−	3186.97i	−0.852596	−	1.47674i	0.0262621	−	0.999655i	$-0.491640\pi$
$168$	−450.000			−0.206656
$169$	1943.50	−	1024.51i	0.884615	−	0.466321i
$170$	−259.000			−0.116849
$171$	−135.000	−	233.827i	−0.0603726	−	0.104568i
$172$	−861.000	−	1491.30i	−0.381690	−	0.661106i
$173$	−2073.00	+	3590.54i	−0.911025	+	1.57794i	−0.0984052	+	0.995146i	$0.531374\pi$
$173$	−2073.00	+	3590.54i	−0.911025	+	1.57794i	−0.812619	+	0.582795i	$0.801959\pi$
$174$	339.000			0.147698
$175$	−380.000	+	658.179i	−0.164145	+	0.284307i
$176$	451.000	−	781.155i	0.193156	−	0.334555i
$177$	1728.00			0.733810
$178$	97.0000	−	168.009i	0.0408453	−	0.0707461i
$179$	−1837.00	−	3181.78i	−0.767060	−	1.32859i	−0.939150	−	0.343506i	$-0.888385\pi$
$179$	−1837.00	−	3181.78i	−0.767060	−	1.32859i	0.172090	−	0.985081i	$-0.444948\pi$
$180$	220.500	+	381.917i	0.0913061	+	0.158147i
$181$	−3283.00			−1.34820			−0.674098	−	0.738642i	$-0.735467\pi$
$181$	−3283.00			−1.34820			−0.674098	+	0.738642i	$0.735467\pi$
$182$	−455.000	+	112.583i	−0.185312	+	0.0458529i
$183$	−1905.00			−0.769517
$184$	1215.00	+	2104.44i	0.486799	+	0.843160i
$185$	−45.5000	−	78.8083i	−0.0180823	−	0.0313195i
$186$	294.000	−	509.223i	0.115899	−	0.200742i
$187$	−814.000			−0.318319
$188$	−1617.00	+	2800.73i	−0.627297	+	1.08651i
$189$	135.000	−	233.827i	0.0519566	−	0.0899915i
$190$	−210.000			−0.0801842
$191$	298.000	−	516.151i	0.112893	−	0.195536i	−0.804043	−	0.594572i	$-0.797322\pi$
$191$	298.000	−	516.151i	0.112893	−	0.195536i	0.916935	+	0.399036i	$0.130655\pi$
$192$	250.500	+	433.879i	0.0941577	+	0.163086i
$193$	196.500	+	340.348i	0.0732869	+	0.126937i	0.900340	−	0.435187i	$-0.143318\pi$
$193$	196.500	+	340.348i	0.0732869	+	0.126937i	−0.827053	+	0.562124i	$0.809984\pi$
$194$	1202.00			0.444838
$195$	682.500	+	709.275i	0.250640	+	0.260473i
$196$	1701.00			0.619898
$197$	1761.00	+	3050.14i	0.636884	+	1.10311i	0.986113	+	0.166077i	$0.0531101\pi$
$197$	1761.00	+	3050.14i	0.636884	+	1.10311i	−0.349229	+	0.937037i	$0.613557\pi$
$198$	−99.0000	−	171.473i	−0.0355335	−	0.0615457i
$199$	−1009.00	+	1747.64i	−0.359428	+	0.622547i	−0.987865	−	0.155313i	$-0.950361\pi$
$199$	−1009.00	+	1747.64i	−0.359428	+	0.622547i	0.628438	+	0.777860i	$0.283695\pi$
$200$	−1140.00			−0.403051
$201$	−303.000	+	524.811i	−0.106328	+	0.184166i
$202$	−214.500	+	371.525i	−0.0747137	+	0.129408i
$203$	1130.00			0.390692
$204$	388.500	−	672.902i	0.133335	−	0.230944i
$205$	−997.500	−	1727.72i	−0.339846	−	0.588630i
$206$	−651.000	−	1127.57i	−0.220181	−	0.381365i
$207$	−1458.00			−0.489556
$208$	1332.50	+	1384.77i	0.444194	+	0.461619i
$209$	−660.000			−0.218436
$210$	−105.000	−	181.865i	−0.0345033	−	0.0597614i
$211$	−80.0000	−	138.564i	−0.0261016	−	0.0452092i	0.852680	−	0.522434i	$-0.174976\pi$
$211$	−80.0000	−	138.564i	−0.0261016	−	0.0452092i	−0.878781	+	0.477225i	$0.841643\pi$
$212$	−1879.50	+	3255.39i	−0.608890	+	1.05463i
$213$	−3258.00			−1.04805
$214$	−669.000	+	1158.74i	−0.213700	+	0.370140i
$215$	861.000	−	1491.30i	0.273115	−	0.473049i
$216$	405.000			0.127578
$217$	980.000	−	1697.41i	0.306575	−	0.531003i
$218$	−517.000	−	895.470i	−0.160622	−	0.278206i
$219$	1207.50	+	2091.45i	0.372581	+	0.645330i
$220$	1078.00			0.330358
$221$	481.000	−	1666.23i	0.146405	−	0.507163i
$222$	−39.0000			−0.0117906
$223$	−2036.00	−	3526.46i	−0.611393	−	1.05896i	−0.991006	−	0.133818i	$-0.957276\pi$
$223$	−2036.00	−	3526.46i	−0.611393	−	1.05896i	0.379613	−	0.925145i	$-0.376057\pi$
$224$	−805.000	−	1394.30i	−0.240118	−	0.415896i
$225$	342.000	−	592.361i	0.101333	−	0.175514i
$226$	−1077.00			−0.316995
$227$	2897.00	−	5017.75i	0.847051	−	1.46714i	−0.0367765	−	0.999324i	$-0.511709\pi$
$227$	2897.00	−	5017.75i	0.847051	−	1.46714i	0.883828	−	0.467812i	$-0.154958\pi$
$228$	315.000	−	545.596i	0.0914973	−	0.158478i
$229$	6482.00			1.87049			0.935246	−	0.353999i	$-0.115178\pi$
$229$	6482.00			1.87049			0.935246	+	0.353999i	$0.115178\pi$
$230$	−567.000	+	982.073i	−0.162552	+	0.281548i
$231$	−330.000	−	571.577i	−0.0939931	−	0.162801i
$232$	847.500	+	1467.91i	0.239832	+	0.415402i
$233$	6890.00			1.93725			0.968624	−	0.248530i	$-0.0799474\pi$
$233$	6890.00			1.93725			0.968624	+	0.248530i	$0.0799474\pi$
$234$	409.500	−	101.325i	0.114401	−	0.0283069i
$235$	−3234.00			−0.897714
$236$	2016.00	+	3491.81i	0.556061	+	0.963126i
$237$	−1326.00	−	2296.70i	−0.363430	−	0.629480i
$238$	−185.000	+	320.429i	−0.0503856	+	0.0872704i
$239$	2466.00			0.667415			0.333708	−	0.942677i	$-0.391700\pi$
$239$	2466.00			0.667415			0.333708	+	0.942677i	$0.391700\pi$
$240$	−430.500	+	745.648i	−0.115786	+	0.200547i
$241$	1808.50	−	3132.41i	0.483385	−	0.837247i	−0.516433	−	0.856327i	$-0.672741\pi$
$241$	1808.50	−	3132.41i	0.483385	−	0.837247i	0.999818	+	0.0190805i	$0.00607389\pi$
$242$	847.000			0.224989
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−2222.50	−	3849.48i	−0.583119	−	1.00999i
$245$	850.500	+	1473.11i	0.221781	+	0.384137i
$246$	−855.000			−0.221597
$247$	390.000	−	1351.00i	0.100466	−	0.348024i
$248$	2940.00			0.752783
$249$	−777.000	−	1345.80i	−0.197753	−	0.342517i
$250$	−703.500	−	1218.50i	−0.177973	−	0.308258i
$251$	−2430.00	+	4208.88i	−0.611077	+	1.05842i	0.379983	+	0.924994i	$0.375930\pi$
$251$	−2430.00	+	4208.88i	−0.611077	+	1.05842i	−0.991059	+	0.133422i	$0.957403\pi$
$252$	630.000			0.157485
$253$	−1782.00	+	3086.51i	−0.442820	+	0.766986i
$254$	−494.000	+	855.633i	−0.122033	+	0.211367i
$255$	777.000			0.190814
$256$	59.5000	−	103.057i	0.0145264	−	0.0251604i
$257$	−282.500	−	489.304i	−0.0685676	−	0.118763i	0.829703	−	0.558204i	$-0.188510\pi$
$257$	−282.500	−	489.304i	−0.0685676	−	0.118763i	−0.898271	+	0.439442i	$0.855176\pi$
$258$	−369.000	−	639.127i	−0.0890424	−	0.154226i
$259$	−130.000			−0.0311884
$260$	−637.000	+	2206.63i	−0.151943	+	0.526344i
$261$	−1017.00			−0.241190
$262$	280.000	+	484.974i	0.0660246	+	0.114358i
$263$	249.000	+	431.281i	0.0583802	+	0.101118i	0.893738	−	0.448588i	$-0.148073\pi$
$263$	249.000	+	431.281i	0.0583802	+	0.101118i	−0.835358	+	0.549706i	$0.814740\pi$
$264$	495.000	−	857.365i	0.115398	−	0.199876i
$265$	−3759.00			−0.871372
$266$	−150.000	+	259.808i	−0.0345755	+	0.0598866i
$267$	−291.000	+	504.027i	−0.0667000	+	0.115528i
$268$	−1414.00			−0.322290
$269$	−2773.00	+	4802.98i	−0.628523	+	1.08863i	0.359325	+	0.933213i	$0.383007\pi$
$269$	−2773.00	+	4802.98i	−0.628523	+	1.08863i	−0.987848	+	0.155422i	$0.950326\pi$
$270$	94.5000	+	163.679i	0.0213003	+	0.0368932i
$271$	1128.00	+	1953.75i	0.252845	+	0.437941i	0.964308	−	0.264783i	$-0.0853002\pi$
$271$	1128.00	+	1953.75i	0.252845	+	0.437941i	−0.711463	+	0.702724i	$0.751967\pi$
$272$	1517.00			0.338168
$273$	1365.00	−	337.750i	0.302614	−	0.0748775i
$274$	519.000			0.114430
$275$	−836.000	−	1447.99i	−0.183319	−	0.317518i
$276$	−1701.00	−	2946.22i	−0.370972	−	0.642542i
$277$	−1154.50	+	1999.65i	−0.250423	+	0.433745i	−0.963642	−	0.267196i	$-0.913903\pi$
$277$	−1154.50	+	1999.65i	−0.250423	+	0.433745i	0.713219	+	0.700941i	$0.247236\pi$
$278$	348.000			0.0750779
$279$	−882.000	+	1527.67i	−0.189262	+	0.327811i
$280$	525.000	−	909.327i	0.112053	−	0.194081i
$281$	5833.00			1.23832			0.619159	−	0.785265i	$-0.287473\pi$
$281$	5833.00			1.23832			0.619159	+	0.785265i	$0.287473\pi$
$282$	−693.000	+	1200.31i	−0.146339	+	0.253466i
$283$	−825.000	−	1428.94i	−0.173290	−	0.300148i	0.766278	−	0.642509i	$-0.222107\pi$
$283$	−825.000	−	1428.94i	−0.173290	−	0.300148i	−0.939568	+	0.342362i	$0.888773\pi$
$284$	−3801.00	−	6583.53i	−0.794183	−	1.37556i
$285$	630.000			0.130940
$286$	286.000	−	990.733i	0.0591312	−	0.204837i
$287$	−2850.00			−0.586168
$288$	724.500	+	1254.87i	0.148235	+	0.256750i
$289$	1772.00	+	3069.19i	0.360676	+	0.624709i
$290$	−395.500	+	685.026i	−0.0800847	+	0.138711i
$291$	−3606.00			−0.726417
$292$	−2817.50	+	4880.05i	−0.564663	+	0.978026i
$293$	−1495.50	+	2590.28i	−0.298184	+	0.516471i	−0.975721	−	0.219019i	$-0.929714\pi$
$293$	−1495.50	+	2590.28i	−0.298184	+	0.516471i	0.677536	+	0.735489i	$0.263048\pi$
$294$	729.000			0.144613
$295$	−2016.00	+	3491.81i	−0.397885	+	0.689157i
$296$	−97.5000	−	168.875i	−0.0191455	−	0.0331610i
$297$	297.000	+	514.419i	0.0580259	+	0.100504i
$298$	645.000			0.125382
$299$	−5265.00	−	5471.55i	−1.01834	−	1.05829i
$300$	1596.00			0.307150
$301$	−1230.00	−	2130.42i	−0.235535	−	0.407959i
$302$	1457.00	+	2523.60i	0.277619	+	0.480850i
$303$	643.500	−	1114.57i	0.122007	−	0.211322i
$304$	1230.00			0.232057
$305$	2222.50	−	3849.48i	0.417246	−	0.722691i
$306$	166.500	−	288.386i	0.0311051	−	0.0538757i
$307$	−2422.00			−0.450263			−0.225132	−	0.974328i	$-0.572281\pi$
$307$	−2422.00			−0.450263			−0.225132	+	0.974328i	$0.572281\pi$
$308$	770.000	−	1333.68i	0.142451	−	0.246732i
$309$	1953.00	+	3382.70i	0.359554	+	0.622766i
$310$	686.000	+	1188.19i	0.125684	+	0.217692i
$311$	−3402.00			−0.620288			−0.310144	−	0.950690i	$-0.600377\pi$
$311$	−3402.00			−0.620288			−0.310144	+	0.950690i	$0.600377\pi$
$312$	1462.50	+	1519.87i	0.265377	+	0.275788i
$313$	2310.00			0.417153			0.208577	−	0.978006i	$-0.433117\pi$
$313$	2310.00			0.417153			0.208577	+	0.978006i	$0.433117\pi$
$314$	−1039.50	−	1800.47i	−0.186823	−	0.323587i
$315$	315.000	+	545.596i	0.0563436	+	0.0975900i
$316$	3094.00	−	5358.97i	0.550795	−	0.954004i
$317$	−257.000			−0.0455349			−0.0227674	−	0.999741i	$-0.507248\pi$
$317$	−257.000			−0.0455349			−0.0227674	+	0.999741i	$0.507248\pi$
$318$	−805.500	+	1395.17i	−0.142045	+	0.246029i
$319$	−1243.00	+	2152.94i	−0.218165	+	0.377873i
$320$	−1169.00			−0.204216
$321$	2007.00	−	3476.23i	0.348971	−	0.604436i
$322$	810.000	+	1402.96i	0.140185	+	0.242807i
$323$	−555.000	−	961.288i	−0.0956069	−	0.165596i
$324$	−567.000			−0.0972222
$325$	3458.00	−	855.633i	0.590201	−	0.146037i
$326$	−1700.00			−0.288817
$327$	1551.00	+	2686.41i	0.262295	+	0.454308i
$328$	−2137.50	−	3702.26i	−0.359828	−	0.623241i
$329$	−2310.00	+	4001.04i	−0.387096	+	0.670469i
$330$	462.000			0.0770675
$331$	−514.000	+	890.274i	−0.0853535	+	0.147837i	−0.905542	−	0.424257i	$-0.860535\pi$
$331$	−514.000	+	890.274i	−0.0853535	+	0.147837i	0.820188	+	0.572094i	$0.193869\pi$
$332$	1813.00	−	3140.21i	0.299703	−	0.519100i
$333$	117.000			0.0192539
$334$	1840.00	−	3186.97i	0.301438	−	0.522106i
$335$	−707.000	−	1224.56i	−0.115306	−	0.199716i
$336$	615.000	+	1065.21i	0.0998542	+	0.172952i
$337$	2487.00			0.402005			0.201002	−	0.979591i	$-0.435580\pi$
$337$	2487.00			0.402005			0.201002	+	0.979591i	$0.435580\pi$
$338$	1859.00	+	1170.87i	0.299161	+	0.188422i
$339$	3231.00			0.517651
$340$	906.500	+	1570.10i	0.144594	+	0.250444i
$341$	2156.00	+	3734.30i	0.342387	+	0.593032i
$342$	135.000	−	233.827i	0.0213449	−	0.0369705i
$343$	5860.00			0.922479
$344$	1845.00	−	3195.63i	0.289174	−	0.500863i
$345$	1701.00	−	2946.22i	0.265446	−	0.459765i
$346$	−4146.00			−0.644192
$347$	1425.00	−	2468.17i	0.220455	−	0.381840i	−0.734491	−	0.678618i	$-0.762579\pi$
$347$	1425.00	−	2468.17i	0.220455	−	0.381840i	0.954946	+	0.296779i	$0.0959123\pi$
$348$	−1186.50	−	2055.08i	−0.182767	−	0.316563i
$349$	1009.00	+	1747.64i	0.154758	+	0.268049i	0.932971	−	0.359952i	$-0.117207\pi$
$349$	1009.00	+	1747.64i	0.154758	+	0.268049i	−0.778213	+	0.628001i	$0.783874\pi$
$350$	−760.000			−0.116068
$351$	−1228.50	+	303.975i	−0.186816	+	0.0462250i
$352$	3542.00			0.536333
$353$	2643.50	+	4578.68i	0.398582	+	0.690364i	0.993551	−	0.113385i	$-0.0361692\pi$
$353$	2643.50	+	4578.68i	0.398582	+	0.690364i	−0.594970	+	0.803748i	$0.702836\pi$
$354$	864.000	+	1496.49i	0.129721	+	0.224683i
$355$	3801.00	−	6583.53i	0.568271	−	0.984274i
$356$	−1358.00			−0.202174
$357$	555.000	−	961.288i	0.0822793	−	0.142512i
$358$	1837.00	−	3181.78i	0.271197	−	0.469727i
$359$	−7278.00			−1.06997			−0.534983	−	0.844863i	$-0.679682\pi$
$359$	−7278.00			−1.06997			−0.534983	+	0.844863i	$0.679682\pi$
$360$	−472.500	+	818.394i	−0.0691748	+	0.119814i
$361$	2979.50	+	5160.65i	0.434393	+	0.752390i
$362$	−1641.50	−	2843.16i	−0.238330	−	0.412799i
$363$	−2541.00			−0.367405
$364$	2275.00	+	2364.25i	0.327589	+	0.340440i
$365$	−5635.00			−0.808080
$366$	−952.500	−	1649.78i	−0.136033	−	0.235616i
$367$	2101.00	+	3639.04i	0.298832	+	0.517592i	0.975869	−	0.218357i	$-0.0700697\pi$
$367$	2101.00	+	3639.04i	0.298832	+	0.517592i	−0.677037	+	0.735949i	$0.736736\pi$
$368$	3321.00	−	5752.14i	0.470432	−	0.814813i
$369$	2565.00			0.361866
$370$	45.5000	−	78.8083i	0.00639306	−	0.0110731i
$371$	−2685.00	+	4650.56i	−0.375737	+	0.650795i
$372$	−4116.00			−0.573668
$373$	791.500	−	1370.92i	0.109872	−	0.190304i	−0.805846	−	0.592125i	$-0.798289\pi$
$373$	791.500	−	1370.92i	0.109872	−	0.190304i	0.915718	+	0.401821i	$0.131623\pi$
$374$	−407.000	−	704.945i	−0.0562713	−	0.0974648i
$375$	2110.50	+	3655.49i	0.290629	+	0.503384i
$376$	−6930.00			−0.950499
$377$	−3672.50	−	3816.57i	−0.501707	−	0.521389i
$378$	270.000			0.0367389
$379$	1026.00	+	1777.08i	0.139056	+	0.240851i	0.927139	−	0.374717i	$-0.122260\pi$
$379$	1026.00	+	1777.08i	0.139056	+	0.240851i	−0.788084	+	0.615568i	$0.788927\pi$
$380$	735.000	+	1273.06i	0.0992229	+	0.171859i
$381$	1482.00	−	2566.90i	0.199279	−	0.345161i
$382$	596.000			0.0798273
$383$	3436.00	−	5951.33i	0.458411	−	0.793991i	−0.540466	−	0.841366i	$-0.681752\pi$
$383$	3436.00	−	5951.33i	0.458411	−	0.793991i	0.998877	+	0.0473746i	$0.0150855\pi$
$384$	−2182.50	+	3780.20i	−0.290040	+	0.502363i
$385$	1540.00			0.203859
$386$	−196.500	+	340.348i	−0.0259108	+	0.0448789i
$387$	1107.00	+	1917.38i	0.145406	+	0.251850i
$388$	−4207.00	−	7286.74i	−0.550459	−	0.953423i
$389$	−11653.0			−1.51884			−0.759422	−	0.650598i	$-0.774518\pi$
$389$	−11653.0			−1.51884			−0.759422	+	0.650598i	$0.774518\pi$
$390$	−273.000	+	945.700i	−0.0354459	+	0.122788i
$391$	−5994.00			−0.775268
$392$	1822.50	+	3156.66i	0.234822	+	0.406723i
$393$	−840.000	−	1454.92i	−0.107818	−	0.186746i
$394$	−1761.00	+	3050.14i	−0.225172	+	0.390010i
$395$	6188.00			0.788233
$396$	−693.000	+	1200.31i	−0.0879408	+	0.152318i
$397$	−3067.00	+	5312.20i	−0.387729	+	0.671566i	−0.992144	−	0.125104i	$-0.960074\pi$
$397$	−3067.00	+	5312.20i	−0.387729	+	0.671566i	0.604415	+	0.796670i	$0.293407\pi$
$398$	−2018.00			−0.254154
$399$	450.000	−	779.423i	0.0564616	−	0.0977944i
$400$	1558.00	+	2698.54i	0.194750	+	0.337317i
$401$	5397.50	+	9348.74i	0.672165	+	1.16422i	0.977289	+	0.211912i	$0.0679689\pi$
$401$	5397.50	+	9348.74i	0.672165	+	1.16422i	−0.305124	+	0.952313i	$0.598698\pi$
$402$	−606.000			−0.0751854
$403$	−8918.00	+	2206.63i	−1.10233	+	0.272755i
$404$	3003.00			0.369814
$405$	−283.500	−	491.036i	−0.0347833	−	0.0602464i
$406$	565.000	+	978.609i	0.0690652	+	0.119624i
$407$	143.000	−	247.683i	0.0174158	−	0.0301651i
$408$	1665.00			0.202034
$409$	4244.50	−	7351.69i	0.513147	−	0.888796i	−0.486737	−	0.873549i	$-0.661813\pi$
$409$	4244.50	−	7351.69i	0.513147	−	0.888796i	0.999884	−	0.0152477i	$-0.00485367\pi$
$410$	997.500	−	1727.72i	0.120154	−	0.208112i
$411$	−1557.00			−0.186864
$412$	−4557.00	+	7892.96i	−0.544921	+	0.943830i
$413$	2880.00	+	4988.31i	0.343137	+	0.594331i
$414$	−729.000	−	1262.67i	−0.0865420	−	0.149895i
$415$	3626.00			0.428900
$416$	−2093.00	+	7250.36i	−0.246677	+	0.854515i
$417$	−1044.00			−0.122602
$418$	−330.000	−	571.577i	−0.0386144	−	0.0668821i
$419$	−748.000	−	1295.57i	−0.0872129	−	0.151057i	0.819119	−	0.573623i	$-0.194463\pi$
$419$	−748.000	−	1295.57i	−0.0872129	−	0.151057i	−0.906332	+	0.422566i	$0.861129\pi$
$420$	−735.000	+	1273.06i	−0.0853913	+	0.147902i
$421$	−11695.0			−1.35387			−0.676935	−	0.736043i	$-0.736692\pi$
$421$	−11695.0			−1.35387			−0.676935	+	0.736043i	$0.736692\pi$
$422$	80.0000	−	138.564i	0.00922829	−	0.0159839i
$423$	2079.00	−	3600.93i	0.238970	−	0.413909i
$424$	−8055.00			−0.922607
$425$	1406.00	−	2435.26i	0.160473	−	0.277947i
$426$	−1629.00	−	2821.51i	−0.185271	−	0.320898i
$427$	−3175.00	−	5499.26i	−0.359834	−	0.623250i
$428$	9366.00			1.05776
$429$	−858.000	+	2972.20i	−0.0965609	+	0.334497i
$430$	1722.00			0.193121
$431$	−5295.00	−	9171.21i	−0.591766	−	1.02497i	−0.993995	−	0.109430i	$-0.965098\pi$
$431$	−5295.00	−	9171.21i	−0.591766	−	1.02497i	0.402228	−	0.915539i	$-0.368236\pi$
$432$	−553.500	−	958.690i	−0.0616442	−	0.106771i
$433$	6974.50	−	12080.2i	0.774072	−	1.34073i	−0.161243	−	0.986915i	$-0.551550\pi$
$433$	6974.50	−	12080.2i	0.774072	−	1.34073i	0.935315	−	0.353817i	$-0.115116\pi$
$434$	1960.00			0.216781
$435$	1186.50	−	2055.08i	0.130778	−	0.226514i
$436$	−3619.00	+	6268.29i	−0.397520	+	0.688525i
$437$	−4860.00			−0.532003
$438$	−1207.50	+	2091.45i	−0.131727	+	0.228158i
$439$	5363.00	+	9288.99i	0.583057	+	1.00988i	0.995115	+	0.0987266i	$0.0314769\pi$
$439$	5363.00	+	9288.99i	0.583057	+	1.00988i	−0.412058	+	0.911158i	$0.635190\pi$
$440$	1155.00	+	2000.52i	0.125142	+	0.216752i
$441$	−2187.00			−0.236152
$442$	1683.50	−	416.558i	0.181167	−	0.0448273i
$443$	16228.0			1.74044			0.870221	−	0.492662i	$-0.163976\pi$
$443$	16228.0			1.74044			0.870221	+	0.492662i	$0.163976\pi$
$444$	136.500	+	236.425i	0.0145901	+	0.0252708i
$445$	−679.000	−	1176.06i	−0.0723319	−	0.125282i
$446$	2036.00	−	3526.46i	0.216160	−	0.374400i
$447$	−1935.00			−0.204748
$448$	−835.000	+	1446.26i	−0.0880581	+	0.152521i
$449$	−3769.00	+	6528.10i	−0.396147	+	0.686147i	−0.993247	−	0.116020i	$-0.962986\pi$
$449$	−3769.00	+	6528.10i	−0.396147	+	0.686147i	0.597100	+	0.802167i	$0.296320\pi$
$450$	684.000			0.0716535
$451$	3135.00	−	5429.98i	0.327320	−	0.566935i
$452$	3769.50	+	6528.97i	0.392262	+	0.679417i
$453$	−4371.00	−	7570.79i	−0.453350	−	0.785225i
$454$	5794.00			0.598956
$455$	−910.000	+	3152.33i	−0.0937614	+	0.324799i
$456$	1350.00			0.138639
$457$	−7769.50	−	13457.2i	−0.795278	−	1.37746i	−0.922663	−	0.385608i	$-0.873992\pi$
$457$	−7769.50	−	13457.2i	−0.795278	−	1.37746i	0.127385	−	0.991853i	$-0.459342\pi$
$458$	3241.00	+	5613.58i	0.330659	+	0.572719i
$459$	−499.500	+	865.159i	−0.0507945	+	0.0879786i
$460$	7938.00			0.804589
$461$	−2405.50	+	4166.45i	−0.243027	+	0.420935i	−0.961575	−	0.274543i	$-0.911474\pi$
$461$	−2405.50	+	4166.45i	−0.243027	+	0.420935i	0.718548	+	0.695477i	$0.244807\pi$
$462$	330.000	−	571.577i	0.0332316	−	0.0575588i
$463$	562.000			0.0564111			0.0282056	−	0.999602i	$-0.491021\pi$
$463$	562.000			0.0564111			0.0282056	+	0.999602i	$0.491021\pi$
$464$	2316.50	−	4012.30i	0.231769	−	0.401436i
$465$	−2058.00	−	3564.56i	−0.205242	−	0.355489i
$466$	3445.00	+	5966.92i	0.342460	+	0.593159i
$467$	4914.00			0.486922			0.243461	−	0.969911i	$-0.421717\pi$
$467$	4914.00			0.486922			0.243461	+	0.969911i	$0.421717\pi$
$468$	−2047.50	−	2127.82i	−0.202234	−	0.210168i
$469$	−2020.00			−0.198880
$470$	−1617.00	−	2800.73i	−0.158695	−	0.274868i
$471$	3118.50	+	5401.40i	0.305080	+	0.528415i
$472$	−4320.00	+	7482.46i	−0.421280	+	0.729678i
$473$	5412.00			0.526097
$474$	1326.00	−	2296.70i	0.128492	−	0.222555i
$475$	1140.00	−	1974.54i	0.110120	−	0.190733i
$476$	2590.00			0.249396
$477$	2416.50	−	4185.50i	0.231958	−	0.401763i
$478$	1233.00	+	2135.62i	0.117983	+	0.204353i
$479$	1800.00	+	3117.69i	0.171700	+	0.297392i	0.939014	−	0.343878i	$-0.111741\pi$
$479$	1800.00	+	3117.69i	0.171700	+	0.297392i	−0.767315	+	0.641271i	$0.778407\pi$
$480$	−3381.00			−0.321502
$481$	422.500	+	439.075i	0.0400506	+	0.0416218i
$482$	3617.00			0.341805
$483$	−2430.00	−	4208.88i	−0.228921	−	0.396503i
$484$	−2964.50	−	5134.66i	−0.278409	−	0.482219i
$485$	4207.00	−	7286.74i	0.393876	−	0.682214i
$486$	−243.000			−0.0226805
$487$	8565.00	−	14835.0i	0.796955	−	1.38037i	−0.124635	−	0.992203i	$-0.539776\pi$
$487$	8565.00	−	14835.0i	0.796955	−	1.38037i	0.921590	−	0.388164i	$-0.126891\pi$
$488$	4762.50	−	8248.89i	0.441779	−	0.765184i
$489$	5100.00			0.471636
$490$	−850.500	+	1473.11i	−0.0784116	+	0.135813i
$491$	5919.00	+	10252.0i	0.544034	+	0.942295i	0.998667	+	0.0516158i	$0.0164371\pi$
$491$	5919.00	+	10252.0i	0.544034	+	0.942295i	−0.454633	+	0.890679i	$0.650230\pi$
$492$	2992.50	+	5183.16i	0.274212	+	0.474949i
$493$	−4181.00			−0.381953
$494$	1365.00	−	337.750i	0.124320	−	0.0307613i
$495$	−1386.00			−0.125851
$496$	−4018.00	−	6959.38i	−0.363737	−	0.630011i
$497$	−5430.00	−	9405.04i	−0.490078	−	0.848840i
$498$	777.000	−	1345.80i	0.0699161	−	0.121098i
$499$	8976.00			0.805252			0.402626	−	0.915364i	$-0.368097\pi$
$499$	8976.00			0.805252			0.402626	+	0.915364i	$0.368097\pi$
$500$	−4924.50	+	8529.48i	−0.440461	+	0.762900i
$501$	−5520.00	+	9560.92i	−0.492246	+	0.852596i
$502$	−4860.00			−0.432096
$503$	−841.000	+	1456.65i	−0.0745494	+	0.129123i	−0.900890	−	0.434047i	$-0.857085\pi$
$503$	−841.000	+	1456.65i	−0.0745494	+	0.129123i	0.826341	+	0.563170i	$0.190419\pi$
$504$	675.000	+	1169.13i	0.0596565	+	0.103328i
$505$	1501.50	+	2600.67i	0.132309	+	0.229165i
$506$	−3564.00			−0.313121
$507$	−5577.00	−	3512.60i	−0.488527	−	0.307692i
$508$	6916.00			0.604031
$509$	−7583.50	−	13135.0i	−0.660379	−	1.14381i	−0.980516	−	0.196438i	$-0.937062\pi$
$509$	−7583.50	−	13135.0i	−0.660379	−	1.14381i	0.320138	−	0.947371i	$-0.396271\pi$
$510$	388.500	+	672.902i	0.0337315	+	0.0584247i
$511$	−4025.00	+	6971.50i	−0.348445	+	0.603525i
$512$	−11521.0			−0.994455
$513$	−405.000	+	701.481i	−0.0348561	+	0.0603726i
$514$	282.500	−	489.304i	0.0242423	−	0.0419889i
$515$	−9114.00			−0.779827
$516$	−2583.00	+	4473.89i	−0.220369	+	0.381690i
$517$	−5082.00	−	8802.28i	−0.432314	−	0.748789i
$518$	−65.0000	−	112.583i	−0.00551339	−	0.00954947i
$519$	12438.0			1.05196
$520$	−4777.50	+	1182.12i	−0.402899	+	0.0996915i
$521$	−6783.00			−0.570381			−0.285191	−	0.958471i	$-0.592057\pi$
$521$	−6783.00			−0.570381			−0.285191	+	0.958471i	$0.592057\pi$
$522$	−508.500	−	880.748i	−0.0426369	−	0.0738492i
$523$	6959.00	+	12053.3i	0.581828	+	1.00775i	0.995263	+	0.0972214i	$0.0309955\pi$
$523$	6959.00	+	12053.3i	0.581828	+	1.00775i	−0.413435	+	0.910534i	$0.635671\pi$
$524$	1960.00	−	3394.82i	0.163403	−	0.283022i
$525$	2280.00			0.189538
$526$	−249.000	+	431.281i	−0.0206405	+	0.0357504i
$527$	−3626.00	+	6280.42i	−0.299717	+	0.519126i
$528$	−2706.00			−0.223037
$529$	−7038.50	+	12191.0i	−0.578491	+	1.00198i
$530$	−1879.50	−	3255.39i	−0.154038	−	0.266802i
$531$	−2592.00	−	4489.48i	−0.211833	−	0.366905i
$532$	2100.00			0.171140
$533$	9262.50	+	9625.87i	0.752727	+	0.782257i
$534$	−582.000			−0.0471641
$535$	4683.00	+	8111.19i	0.378437	+	0.655472i
$536$	−1515.00	−	2624.06i	−0.122086	−	0.211459i
$537$	−5511.00	+	9545.33i	−0.442863	+	0.767060i
$538$	−5546.00			−0.444433
$539$	−2673.00	+	4629.77i	−0.213607	+	0.369978i
$540$	661.500	−	1145.75i	0.0527156	−	0.0913061i
$541$	−1335.00			−0.106093			−0.0530463	−	0.998592i	$-0.516893\pi$
$541$	−1335.00			−0.106093			−0.0530463	+	0.998592i	$0.516893\pi$
$542$	−1128.00	+	1953.75i	−0.0893944	+	0.154836i
$543$	4924.50	+	8529.48i	0.389191	+	0.674098i
$544$	2978.50	+	5158.91i	0.234747	+	0.406593i
$545$	−7238.00			−0.568884
$546$	975.000	+	1013.25i	0.0764215	+	0.0794196i
$547$	−3806.00			−0.297501			−0.148750	−	0.988875i	$-0.547525\pi$
$547$	−3806.00			−0.297501			−0.148750	+	0.988875i	$0.547525\pi$
$548$	−1816.50	−	3146.27i	−0.141600	−	0.245259i
$549$	2857.50	+	4949.34i	0.222140	+	0.384759i
$550$	836.000	−	1447.99i	0.0648130	−	0.112259i
$551$	−3390.00			−0.262103
$552$	3645.00	−	6313.33i	0.281053	−	0.486799i
$553$	4420.00	−	7655.66i	0.339887	−	0.588702i
$554$	−2309.00			−0.177076
$555$	−136.500	+	236.425i	−0.0104398	+	0.0180823i
$556$	−1218.00	−	2109.64i	−0.0929041	−	0.160915i
$557$	952.500	+	1649.78i	0.0724573	+	0.125500i	0.899978	−	0.435936i	$-0.143583\pi$
$557$	952.500	+	1649.78i	0.0724573	+	0.125500i	−0.827520	+	0.561436i	$0.810249\pi$
$558$	−1764.00			−0.133828
$559$	−3198.00	+	11078.2i	−0.241970	+	0.838207i
$560$	−2870.00			−0.216571
$561$	1221.00	+	2114.83i	0.0918907	+	0.159159i
$562$	2916.50	+	5051.53i	0.218906	+	0.379156i
$563$	2400.00	−	4156.92i	0.179659	−	0.311178i	−0.762105	−	0.647454i	$-0.775834\pi$
$563$	2400.00	−	4156.92i	0.179659	−	0.311178i	0.941764	+	0.336275i	$0.109167\pi$
$564$	9702.00			0.724340
$565$	−3769.50	+	6528.97i	−0.280680	+	0.486152i
$566$	825.000	−	1428.94i	0.0612674	−	0.106118i
$567$	−810.000			−0.0599944
$568$	8145.00	−	14107.6i	0.601684	−	1.04215i
$569$	−7339.00	−	12711.5i	−0.540715	−	0.936546i	−0.998863	−	0.0476701i	$-0.984820\pi$
$569$	−7339.00	−	12711.5i	−0.540715	−	0.936546i	0.458148	−	0.888876i	$-0.348513\pi$
$570$	315.000	+	545.596i	0.0231472	+	0.0400921i
$571$	−586.000			−0.0429481			−0.0214740	−	0.999769i	$-0.506836\pi$
$571$	−586.000			−0.0429481			−0.0214740	+	0.999769i	$0.506836\pi$
$572$	−7007.00	+	1733.78i	−0.512198	+	0.126736i
$573$	−1788.00			−0.130357
$574$	−1425.00	−	2468.17i	−0.103621	−	0.179477i
$575$	−6156.00	−	10662.5i	−0.446475	−	0.773317i
$576$	751.500	−	1301.64i	0.0543620	−	0.0941577i
$577$	8939.00			0.644949			0.322474	−	0.946578i	$-0.395485\pi$
$577$	8939.00			0.644949			0.322474	+	0.946578i	$0.395485\pi$
$578$	−1772.00	+	3069.19i	−0.127518	+	0.220868i
$579$	589.500	−	1021.04i	0.0423122	−	0.0732869i
$580$	5537.00			0.396399
$581$	2590.00	−	4486.01i	0.184942	−	0.320329i
$582$	−1803.00	−	3122.89i	−0.128414	−	0.222419i
$583$	−5907.00	−	10231.2i	−0.419628	−	0.726816i
$584$	−12075.0			−0.855594
$585$	819.000	−	2837.10i	0.0578829	−	0.200512i
$586$	−2991.00			−0.210848
$587$	6896.00	+	11944.2i	0.484887	+	0.839848i	0.999849	−	0.0173645i	$-0.00552757\pi$
$587$	6896.00	+	11944.2i	0.484887	+	0.839848i	−0.514963	+	0.857213i	$0.672194\pi$
$588$	−2551.50	−	4419.33i	−0.178949	−	0.309949i
$589$	−2940.00	+	5092.23i	−0.205672	+	0.356234i
$590$	−4032.00			−0.281347
$591$	5283.00	−	9150.42i	0.367705	−	0.636884i
$592$	−266.500	+	461.592i	−0.0185018	+	0.0320461i
$593$	9569.00			0.662650			0.331325	−	0.943517i	$-0.392504\pi$
$593$	9569.00			0.662650			0.331325	+	0.943517i	$0.392504\pi$
$594$	−297.000	+	514.419i	−0.0205152	+	0.0355335i
$595$	1295.00	+	2243.01i	0.0892266	+	0.154545i
$596$	−2257.50	−	3910.10i	−0.155152	−	0.268732i
$597$	6054.00			0.415031
$598$	2106.00	−	7295.40i	0.144015	−	0.498881i
$599$	−5192.00			−0.354156			−0.177078	−	0.984197i	$-0.556664\pi$
$599$	−5192.00			−0.354156			−0.177078	+	0.984197i	$0.556664\pi$
$600$	1710.00	+	2961.81i	0.116351	+	0.201525i
$601$	1838.50	+	3184.38i	0.124782	+	0.216129i	0.921648	−	0.388028i	$-0.126844\pi$
$601$	1838.50	+	3184.38i	0.124782	+	0.216129i	−0.796866	+	0.604156i	$0.793510\pi$
$602$	1230.00	−	2130.42i	0.0832742	−	0.144235i
$603$	1818.00			0.122777
$604$	10199.0	−	17665.2i	0.687072	−	1.19004i
$605$	2964.50	−	5134.66i	0.199213	−	0.345048i
$606$	1287.00			0.0862719
$607$	5480.00	−	9491.64i	0.366435	−	0.634685i	−0.622570	−	0.782564i	$-0.713911\pi$
$607$	5480.00	−	9491.64i	0.366435	−	0.634685i	0.989005	+	0.147879i	$0.0472447\pi$
$608$	2415.00	+	4182.90i	0.161087	+	0.279012i
$609$	−1695.00	−	2935.83i	−0.112783	−	0.195346i
$610$	4445.00			0.295037
$611$	21021.0	−	5201.35i	1.39185	−	0.344393i
$612$	−2331.00			−0.153963
$613$	13013.5	+	22540.0i	0.857439	+	1.48513i	0.874363	+	0.485272i	$0.161279\pi$
$613$	13013.5	+	22540.0i	0.857439	+	1.48513i	−0.0169241	+	0.999857i	$0.505387\pi$
$614$	−1211.00	−	2097.51i	−0.0795961	−	0.137864i
$615$	−2992.50	+	5183.16i	−0.196210	+	0.339846i
$616$	3300.00			0.215845
$617$	−8840.50	+	15312.2i	−0.576832	+	0.999102i	0.419008	+	0.907982i	$0.362378\pi$
$617$	−8840.50	+	15312.2i	−0.576832	+	0.999102i	−0.995840	+	0.0911193i	$0.970956\pi$
$618$	−1953.00	+	3382.70i	−0.127122	+	0.220181i
$619$	3192.00			0.207265			0.103633	−	0.994616i	$-0.466953\pi$
$619$	3192.00			0.207265			0.103633	+	0.994616i	$0.466953\pi$
$620$	4802.00	−	8317.31i	0.311053	−	0.538760i
$621$	2187.00	+	3788.00i	0.141323	+	0.244778i
$622$	−1701.00	−	2946.22i	−0.109653	−	0.189924i
$623$	−1940.00			−0.124758
$624$	1599.00	−	5539.10i	0.102582	−	0.355355i
$625$	−349.000			−0.0223360
$626$	1155.00	+	2000.52i	0.0737429	+	0.127727i
$627$	990.000	+	1714.73i	0.0630571	+	0.109218i
$628$	−7276.50	+	12603.3i	−0.462363	+	0.800836i
$629$	481.000			0.0304908
$630$	−315.000	+	545.596i	−0.0199205	+	0.0345033i
$631$	−3790.00	+	6564.47i	−0.239109	+	0.414148i	−0.960459	−	0.278422i	$-0.910189\pi$
$631$	−3790.00	+	6564.47i	−0.239109	+	0.414148i	0.721350	+	0.692571i	$0.243522\pi$
$632$	13260.0			0.834580
$633$	−240.000	+	415.692i	−0.0150697	+	0.0261016i
$634$	−128.500	−	222.569i	−0.00804951	−	0.0139422i
$635$	3458.00	+	5989.43i	0.216105	+	0.374304i
$636$	11277.0			0.703085
$637$	−7897.50	−	8207.32i	−0.491225	−	0.510496i
$638$	−2486.00			−0.154266
$639$	4887.00	+	8464.53i	0.302546	+	0.524025i
$640$	−5092.50	−	8820.47i	−0.314529	−	0.544781i
$641$	13853.5	−	23995.0i	0.853635	−	1.47854i	−0.0242696	−	0.999705i	$-0.507726\pi$
$641$	13853.5	−	23995.0i	0.853635	−	1.47854i	0.877905	−	0.478835i	$-0.158941\pi$
$642$	4014.00			0.246760
$643$	−5608.00	+	9713.34i	−0.343947	+	0.595734i	−0.985162	−	0.171628i	$-0.945097\pi$
$643$	−5608.00	+	9713.34i	−0.343947	+	0.595734i	0.641215	+	0.767361i	$0.278431\pi$
$644$	5670.00	−	9820.73i	0.346940	−	0.600918i
$645$	−5166.00			−0.315366
$646$	555.000	−	961.288i	0.0338021	−	0.0585470i
$647$	1268.00	+	2196.24i	0.0770483	+	0.133452i	0.901975	−	0.431788i	$-0.142117\pi$
$647$	1268.00	+	2196.24i	0.0770483	+	0.133452i	−0.824927	+	0.565239i	$0.808784\pi$
$648$	−607.500	−	1052.22i	−0.0368285	−	0.0637888i
$649$	−12672.0			−0.766440
$650$	2470.00	+	2566.90i	0.149048	+	0.154895i
$651$	−5880.00			−0.354002
$652$	5950.00	+	10305.7i	0.357393	+	0.619022i
$653$	−8865.00	−	15354.6i	−0.531262	−	0.920173i	−0.999334	−	0.0364829i	$-0.988385\pi$
$653$	−8865.00	−	15354.6i	−0.531262	−	0.920173i	0.468072	−	0.883690i	$-0.344949\pi$
$654$	−1551.00	+	2686.41i	−0.0927353	+	0.160622i
$655$	3920.00			0.233843
$656$	−5842.50	+	10119.5i	−0.347731	+	0.602287i
$657$	3622.50	−	6274.35i	0.215110	−	0.372581i
$658$	−4620.00			−0.273718
$659$	−9460.00	+	16385.2i	−0.559195	+	0.968554i	0.438369	+	0.898795i	$0.355556\pi$
$659$	−9460.00	+	16385.2i	−0.559195	+	0.968554i	−0.997564	+	0.0697586i	$0.977777\pi$
$660$	−1617.00	−	2800.73i	−0.0953661	−	0.165179i
$661$	−2620.50	−	4538.84i	−0.154199	−	0.267081i	0.778568	−	0.627560i	$-0.215946\pi$
$661$	−2620.50	−	4538.84i	−0.154199	−	0.267081i	−0.932767	+	0.360480i	$0.882613\pi$
$662$	−1028.00			−0.0603540
$663$	−5050.50	+	1249.67i	−0.295845	+	0.0732026i
$664$	7770.00			0.454118
$665$	1050.00	+	1818.65i	0.0612290	+	0.106052i
$666$	58.5000	+	101.325i	0.00340365	+	0.00589529i
$667$	−9153.00	+	15853.5i	−0.531343	+	0.920313i
$668$	−25760.0			−1.49204
$669$	−6108.00	+	10579.4i	−0.352988	+	0.611393i
$670$	707.000	−	1224.56i	0.0407669	−	0.0706103i
$671$	13970.0			0.803735
$672$	−2415.00	+	4182.90i	−0.138632	+	0.240118i
$673$	−10233.5	−	17724.9i	−0.586140	−	1.01522i	−0.994732	−	0.102508i	$-0.967313\pi$
$673$	−10233.5	−	17724.9i	−0.586140	−	1.01522i	0.408592	−	0.912717i	$-0.366020\pi$
$674$	1243.50	+	2153.81i	0.0710650	+	0.123088i
$675$	−2052.00			−0.117010
$676$	591.500	−	15367.6i	0.0336538	−	0.874353i
$677$	−70.0000			−0.00397388			−0.00198694	−	0.999998i	$-0.500632\pi$
$677$	−70.0000			−0.00397388			−0.00198694	+	0.999998i	$0.500632\pi$
$678$	1615.50	+	2798.13i	0.0915087	+	0.158498i
$679$	−6010.00	−	10409.6i	−0.339680	−	0.588343i
$680$	−1942.50	+	3364.51i	−0.109546	+	0.189740i
$681$	−17382.0			−0.978091
$682$	−2156.00	+	3734.30i	−0.121052	+	0.209668i
$683$	−3216.00	+	5570.28i	−0.180171	+	0.312065i	−0.941939	−	0.335785i	$-0.890998\pi$
$683$	−3216.00	+	5570.28i	−0.180171	+	0.312065i	0.761768	+	0.647850i	$0.224332\pi$
$684$	−1890.00			−0.105652
$685$	1816.50	−	3146.27i	0.101321	−	0.175493i
$686$	2930.00	+	5074.91i	0.163073	+	0.282450i
$687$	−9723.00	−	16840.7i	−0.539964	−	0.935246i
$688$	−10086.0			−0.558903
$689$	24433.5	−	6045.72i	1.35100	−	0.334287i
$690$	3402.00			0.187698
$691$	3333.00	+	5772.93i	0.183492	+	0.317818i	0.943067	−	0.332601i	$-0.107926\pi$
$691$	3333.00	+	5772.93i	0.183492	+	0.317818i	−0.759575	+	0.650420i	$0.774593\pi$
$692$	14511.0	+	25133.8i	0.797147	+	1.38070i
$693$	−990.000	+	1714.73i	−0.0542669	+	0.0939931i
$694$	2850.00			0.155885
$695$	1218.00	−	2109.64i	0.0664768	−	0.115141i
$696$	2542.50	−	4403.74i	0.138467	−	0.239832i
$697$	10545.0			0.573056
$698$	−1009.00	+	1747.64i	−0.0547152	+	0.0947695i
$699$	−10335.0	−	17900.7i	−0.559235	−	0.968624i
$700$	2660.00	+	4607.26i	0.143626	+	0.248768i
$701$	−14054.0			−0.757221			−0.378611	−	0.925556i	$-0.623598\pi$
$701$	−14054.0			−0.757221			−0.378611	+	0.925556i	$0.623598\pi$
$702$	−877.500	−	911.925i	−0.0471782	−	0.0490290i
$703$	390.000			0.0209234
$704$	−1837.00	−	3181.78i	−0.0983445	−	0.170338i
$705$	4851.00	+	8402.18i	0.259148	+	0.448857i
$706$	−2643.50	+	4578.68i	−0.140920	+	0.244080i
$707$	4290.00			0.228207
$708$	6048.00	−	10475.4i	0.321042	−	0.556061i
$709$	35.5000	−	61.4878i	0.00188044	−	0.00325701i	−0.865084	−	0.501628i	$-0.832735\pi$
$709$	35.5000	−	61.4878i	0.00188044	−	0.00325701i	0.866964	+	0.498371i	$0.166068\pi$
$710$	7602.00			0.401828
$711$	−3978.00	+	6890.10i	−0.209827	+	0.363430i
$712$	−1455.00	−	2520.13i	−0.0765849	−	0.132649i
$713$	15876.0	+	27498.0i	0.833886	+	1.44433i
$714$	1110.00			0.0581803
$715$	−5005.00	−	5201.35i	−0.261785	−	0.272055i
$716$	−25718.0			−1.34236
$717$	−3699.00	−	6406.86i	−0.192666	−	0.333708i
$718$	−3639.00	−	6302.93i	−0.189145	−	0.327609i
$719$	−1968.00	+	3408.68i	−0.102078	+	0.176804i	−0.912541	−	0.408986i	$-0.865882\pi$
$719$	−1968.00	+	3408.68i	−0.102078	+	0.176804i	0.810463	+	0.585790i	$0.199216\pi$
$720$	2583.00			0.133698
$721$	−6510.00	+	11275.7i	−0.336262	+	0.582423i
$722$	−2979.50	+	5160.65i	−0.153581	+	0.266010i
$723$	−10851.0			−0.558165
$724$	−11490.5	+	19902.1i	−0.589836	+	1.02163i
$725$	−4294.00	−	7437.43i	−0.219966	−	0.380992i
$726$	−1270.50	−	2200.57i	−0.0649486	−	0.112494i
$727$	34202.0			1.74482			0.872409	−	0.488777i	$-0.162557\pi$
$727$	34202.0			1.74482			0.872409	+	0.488777i	$0.162557\pi$
$728$	−1950.00	+	6755.00i	−0.0992745	+	0.343897i
$729$	729.000			0.0370370
$730$	−2817.50	−	4880.05i	−0.142850	−	0.247423i
$731$	4551.00	+	7882.56i	0.230267	+	0.398833i
$732$	−6667.50	+	11548.4i	−0.336664	+	0.583119i
$733$	−27363.0			−1.37882			−0.689410	−	0.724371i	$-0.742130\pi$
$733$	−27363.0			−1.37882			−0.689410	+	0.724371i	$0.742130\pi$
$734$	−2101.00	+	3639.04i	−0.105653	+	0.182996i
$735$	2551.50	−	4419.33i	0.128046	−	0.221781i
$736$	26082.0			1.30624
$737$	2222.00	−	3848.62i	0.111056	−	0.192355i
$738$	1282.50	+	2221.36i	0.0639695	+	0.110798i
$739$	−10888.0	−	18858.6i	−0.541978	−	0.938733i	−0.998790	−	0.0491701i	$-0.984342\pi$
$739$	−10888.0	−	18858.6i	−0.541978	−	0.938733i	0.456813	−	0.889563i	$-0.348991\pi$
$740$	−637.000			−0.0316440
$741$	−4095.00	+	1013.25i	−0.203014	+	0.0502330i
$742$	−5370.00			−0.265686
$743$	−1242.00	−	2151.21i	−0.0613251	−	0.106218i	0.833733	−	0.552168i	$-0.186199\pi$
$743$	−1242.00	−	2151.21i	−0.0613251	−	0.106218i	−0.895058	+	0.445950i	$0.852866\pi$
$744$	−4410.00	−	7638.34i	−0.217310	−	0.376392i
$745$	2257.50	−	3910.10i	0.111018	−	0.192289i
$746$	1583.00			0.0776914
$747$	−2331.00	+	4037.41i	−0.114172	+	0.197753i
$748$	−2849.00	+	4934.61i	−0.139264	+	0.241213i
$749$	13380.0			0.652730
$750$	−2110.50	+	3655.49i	−0.102753	+	0.177973i
$751$	−16453.0	−	28497.4i	−0.799439	−	1.38467i	−0.919982	−	0.391960i	$-0.871797\pi$
$751$	−16453.0	−	28497.4i	−0.799439	−	1.38467i	0.120543	−	0.992708i	$-0.461536\pi$
$752$	9471.00	+	16404.3i	0.459271	+	0.795481i
$753$	14580.0			0.705611
$754$	1469.00	−	5088.77i	0.0709520	−	0.245785i
$755$	20398.0			0.983257
$756$	−945.000	−	1636.79i	−0.0454621	−	0.0787426i
$757$	1957.00	+	3389.62i	0.0939609	+	0.162745i	0.909174	−	0.416415i	$-0.136714\pi$
$757$	1957.00	+	3389.62i	0.0939609	+	0.162745i	−0.815214	+	0.579160i	$0.803380\pi$
$758$	−1026.00	+	1777.08i	−0.0491636	+	0.0851538i
$759$	10692.0			0.511324
$760$	−1575.00	+	2727.98i	−0.0751727	+	0.130203i
$761$	16519.0	−	28611.7i	0.786877	−	1.36291i	−0.140995	−	0.990010i	$-0.545030\pi$
$761$	16519.0	−	28611.7i	0.786877	−	1.36291i	0.927871	−	0.372900i	$-0.121637\pi$
$762$	2964.00			0.140911
$763$	−5170.00	+	8954.70i	−0.245303	+	0.424878i
$764$	−2086.00	−	3613.06i	−0.0987812	−	0.171094i
$765$	−1165.50	−	2018.71i	−0.0550833	−	0.0954071i
$766$	6872.00			0.324145
$767$	7488.00	−	25939.2i	0.352511	−	1.22113i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +7.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(5.00000 - 8.66025i) q^{7} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.50000 - 6.06218i) q^{4} +7.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(5.00000 - 8.66025i) q^{7} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(3.50000 + 6.06218i) q^{10} +(11.0000 + 19.0526i) q^{11} -21.0000 q^{12} +(-45.5000 + 11.2583i) q^{13} +10.0000 q^{14} +(-10.5000 - 18.1865i) q^{15} +(-20.5000 - 35.5070i) q^{16} +(-18.5000 + 32.0429i) q^{17} -9.00000 q^{18} +(-15.0000 + 25.9808i) q^{19} +(24.5000 - 42.4352i) q^{20} -30.0000 q^{21} +(-11.0000 + 19.0526i) q^{22} +(81.0000 + 140.296i) q^{23} +(-22.5000 - 38.9711i) q^{24} -76.0000 q^{25} +(-32.5000 - 33.7750i) q^{26} +27.0000 q^{27} +(-35.0000 - 60.6218i) q^{28} +(56.5000 + 97.8609i) q^{29} +(10.5000 - 18.1865i) q^{30} +196.000 q^{31} +(80.5000 - 139.430i) q^{32} +(33.0000 - 57.1577i) q^{33} -37.0000 q^{34} +(35.0000 - 60.6218i) q^{35} +(31.5000 + 54.5596i) q^{36} +(-6.50000 - 11.2583i) q^{37} -30.0000 q^{38} +(97.5000 + 101.325i) q^{39} +105.000 q^{40} +(-142.500 - 246.817i) q^{41} +(-15.0000 - 25.9808i) q^{42} +(123.000 - 213.042i) q^{43} +154.000 q^{44} +(-31.5000 + 54.5596i) q^{45} +(-81.0000 + 140.296i) q^{46} -462.000 q^{47} +(-61.5000 + 106.521i) q^{48} +(121.500 + 210.444i) q^{49} +(-38.0000 - 65.8179i) q^{50} +111.000 q^{51} +(-91.0000 + 315.233i) q^{52} -537.000 q^{53} +(13.5000 + 23.3827i) q^{54} +(77.0000 + 133.368i) q^{55} +(75.0000 - 129.904i) q^{56} +90.0000 q^{57} +(-56.5000 + 97.8609i) q^{58} +(-288.000 + 498.831i) q^{59} -147.000 q^{60} +(317.500 - 549.926i) q^{61} +(98.0000 + 169.741i) q^{62} +(45.0000 + 77.9423i) q^{63} -167.000 q^{64} +(-318.500 + 78.8083i) q^{65} +66.0000 q^{66} +(-101.000 - 174.937i) q^{67} +(129.500 + 224.301i) q^{68} +(243.000 - 420.888i) q^{69} +70.0000 q^{70} +(543.000 - 940.504i) q^{71} +(-67.5000 + 116.913i) q^{72} -805.000 q^{73} +(6.50000 - 11.2583i) q^{74} +(114.000 + 197.454i) q^{75} +(105.000 + 181.865i) q^{76} +220.000 q^{77} +(-39.0000 + 135.100i) q^{78} +884.000 q^{79} +(-143.500 - 248.549i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(142.500 - 246.817i) q^{82} +518.000 q^{83} +(-105.000 + 181.865i) q^{84} +(-129.500 + 224.301i) q^{85} +246.000 q^{86} +(169.500 - 293.583i) q^{87} +(165.000 + 285.788i) q^{88} +(-97.0000 - 168.009i) q^{89} -63.0000 q^{90} +(-130.000 + 450.333i) q^{91} +1134.00 q^{92} +(-294.000 - 509.223i) q^{93} +(-231.000 - 400.104i) q^{94} +(-105.000 + 181.865i) q^{95} -483.000 q^{96} +(601.000 - 1040.96i) q^{97} +(-121.500 + 210.444i) q^{98} -198.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} + 7 q^{4} + 14 q^{5} + 3 q^{6} + 10 q^{7} + 30 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 + 7 * q^4 + 14 * q^5 + 3 * q^6 + 10 * q^7 + 30 * q^8 - 9 * q^9	\( 2 q + q^{2} - 3 q^{3} + 7 q^{4} + 14 q^{5} + 3 q^{6} + 10 q^{7} + 30 q^{8} - 9 q^{9} + 7 q^{10} + 22 q^{11} - 42 q^{12} - 91 q^{13} + 20 q^{14} - 21 q^{15} - 41 q^{16} - 37 q^{17} - 18 q^{18} - 30 q^{19} + 49 q^{20} - 60 q^{21} - 22 q^{22} + 162 q^{23} - 45 q^{24} - 152 q^{25} - 65 q^{26} + 54 q^{27} - 70 q^{28} + 113 q^{29} + 21 q^{30} + 392 q^{31} + 161 q^{32} + 66 q^{33} - 74 q^{34} + 70 q^{35} + 63 q^{36} - 13 q^{37} - 60 q^{38} + 195 q^{39} + 210 q^{40} - 285 q^{41} - 30 q^{42} + 246 q^{43} + 308 q^{44} - 63 q^{45} - 162 q^{46} - 924 q^{47} - 123 q^{48} + 243 q^{49} - 76 q^{50} + 222 q^{51} - 182 q^{52} - 1074 q^{53} + 27 q^{54} + 154 q^{55} + 150 q^{56} + 180 q^{57} - 113 q^{58} - 576 q^{59} - 294 q^{60} + 635 q^{61} + 196 q^{62} + 90 q^{63} - 334 q^{64} - 637 q^{65} + 132 q^{66} - 202 q^{67} + 259 q^{68} + 486 q^{69} + 140 q^{70} + 1086 q^{71} - 135 q^{72} - 1610 q^{73} + 13 q^{74} + 228 q^{75} + 210 q^{76} + 440 q^{77} - 78 q^{78} + 1768 q^{79} - 287 q^{80} - 81 q^{81} + 285 q^{82} + 1036 q^{83} - 210 q^{84} - 259 q^{85} + 492 q^{86} + 339 q^{87} + 330 q^{88} - 194 q^{89} - 126 q^{90} - 260 q^{91} + 2268 q^{92} - 588 q^{93} - 462 q^{94} - 210 q^{95} - 966 q^{96} + 1202 q^{97} - 243 q^{98} - 396 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 + 7 * q^4 + 14 * q^5 + 3 * q^6 + 10 * q^7 + 30 * q^8 - 9 * q^9 + 7 * q^10 + 22 * q^11 - 42 * q^12 - 91 * q^13 + 20 * q^14 - 21 * q^15 - 41 * q^16 - 37 * q^17 - 18 * q^18 - 30 * q^19 + 49 * q^20 - 60 * q^21 - 22 * q^22 + 162 * q^23 - 45 * q^24 - 152 * q^25 - 65 * q^26 + 54 * q^27 - 70 * q^28 + 113 * q^29 + 21 * q^30 + 392 * q^31 + 161 * q^32 + 66 * q^33 - 74 * q^34 + 70 * q^35 + 63 * q^36 - 13 * q^37 - 60 * q^38 + 195 * q^39 + 210 * q^40 - 285 * q^41 - 30 * q^42 + 246 * q^43 + 308 * q^44 - 63 * q^45 - 162 * q^46 - 924 * q^47 - 123 * q^48 + 243 * q^49 - 76 * q^50 + 222 * q^51 - 182 * q^52 - 1074 * q^53 + 27 * q^54 + 154 * q^55 + 150 * q^56 + 180 * q^57 - 113 * q^58 - 576 * q^59 - 294 * q^60 + 635 * q^61 + 196 * q^62 + 90 * q^63 - 334 * q^64 - 637 * q^65 + 132 * q^66 - 202 * q^67 + 259 * q^68 + 486 * q^69 + 140 * q^70 + 1086 * q^71 - 135 * q^72 - 1610 * q^73 + 13 * q^74 + 228 * q^75 + 210 * q^76 + 440 * q^77 - 78 * q^78 + 1768 * q^79 - 287 * q^80 - 81 * q^81 + 285 * q^82 + 1036 * q^83 - 210 * q^84 - 259 * q^85 + 492 * q^86 + 339 * q^87 + 330 * q^88 - 194 * q^89 - 126 * q^90 - 260 * q^91 + 2268 * q^92 - 588 * q^93 - 462 * q^94 - 210 * q^95 - 966 * q^96 + 1202 * q^97 - 243 * q^98 - 396 * q^99

Introduction

L-functions

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