LMFDB - Embedded newform 114.4.e.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(7,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, 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("114.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.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:	$6.72621774065$
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			49.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	114.49
Dual form			114.4.e.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +(3.00000 + 5.19615i) q^{6} +19.0000 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +(3.00000 + 5.19615i) q^{6} +19.0000 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.00000 - 10.3923i) q^{10} +32.0000 q^{11} +12.0000 q^{12} +(-40.5000 - 70.1481i) q^{13} +(19.0000 - 32.9090i) q^{14} +(9.00000 + 15.5885i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(62.0000 - 107.387i) q^{17} -18.0000 q^{18} +(76.0000 + 32.9090i) q^{19} -24.0000 q^{20} +(-28.5000 + 49.3634i) q^{21} +(32.0000 - 55.4256i) q^{22} +(-49.0000 - 84.8705i) q^{23} +(12.0000 - 20.7846i) q^{24} +(44.5000 + 77.0763i) q^{25} -162.000 q^{26} +27.0000 q^{27} +(-38.0000 - 65.8179i) q^{28} +(150.000 + 259.808i) q^{29} +36.0000 q^{30} -225.000 q^{31} +(16.0000 + 27.7128i) q^{32} +(-48.0000 + 83.1384i) q^{33} +(-124.000 - 214.774i) q^{34} +(57.0000 - 98.7269i) q^{35} +(-18.0000 + 31.1769i) q^{36} -293.000 q^{37} +(133.000 - 98.7269i) q^{38} +243.000 q^{39} +(-24.0000 + 41.5692i) q^{40} +(-88.0000 + 152.420i) q^{41} +(57.0000 + 98.7269i) q^{42} +(55.5000 - 96.1288i) q^{43} +(-64.0000 - 110.851i) q^{44} -54.0000 q^{45} -196.000 q^{46} +(275.000 + 476.314i) q^{47} +(-24.0000 - 41.5692i) q^{48} +18.0000 q^{49} +178.000 q^{50} +(186.000 + 322.161i) q^{51} +(-162.000 + 280.592i) q^{52} +(241.000 + 417.424i) q^{53} +(27.0000 - 46.7654i) q^{54} +(96.0000 - 166.277i) q^{55} -152.000 q^{56} +(-199.500 + 148.090i) q^{57} +600.000 q^{58} +(248.000 - 429.549i) q^{59} +(36.0000 - 62.3538i) q^{60} +(-77.5000 - 134.234i) q^{61} +(-225.000 + 389.711i) q^{62} +(-85.5000 - 148.090i) q^{63} +64.0000 q^{64} -486.000 q^{65} +(96.0000 + 166.277i) q^{66} +(-232.500 - 402.702i) q^{67} -496.000 q^{68} +294.000 q^{69} +(-114.000 - 197.454i) q^{70} +(55.0000 - 95.2628i) q^{71} +(36.0000 + 62.3538i) q^{72} +(-408.500 + 707.543i) q^{73} +(-293.000 + 507.491i) q^{74} -267.000 q^{75} +(-38.0000 - 329.090i) q^{76} +608.000 q^{77} +(243.000 - 420.888i) q^{78} +(-129.500 + 224.301i) q^{79} +(48.0000 + 83.1384i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(176.000 + 304.841i) q^{82} -56.0000 q^{83} +228.000 q^{84} +(-372.000 - 644.323i) q^{85} +(-111.000 - 192.258i) q^{86} -900.000 q^{87} -256.000 q^{88} +(-154.000 - 266.736i) q^{89} +(-54.0000 + 93.5307i) q^{90} +(-769.500 - 1332.81i) q^{91} +(-196.000 + 339.482i) q^{92} +(337.500 - 584.567i) q^{93} +1100.00 q^{94} +(399.000 - 296.181i) q^{95} -96.0000 q^{96} +(575.000 - 995.929i) q^{97} +(18.0000 - 31.1769i) q^{98} +(-144.000 - 249.415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} + 6 q^{6} + 38 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 + 6 * q^6 + 38 * q^7 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} + 6 q^{6} + 38 q^{7} - 16 q^{8} - 9 q^{9} - 12 q^{10} + 64 q^{11} + 24 q^{12} - 81 q^{13} + 38 q^{14} + 18 q^{15} - 16 q^{16} + 124 q^{17} - 36 q^{18} + 152 q^{19} - 48 q^{20} - 57 q^{21} + 64 q^{22} - 98 q^{23} + 24 q^{24} + 89 q^{25} - 324 q^{26} + 54 q^{27} - 76 q^{28} + 300 q^{29} + 72 q^{30} - 450 q^{31} + 32 q^{32} - 96 q^{33} - 248 q^{34} + 114 q^{35} - 36 q^{36} - 586 q^{37} + 266 q^{38} + 486 q^{39} - 48 q^{40} - 176 q^{41} + 114 q^{42} + 111 q^{43} - 128 q^{44} - 108 q^{45} - 392 q^{46} + 550 q^{47} - 48 q^{48} + 36 q^{49} + 356 q^{50} + 372 q^{51} - 324 q^{52} + 482 q^{53} + 54 q^{54} + 192 q^{55} - 304 q^{56} - 399 q^{57} + 1200 q^{58} + 496 q^{59} + 72 q^{60} - 155 q^{61} - 450 q^{62} - 171 q^{63} + 128 q^{64} - 972 q^{65} + 192 q^{66} - 465 q^{67} - 992 q^{68} + 588 q^{69} - 228 q^{70} + 110 q^{71} + 72 q^{72} - 817 q^{73} - 586 q^{74} - 534 q^{75} - 76 q^{76} + 1216 q^{77} + 486 q^{78} - 259 q^{79} + 96 q^{80} - 81 q^{81} + 352 q^{82} - 112 q^{83} + 456 q^{84} - 744 q^{85} - 222 q^{86} - 1800 q^{87} - 512 q^{88} - 308 q^{89} - 108 q^{90} - 1539 q^{91} - 392 q^{92} + 675 q^{93} + 2200 q^{94} + 798 q^{95} - 192 q^{96} + 1150 q^{97} + 36 q^{98} - 288 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 + 6 * q^6 + 38 * q^7 - 16 * q^8 - 9 * q^9 - 12 * q^10 + 64 * q^11 + 24 * q^12 - 81 * q^13 + 38 * q^14 + 18 * q^15 - 16 * q^16 + 124 * q^17 - 36 * q^18 + 152 * q^19 - 48 * q^20 - 57 * q^21 + 64 * q^22 - 98 * q^23 + 24 * q^24 + 89 * q^25 - 324 * q^26 + 54 * q^27 - 76 * q^28 + 300 * q^29 + 72 * q^30 - 450 * q^31 + 32 * q^32 - 96 * q^33 - 248 * q^34 + 114 * q^35 - 36 * q^36 - 586 * q^37 + 266 * q^38 + 486 * q^39 - 48 * q^40 - 176 * q^41 + 114 * q^42 + 111 * q^43 - 128 * q^44 - 108 * q^45 - 392 * q^46 + 550 * q^47 - 48 * q^48 + 36 * q^49 + 356 * q^50 + 372 * q^51 - 324 * q^52 + 482 * q^53 + 54 * q^54 + 192 * q^55 - 304 * q^56 - 399 * q^57 + 1200 * q^58 + 496 * q^59 + 72 * q^60 - 155 * q^61 - 450 * q^62 - 171 * q^63 + 128 * q^64 - 972 * q^65 + 192 * q^66 - 465 * q^67 - 992 * q^68 + 588 * q^69 - 228 * q^70 + 110 * q^71 + 72 * q^72 - 817 * q^73 - 586 * q^74 - 534 * q^75 - 76 * q^76 + 1216 * q^77 + 486 * q^78 - 259 * q^79 + 96 * q^80 - 81 * q^81 + 352 * q^82 - 112 * q^83 + 456 * q^84 - 744 * q^85 - 222 * q^86 - 1800 * q^87 - 512 * q^88 - 308 * q^89 - 108 * q^90 - 1539 * q^91 - 392 * q^92 + 675 * q^93 + 2200 * q^94 + 798 * q^95 - 192 * q^96 + 1150 * q^97 + 36 * q^98 - 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	3.00000	−	5.19615i	0.268328	−	0.464758i	−0.700102	−	0.714043i	$-0.746862\pi$
$5$	3.00000	−	5.19615i	0.268328	−	0.464758i	0.968430	+	0.249285i	$0.0801955\pi$
$6$	3.00000	+	5.19615i	0.204124	+	0.353553i
$7$	19.0000			1.02590			0.512952	−	0.858417i	$-0.328552\pi$
$7$	19.0000			1.02590			0.512952	+	0.858417i	$0.328552\pi$
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−6.00000	−	10.3923i	−0.189737	−	0.328634i
$11$	32.0000			0.877124			0.438562	−	0.898701i	$-0.355488\pi$
$11$	32.0000			0.877124			0.438562	+	0.898701i	$0.355488\pi$
$12$	12.0000			0.288675
$13$	−40.5000	−	70.1481i	−0.864052	−	1.49658i	−0.867985	−	0.496590i	$-0.834585\pi$
$13$	−40.5000	−	70.1481i	−0.864052	−	1.49658i	0.00393295	−	0.999992i	$-0.498748\pi$
$14$	19.0000	−	32.9090i	0.362712	−	0.628235i
$15$	9.00000	+	15.5885i	0.154919	+	0.268328i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	62.0000	−	107.387i	0.884542	−	1.53207i	0.0383036	−	0.999266i	$-0.487805\pi$
$17$	62.0000	−	107.387i	0.884542	−	1.53207i	0.846238	−	0.532805i	$-0.178862\pi$
$18$	−18.0000			−0.235702
$19$	76.0000	+	32.9090i	0.917663	+	0.397360i
$19$	76.0000	+	32.9090i	0.917663	+	0.397360i
$20$	−24.0000			−0.268328
$21$	−28.5000	+	49.3634i	−0.296153	+	0.512952i
$22$	32.0000	−	55.4256i	0.310110	−	0.537127i
$23$	−49.0000	−	84.8705i	−0.444226	−	0.769423i	0.553772	−	0.832669i	$-0.313188\pi$
$23$	−49.0000	−	84.8705i	−0.444226	−	0.769423i	−0.997998	+	0.0632460i	$0.979855\pi$
$24$	12.0000	−	20.7846i	0.102062	−	0.176777i
$25$	44.5000	+	77.0763i	0.356000	+	0.616610i
$26$	−162.000			−1.22195
$27$	27.0000			0.192450
$28$	−38.0000	−	65.8179i	−0.256476	−	0.444229i
$29$	150.000	+	259.808i	0.960493	+	1.66362i	0.721265	+	0.692660i	$0.243561\pi$
$29$	150.000	+	259.808i	0.960493	+	1.66362i	0.239228	+	0.970963i	$0.423106\pi$
$30$	36.0000			0.219089
$31$	−225.000			−1.30359			−0.651793	−	0.758397i	$-0.725983\pi$
$31$	−225.000			−1.30359			−0.651793	+	0.758397i	$0.725983\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−48.0000	+	83.1384i	−0.253204	+	0.438562i
$34$	−124.000	−	214.774i	−0.625465	−	1.08334i
$35$	57.0000	−	98.7269i	0.275279	−	0.476797i
$36$	−18.0000	+	31.1769i	−0.0833333	+	0.144338i
$37$	−293.000			−1.30186			−0.650931	−	0.759137i	$-0.725621\pi$
$37$	−293.000			−1.30186			−0.650931	+	0.759137i	$0.725621\pi$
$38$	133.000	−	98.7269i	0.567775	−	0.421464i
$39$	243.000			0.997722
$40$	−24.0000	+	41.5692i	−0.0948683	+	0.164317i
$41$	−88.0000	+	152.420i	−0.335202	+	0.580587i	−0.983524	−	0.180779i	$-0.942138\pi$
$41$	−88.0000	+	152.420i	−0.335202	+	0.580587i	0.648321	+	0.761367i	$0.275471\pi$
$42$	57.0000	+	98.7269i	0.209412	+	0.362712i
$43$	55.5000	−	96.1288i	0.196830	−	0.340919i	−0.750669	−	0.660678i	$-0.770269\pi$
$43$	55.5000	−	96.1288i	0.196830	−	0.340919i	0.947499	+	0.319759i	$0.103602\pi$
$44$	−64.0000	−	110.851i	−0.219281	−	0.379806i
$45$	−54.0000			−0.178885
$46$	−196.000			−0.628231
$47$	275.000	+	476.314i	0.853465	+	1.47825i	0.878061	+	0.478548i	$0.158837\pi$
$47$	275.000	+	476.314i	0.853465	+	1.47825i	−0.0245961	+	0.999697i	$0.507830\pi$
$48$	−24.0000	−	41.5692i	−0.0721688	−	0.125000i
$49$	18.0000			0.0524781
$50$	178.000			0.503460
$51$	186.000	+	322.161i	0.510690	+	0.884542i
$52$	−162.000	+	280.592i	−0.432026	+	0.748291i
$53$	241.000	+	417.424i	0.624602	+	1.08184i	0.988618	+	0.150449i	$0.0480720\pi$
$53$	241.000	+	417.424i	0.624602	+	1.08184i	−0.364016	+	0.931393i	$0.618595\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	96.0000	−	166.277i	0.235357	−	0.407650i
$56$	−152.000			−0.362712
$57$	−199.500	+	148.090i	−0.463586	+	0.344124i
$58$	600.000			1.35834
$59$	248.000	−	429.549i	0.547235	−	0.947838i	−0.451228	−	0.892409i	$-0.649014\pi$
$59$	248.000	−	429.549i	0.547235	−	0.947838i	0.998463	−	0.0554296i	$-0.0176528\pi$
$60$	36.0000	−	62.3538i	0.0774597	−	0.134164i
$61$	−77.5000	−	134.234i	−0.162670	−	0.281752i	0.773156	−	0.634216i	$-0.218677\pi$
$61$	−77.5000	−	134.234i	−0.162670	−	0.281752i	−0.935825	+	0.352464i	$0.885344\pi$
$62$	−225.000	+	389.711i	−0.460888	+	0.798281i
$63$	−85.5000	−	148.090i	−0.170984	−	0.296153i
$64$	64.0000			0.125000
$65$	−486.000			−0.927398
$66$	96.0000	+	166.277i	0.179042	+	0.310110i
$67$	−232.500	−	402.702i	−0.423946	−	0.734296i	0.572375	−	0.819992i	$-0.306022\pi$
$67$	−232.500	−	402.702i	−0.423946	−	0.734296i	−0.996321	+	0.0856955i	$0.972689\pi$
$68$	−496.000			−0.884542
$69$	294.000			0.512948
$70$	−114.000	−	197.454i	−0.194652	−	0.337146i
$71$	55.0000	−	95.2628i	0.0919338	−	0.159234i	−0.816391	−	0.577500i	$-0.804029\pi$
$71$	55.0000	−	95.2628i	0.0919338	−	0.159234i	0.908325	+	0.418266i	$0.137362\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	−408.500	+	707.543i	−0.654949	+	1.13441i	0.326957	+	0.945039i	$0.393977\pi$
$73$	−408.500	+	707.543i	−0.654949	+	1.13441i	−0.981906	+	0.189366i	$0.939357\pi$
$74$	−293.000	+	507.491i	−0.460278	+	0.797225i
$75$	−267.000			−0.411073
$76$	−38.0000	−	329.090i	−0.0573539	−	0.496700i
$77$	608.000			0.899845
$78$	243.000	−	420.888i	0.352748	−	0.610977i
$79$	−129.500	+	224.301i	−0.184429	+	0.319440i	−0.943384	−	0.331703i	$-0.892377\pi$
$79$	−129.500	+	224.301i	−0.184429	+	0.319440i	0.758955	+	0.651143i	$0.225710\pi$
$80$	48.0000	+	83.1384i	0.0670820	+	0.116190i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	176.000	+	304.841i	0.237024	+	0.410537i
$83$	−56.0000			−0.0740578			−0.0370289	−	0.999314i	$-0.511789\pi$
$83$	−56.0000			−0.0740578			−0.0370289	+	0.999314i	$0.511789\pi$
$84$	228.000			0.296153
$85$	−372.000	−	644.323i	−0.474695	−	0.822196i
$86$	−111.000	−	192.258i	−0.139180	−	0.241066i
$87$	−900.000			−1.10908
$88$	−256.000			−0.310110
$89$	−154.000	−	266.736i	−0.183415	−	0.317685i	0.759626	−	0.650360i	$-0.225382\pi$
$89$	−154.000	−	266.736i	−0.183415	−	0.317685i	−0.943041	+	0.332675i	$0.892049\pi$
$90$	−54.0000	+	93.5307i	−0.0632456	+	0.109545i
$91$	−769.500	−	1332.81i	−0.886434	−	1.53535i
$92$	−196.000	+	339.482i	−0.222113	+	0.384711i
$93$	337.500	−	584.567i	0.376313	−	0.651793i
$94$	1100.00			1.20698
$95$	399.000	−	296.181i	0.430911	−	0.319868i
$96$	−96.0000			−0.102062
$97$	575.000	−	995.929i	0.601880	−	1.04249i	−0.390656	−	0.920537i	$-0.627752\pi$
$97$	575.000	−	995.929i	0.601880	−	1.04249i	0.992536	−	0.121951i	$-0.0389150\pi$
$98$	18.0000	−	31.1769i	0.0185538	−	0.0321362i
$99$	−144.000	−	249.415i	−0.146187	−	0.253204i
$100$	178.000	−	308.305i	0.178000	−	0.308305i
$101$	289.000	+	500.563i	0.284719	+	0.493147i	0.972541	−	0.232732i	$-0.0747665\pi$
$101$	289.000	+	500.563i	0.284719	+	0.493147i	−0.687822	+	0.725879i	$0.741433\pi$
$102$	744.000			0.722225
$103$	819.000			0.783480			0.391740	−	0.920076i	$-0.371873\pi$
$103$	819.000			0.783480			0.391740	+	0.920076i	$0.371873\pi$
$104$	324.000	+	561.184i	0.305489	+	0.529122i
$105$	171.000	+	296.181i	0.158932	+	0.275279i
$106$	964.000			0.883320
$107$	262.000			0.236715			0.118357	−	0.992971i	$-0.462237\pi$
$107$	262.000			0.236715			0.118357	+	0.992971i	$0.462237\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	−517.000	+	895.470i	−0.454308	+	0.786885i	−0.998648	−	0.0519796i	$-0.983447\pi$
$109$	−517.000	+	895.470i	−0.454308	+	0.786885i	0.544340	+	0.838865i	$0.316780\pi$
$110$	−192.000	−	332.554i	−0.166423	−	0.288252i
$111$	439.500	−	761.236i	0.375815	−	0.650931i
$112$	−152.000	+	263.272i	−0.128238	+	0.222115i
$113$	−1324.00			−1.10223			−0.551113	−	0.834431i	$-0.685797\pi$
$113$	−1324.00			−1.10223			−0.551113	+	0.834431i	$0.685797\pi$
$114$	57.0000	+	493.634i	0.0468293	+	0.405554i
$115$	−588.000			−0.476794
$116$	600.000	−	1039.23i	0.480247	−	0.831811i
$117$	−364.500	+	631.333i	−0.288017	+	0.498861i
$118$	−496.000	−	859.097i	−0.386953	−	0.670223i
$119$	1178.00	−	2040.36i	0.907454	−	1.57176i
$120$	−72.0000	−	124.708i	−0.0547723	−	0.0948683i
$121$	−307.000			−0.230654
$122$	−310.000			−0.230050
$123$	−264.000	−	457.261i	−0.193529	−	0.335202i
$124$	450.000	+	779.423i	0.325897	+	0.564470i
$125$	1284.00			0.918756
$126$	−342.000			−0.241808
$127$	718.000	+	1243.61i	0.501671	+	0.868919i	0.999998	+	0.00193040i	$0.000614466\pi$
$127$	718.000	+	1243.61i	0.501671	+	0.868919i	−0.498327	+	0.866989i	$0.666052\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	166.500	+	288.386i	0.113640	+	0.196830i
$130$	−486.000	+	841.777i	−0.327885	+	0.567913i
$131$	189.000	−	327.358i	0.126053	−	0.218331i	−0.796091	−	0.605177i	$-0.793102\pi$
$131$	189.000	−	327.358i	0.126053	−	0.218331i	0.922144	+	0.386846i	$0.126436\pi$
$132$	384.000			0.253204
$133$	1444.00	+	625.270i	0.941434	+	0.407653i
$134$	−930.000			−0.599550
$135$	81.0000	−	140.296i	0.0516398	−	0.0894427i
$136$	−496.000	+	859.097i	−0.312733	+	0.541669i
$137$	−531.000	−	919.719i	−0.331142	−	0.573554i	0.651594	−	0.758568i	$-0.274100\pi$
$137$	−531.000	−	919.719i	−0.331142	−	0.573554i	−0.982736	+	0.185014i	$0.940767\pi$
$138$	294.000	−	509.223i	0.181355	−	0.314115i
$139$	936.500	+	1622.07i	0.571460	+	0.989797i	0.996416	+	0.0845835i	$0.0269560\pi$
$139$	936.500	+	1622.07i	0.571460	+	0.989797i	−0.424957	+	0.905214i	$0.639711\pi$
$140$	−456.000			−0.275279
$141$	−1650.00			−0.985497
$142$	−110.000	−	190.526i	−0.0650070	−	0.112595i
$143$	−1296.00	−	2244.74i	−0.757881	−	1.31269i
$144$	144.000			0.0833333
$145$	1800.00			1.03091
$146$	817.000	+	1415.09i	0.463119	+	0.802146i
$147$	−27.0000	+	46.7654i	−0.0151491	+	0.0262391i
$148$	586.000	+	1014.98i	0.325466	+	0.563723i
$149$	−686.000	+	1188.19i	−0.377177	+	0.653289i	−0.990650	−	0.136426i	$-0.956438\pi$
$149$	−686.000	+	1188.19i	−0.377177	+	0.653289i	0.613474	+	0.789715i	$0.289772\pi$
$150$	−267.000	+	462.458i	−0.145336	+	0.251730i
$151$	−3296.00			−1.77632			−0.888161	−	0.459532i	$-0.848017\pi$
$151$	−3296.00			−1.77632			−0.888161	+	0.459532i	$0.848017\pi$
$152$	−608.000	−	263.272i	−0.324443	−	0.140488i
$153$	−1116.00			−0.589694
$154$	608.000	−	1053.09i	0.318143	−	0.551040i
$155$	−675.000	+	1169.13i	−0.349789	+	0.605852i
$156$	−486.000	−	841.777i	−0.249430	−	0.432026i
$157$	−883.500	+	1530.27i	−0.449114	+	0.777889i	−0.998329	−	0.0577925i	$-0.981594\pi$
$157$	−883.500	+	1530.27i	−0.449114	+	0.777889i	0.549214	+	0.835682i	$0.314927\pi$
$158$	259.000	+	448.601i	0.130411	+	0.225878i
$159$	−1446.00			−0.721228
$160$	192.000			0.0948683
$161$	−931.000	−	1612.54i	−0.455733	−	0.789353i
$162$	81.0000	+	140.296i	0.0392837	+	0.0680414i
$163$	1709.00			0.821222			0.410611	−	0.911811i	$-0.365315\pi$
$163$	1709.00			0.821222			0.410611	+	0.911811i	$0.365315\pi$
$164$	704.000			0.335202
$165$	288.000	+	498.831i	0.135883	+	0.235357i
$166$	−56.0000	+	96.9948i	−0.0261834	+	0.0453510i
$167$	1380.00	+	2390.23i	0.639447	+	1.10755i	0.985554	+	0.169359i	$0.0541699\pi$
$167$	1380.00	+	2390.23i	0.639447	+	1.10755i	−0.346108	+	0.938195i	$0.612497\pi$
$168$	228.000	−	394.908i	0.104706	−	0.181356i
$169$	−2182.00	+	3779.33i	−0.993173	+	1.72023i
$170$	−1488.00			−0.671320
$171$	−85.5000	−	740.452i	−0.0382360	−	0.331133i
$172$	−444.000			−0.196830
$173$	738.000	−	1278.25i	0.324330	−	0.561756i	−0.657046	−	0.753850i	$-0.728194\pi$
$173$	738.000	−	1278.25i	0.324330	−	0.561756i	0.981377	+	0.192094i	$0.0615278\pi$
$174$	−900.000	+	1558.85i	−0.392120	+	0.679171i
$175$	845.500	+	1464.45i	0.365222	+	0.632582i
$176$	−256.000	+	443.405i	−0.109640	+	0.189903i
$177$	744.000	+	1288.65i	0.315946	+	0.547235i
$178$	−616.000			−0.259388
$179$	26.0000			0.0108566			0.00542830	−	0.999985i	$-0.498272\pi$
$179$	26.0000			0.0108566			0.00542830	+	0.999985i	$0.498272\pi$
$180$	108.000	+	187.061i	0.0447214	+	0.0774597i
$181$	1797.00	+	3112.50i	0.737956	+	1.27818i	0.953414	+	0.301664i	$0.0975420\pi$
$181$	1797.00	+	3112.50i	0.737956	+	1.27818i	−0.215459	+	0.976513i	$0.569125\pi$
$182$	−3078.00			−1.25361
$183$	465.000			0.187835
$184$	392.000	+	678.964i	0.157058	+	0.272032i
$185$	−879.000	+	1522.47i	−0.349326	+	0.605051i
$186$	−675.000	−	1169.13i	−0.266094	−	0.460888i
$187$	1984.00	−	3436.39i	0.775853	−	1.34382i
$188$	1100.00	−	1905.26i	0.426733	−	0.739123i
$189$	513.000			0.197435
$190$	−114.000	−	987.269i	−0.0435286	−	0.376969i
$191$	314.000			0.118954			0.0594771	−	0.998230i	$-0.481057\pi$
$191$	314.000			0.118954			0.0594771	+	0.998230i	$0.481057\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	462.500	−	801.073i	0.172495	−	0.298770i	−0.766797	−	0.641890i	$-0.778151\pi$
$193$	462.500	−	801.073i	0.172495	−	0.298770i	0.939291	+	0.343120i	$0.111484\pi$
$194$	−1150.00	−	1991.86i	−0.425594	−	0.737150i
$195$	729.000	−	1262.67i	0.267717	−	0.463699i
$196$	−36.0000	−	62.3538i	−0.0131195	−	0.0227237i
$197$	1244.00			0.449905			0.224953	−	0.974370i	$-0.427777\pi$
$197$	1244.00			0.449905			0.224953	+	0.974370i	$0.427777\pi$
$198$	−576.000			−0.206740
$199$	−1745.50	−	3023.29i	−0.621785	−	1.07696i	−0.989153	−	0.146888i	$-0.953074\pi$
$199$	−1745.50	−	3023.29i	−0.621785	−	1.07696i	0.367368	−	0.930076i	$-0.380259\pi$
$200$	−356.000	−	616.610i	−0.125865	−	0.218005i
$201$	1395.00			0.489531
$202$	1156.00			0.402653
$203$	2850.00	+	4936.34i	0.985373	+	1.70672i
$204$	744.000	−	1288.65i	0.255345	−	0.442271i
$205$	528.000	+	914.523i	0.179888	+	0.311576i
$206$	819.000	−	1418.55i	0.277002	−	0.479782i
$207$	−441.000	+	763.834i	−0.148075	+	0.256474i
$208$	1296.00			0.432026
$209$	2432.00	+	1053.09i	0.804904	+	0.348534i
$210$	684.000			0.224764
$211$	2288.50	−	3963.80i	0.746667	−	1.29327i	−0.202744	−	0.979232i	$-0.564986\pi$
$211$	2288.50	−	3963.80i	0.746667	−	1.29327i	0.949412	−	0.314034i	$-0.101681\pi$
$212$	964.000	−	1669.70i	0.312301	−	0.540921i
$213$	165.000	+	285.788i	0.0530780	+	0.0919338i
$214$	262.000	−	453.797i	0.0836914	−	0.144958i
$215$	−333.000	−	576.773i	−0.105630	−	0.182956i
$216$	−216.000			−0.0680414
$217$	−4275.00			−1.33735
$218$	1034.00	+	1790.94i	0.321245	+	0.556412i
$219$	−1225.50	−	2122.63i	−0.378135	−	0.654949i
$220$	−768.000			−0.235357
$221$	−10044.0			−3.05716
$222$	−879.000	−	1522.47i	−0.265742	−	0.460278i
$223$	−1147.50	+	1987.53i	−0.344584	+	0.596837i	−0.985278	−	0.170959i	$-0.945313\pi$
$223$	−1147.50	+	1987.53i	−0.344584	+	0.596837i	0.640694	+	0.767796i	$0.278647\pi$
$224$	304.000	+	526.543i	0.0906779	+	0.157059i
$225$	400.500	−	693.686i	0.118667	−	0.205537i
$226$	−1324.00	+	2293.24i	−0.389695	+	0.674972i
$227$	2518.00			0.736236			0.368118	−	0.929779i	$-0.380002\pi$
$227$	2518.00			0.736236			0.368118	+	0.929779i	$0.380002\pi$
$228$	912.000	+	394.908i	0.264906	+	0.114708i
$229$	5401.00			1.55855			0.779275	−	0.626682i	$-0.215587\pi$
$229$	5401.00			1.55855			0.779275	+	0.626682i	$0.215587\pi$
$230$	−588.000	+	1018.45i	−0.168572	+	0.291975i
$231$	−912.000	+	1579.63i	−0.259763	+	0.449922i
$232$	−1200.00	−	2078.46i	−0.339586	−	0.588180i
$233$	3039.00	−	5263.70i	0.854470	−	1.47999i	−0.0226658	−	0.999743i	$-0.507215\pi$
$233$	3039.00	−	5263.70i	0.854470	−	1.47999i	0.877136	−	0.480242i	$-0.159451\pi$
$234$	729.000	+	1262.67i	0.203659	+	0.352748i
$235$	3300.00			0.916035
$236$	−1984.00			−0.547235
$237$	−388.500	−	672.902i	−0.106480	−	0.184429i
$238$	−2356.00	−	4080.71i	−0.641667	−	1.11140i
$239$	1062.00			0.287427			0.143714	−	0.989619i	$-0.454096\pi$
$239$	1062.00			0.287427			0.143714	+	0.989619i	$0.454096\pi$
$240$	−288.000			−0.0774597
$241$	2309.50	+	4000.17i	0.617294	+	1.06919i	0.989977	+	0.141227i	$0.0451046\pi$
$241$	2309.50	+	4000.17i	0.617294	+	1.06919i	−0.372683	+	0.927959i	$0.621562\pi$
$242$	−307.000	+	531.740i	−0.0815484	+	0.141246i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	−310.000	+	536.936i	−0.0813349	+	0.140876i
$245$	54.0000	−	93.5307i	0.0140814	−	0.0243896i
$246$	−1056.00			−0.273691
$247$	−769.500	−	6664.07i	−0.198227	−	1.71670i
$248$	1800.00			0.460888
$249$	84.0000	−	145.492i	0.0213786	−	0.0370289i
$250$	1284.00	−	2223.95i	0.324829	−	0.562621i
$251$	−1089.00	−	1886.20i	−0.273853	−	0.474327i	0.695992	−	0.718049i	$-0.254965\pi$
$251$	−1089.00	−	1886.20i	−0.273853	−	0.474327i	−0.969845	+	0.243722i	$0.921631\pi$
$252$	−342.000	+	592.361i	−0.0854920	+	0.148076i
$253$	−1568.00	−	2715.86i	−0.389642	−	0.674879i
$254$	2872.00			0.709470
$255$	2232.00			0.548130
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	315.000	+	545.596i	0.0764559	+	0.132425i	0.901718	−	0.432324i	$-0.142306\pi$
$257$	315.000	+	545.596i	0.0764559	+	0.132425i	−0.825263	+	0.564749i	$0.808973\pi$
$258$	666.000			0.160711
$259$	−5567.00			−1.33559
$260$	972.000	+	1683.55i	0.231850	+	0.401575i
$261$	1350.00	−	2338.27i	0.320164	−	0.554541i
$262$	−378.000	−	654.715i	−0.0891333	−	0.154383i
$263$	−1371.00	+	2374.64i	−0.321443	+	0.556755i	−0.980786	−	0.195087i	$-0.937501\pi$
$263$	−1371.00	+	2374.64i	−0.321443	+	0.556755i	0.659343	+	0.751842i	$0.270834\pi$
$264$	384.000	−	665.108i	0.0895211	−	0.155055i
$265$	2892.00			0.670393
$266$	2527.00	−	1875.81i	0.582482	−	0.432381i
$267$	924.000			0.211790
$268$	−930.000	+	1610.81i	−0.211973	+	0.367148i
$269$	−1046.00	+	1811.73i	−0.237085	+	0.410642i	−0.959876	−	0.280423i	$-0.909525\pi$
$269$	−1046.00	+	1811.73i	−0.237085	+	0.410642i	0.722792	+	0.691066i	$0.242859\pi$
$270$	−162.000	−	280.592i	−0.0365148	−	0.0632456i
$271$	−2716.00	+	4704.25i	−0.608802	+	1.05448i	0.382637	+	0.923899i	$0.375016\pi$
$271$	−2716.00	+	4704.25i	−0.608802	+	1.05448i	−0.991438	+	0.130576i	$0.958317\pi$
$272$	992.000	+	1718.19i	0.221135	+	0.383018i
$273$	4617.00			1.02357
$274$	−2124.00			−0.468305
$275$	1424.00	+	2466.44i	0.312256	+	0.540843i
$276$	−588.000	−	1018.45i	−0.128237	−	0.222113i
$277$	−2834.00			−0.614724			−0.307362	−	0.951593i	$-0.599446\pi$
$277$	−2834.00			−0.614724			−0.307362	+	0.951593i	$0.599446\pi$
$278$	3746.00			0.808166
$279$	1012.50	+	1753.70i	0.217264	+	0.376313i
$280$	−456.000	+	789.815i	−0.0973258	+	0.168573i
$281$	−2845.00	−	4927.68i	−0.603980	−	1.04612i	−0.992212	−	0.124563i	$-0.960247\pi$
$281$	−2845.00	−	4927.68i	−0.603980	−	1.04612i	0.388231	−	0.921562i	$-0.373086\pi$
$282$	−1650.00	+	2857.88i	−0.348426	+	0.603491i
$283$	2194.00	−	3800.12i	0.460847	−	0.798211i	−0.538156	−	0.842845i	$-0.680879\pi$
$283$	2194.00	−	3800.12i	0.460847	−	0.798211i	0.999003	+	0.0446343i	$0.0142123\pi$
$284$	−440.000			−0.0919338
$285$	171.000	+	1480.90i	0.0355409	+	0.307794i
$286$	−5184.00			−1.07181
$287$	−1672.00	+	2895.99i	−0.343885	+	0.595627i
$288$	144.000	−	249.415i	0.0294628	−	0.0510310i
$289$	−5231.50	−	9061.22i	−1.06483	−	1.84434i
$290$	1800.00	−	3117.69i	0.364482	−	0.631301i
$291$	1725.00	+	2987.79i	0.347496	+	0.601880i
$292$	3268.00			0.654949
$293$	−1658.00			−0.330585			−0.165292	−	0.986245i	$-0.552857\pi$
$293$	−1658.00			−0.330585			−0.165292	+	0.986245i	$0.552857\pi$
$294$	54.0000	+	93.5307i	0.0107121	+	0.0185538i
$295$	−1488.00	−	2577.29i	−0.293677	−	0.508663i
$296$	2344.00			0.460278
$297$	864.000			0.168803
$298$	1372.00	+	2376.37i	0.266704	+	0.461945i
$299$	−3969.00	+	6874.51i	−0.767670	+	1.32964i
$300$	534.000	+	924.915i	0.102768	+	0.178000i
$301$	1054.50	−	1826.45i	0.201928	−	0.349750i
$302$	−3296.00	+	5708.84i	−0.628025	+	1.08777i
$303$	−1734.00			−0.328765
$304$	−1064.00	+	789.815i	−0.200739	+	0.149010i
$305$	−930.000			−0.174596
$306$	−1116.00	+	1932.97i	−0.208488	+	0.361113i
$307$	−402.000	+	696.284i	−0.0747340	+	0.129443i	−0.900971	−	0.433880i	$-0.857144\pi$
$307$	−402.000	+	696.284i	−0.0747340	+	0.129443i	0.826237	+	0.563323i	$0.190477\pi$
$308$	−1216.00	−	2106.17i	−0.224961	−	0.389644i
$309$	−1228.50	+	2127.82i	−0.226171	+	0.391740i
$310$	1350.00	+	2338.27i	0.247338	+	0.428402i
$311$	−3172.00			−0.578352			−0.289176	−	0.957276i	$-0.593381\pi$
$311$	−3172.00			−0.578352			−0.289176	+	0.957276i	$0.593381\pi$
$312$	−1944.00			−0.352748
$313$	−1917.00	−	3320.34i	−0.346183	−	0.599606i	0.639385	−	0.768887i	$-0.279189\pi$
$313$	−1917.00	−	3320.34i	−0.346183	−	0.599606i	−0.985568	+	0.169280i	$0.945856\pi$
$314$	1767.00	+	3060.53i	0.317572	+	0.550051i
$315$	−1026.00			−0.183519
$316$	1036.00			0.184429
$317$	−1461.00	−	2530.53i	−0.258858	−	0.448355i	0.707078	−	0.707135i	$-0.250013\pi$
$317$	−1461.00	−	2530.53i	−0.258858	−	0.448355i	−0.965936	+	0.258780i	$0.916679\pi$
$318$	−1446.00	+	2504.55i	−0.254993	+	0.441660i
$319$	4800.00	+	8313.84i	0.842471	+	1.45920i
$320$	192.000	−	332.554i	0.0335410	−	0.0580948i
$321$	−393.000	+	680.696i	−0.0683337	+	0.118357i
$322$	−3724.00			−0.644504
$323$	8246.00	−	6121.07i	1.42049	−	1.05444i
$324$	324.000			0.0555556
$325$	3604.50	−	6243.18i	0.615205	−	1.06557i
$326$	1709.00	−	2960.07i	0.290346	−	0.502894i
$327$	−1551.00	−	2686.41i	−0.262295	−	0.454308i
$328$	704.000	−	1219.36i	0.118512	−	0.205269i
$329$	5225.00	+	9049.97i	0.875573	+	1.51654i
$330$	1152.00			0.192168
$331$	−4359.00			−0.723844			−0.361922	−	0.932208i	$-0.617879\pi$
$331$	−4359.00			−0.723844			−0.361922	+	0.932208i	$0.617879\pi$
$332$	112.000	+	193.990i	0.0185145	+	0.0320680i
$333$	1318.50	+	2283.71i	0.216977	+	0.375815i
$334$	5520.00			0.904314
$335$	−2790.00			−0.455027
$336$	−456.000	−	789.815i	−0.0740382	−	0.128238i
$337$	−4364.50	+	7559.54i	−0.705488	+	1.22194i	0.261027	+	0.965331i	$0.415939\pi$
$337$	−4364.50	+	7559.54i	−0.705488	+	1.22194i	−0.966515	+	0.256610i	$0.917395\pi$
$338$	4364.00	+	7558.67i	0.702279	+	1.21638i
$339$	1986.00	−	3439.85i	0.318185	−	0.551113i
$340$	−1488.00	+	2577.29i	−0.237347	+	0.411098i
$341$	−7200.00			−1.14341
$342$	−1368.00	−	592.361i	−0.216295	−	0.0936586i
$343$	−6175.00			−0.972066
$344$	−444.000	+	769.031i	−0.0695898	+	0.120533i
$345$	882.000	−	1527.67i	0.137639	−	0.238397i
$346$	−1476.00	−	2556.51i	−0.229336	−	0.397222i
$347$	−19.0000	+	32.9090i	−0.00293940	+	0.00509120i	−0.867491	−	0.497452i	$-0.834269\pi$
$347$	−19.0000	+	32.9090i	−0.00293940	+	0.00509120i	0.864552	+	0.502543i	$0.167602\pi$
$348$	1800.00	+	3117.69i	0.277270	+	0.480247i
$349$	6103.00			0.936063			0.468032	−	0.883712i	$-0.344963\pi$
$349$	6103.00			0.936063			0.468032	+	0.883712i	$0.344963\pi$
$350$	3382.00			0.516501
$351$	−1093.50	−	1894.00i	−0.166287	−	0.288017i
$352$	512.000	+	886.810i	0.0775275	+	0.134282i
$353$	−12198.0			−1.83919			−0.919595	−	0.392868i	$-0.871483\pi$
$353$	−12198.0			−1.83919			−0.919595	+	0.392868i	$0.871483\pi$
$354$	2976.00			0.446815
$355$	−330.000	−	571.577i	−0.0493368	−	0.0854539i
$356$	−616.000	+	1066.94i	−0.0917077	+	0.158842i
$357$	3534.00	+	6121.07i	0.523919	+	0.907454i
$358$	26.0000	−	45.0333i	0.00383839	−	0.00664828i
$359$	−1494.00	+	2587.68i	−0.219639	+	0.380425i	−0.954698	−	0.297578i	$-0.903821\pi$
$359$	−1494.00	+	2587.68i	−0.219639	+	0.380425i	0.735059	+	0.678003i	$0.237155\pi$
$360$	432.000			0.0632456
$361$	4693.00	+	5002.16i	0.684211	+	0.729285i
$362$	7188.00			1.04363
$363$	460.500	−	797.609i	0.0665840	−	0.115327i
$364$	−3078.00	+	5331.25i	−0.443217	+	0.767675i
$365$	2451.00	+	4245.26i	0.351483	+	0.608786i
$366$	465.000	−	805.404i	0.0664097	−	0.115025i
$367$	−1052.50	−	1822.98i	−0.149700	−	0.259289i	0.781416	−	0.624010i	$-0.214498\pi$
$367$	−1052.50	−	1822.98i	−0.149700	−	0.259289i	−0.931117	+	0.364721i	$0.881164\pi$
$368$	1568.00			0.222113
$369$	1584.00			0.223468
$370$	1758.00	+	3044.95i	0.247011	+	0.427836i
$371$	4579.00	+	7931.06i	0.640781	+	1.10987i
$372$	−2700.00			−0.376313
$373$	−2494.00			−0.346205			−0.173102	−	0.984904i	$-0.555379\pi$
$373$	−2494.00			−0.346205			−0.173102	+	0.984904i	$0.555379\pi$
$374$	−3968.00	−	6872.78i	−0.548611	−	0.950222i
$375$	−1926.00	+	3335.93i	−0.265222	+	0.459378i
$376$	−2200.00	−	3810.51i	−0.301746	−	0.522639i
$377$	12150.0	−	21044.4i	1.65983	−	2.87491i
$378$	513.000	−	888.542i	0.0698039	−	0.120904i
$379$	5729.00			0.776462			0.388231	−	0.921562i	$-0.373086\pi$
$379$	5729.00			0.776462			0.388231	+	0.921562i	$0.373086\pi$
$380$	−1824.00	−	789.815i	−0.246235	−	0.106623i
$381$	−4308.00			−0.579280
$382$	314.000	−	543.864i	0.0420566	−	0.0728442i
$383$	5008.00	−	8674.11i	0.668138	−	1.15725i	−0.310286	−	0.950643i	$-0.600425\pi$
$383$	5008.00	−	8674.11i	0.668138	−	1.15725i	0.978424	−	0.206606i	$-0.0662418\pi$
$384$	192.000	+	332.554i	0.0255155	+	0.0441942i
$385$	1824.00	−	3159.26i	0.241454	−	0.418210i
$386$	−925.000	−	1602.15i	−0.121972	−	0.211262i
$387$	−999.000			−0.131220
$388$	−4600.00			−0.601880
$389$	−2909.00	−	5038.54i	−0.379157	−	0.656720i	0.611783	−	0.791026i	$-0.290453\pi$
$389$	−2909.00	−	5038.54i	−0.379157	−	0.656720i	−0.990940	+	0.134306i	$0.957119\pi$
$390$	−1458.00	−	2525.33i	−0.189304	−	0.327885i
$391$	−12152.0			−1.57175
$392$	−144.000			−0.0185538
$393$	567.000	+	982.073i	0.0727770	+	0.126053i
$394$	1244.00	−	2154.67i	0.159066	−	0.275510i
$395$	777.000	+	1345.80i	0.0989750	+	0.171430i
$396$	−576.000	+	997.661i	−0.0730937	+	0.126602i
$397$	2074.50	−	3593.14i	0.262257	−	0.454243i	−0.704584	−	0.709621i	$-0.748866\pi$
$397$	2074.50	−	3593.14i	0.262257	−	0.454243i	0.966841	+	0.255377i	$0.0821997\pi$
$398$	−6982.00			−0.879337
$399$	−3790.50	+	2813.72i	−0.475595	+	0.353038i
$400$	−1424.00			−0.178000
$401$	−4536.00	+	7856.58i	−0.564880	+	0.978402i	0.432180	+	0.901787i	$0.357744\pi$
$401$	−4536.00	+	7856.58i	−0.564880	+	0.978402i	−0.997061	+	0.0766144i	$0.975589\pi$
$402$	1395.00	−	2416.21i	0.173075	−	0.299775i
$403$	9112.50	+	15783.3i	1.12637	+	1.95093i
$404$	1156.00	−	2002.25i	0.142359	−	0.246574i
$405$	243.000	+	420.888i	0.0298142	+	0.0516398i
$406$	11400.0			1.39353
$407$	−9376.00			−1.14189
$408$	−1488.00	−	2577.29i	−0.180556	−	0.312733i
$409$	−4347.00	−	7529.22i	−0.525539	−	0.910260i	−0.999558	−	0.0297450i	$-0.990530\pi$
$409$	−4347.00	−	7529.22i	−0.525539	−	0.910260i	0.474019	−	0.880515i	$-0.342803\pi$
$410$	2112.00			0.254401
$411$	3186.00			0.382369
$412$	−1638.00	−	2837.10i	−0.195870	−	0.339257i
$413$	4712.00	−	8161.42i	0.561410	−	0.972391i
$414$	882.000	+	1527.67i	0.104705	+	0.181355i
$415$	−168.000	+	290.985i	−0.0198718	+	0.0344190i
$416$	1296.00	−	2244.74i	0.152744	−	0.264561i
$417$	−5619.00			−0.659865
$418$	4256.00	−	3159.26i	0.498009	−	0.369676i
$419$	−4392.00			−0.512084			−0.256042	−	0.966666i	$-0.582419\pi$
$419$	−4392.00			−0.512084			−0.256042	+	0.966666i	$0.582419\pi$
$420$	684.000	−	1184.72i	0.0794661	−	0.137639i
$421$	−3455.00	+	5984.24i	−0.399968	+	0.692764i	−0.993721	−	0.111882i	$-0.964312\pi$
$421$	−3455.00	+	5984.24i	−0.399968	+	0.692764i	0.593754	+	0.804647i	$0.297645\pi$
$422$	−4577.00	−	7927.60i	−0.527974	−	0.914477i
$423$	2475.00	−	4286.83i	0.284488	−	0.492748i
$424$	−1928.00	−	3339.39i	−0.220830	−	0.382489i
$425$	11036.0			1.25959
$426$	660.000			0.0750636
$427$	−1472.50	−	2550.44i	−0.166884	−	0.289051i
$428$	−524.000	−	907.595i	−0.0591787	−	0.102501i
$429$	7776.00			0.875125
$430$	−1332.00			−0.149383
$431$	4441.00	+	7692.04i	0.496324	+	0.859658i	0.999991	−	0.00424003i	$-0.00134965\pi$
$431$	4441.00	+	7692.04i	0.496324	+	0.859658i	−0.503667	+	0.863898i	$0.668016\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−1849.50	−	3203.43i	−0.205269	−	0.355536i	0.744950	−	0.667121i	$-0.232473\pi$
$433$	−1849.50	−	3203.43i	−0.205269	−	0.355536i	−0.950218	+	0.311585i	$0.899140\pi$
$434$	−4275.00	+	7404.52i	−0.472826	+	0.818959i
$435$	−2700.00	+	4676.54i	−0.297598	+	0.515455i
$436$	4136.00			0.454308
$437$	−931.000	−	8062.70i	−0.101913	−	0.882588i
$438$	−4902.00			−0.534764
$439$	8453.50	−	14641.9i	0.919051	−	1.59184i	0.118192	−	0.992991i	$-0.462290\pi$
$439$	8453.50	−	14641.9i	0.919051	−	1.59184i	0.800859	−	0.598853i	$-0.204377\pi$
$440$	−768.000	+	1330.22i	−0.0832113	+	0.144126i
$441$	−81.0000	−	140.296i	−0.00874636	−	0.0151491i
$442$	−10044.0	+	17396.7i	−1.08087	+	1.87212i
$443$	4986.00	+	8636.01i	0.534745	+	0.926205i	0.999176	+	0.0405959i	$0.0129256\pi$
$443$	4986.00	+	8636.01i	0.534745	+	0.926205i	−0.464431	+	0.885609i	$0.653741\pi$
$444$	−3516.00			−0.375815
$445$	−1848.00			−0.196862
$446$	2295.00	+	3975.06i	0.243658	+	0.422028i
$447$	−2058.00	−	3564.56i	−0.217763	−	0.377177i
$448$	1216.00			0.128238
$449$	−10368.0			−1.08975			−0.544873	−	0.838518i	$-0.683422\pi$
$449$	−10368.0			−1.08975			−0.544873	+	0.838518i	$0.683422\pi$
$450$	−801.000	−	1387.37i	−0.0839100	−	0.145336i
$451$	−2816.00	+	4877.46i	−0.294014	+	0.509247i
$452$	2648.00	+	4586.47i	0.275556	+	0.477277i
$453$	4944.00	−	8563.26i	0.512780	−	0.888161i
$454$	2518.00	−	4361.30i	0.260299	−	0.450851i
$455$	−9234.00			−0.951421
$456$	1596.00	−	1184.72i	0.163903	−	0.121666i
$457$	4481.00			0.458670			0.229335	−	0.973348i	$-0.426345\pi$
$457$	4481.00			0.458670			0.229335	+	0.973348i	$0.426345\pi$
$458$	5401.00	−	9354.81i	0.551031	−	0.954414i
$459$	1674.00	−	2899.45i	0.170230	−	0.294847i
$460$	1176.00	+	2036.89i	0.119198	+	0.206458i
$461$	1056.00	−	1829.05i	0.106687	−	0.184788i	−0.807739	−	0.589540i	$-0.799309\pi$
$461$	1056.00	−	1829.05i	0.106687	−	0.184788i	0.914426	+	0.404752i	$0.132642\pi$
$462$	1824.00	+	3159.26i	0.183680	+	0.318143i
$463$	5817.00			0.583885			0.291943	−	0.956436i	$-0.405698\pi$
$463$	5817.00			0.583885			0.291943	+	0.956436i	$0.405698\pi$
$464$	−4800.00			−0.480247
$465$	−2025.00	−	3507.40i	−0.201951	−	0.349789i
$466$	−6078.00	−	10527.4i	−0.604202	−	1.04651i
$467$	9100.00			0.901708			0.450854	−	0.892598i	$-0.351119\pi$
$467$	9100.00			0.901708			0.450854	+	0.892598i	$0.351119\pi$
$468$	2916.00			0.288017
$469$	−4417.50	−	7651.33i	−0.434928	−	0.753317i
$470$	3300.00	−	5715.77i	0.323867	−	0.560955i
$471$	−2650.50	−	4590.80i	−0.259296	−	0.449114i
$472$	−1984.00	+	3436.39i	−0.193477	+	0.335111i
$473$	1776.00	−	3076.12i	0.172644	−	0.299028i
$474$	−1554.00			−0.150586
$475$	845.500	+	7322.24i	0.0816720	+	0.707300i
$476$	−9424.00			−0.907454
$477$	2169.00	−	3756.82i	0.208201	−	0.360614i
$478$	1062.00	−	1839.44i	0.101621	−	0.176012i
$479$	15.0000	+	25.9808i	0.00143083	+	0.00247827i	0.866740	−	0.498760i	$-0.166211\pi$
$479$	15.0000	+	25.9808i	0.00143083	+	0.00247827i	−0.865309	+	0.501239i	$0.832878\pi$
$480$	−288.000	+	498.831i	−0.0273861	+	0.0474342i
$481$	11866.5	+	20553.4i	1.12488	+	1.94834i
$482$	9238.00			0.872986
$483$	5586.00			0.526236
$484$	614.000	+	1063.48i	0.0576634	+	0.0998760i
$485$	−3450.00	−	5975.58i	−0.323003	−	0.559458i
$486$	−486.000			−0.0453609
$487$	−10924.0			−1.01646			−0.508228	−	0.861223i	$-0.669699\pi$
$487$	−10924.0			−1.01646			−0.508228	+	0.861223i	$0.669699\pi$
$488$	620.000	+	1073.87i	0.0575125	+	0.0996145i
$489$	−2563.50	+	4440.11i	−0.237066	+	0.410611i
$490$	−108.000	−	187.061i	−0.00995703	−	0.0172461i
$491$	−3669.00	+	6354.89i	−0.337229	+	0.584099i	−0.983911	−	0.178662i	$-0.942823\pi$
$491$	−3669.00	+	6354.89i	−0.337229	+	0.584099i	0.646681	+	0.762761i	$0.276156\pi$
$492$	−1056.00	+	1829.05i	−0.0967645	+	0.167601i
$493$	37200.0			3.39838
$494$	−12312.0	−	5331.25i	−1.12134	−	0.485555i
$495$	−1728.00			−0.156905
$496$	1800.00	−	3117.69i	0.162948	−	0.282235i
$497$	1045.00	−	1809.99i	0.0943152	−	0.163359i
$498$	−168.000	−	290.985i	−0.0151170	−	0.0261834i
$499$	4260.50	−	7379.40i	0.382217	−	0.662019i	−0.609162	−	0.793046i	$-0.708494\pi$
$499$	4260.50	−	7379.40i	0.382217	−	0.662019i	0.991379	+	0.131027i	$0.0418274\pi$
$500$	−2568.00	−	4447.91i	−0.229689	−	0.397833i
$501$	−8280.00			−0.738369
$502$	−4356.00			−0.387286
$503$	2750.00	+	4763.14i	0.243770	+	0.422222i	0.961785	−	0.273805i	$-0.0882824\pi$
$503$	2750.00	+	4763.14i	0.243770	+	0.422222i	−0.718015	+	0.696028i	$0.754949\pi$
$504$	684.000	+	1184.72i	0.0604519	+	0.104706i
$505$	3468.00			0.305592
$506$	−6272.00			−0.551036
$507$	−6546.00	−	11338.0i	−0.573408	−	0.993173i
$508$	2872.00	−	4974.45i	0.250835	−	0.434460i
$509$	−2969.00	−	5142.46i	−0.258543	−	0.447810i	0.707309	−	0.706905i	$-0.249909\pi$
$509$	−2969.00	−	5142.46i	−0.258543	−	0.447810i	−0.965852	+	0.259095i	$0.916576\pi$
$510$	2232.00	−	3865.94i	0.193793	−	0.335660i
$511$	−7761.50	+	13443.3i	−0.671915	+	1.16379i
$512$	−512.000			−0.0441942
$513$	2052.00	+	888.542i	0.176604	+	0.0764719i
$514$	1260.00			0.108125
$515$	2457.00	−	4255.65i	0.210230	−	0.364129i
$516$	666.000	−	1153.55i	0.0568198	−	0.0984148i
$517$	8800.00	+	15242.0i	0.748595	+	1.29660i
$518$	−5567.00	+	9642.33i	−0.472201	+	0.817876i
$519$	2214.00	+	3834.76i	0.187252	+	0.324330i
$520$	3888.00			0.327885
$521$	−2884.00			−0.242515			−0.121258	−	0.992621i	$-0.538693\pi$
$521$	−2884.00			−0.242515			−0.121258	+	0.992621i	$0.538693\pi$
$522$	−2700.00	−	4676.54i	−0.226390	−	0.392120i
$523$	5330.50	+	9232.70i	0.445672	+	0.771927i	0.998099	−	0.0616348i	$-0.0196314\pi$
$523$	5330.50	+	9232.70i	0.445672	+	0.771927i	−0.552427	+	0.833561i	$0.686298\pi$
$524$	−1512.00			−0.126053
$525$	−5073.00			−0.421722
$526$	2742.00	+	4749.28i	0.227294	+	0.393686i
$527$	−13950.0	+	24162.1i	−1.15308	+	1.99719i
$528$	−768.000	−	1330.22i	−0.0633010	−	0.109640i
$529$	1281.50	−	2219.62i	0.105326	−	0.182430i
$530$	2892.00	−	5009.09i	0.237020	−	0.410530i
$531$	−4464.00			−0.364823
$532$	−722.000	−	6252.70i	−0.0588396	−	0.509566i
$533$	14256.0			1.15853
$534$	924.000	−	1600.41i	0.0748790	−	0.129694i
$535$	786.000	−	1361.39i	0.0635173	−	0.110015i
$536$	1860.00	+	3221.61i	0.149888	+	0.259613i
$537$	−39.0000	+	67.5500i	−0.00313403	+	0.00542830i
$538$	2092.00	+	3623.45i	0.167644	+	0.290368i
$539$	576.000			0.0460298
$540$	−648.000			−0.0516398
$541$	−2942.50	−	5096.56i	−0.233841	−	0.405024i	0.725094	−	0.688650i	$-0.241796\pi$
$541$	−2942.50	−	5096.56i	−0.233841	−	0.405024i	−0.958935	+	0.283625i	$0.908463\pi$
$542$	5432.00	+	9408.50i	0.430488	+	0.745627i
$543$	−10782.0			−0.852118
$544$	3968.00			0.312733
$545$	3102.00	+	5372.82i	0.243807	+	0.422287i
$546$	4617.00	−	7996.88i	0.361885	−	0.626804i
$547$	−818.500	−	1417.68i	−0.0639790	−	0.110815i	0.832262	−	0.554383i	$-0.187046\pi$
$547$	−818.500	−	1417.68i	−0.0639790	−	0.110815i	−0.896241	+	0.443568i	$0.853712\pi$
$548$	−2124.00	+	3678.88i	−0.165571	+	0.286777i
$549$	−697.500	+	1208.11i	−0.0542233	+	0.0939175i
$550$	5696.00			0.441597
$551$	2850.00	+	24681.7i	0.220352	+	1.90831i
$552$	−2352.00			−0.181355
$553$	−2460.50	+	4261.71i	−0.189206	+	0.327715i
$554$	−2834.00	+	4908.63i	−0.217338	+	0.376440i
$555$	−2637.00	−	4567.42i	−0.201684	−	0.349326i
$556$	3746.00	−	6488.26i	0.285730	−	0.494899i
$557$	−3235.00	−	5603.18i	−0.246089	−	0.426238i	0.716349	−	0.697743i	$-0.245812\pi$
$557$	−3235.00	−	5603.18i	−0.246089	−	0.426238i	−0.962437	+	0.271505i	$0.912479\pi$
$558$	4050.00			0.307258
$559$	−8991.00			−0.680284
$560$	912.000	+	1579.63i	0.0688197	+	0.119199i
$561$	5952.00	+	10309.2i	0.447939	+	0.775853i
$562$	−11380.0			−0.854157
$563$	14898.0			1.11523			0.557616	−	0.830099i	$-0.311716\pi$
$563$	14898.0			1.11523			0.557616	+	0.830099i	$0.311716\pi$
$564$	3300.00	+	5715.77i	0.246374	+	0.426733i
$565$	−3972.00	+	6879.71i	−0.295758	+	0.512268i
$566$	−4388.00	−	7600.24i	−0.325868	−	0.564420i
$567$	−769.500	+	1332.81i	−0.0569946	+	0.0987176i
$568$	−440.000	+	762.102i	−0.0325035	+	0.0562977i
$569$	−13260.0			−0.976956			−0.488478	−	0.872576i	$-0.662448\pi$
$569$	−13260.0			−0.976956			−0.488478	+	0.872576i	$0.662448\pi$
$570$	2736.00	+	1184.72i	0.201050	+	0.0870572i
$571$	−6097.00			−0.446850			−0.223425	−	0.974721i	$-0.571724\pi$
$571$	−6097.00			−0.446850			−0.223425	+	0.974721i	$0.571724\pi$
$572$	−5184.00	+	8978.95i	−0.378940	+	0.656344i
$573$	−471.000	+	815.796i	−0.0343391	+	0.0594771i
$574$	3344.00	+	5791.98i	0.243164	+	0.421172i
$575$	4361.00	−	7553.47i	0.316289	−	0.547829i
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−5594.00			−0.403607			−0.201804	−	0.979426i	$-0.564680\pi$
$577$	−5594.00			−0.403607			−0.201804	+	0.979426i	$0.564680\pi$
$578$	−20926.0			−1.50589
$579$	1387.50	+	2403.22i	0.0995899	+	0.172495i
$580$	−3600.00	−	6235.38i	−0.257727	−	0.446397i
$581$	−1064.00			−0.0759762
$582$	6900.00			0.491433
$583$	7712.00	+	13357.6i	0.547853	+	0.948910i
$584$	3268.00	−	5660.34i	0.231560	−	0.401073i
$585$	2187.00	+	3788.00i	0.154566	+	0.267717i
$586$	−1658.00	+	2871.74i	−0.116879	+	0.202441i
$587$	9038.00	−	15654.3i	0.635499	−	1.10072i	−0.350910	−	0.936409i	$-0.614128\pi$
$587$	9038.00	−	15654.3i	0.635499	−	1.10072i	0.986409	−	0.164308i	$-0.0525391\pi$
$588$	216.000			0.0151491
$589$	−17100.0	−	7404.52i	−1.19625	−	0.517993i
$590$	−5952.00			−0.415322
$591$	−1866.00	+	3232.01i	−0.129876	+	0.224953i
$592$	2344.00	−	4059.93i	0.162733	−	0.281861i
$593$	−11464.0	−	19856.2i	−0.793879	−	1.37504i	−0.923549	−	0.383481i	$-0.874725\pi$
$593$	−11464.0	−	19856.2i	−0.793879	−	1.37504i	0.129670	−	0.991557i	$-0.458608\pi$
$594$	864.000	−	1496.49i	0.0596807	−	0.103370i
$595$	−7068.00	−	12242.1i	−0.486991	−	0.843493i
$596$	5488.00			0.377177
$597$	10473.0			0.717975
$598$	7938.00	+	13749.0i	0.542824	+	0.940199i
$599$	5896.00	+	10212.2i	0.402177	+	0.696591i	0.993988	−	0.109485i	$-0.0349203\pi$
$599$	5896.00	+	10212.2i	0.402177	+	0.696591i	−0.591811	+	0.806076i	$0.701587\pi$
$600$	2136.00			0.145336
$601$	−15585.0			−1.05778			−0.528890	−	0.848691i	$-0.677391\pi$
$601$	−15585.0			−1.05778			−0.528890	+	0.848691i	$0.677391\pi$
$602$	−2109.00	−	3652.90i	−0.142785	−	0.247310i
$603$	−2092.50	+	3624.32i	−0.141315	+	0.244765i
$604$	6592.00	+	11417.7i	0.444081	+	0.769170i
$605$	−921.000	+	1595.22i	−0.0618909	+	0.107198i
$606$	−1734.00	+	3003.38i	−0.116236	+	0.201326i
$607$	−27181.0			−1.81753			−0.908767	−	0.417305i	$-0.862975\pi$
$607$	−27181.0			−1.81753			−0.908767	+	0.417305i	$0.862975\pi$
$608$	304.000	+	2632.72i	0.0202777	+	0.175610i
$609$	−17100.0			−1.13781
$610$	−930.000	+	1610.81i	−0.0617289	+	0.106918i
$611$	22275.0	−	38581.4i	1.47488	−	2.55456i
$612$	2232.00	+	3865.94i	0.147424	+	0.255345i
$613$	−6913.00	+	11973.7i	−0.455487	+	0.788926i	−0.998716	−	0.0506581i	$-0.983868\pi$
$613$	−6913.00	+	11973.7i	−0.455487	+	0.788926i	0.543229	+	0.839584i	$0.317201\pi$
$614$	804.000	+	1392.57i	0.0528450	+	0.0915301i
$615$	−3168.00			−0.207717
$616$	−4864.00			−0.318143
$617$	6222.00	+	10776.8i	0.405978	+	0.703174i	0.994435	−	0.105354i	$-0.0335977\pi$
$617$	6222.00	+	10776.8i	0.405978	+	0.703174i	−0.588457	+	0.808529i	$0.700264\pi$
$618$	2457.00	+	4255.65i	0.159927	+	0.277002i
$619$	−137.000			−0.00889579			−0.00444790	−	0.999990i	$-0.501416\pi$
$619$	−137.000			−0.00889579			−0.00444790	+	0.999990i	$0.501416\pi$
$620$	5400.00			0.349789
$621$	−1323.00	−	2291.50i	−0.0854914	−	0.148075i
$622$	−3172.00	+	5494.07i	−0.204478	+	0.354167i
$623$	−2926.00	−	5067.98i	−0.188166	−	0.325914i
$624$	−1944.00	+	3367.11i	−0.124715	+	0.216013i
$625$	−1710.50	+	2962.67i	−0.109472	+	0.189611i
$626$	−7668.00			−0.489577
$627$	−6384.00	+	4738.89i	−0.406623	+	0.301839i
$628$	7068.00			0.449114
$629$	−18166.0	+	31464.4i	−1.15155	+	1.99455i
$630$	−1026.00	+	1777.08i	−0.0648838	+	0.112382i
$631$	5130.50	+	8886.29i	0.323680	+	0.560630i	0.981244	−	0.192768i	$-0.0617466\pi$
$631$	5130.50	+	8886.29i	0.323680	+	0.560630i	−0.657564	+	0.753398i	$0.728413\pi$
$632$	1036.00	−	1794.40i	0.0652055	−	0.112939i
$633$	6865.50	+	11891.4i	0.431089	+	0.746667i
$634$	−5844.00			−0.366080
$635$	8616.00			0.538450
$636$	2892.00	+	5009.09i	0.180307	+	0.312301i
$637$	−729.000	−	1262.67i	−0.0453438	−	0.0785378i
$638$	19200.0			1.19143
$639$	−990.000			−0.0612892
$640$	−384.000	−	665.108i	−0.0237171	−	0.0410792i
$641$	4625.00	−	8010.73i	0.284987	−	0.493612i	−0.687619	−	0.726072i	$-0.741344\pi$
$641$	4625.00	−	8010.73i	0.284987	−	0.493612i	0.972606	+	0.232460i	$0.0746775\pi$
$642$	786.000	+	1361.39i	0.0483192	+	0.0836914i
$643$	8264.50	−	14314.5i	0.506874	−	0.877932i	−0.493094	−	0.869976i	$-0.664134\pi$
$643$	8264.50	−	14314.5i	0.506874	−	0.877932i	0.999968	−	0.00795583i	$-0.00253245\pi$
$644$	−3724.00	+	6450.16i	−0.227867	+	0.394677i
$645$	1998.00			0.121971
$646$	−2356.00	−	20403.6i	−0.143492	−	1.24267i
$647$	13884.0			0.843642			0.421821	−	0.906679i	$-0.361391\pi$
$647$	13884.0			0.843642			0.421821	+	0.906679i	$0.361391\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	7936.00	−	13745.6i	0.479993	−	0.831372i
$650$	−7209.00	−	12486.4i	−0.435016	−	0.753469i
$651$	6412.50	−	11106.8i	0.386061	−	0.668677i
$652$	−3418.00	−	5920.15i	−0.205306	−	0.355600i
$653$	−20538.0			−1.23080			−0.615401	−	0.788214i	$-0.711006\pi$
$653$	−20538.0			−1.23080			−0.615401	+	0.788214i	$0.711006\pi$
$654$	−6204.00			−0.370941
$655$	−1134.00	−	1964.15i	−0.0676474	−	0.117169i
$656$	−1408.00	−	2438.73i	−0.0838006	−	0.145147i
$657$	7353.00			0.436633
$658$	20900.0			1.23825
$659$	−7624.00	−	13205.2i	−0.450666	−	0.780576i	0.547762	−	0.836635i	$-0.315480\pi$
$659$	−7624.00	−	13205.2i	−0.450666	−	0.780576i	−0.998428	+	0.0560582i	$0.982147\pi$
$660$	1152.00	−	1995.32i	0.0679417	−	0.117679i
$661$	−12413.0	−	21499.9i	−0.730423	−	1.26513i	−0.956702	−	0.291068i	$-0.905990\pi$
$661$	−12413.0	−	21499.9i	−0.730423	−	1.26513i	0.226279	−	0.974062i	$-0.427344\pi$
$662$	−4359.00	+	7550.01i	−0.255917	+	0.443262i
$663$	15066.0	−	26095.1i	0.882526	−	1.52858i
$664$	448.000			0.0261834
$665$	7581.00	−	5627.43i	0.442073	−	0.328154i
$666$	5274.00			0.306852
$667$	14700.0	−	25461.1i	0.853353	−	1.47805i
$668$	5520.00	−	9560.92i	0.319723	−	0.553777i
$669$	−3442.50	−	5962.58i	−0.198946	−	0.344584i
$670$	−2790.00	+	4832.42i	−0.160876	+	0.278646i
$671$	−2480.00	−	4295.49i	−0.142682	−	0.247132i
$672$	−1824.00			−0.104706
$673$	10907.0			0.624716			0.312358	−	0.949964i	$-0.398881\pi$
$673$	10907.0			0.624716			0.312358	+	0.949964i	$0.398881\pi$
$674$	8729.00	+	15119.1i	0.498855	+	0.864043i
$675$	1201.50	+	2081.06i	0.0685122	+	0.118667i
$676$	17456.0			0.993173
$677$	7386.00			0.419301			0.209651	−	0.977776i	$-0.432767\pi$
$677$	7386.00			0.419301			0.209651	+	0.977776i	$0.432767\pi$
$678$	−3972.00	−	6879.71i	−0.224991	−	0.389695i
$679$	10925.0	−	18922.7i	0.617471	−	1.06949i
$680$	2976.00	+	5154.58i	0.167830	+	0.290690i
$681$	−3777.00	+	6541.96i	−0.212533	+	0.368118i
$682$	−7200.00	+	12470.8i	−0.404255	+	0.700191i
$683$	16542.0			0.926738			0.463369	−	0.886165i	$-0.346640\pi$
$683$	16542.0			0.926738			0.463369	+	0.886165i	$0.346640\pi$
$684$	−2394.00	+	1777.08i	−0.133826	+	0.0993399i
$685$	−6372.00			−0.355418
$686$	−6175.00	+	10695.4i	−0.343677	+	0.595266i
$687$	−8101.50	+	14032.2i	−0.449915	+	0.779275i
$688$	888.000	+	1538.06i	0.0492074	+	0.0852297i
$689$	19521.0	−	33811.4i	1.07938	−	1.86954i
$690$	−1764.00	−	3055.34i	−0.0973251	−	0.168572i
$691$	1972.00			0.108565			0.0542825	−	0.998526i	$-0.482713\pi$
$691$	1972.00			0.108565			0.0542825	+	0.998526i	$0.482713\pi$
$692$	−5904.00			−0.324330
$693$	−2736.00	−	4738.89i	−0.149974	−	0.259763i
$694$	38.0000	+	65.8179i	0.00207847	+	0.00360002i
$695$	11238.0			0.613355
$696$	7200.00			0.392120
$697$	10912.0	+	18900.1i	0.593001	+	1.02711i
$698$	6103.00	−	10570.7i	0.330948	−	0.573219i
$699$	9117.00	+	15791.1i	0.493328	+	0.854470i
$700$	3382.00	−	5857.80i	0.182611	−	0.316291i
$701$	2207.00	−	3822.64i	0.118912	−	0.205961i	−0.800425	−	0.599433i	$-0.795393\pi$
$701$	2207.00	−	3822.64i	0.118912	−	0.205961i	0.919337	+	0.393472i	$0.128726\pi$
$702$	−4374.00			−0.235165
$703$	−22268.0	−	9642.33i	−1.19467	−	0.517308i
$704$	2048.00			0.109640
$705$	−4950.00	+	8573.65i	−0.264437	+	0.458018i
$706$	−12198.0	+	21127.6i	−0.650252	+	1.12627i
$707$	5491.00	+	9510.69i	0.292094	+	0.505921i
$708$	2976.00	−	5154.58i	0.157973	−	0.273617i
$709$	−15344.5	−	26577.5i	−0.812799	−	1.40781i	−0.910897	−	0.412633i	$-0.864609\pi$
$709$	−15344.5	−	26577.5i	−0.812799	−	1.40781i	0.0980979	−	0.995177i	$-0.468724\pi$
$710$	−1320.00			−0.0697728
$711$	2331.00			0.122953
$712$	1232.00	+	2133.89i	0.0648471	+	0.112319i
$713$	11025.0	+	19095.9i	0.579088	+	1.00301i
$714$	14136.0			0.740933
$715$	−15552.0			−0.813443
$716$	−52.0000	−	90.0666i	−0.00271415	−	0.00470105i
$717$	−1593.00	+	2759.16i	−0.0829730	+	0.143714i
$718$	2988.00	+	5175.37i	0.155308	+	0.269001i
$719$	10865.0	−	18818.7i	0.563555	−	0.976106i	−0.433627	−	0.901092i	$-0.642767\pi$
$719$	10865.0	−	18818.7i	0.563555	−	0.976106i	0.997182	−	0.0750138i	$-0.0239001\pi$
$720$	432.000	−	748.246i	0.0223607	−	0.0387298i
$721$	15561.0			0.803775
$722$	13357.0	−	3126.35i	0.688499	−	0.161151i
$723$	−13857.0			−0.712790
$724$	7188.00	−	12450.0i	0.368978	−	0.639088i
$725$	−13350.0	+	23122.9i	−0.683871	+	1.18450i
$726$	−921.000	−	1595.22i	−0.0470820	−	0.0815484i
$727$	−1361.50	+	2358.19i	−0.0694570	+	0.120303i	−0.898662	−	0.438641i	$-0.855460\pi$
$727$	−1361.50	+	2358.19i	−0.0694570	+	0.120303i	0.829205	+	0.558944i	$0.188793\pi$
$728$	6156.00	+	10662.5i	0.313402	+	0.542828i
$729$	729.000			0.0370370
$730$	9804.00			0.497072
$731$	−6882.00	−	11920.0i	−0.348208	−	0.603114i
$732$	−930.000	−	1610.81i	−0.0469587	−	0.0813349i
$733$	−26186.0			−1.31951			−0.659756	−	0.751480i	$-0.729340\pi$
$733$	−26186.0			−1.31951			−0.659756	+	0.751480i	$0.729340\pi$
$734$	−4210.00			−0.211708
$735$	162.000	+	280.592i	0.00812988	+	0.0140814i
$736$	1568.00	−	2715.86i	0.0785289	−	0.136016i
$737$	−7440.00	−	12886.5i	−0.371853	−	0.644069i
$738$	1584.00	−	2743.57i	0.0790079	−	0.136846i
$739$	4895.50	−	8479.25i	0.243686	−	0.422076i	−0.718075	−	0.695965i	$-0.754977\pi$
$739$	4895.50	−	8479.25i	0.243686	−	0.422076i	0.961761	+	0.273889i	$0.0883101\pi$
$740$	7032.00			0.349326
$741$	18468.0	+	7996.88i	0.915572	+	0.396454i
$742$	18316.0			0.906202
$743$	−2766.00	+	4790.85i	−0.136574	+	0.236554i	−0.926198	−	0.377038i	$-0.876943\pi$
$743$	−2766.00	+	4790.85i	−0.136574	+	0.236554i	0.789623	+	0.613592i	$0.210276\pi$
$744$	−2700.00	+	4676.54i	−0.133047	+	0.230444i
$745$	4116.00	+	7129.12i	0.202414	+	0.350592i
$746$	−2494.00	+	4319.73i	−0.122402	+	0.212006i
$747$	252.000	+	436.477i	0.0123430	+	0.0213786i
$748$	−15872.0			−0.775853
$749$	4978.00			0.242847
$750$	3852.00	+	6671.86i	0.187540	+	0.324829i
$751$	−13965.5	−	24189.0i	−0.678573	−	1.17532i	−0.975411	−	0.220395i	$-0.929265\pi$
$751$	−13965.5	−	24189.0i	−0.678573	−	1.17532i	0.296838	−	0.954928i	$-0.404068\pi$
$752$	−8800.00			−0.426733
$753$	6534.00			0.316218
$754$	−24300.0	−	42088.8i	−1.17368	−	2.03287i
$755$	−9888.00	+	17126.5i	−0.476637	+	0.825560i
$756$	−1026.00	−	1777.08i	−0.0493588	−	0.0854920i
$757$	−12830.5	+	22223.1i	−0.616027	+	1.06699i	0.374176	+	0.927358i	$0.377925\pi$
$757$	−12830.5	+	22223.1i	−0.616027	+	1.06699i	−0.990203	+	0.139633i	$0.955408\pi$
$758$	5729.00	−	9922.92i	0.274521	−	0.475484i
$759$	9408.00			0.449919
$760$	−3192.00	+	2369.45i	−0.152350	+	0.113091i
$761$	−16868.0			−0.803501			−0.401751	−	0.915749i	$-0.631598\pi$
$761$	−16868.0			−0.803501			−0.401751	+	0.915749i	$0.631598\pi$
$762$	−4308.00	+	7461.67i	−0.204806	+	0.354735i
$763$	−9823.00	+	17013.9i	−0.466077	+	0.807268i
$764$	−628.000	−	1087.73i	−0.0297385	−	0.0515087i
$765$	−3348.00	+	5798.91i	−0.158232	+	0.274065i
$766$	−10016.0	−	17348.2i	−0.472445	−	0.818299i
$767$	−40176.0			−1.89136
$768$	768.000			0.0360844
$769$	−2845.50	−	4928.55i	−0.133435	−	0.231116i	0.791564	−	0.611087i	$-0.209267\pi$
$769$	−2845.50	−	4928.55i	−0.133435	−	0.231116i	−0.924998	+	0.379971i	$0.875934\pi$
$770$	−3648.00	−	6318.52i	−0.170733	−	0.295719i
$771$	−1890.00			−0.0882836
$772$	−3700.00			−0.172495
$773$	9459.00	+	16383.5i	0.440125	+	0.762319i	0.997698	−	0.0678089i	$-0.0216008\pi$
$773$	9459.00	+	16383.5i	0.440125	+	0.762319i	−0.557573	+	0.830128i	$0.688267\pi$
$774$	−999.000	+	1730.32i	−0.0463932	+	0.0803553i
$775$	−10012.5	−	17342.2i	−0.464077	−	0.803805i
$776$	−4600.00	+	7967.43i	−0.212797	+	0.368575i
$777$	8350.50	−	14463.5i	0.385550	−	0.667793i
$778$	−11636.0			−0.536209
$779$	−11704.0	+	8687.97i	−0.538305	+	0.399588i
$780$	−5832.00			−0.267717
$781$	1760.00	−	3048.41i	0.0806373	−	0.139668i
$782$	−12152.0	+	21047.9i	−0.555696	+	0.962495i
$783$	4050.00	+	7014.81i	0.184847	+	0.320164i
$784$	−144.000	+	249.415i	−0.00655977	+	0.0113618i
$785$	5301.00	+	9181.60i	0.241020	+	0.417459i
$786$	2268.00			0.102922
$787$	29191.0			1.32217			0.661084	−	0.750312i	$-0.270097\pi$
$787$	29191.0			1.32217			0.661084	+	0.750312i	$0.270097\pi$
$788$	−2488.00	−	4309.34i	−0.112476	−	0.194815i
$789$	−4113.00	−	7123.92i	−0.185585	−	0.321443i
$790$	3108.00			0.139972
$791$	−25156.0			−1.13078
$792$	1152.00	+	1995.32i	0.0516850	+	0.0895211i
$793$	−6277.50	+	10872.9i	−0.281110	+	0.486898i
$794$	−4149.00	−	7186.28i	−0.185444	−	0.321198i
$795$	−4338.00	+	7513.64i	−0.193526	+	0.335197i
$796$	−6982.00	+	12093.2i	−0.310892	+	0.538482i
$797$	22594.0			1.00417			0.502083	−	0.864819i	$-0.332567\pi$
$797$	22594.0			1.00417			0.502083	+	0.864819i	$0.332567\pi$
$798$	1083.00	+	9379.06i	0.0480423	+	0.416059i
$799$	68200.0			3.01970
$800$	−1424.00	+	2466.44i	−0.0629325	+	0.109002i
$801$	−1386.00	+	2400.62i	−0.0611385	+	0.105895i
$802$	9072.00	+	15713.2i	0.399431	+	0.691834i
$803$	−13072.0	+	22641.4i	−0.574472	+	0.995014i
$804$	−2790.00	−	4832.42i	−0.122383	−	0.211973i
$805$	−11172.0			−0.489144
$806$	36450.0			1.59292
$807$	−3138.00	−	5435.18i	−0.136881	−	0.237085i
$808$	−2312.00	−	4004.50i	−0.100663	−	0.174354i
$809$	522.000			0.0226855			0.0113427	−	0.999936i	$-0.496389\pi$
$809$	522.000			0.0226855			0.0113427	+	0.999936i	$0.496389\pi$
$810$	972.000			0.0421637
$811$	6040.00	+	10461.6i	0.261520	+	0.452967i	0.966646	−	0.256116i	$-0.0824428\pi$
$811$	6040.00	+	10461.6i	0.261520	+	0.452967i	−0.705126	+	0.709082i	$0.749109\pi$
$812$	11400.0	−	19745.4i	0.492687	−	0.853358i
$813$	−8148.00	−	14112.7i	−0.351492	−	0.608802i
$814$	−9376.00	+	16239.7i	−0.403721	+	0.699265i
$815$	5127.00	−	8880.22i	0.220357	−	0.381670i
$816$	−5952.00			−0.255345
$817$	7381.50	−	5479.34i	0.316091	−	0.234636i
$818$	−17388.0			−0.743224
$819$	−6925.50	+	11995.3i	−0.295478	+	0.511783i
$820$	2112.00	−	3658.09i	0.0899442	−	0.155788i
$821$	18234.0	+	31582.2i	0.775117	+	1.34254i	0.934729	+	0.355362i	$0.115642\pi$
$821$	18234.0	+	31582.2i	0.775117	+	1.34254i	−0.159612	+	0.987180i	$0.551024\pi$
$822$	3186.00	−	5518.31i	0.135188	−	0.234152i
$823$	−9344.00	−	16184.3i	−0.395761	−	0.685478i	0.597437	−	0.801916i	$-0.296186\pi$
$823$	−9344.00	−	16184.3i	−0.395761	−	0.685478i	−0.993198	+	0.116438i	$0.962852\pi$
$824$	−6552.00			−0.277002
$825$	−8544.00			−0.360562
$826$	−9424.00	−	16322.8i	−0.396977	−	0.687584i
$827$	−2988.00	−	5175.37i	−0.125638	−	0.217612i	0.796344	−	0.604844i	$-0.206765\pi$
$827$	−2988.00	−	5175.37i	−0.125638	−	0.217612i	−0.921982	+	0.387232i	$0.873431\pi$
$828$	3528.00			0.148075
$829$	−11167.0			−0.467848			−0.233924	−	0.972255i	$-0.575157\pi$
$829$	−11167.0			−0.467848			−0.233924	+	0.972255i	$0.575157\pi$
$830$	336.000	+	581.969i	0.0140515	+	0.0243379i
$831$	4251.00	−	7362.95i	0.177456	−	0.307362i
$832$	−2592.00	−	4489.48i	−0.108007	−	0.187073i
$833$	1116.00	−	1932.97i	0.0464191	−	0.0804002i
$834$	−5619.00	+	9732.39i	−0.233297	+	0.404083i
$835$	16560.0			0.686326
$836$	−1216.00	−	10530.9i	−0.0503065	−	0.435667i
$837$	−6075.00			−0.250875
$838$	−4392.00	+	7607.17i	−0.181049	+	0.313586i
$839$	−10035.0	+	17381.1i	−0.412928	+	0.715212i	−0.995208	−	0.0977756i	$-0.968827\pi$
$839$	−10035.0	+	17381.1i	−0.412928	+	0.715212i	0.582280	+	0.812988i	$0.302161\pi$
$840$	−1368.00	−	2369.45i	−0.0561911	−	0.0973258i
$841$	−32805.5	+	56820.8i	−1.34509	+	2.32977i
$842$	6910.00	+	11968.5i	0.282820	+	0.489858i
$843$	17070.0			0.697416
$844$	−18308.0			−0.746667
$845$	13092.0	+	22676.0i	0.532992	+	0.923170i
$846$	−4950.00	−	8573.65i	−0.201164	−	0.348426i
$847$	−5833.00			−0.236628
$848$	−7712.00			−0.312301
$849$	6582.00	+	11400.4i	0.266070	+	0.460847i
$850$	11036.0	−	19114.9i	0.445331	−	0.771337i
$851$	14357.0	+	24867.1i	0.578322	+	1.00168i
$852$	660.000	−	1143.15i	0.0265390	−	0.0459669i
$853$	−5413.50	+	9376.46i	−0.217297	+	0.376370i	−0.953981	−	0.299868i	$-0.903057\pi$
$853$	−5413.50	+	9376.46i	−0.217297	+	0.376370i	0.736683	+	0.676238i	$0.236391\pi$
$854$	−5890.00			−0.236009
$855$	−4104.00	−	1777.08i	−0.164157	−	0.0710819i
$856$	−2096.00			−0.0836914
$857$	11307.0	−	19584.3i	0.450688	−	0.780615i	−0.547741	−	0.836648i	$-0.684512\pi$
$857$	11307.0	−	19584.3i	0.450688	−	0.780615i	0.998429	+	0.0560333i	$0.0178453\pi$
$858$	7776.00	−	13468.4i	0.309404	−	0.535903i
$859$	13169.5	+	22810.2i	0.523094	+	0.906025i	0.999639	+	0.0268749i	$0.00855558\pi$
$859$	13169.5	+	22810.2i	0.523094	+	0.906025i	−0.476545	+	0.879150i	$0.658111\pi$
$860$	−1332.00	+	2307.09i	−0.0528149	+	0.0914781i
$861$	−5016.00	−	8687.97i	−0.198542	−	0.343885i
$862$	17764.0			0.701907
$863$	20458.0			0.806951			0.403475	−	0.914991i	$-0.367802\pi$
$863$	20458.0			0.806951			0.403475	+	0.914991i	$0.367802\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	−4428.00	−	7669.52i	−0.174054	−	0.301470i
$866$	−7398.00			−0.290294
$867$	31389.0			1.22956
$868$	8550.00	+	14809.0i	0.334339	+	0.579091i
$869$	−4144.00	+	7177.62i	−0.161767	+	0.280189i
$870$	5400.00	+	9353.07i	0.210434	+	0.364482i
$871$	−18832.5	+	32618.8i	−0.732623	+	1.26894i
$872$	4136.00	−	7163.76i	0.160622	−	0.278206i
$873$	−10350.0			−0.401254
$874$	−14896.0	−	6450.16i	−0.576504	−	0.249634i
$875$	24396.0			0.942555
$876$	−4902.00	+	8490.51i	−0.189068	+	0.327475i
$877$	8160.50	−	14134.4i	0.314208	−	0.544224i	−0.665061	−	0.746789i	$-0.731594\pi$
$877$	8160.50	−	14134.4i	0.314208	−	0.544224i	0.979269	+	0.202565i	$0.0649277\pi$
$878$	−16907.0	−	29283.8i	−0.649867	−	1.12560i
$879$	2487.00	−	4307.61i	0.0954317	−	0.165292i
$880$	1536.00	+	2660.43i	0.0588393	+	0.101913i
$881$	−15990.0			−0.611483			−0.305742	−	0.952115i	$-0.598904\pi$
$881$	−15990.0			−0.611483			−0.305742	+	0.952115i	$0.598904\pi$
$882$	−324.000			−0.0123692
$883$	−6412.50	−	11106.8i	−0.244392	−	0.423299i	0.717569	−	0.696488i	$-0.245255\pi$
$883$	−6412.50	−	11106.8i	−0.244392	−	0.423299i	−0.961960	+	0.273189i	$0.911922\pi$
$884$	20088.0	+	34793.4i	0.764290	+	1.32379i
$885$	8928.00			0.339109
$886$	19944.0			0.756244
$887$	−11238.0	−	19464.8i	−0.425406	−	0.736825i	0.571052	−	0.820914i	$-0.306535\pi$
$887$	−11238.0	−	19464.8i	−0.425406	−	0.736825i	−0.996458	+	0.0840889i	$0.973202\pi$
$888$	−3516.00	+	6089.89i	−0.132871	+	0.230139i
$889$	13642.0	+	23628.6i	0.514666	+	0.891428i
$890$	−1848.00	+	3200.83i	−0.0696012	+	0.120553i
$891$	−1296.00	+	2244.74i	−0.0487291	+	0.0844013i
$892$	9180.00			0.344584
$893$	5225.00	+	45249.8i	0.195798	+	1.69566i
$894$	−8232.00			−0.307963
$895$	78.0000	−	135.100i	0.00291313	−	0.00504569i
$896$	1216.00	−	2106.17i	0.0453390	−	0.0785294i
$897$	−11907.0	−	20623.5i	−0.443214	−	0.767670i
$898$	−10368.0	+	17957.9i	−0.385284	+	0.667331i
$899$	−33750.0	−	58456.7i	−1.25209	−	2.16868i
$900$	−3204.00			−0.118667
$901$	59768.0			2.20995
$902$	5632.00	+	9754.91i	0.207899	+	0.360092i
$903$	3163.50	+	5479.34i	0.116583	+	0.201928i
$904$	10592.0			0.389695
$905$	21564.0			0.792057
$906$	−9888.00	−	17126.5i	−0.362590	−	0.628025i
$907$	1102.00	−	1908.72i	0.0403432	−	0.0698765i	−0.845149	−	0.534531i	$-0.820488\pi$
$907$	1102.00	−	1908.72i	0.0403432	−	0.0698765i	0.885492	+	0.464655i	$0.153822\pi$
$908$	−5036.00	−	8722.61i	−0.184059	−	0.318799i
$909$	2601.00	−	4505.06i	0.0949062	−	0.164382i
$910$	−9234.00	+	15993.8i	−0.336378	+	0.582624i
$911$	−32472.0			−1.18095			−0.590475	−	0.807056i	$-0.701060\pi$
$911$	−32472.0			−1.18095			−0.590475	+	0.807056i	$0.701060\pi$
$912$	−456.000	−	3949.08i	−0.0165567	−	0.143385i
$913$	−1792.00			−0.0649579
$914$	4481.00	−	7761.32i	0.162164	−	0.280877i
$915$	1395.00	−	2416.21i	0.0504014	−	0.0872978i
$916$	−10802.0	−	18709.6i	−0.389638	−	0.674872i
$917$	3591.00	−	6219.79i	0.129319	−	0.223987i
$918$	−3348.00	−	5798.91i	−0.120371	−	0.208488i
$919$	−6095.00			−0.218776			−0.109388	−	0.993999i	$-0.534889\pi$
$919$	−6095.00			−0.218776			−0.109388	+	0.993999i	$0.534889\pi$
$920$	4704.00			0.168572
$921$	−1206.00	−	2088.85i	−0.0431477	−	0.0747340i
$922$	−2112.00	−	3658.09i	−0.0754393	−	0.130665i
$923$	−8910.00			−0.317742
$924$	7296.00			0.259763
$925$	−13038.5	−	22583.3i	−0.463463	−	0.802741i
$926$	5817.00	−	10075.3i	0.206435	−	0.357555i
$927$	−3685.50	−	6383.47i	−0.130580	−	0.226171i
$928$	−4800.00	+	8313.84i	−0.169793	+	0.294090i
$929$	−21993.0	+	38093.0i	−0.776714	+	1.34531i	0.157113	+	0.987581i	$0.449781\pi$
$929$	−21993.0	+	38093.0i	−0.776714	+	1.34531i	−0.933826	+	0.357727i	$0.883552\pi$
$930$	−8100.00			−0.285602
$931$	1368.00	+	592.361i	0.0481572	+	0.0208527i
$932$	−24312.0			−0.854470
$933$	4758.00	−	8241.10i	0.166956	−	0.289176i
$934$	9100.00	−	15761.7i	0.318802	−	0.552181i
$935$	−11904.0	−	20618.3i	−0.416366	−	0.721167i
$936$	2916.00	−	5050.66i	0.101830	−	0.176374i
$937$	−11075.5	−	19183.3i	−0.386148	−	0.668828i	0.605780	−	0.795632i	$-0.292861\pi$
$937$	−11075.5	−	19183.3i	−0.386148	−	0.668828i	−0.991928	+	0.126804i	$0.959528\pi$
$938$	−17670.0			−0.615081
$939$	11502.0			0.399738
$940$	−6600.00	−	11431.5i	−0.229009	−	0.396655i
$941$	−6700.00	−	11604.7i	−0.232108	−	0.402023i	0.726320	−	0.687357i	$-0.241229\pi$
$941$	−6700.00	−	11604.7i	−0.232108	−	0.402023i	−0.958428	+	0.285333i	$0.907896\pi$
$942$	−10602.0			−0.366700
$943$	17248.0			0.595623
$944$	3968.00	+	6872.78i	0.136809	+	0.236960i
$945$	1539.00	−	2665.63i	0.0529774	−	0.0917596i
$946$	−3552.00	−	6152.24i	−0.122078	−	0.211445i
$947$	27197.0	−	47106.6i	0.933246	−	1.61643i	0.155513	−	0.987834i	$-0.450297\pi$
$947$	27197.0	−	47106.6i	0.933246	−	1.61643i	0.777733	−	0.628595i	$-0.216370\pi$
$948$	−1554.00	+	2691.61i	−0.0532401	+	0.0922145i
$949$	66177.0			2.26364
$950$	13528.0	+	5857.80i	0.462007	+	0.200055i
$951$	8766.00			0.298903
$952$	−9424.00	+	16322.8i	−0.320834	+	0.555700i
$953$	−6828.00	+	11826.4i	−0.232089	+	0.401990i	−0.958423	−	0.285353i	$-0.907889\pi$
$953$	−6828.00	+	11826.4i	−0.232089	+	0.401990i	0.726334	+	0.687342i	$0.241223\pi$
$954$	−4338.00	−	7513.64i	−0.147220	−	0.254993i
$955$	942.000	−	1631.59i	0.0319187	−	0.0552849i
$956$	−2124.00	−	3678.88i	−0.0718568	−	0.124460i
$957$	−28800.0			−0.972802
$958$	60.0000			0.00202350
$959$	−10089.0	−	17474.7i	−0.339719	−	0.588411i
$960$	576.000	+	997.661i	0.0193649	+	0.0335410i
$961$	20834.0			0.699339
$962$	47466.0			1.59082
$963$	−1179.00	−	2042.09i	−0.0394525	−	0.0683337i
$964$	9238.00	−	16000.7i	0.308647	−	0.534593i
$965$	−2775.00	−	4806.44i	−0.0925704	−	0.160337i
$966$	5586.00	−	9675.24i	0.186052	−	0.322252i
$967$	−12340.5	+	21374.4i	−0.410386	+	0.710810i	−0.994932	−	0.100551i	$-0.967940\pi$
$967$	−12340.5	+	21374.4i	−0.410386	+	0.710810i	0.584545	+	0.811361i	$0.301273\pi$
$968$	2456.00			0.0815484
$969$	3534.00	+	30605.3i	0.117160	+	1.01464i
$970$	−13800.0			−0.456795
$971$	−23211.0	+	40202.6i	−0.767123	+	1.32870i	0.171994	+	0.985098i	$0.444979\pi$
$971$	−23211.0	+	40202.6i	−0.767123	+	1.32870i	−0.939117	+	0.343598i	$0.888354\pi$
$972$	−486.000	+	841.777i	−0.0160375	+	0.0277778i
$973$	17793.5	+	30819.2i	0.586263	+	1.01544i
$974$	−10924.0	+	18920.9i	−0.359371	+	0.622449i
$975$	10813.5	+	18729.5i	0.355189	+	0.615205i
$976$	2480.00			0.0813349
$977$	10266.0			0.336170			0.168085	−	0.985772i	$-0.446242\pi$
$977$	10266.0			0.336170			0.168085	+	0.985772i	$0.446242\pi$
$978$	5127.00	+	8880.22i	0.167631	+	0.290346i
$979$	−4928.00	−	8535.55i	−0.160878	−	0.278649i
$980$	−432.000			−0.0140814
$981$	9306.00			0.302872
$982$	7338.00	+	12709.8i	0.238457	+	0.413020i
$983$	14106.0	−	24432.3i	0.457692	−	0.792746i	−0.541146	−	0.840928i	$-0.682009\pi$
$983$	14106.0	−	24432.3i	0.457692	−	0.792746i	0.998839	+	0.0481822i	$0.0153428\pi$
$984$	2112.00	+	3658.09i	0.0684229	+	0.118512i
$985$	3732.00	−	6464.01i	0.120722	−	0.209097i
$986$	37200.0	−	64432.3i	1.20151	−	2.08108i
$987$	−31350.0			−1.01102
$988$	−21546.0	+	15993.8i	−0.693795	+	0.515009i
$989$	−10878.0			−0.349747
$990$	−1728.00	+	2992.98i	−0.0554742	+	0.0960841i
$991$	−20448.5	+	35417.8i	−0.655467	+	1.13530i	0.326309	+	0.945263i	$0.394195\pi$
$991$	−20448.5	+	35417.8i	−0.655467	+	1.13530i	−0.981776	+	0.190039i	$0.939138\pi$
$992$	−3600.00	−	6235.38i	−0.115222	−	0.199570i
$993$	6538.50	−	11325.0i	0.208956	−	0.361922i
$994$	−2090.00	−	3619.99i	−0.0666909	−	0.115512i
$995$	−20946.0			−0.667370
$996$	−672.000			−0.0213786
$997$	7410.50	+	12835.4i	0.235399	+	0.407723i	0.959389	−	0.282088i	$-0.0910270\pi$
$997$	7410.50	+	12835.4i	0.235399	+	0.407723i	−0.723990	+	0.689811i	$0.757694\pi$
$998$	−8521.00	−	14758.8i	−0.270268	−	0.468118i
$999$	−7911.00			−0.250544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.e.b.49.1	yes	2
3.2	odd	2		342.4.g.a.163.1		2
19.7	even	3	inner	114.4.e.b.7.1	✓	2
19.8	odd	6		2166.4.a.e.1.1		1
19.11	even	3		2166.4.a.b.1.1		1
57.26	odd	6		342.4.g.a.235.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.b.7.1	✓	2	19.7	even	3	inner
114.4.e.b.49.1	yes	2	1.1	even	1	trivial
342.4.g.a.163.1		2	3.2	odd	2
342.4.g.a.235.1		2	57.26	odd	6
2166.4.a.b.1.1		1	19.11	even	3
2166.4.a.e.1.1		1	19.8	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +(3.00000 + 5.19615i) q^{6} +19.0000 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +(3.00000 + 5.19615i) q^{6} +19.0000 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.00000 - 10.3923i) q^{10} +32.0000 q^{11} +12.0000 q^{12} +(-40.5000 - 70.1481i) q^{13} +(19.0000 - 32.9090i) q^{14} +(9.00000 + 15.5885i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(62.0000 - 107.387i) q^{17} -18.0000 q^{18} +(76.0000 + 32.9090i) q^{19} -24.0000 q^{20} +(-28.5000 + 49.3634i) q^{21} +(32.0000 - 55.4256i) q^{22} +(-49.0000 - 84.8705i) q^{23} +(12.0000 - 20.7846i) q^{24} +(44.5000 + 77.0763i) q^{25} -162.000 q^{26} +27.0000 q^{27} +(-38.0000 - 65.8179i) q^{28} +(150.000 + 259.808i) q^{29} +36.0000 q^{30} -225.000 q^{31} +(16.0000 + 27.7128i) q^{32} +(-48.0000 + 83.1384i) q^{33} +(-124.000 - 214.774i) q^{34} +(57.0000 - 98.7269i) q^{35} +(-18.0000 + 31.1769i) q^{36} -293.000 q^{37} +(133.000 - 98.7269i) q^{38} +243.000 q^{39} +(-24.0000 + 41.5692i) q^{40} +(-88.0000 + 152.420i) q^{41} +(57.0000 + 98.7269i) q^{42} +(55.5000 - 96.1288i) q^{43} +(-64.0000 - 110.851i) q^{44} -54.0000 q^{45} -196.000 q^{46} +(275.000 + 476.314i) q^{47} +(-24.0000 - 41.5692i) q^{48} +18.0000 q^{49} +178.000 q^{50} +(186.000 + 322.161i) q^{51} +(-162.000 + 280.592i) q^{52} +(241.000 + 417.424i) q^{53} +(27.0000 - 46.7654i) q^{54} +(96.0000 - 166.277i) q^{55} -152.000 q^{56} +(-199.500 + 148.090i) q^{57} +600.000 q^{58} +(248.000 - 429.549i) q^{59} +(36.0000 - 62.3538i) q^{60} +(-77.5000 - 134.234i) q^{61} +(-225.000 + 389.711i) q^{62} +(-85.5000 - 148.090i) q^{63} +64.0000 q^{64} -486.000 q^{65} +(96.0000 + 166.277i) q^{66} +(-232.500 - 402.702i) q^{67} -496.000 q^{68} +294.000 q^{69} +(-114.000 - 197.454i) q^{70} +(55.0000 - 95.2628i) q^{71} +(36.0000 + 62.3538i) q^{72} +(-408.500 + 707.543i) q^{73} +(-293.000 + 507.491i) q^{74} -267.000 q^{75} +(-38.0000 - 329.090i) q^{76} +608.000 q^{77} +(243.000 - 420.888i) q^{78} +(-129.500 + 224.301i) q^{79} +(48.0000 + 83.1384i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(176.000 + 304.841i) q^{82} -56.0000 q^{83} +228.000 q^{84} +(-372.000 - 644.323i) q^{85} +(-111.000 - 192.258i) q^{86} -900.000 q^{87} -256.000 q^{88} +(-154.000 - 266.736i) q^{89} +(-54.0000 + 93.5307i) q^{90} +(-769.500 - 1332.81i) q^{91} +(-196.000 + 339.482i) q^{92} +(337.500 - 584.567i) q^{93} +1100.00 q^{94} +(399.000 - 296.181i) q^{95} -96.0000 q^{96} +(575.000 - 995.929i) q^{97} +(18.0000 - 31.1769i) q^{98} +(-144.000 - 249.415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} + 6 q^{6} + 38 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 + 6 * q^6 + 38 * q^7 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} + 6 q^{6} + 38 q^{7} - 16 q^{8} - 9 q^{9} - 12 q^{10} + 64 q^{11} + 24 q^{12} - 81 q^{13} + 38 q^{14} + 18 q^{15} - 16 q^{16} + 124 q^{17} - 36 q^{18} + 152 q^{19} - 48 q^{20} - 57 q^{21} + 64 q^{22} - 98 q^{23} + 24 q^{24} + 89 q^{25} - 324 q^{26} + 54 q^{27} - 76 q^{28} + 300 q^{29} + 72 q^{30} - 450 q^{31} + 32 q^{32} - 96 q^{33} - 248 q^{34} + 114 q^{35} - 36 q^{36} - 586 q^{37} + 266 q^{38} + 486 q^{39} - 48 q^{40} - 176 q^{41} + 114 q^{42} + 111 q^{43} - 128 q^{44} - 108 q^{45} - 392 q^{46} + 550 q^{47} - 48 q^{48} + 36 q^{49} + 356 q^{50} + 372 q^{51} - 324 q^{52} + 482 q^{53} + 54 q^{54} + 192 q^{55} - 304 q^{56} - 399 q^{57} + 1200 q^{58} + 496 q^{59} + 72 q^{60} - 155 q^{61} - 450 q^{62} - 171 q^{63} + 128 q^{64} - 972 q^{65} + 192 q^{66} - 465 q^{67} - 992 q^{68} + 588 q^{69} - 228 q^{70} + 110 q^{71} + 72 q^{72} - 817 q^{73} - 586 q^{74} - 534 q^{75} - 76 q^{76} + 1216 q^{77} + 486 q^{78} - 259 q^{79} + 96 q^{80} - 81 q^{81} + 352 q^{82} - 112 q^{83} + 456 q^{84} - 744 q^{85} - 222 q^{86} - 1800 q^{87} - 512 q^{88} - 308 q^{89} - 108 q^{90} - 1539 q^{91} - 392 q^{92} + 675 q^{93} + 2200 q^{94} + 798 q^{95} - 192 q^{96} + 1150 q^{97} + 36 q^{98} - 288 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 + 6 * q^6 + 38 * q^7 - 16 * q^8 - 9 * q^9 - 12 * q^10 + 64 * q^11 + 24 * q^12 - 81 * q^13 + 38 * q^14 + 18 * q^15 - 16 * q^16 + 124 * q^17 - 36 * q^18 + 152 * q^19 - 48 * q^20 - 57 * q^21 + 64 * q^22 - 98 * q^23 + 24 * q^24 + 89 * q^25 - 324 * q^26 + 54 * q^27 - 76 * q^28 + 300 * q^29 + 72 * q^30 - 450 * q^31 + 32 * q^32 - 96 * q^33 - 248 * q^34 + 114 * q^35 - 36 * q^36 - 586 * q^37 + 266 * q^38 + 486 * q^39 - 48 * q^40 - 176 * q^41 + 114 * q^42 + 111 * q^43 - 128 * q^44 - 108 * q^45 - 392 * q^46 + 550 * q^47 - 48 * q^48 + 36 * q^49 + 356 * q^50 + 372 * q^51 - 324 * q^52 + 482 * q^53 + 54 * q^54 + 192 * q^55 - 304 * q^56 - 399 * q^57 + 1200 * q^58 + 496 * q^59 + 72 * q^60 - 155 * q^61 - 450 * q^62 - 171 * q^63 + 128 * q^64 - 972 * q^65 + 192 * q^66 - 465 * q^67 - 992 * q^68 + 588 * q^69 - 228 * q^70 + 110 * q^71 + 72 * q^72 - 817 * q^73 - 586 * q^74 - 534 * q^75 - 76 * q^76 + 1216 * q^77 + 486 * q^78 - 259 * q^79 + 96 * q^80 - 81 * q^81 + 352 * q^82 - 112 * q^83 + 456 * q^84 - 744 * q^85 - 222 * q^86 - 1800 * q^87 - 512 * q^88 - 308 * q^89 - 108 * q^90 - 1539 * q^91 - 392 * q^92 + 675 * q^93 + 2200 * q^94 + 798 * q^95 - 192 * q^96 + 1150 * q^97 + 36 * q^98 - 288 * q^99

Introduction

L-functions

Modular forms

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