LMFDB - Embedded newform 99.4.e.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.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:	$5.84118909057$
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			67.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	99.67
Dual form			99.4.e.a.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(9.50000 - 16.4545i) q^{5} -20.7846i q^{6} +(13.0000 + 22.5167i) q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(9.50000 - 16.4545i) q^{5} -20.7846i q^{6} +(13.0000 + 22.5167i) q^{7} +(13.5000 + 23.3827i) q^{9} +76.0000 q^{10} +(-5.50000 - 9.52628i) q^{11} +(36.0000 - 20.7846i) q^{12} +(28.0000 - 48.4974i) q^{13} +(-52.0000 + 90.0666i) q^{14} +(-85.5000 + 49.3634i) q^{15} +(32.0000 + 55.4256i) q^{16} +104.000 q^{17} +(-54.0000 + 93.5307i) q^{18} -96.0000 q^{19} +(76.0000 + 131.636i) q^{20} -135.100i q^{21} +(22.0000 - 38.1051i) q^{22} +(-20.0000 + 34.6410i) q^{23} +(-118.000 - 204.382i) q^{25} +224.000 q^{26} -140.296i q^{27} -208.000 q^{28} +(-9.00000 - 15.5885i) q^{29} +(-342.000 - 197.454i) q^{30} +(-24.5000 + 42.4352i) q^{31} +(-128.000 + 221.703i) q^{32} +57.1577i q^{33} +(208.000 + 360.267i) q^{34} +494.000 q^{35} -216.000 q^{36} +75.0000 q^{37} +(-192.000 - 332.554i) q^{38} +(-252.000 + 145.492i) q^{39} +(-148.000 + 256.344i) q^{41} +(468.000 - 270.200i) q^{42} +(-186.000 - 322.161i) q^{43} +88.0000 q^{44} +513.000 q^{45} -160.000 q^{46} +(74.5000 + 129.038i) q^{47} -332.554i q^{48} +(-166.500 + 288.386i) q^{49} +(472.000 - 817.528i) q^{50} +(-468.000 - 270.200i) q^{51} +(224.000 + 387.979i) q^{52} -417.000 q^{53} +(486.000 - 280.592i) q^{54} -209.000 q^{55} +(432.000 + 249.415i) q^{57} +(36.0000 - 62.3538i) q^{58} +(8.50000 - 14.7224i) q^{59} -789.815i q^{60} +(-45.0000 - 77.9423i) q^{61} -196.000 q^{62} +(-351.000 + 607.950i) q^{63} -512.000 q^{64} +(-532.000 - 921.451i) q^{65} +(-198.000 + 114.315i) q^{66} +(-536.500 + 929.245i) q^{67} +(-416.000 + 720.533i) q^{68} +(180.000 - 103.923i) q^{69} +(988.000 + 1711.27i) q^{70} -285.000 q^{71} -962.000 q^{73} +(150.000 + 259.808i) q^{74} +1226.29i q^{75} +(384.000 - 665.108i) q^{76} +(143.000 - 247.683i) q^{77} +(-1008.00 - 581.969i) q^{78} +(-298.000 - 516.151i) q^{79} +1216.00 q^{80} +(-364.500 + 631.333i) q^{81} -1184.00 q^{82} +(249.000 + 431.281i) q^{83} +(936.000 + 540.400i) q^{84} +(988.000 - 1711.27i) q^{85} +(744.000 - 1288.65i) q^{86} +93.5307i q^{87} +1230.00 q^{89} +(1026.00 + 1777.08i) q^{90} +1456.00 q^{91} +(-160.000 - 277.128i) q^{92} +(220.500 - 127.306i) q^{93} +(-298.000 + 516.151i) q^{94} +(-912.000 + 1579.63i) q^{95} +(1152.00 - 665.108i) q^{96} +(165.500 + 286.654i) q^{97} -1332.00 q^{98} +(148.500 - 257.210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 9 q^{3} - 8 q^{4} + 19 q^{5} + 26 q^{7} + 27 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 9 * q^3 - 8 * q^4 + 19 * q^5 + 26 * q^7 + 27 * q^9	\( 2 q + 4 q^{2} - 9 q^{3} - 8 q^{4} + 19 q^{5} + 26 q^{7} + 27 q^{9} + 152 q^{10} - 11 q^{11} + 72 q^{12} + 56 q^{13} - 104 q^{14} - 171 q^{15} + 64 q^{16} + 208 q^{17} - 108 q^{18} - 192 q^{19} + 152 q^{20} + 44 q^{22} - 40 q^{23} - 236 q^{25} + 448 q^{26} - 416 q^{28} - 18 q^{29} - 684 q^{30} - 49 q^{31} - 256 q^{32} + 416 q^{34} + 988 q^{35} - 432 q^{36} + 150 q^{37} - 384 q^{38} - 504 q^{39} - 296 q^{41} + 936 q^{42} - 372 q^{43} + 176 q^{44} + 1026 q^{45} - 320 q^{46} + 149 q^{47} - 333 q^{49} + 944 q^{50} - 936 q^{51} + 448 q^{52} - 834 q^{53} + 972 q^{54} - 418 q^{55} + 864 q^{57} + 72 q^{58} + 17 q^{59} - 90 q^{61} - 392 q^{62} - 702 q^{63} - 1024 q^{64} - 1064 q^{65} - 396 q^{66} - 1073 q^{67} - 832 q^{68} + 360 q^{69} + 1976 q^{70} - 570 q^{71} - 1924 q^{73} + 300 q^{74} + 768 q^{76} + 286 q^{77} - 2016 q^{78} - 596 q^{79} + 2432 q^{80} - 729 q^{81} - 2368 q^{82} + 498 q^{83} + 1872 q^{84} + 1976 q^{85} + 1488 q^{86} + 2460 q^{89} + 2052 q^{90} + 2912 q^{91} - 320 q^{92} + 441 q^{93} - 596 q^{94} - 1824 q^{95} + 2304 q^{96} + 331 q^{97} - 2664 q^{98} + 297 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 8 * q^4 + 19 * q^5 + 26 * q^7 + 27 * q^9 + 152 * q^10 - 11 * q^11 + 72 * q^12 + 56 * q^13 - 104 * q^14 - 171 * q^15 + 64 * q^16 + 208 * q^17 - 108 * q^18 - 192 * q^19 + 152 * q^20 + 44 * q^22 - 40 * q^23 - 236 * q^25 + 448 * q^26 - 416 * q^28 - 18 * q^29 - 684 * q^30 - 49 * q^31 - 256 * q^32 + 416 * q^34 + 988 * q^35 - 432 * q^36 + 150 * q^37 - 384 * q^38 - 504 * q^39 - 296 * q^41 + 936 * q^42 - 372 * q^43 + 176 * q^44 + 1026 * q^45 - 320 * q^46 + 149 * q^47 - 333 * q^49 + 944 * q^50 - 936 * q^51 + 448 * q^52 - 834 * q^53 + 972 * q^54 - 418 * q^55 + 864 * q^57 + 72 * q^58 + 17 * q^59 - 90 * q^61 - 392 * q^62 - 702 * q^63 - 1024 * q^64 - 1064 * q^65 - 396 * q^66 - 1073 * q^67 - 832 * q^68 + 360 * q^69 + 1976 * q^70 - 570 * q^71 - 1924 * q^73 + 300 * q^74 + 768 * q^76 + 286 * q^77 - 2016 * q^78 - 596 * q^79 + 2432 * q^80 - 729 * q^81 - 2368 * q^82 + 498 * q^83 + 1872 * q^84 + 1976 * q^85 + 1488 * q^86 + 2460 * q^89 + 2052 * q^90 + 2912 * q^91 - 320 * q^92 + 441 * q^93 - 596 * q^94 - 1824 * q^95 + 2304 * q^96 + 331 * q^97 - 2664 * q^98 + 297 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$3$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$4$	−4.00000	+	6.92820i	−0.500000	+	0.866025i
$5$	9.50000	−	16.4545i	0.849706	−	1.47173i	−0.0317651	−	0.999495i	$-0.510113\pi$
$5$	9.50000	−	16.4545i	0.849706	−	1.47173i	0.881471	−	0.472238i	$-0.156554\pi$
$6$		−	20.7846i		−	1.41421i
$7$	13.0000	+	22.5167i	0.701934	+	1.21579i	0.967787	+	0.251772i	$0.0810132\pi$
$7$	13.0000	+	22.5167i	0.701934	+	1.21579i	−0.265853	+	0.964014i	$0.585653\pi$
$8$		0			0
$9$	13.5000	+	23.3827i	0.500000	+	0.866025i
$10$	76.0000			2.40333
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$12$	36.0000	−	20.7846i	0.866025	−	0.500000i
$13$	28.0000	−	48.4974i	0.597369	−	1.03467i	−0.395838	−	0.918320i	$-0.629546\pi$
$13$	28.0000	−	48.4974i	0.597369	−	1.03467i	0.993208	−	0.116354i	$-0.0371207\pi$
$14$	−52.0000	+	90.0666i	−0.992685	+	1.71938i
$15$	−85.5000	+	49.3634i	−1.47173	+	0.849706i
$16$	32.0000	+	55.4256i	0.500000	+	0.866025i
$17$	104.000			1.48375			0.741874	−	0.670540i	$-0.233937\pi$
$17$	104.000			1.48375			0.741874	+	0.670540i	$0.233937\pi$
$18$	−54.0000	+	93.5307i	−0.707107	+	1.22474i
$19$	−96.0000			−1.15915			−0.579577	−	0.814918i	$-0.696782\pi$
$19$	−96.0000			−1.15915			−0.579577	+	0.814918i	$0.696782\pi$
$20$	76.0000	+	131.636i	0.849706	+	1.47173i
$21$		−	135.100i		−	1.40387i
$22$	22.0000	−	38.1051i	0.213201	−	0.369274i
$23$	−20.0000	+	34.6410i	−0.181317	+	0.314050i	−0.942329	−	0.334687i	$-0.891369\pi$
$23$	−20.0000	+	34.6410i	−0.181317	+	0.314050i	0.761012	+	0.648737i	$0.224703\pi$
$24$		0			0
$25$	−118.000	−	204.382i	−0.944000	−	1.63506i
$26$	224.000			1.68962
$27$		−	140.296i		−	1.00000i
$28$	−208.000			−1.40387
$29$	−9.00000	−	15.5885i	−0.0576296	−	0.0998174i	0.835771	−	0.549078i	$-0.185021\pi$
$29$	−9.00000	−	15.5885i	−0.0576296	−	0.0998174i	−0.893401	+	0.449260i	$0.851688\pi$
$30$	−342.000	−	197.454i	−2.08135	−	1.20167i
$31$	−24.5000	+	42.4352i	−0.141946	+	0.245858i	−0.928229	−	0.372008i	$-0.878669\pi$
$31$	−24.5000	+	42.4352i	−0.141946	+	0.245858i	0.786283	+	0.617866i	$0.212003\pi$
$32$	−128.000	+	221.703i	−0.707107	+	1.22474i
$33$			57.1577i			0.301511i
$34$	208.000	+	360.267i	1.04917	+	1.81721i
$35$	494.000			2.38575
$36$	−216.000			−1.00000
$37$	75.0000			0.333241			0.166621	−	0.986021i	$-0.446714\pi$
$37$	75.0000			0.333241			0.166621	+	0.986021i	$0.446714\pi$
$38$	−192.000	−	332.554i	−0.819645	−	1.41967i
$39$	−252.000	+	145.492i	−1.03467	+	0.597369i
$40$		0			0
$41$	−148.000	+	256.344i	−0.563749	+	0.976442i	0.433416	+	0.901194i	$0.357308\pi$
$41$	−148.000	+	256.344i	−0.563749	+	0.976442i	−0.997165	+	0.0752481i	$0.976025\pi$
$42$	468.000	−	270.200i	1.71938	−	0.992685i
$43$	−186.000	−	322.161i	−0.659645	−	1.14254i	−0.980708	−	0.195481i	$-0.937373\pi$
$43$	−186.000	−	322.161i	−0.659645	−	1.14254i	0.321063	−	0.947058i	$-0.395960\pi$
$44$	88.0000			0.301511
$45$	513.000			1.69941
$46$	−160.000			−0.512842
$47$	74.5000	+	129.038i	0.231212	+	0.400470i	0.958165	−	0.286217i	$-0.0923977\pi$
$47$	74.5000	+	129.038i	0.231212	+	0.400470i	−0.726953	+	0.686687i	$0.759064\pi$
$48$		−	332.554i		−	1.00000i
$49$	−166.500	+	288.386i	−0.485423	+	0.840777i
$50$	472.000	−	817.528i	1.33502	−	2.31232i
$51$	−468.000	−	270.200i	−1.28496	−	0.741874i
$52$	224.000	+	387.979i	0.597369	+	1.03467i
$53$	−417.000			−1.08074			−0.540371	−	0.841427i	$-0.681716\pi$
$53$	−417.000			−1.08074			−0.540371	+	0.841427i	$0.681716\pi$
$54$	486.000	−	280.592i	1.22474	−	0.707107i
$55$	−209.000			−0.512392
$56$		0			0
$57$	432.000	+	249.415i	1.00386	+	0.579577i
$58$	36.0000	−	62.3538i	0.0815005	−	0.141163i
$59$	8.50000	−	14.7224i	0.0187560	−	0.0324864i	−0.856495	−	0.516155i	$-0.827363\pi$
$59$	8.50000	−	14.7224i	0.0187560	−	0.0324864i	0.875251	+	0.483669i	$0.160696\pi$
$60$		−	789.815i		−	1.69941i
$61$	−45.0000	−	77.9423i	−0.0944534	−	0.163598i	0.814927	−	0.579564i	$-0.196777\pi$
$61$	−45.0000	−	77.9423i	−0.0944534	−	0.163598i	−0.909380	+	0.415966i	$0.863444\pi$
$62$	−196.000			−0.401484
$63$	−351.000	+	607.950i	−0.701934	+	1.21579i
$64$	−512.000			−1.00000
$65$	−532.000	−	921.451i	−1.01518	−	1.75834i
$66$	−198.000	+	114.315i	−0.369274	+	0.213201i
$67$	−536.500	+	929.245i	−0.978267	+	1.69441i	−0.309565	+	0.950878i	$0.600183\pi$
$67$	−536.500	+	929.245i	−0.978267	+	1.69441i	−0.668702	+	0.743530i	$0.733150\pi$
$68$	−416.000	+	720.533i	−0.741874	+	1.28496i
$69$	180.000	−	103.923i	0.314050	−	0.181317i
$70$	988.000	+	1711.27i	1.68698	+	2.92193i
$71$	−285.000			−0.476384			−0.238192	−	0.971218i	$-0.576555\pi$
$71$	−285.000			−0.476384			−0.238192	+	0.971218i	$0.576555\pi$
$72$		0			0
$73$	−962.000			−1.54238			−0.771189	−	0.636606i	$-0.780338\pi$
$73$	−962.000			−1.54238			−0.771189	+	0.636606i	$0.780338\pi$
$74$	150.000	+	259.808i	0.235637	+	0.408135i
$75$			1226.29i			1.88800i
$76$	384.000	−	665.108i	0.579577	−	1.00386i
$77$	143.000	−	247.683i	0.211641	−	0.366573i
$78$	−1008.00	−	581.969i	−1.46325	−	0.844808i
$79$	−298.000	−	516.151i	−0.424400	−	0.735083i	0.571964	−	0.820279i	$-0.306182\pi$
$79$	−298.000	−	516.151i	−0.424400	−	0.735083i	−0.996364	+	0.0851960i	$0.972848\pi$
$80$	1216.00			1.69941
$81$	−364.500	+	631.333i	−0.500000	+	0.866025i
$82$	−1184.00			−1.59452
$83$	249.000	+	431.281i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	249.000	+	431.281i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$	936.000	+	540.400i	1.21579	+	0.701934i
$85$	988.000	−	1711.27i	1.26075	−	2.18368i
$86$	744.000	−	1288.65i	0.932879	−	1.61579i
$87$			93.5307i			0.115259i
$88$		0			0
$89$	1230.00			1.46494			0.732470	−	0.680799i	$-0.238367\pi$
$89$	1230.00			1.46494			0.732470	+	0.680799i	$0.238367\pi$
$90$	1026.00	+	1777.08i	1.20167	+	2.08135i
$91$	1456.00			1.67726
$92$	−160.000	−	277.128i	−0.181317	−	0.314050i
$93$	220.500	−	127.306i	0.245858	−	0.141946i
$94$	−298.000	+	516.151i	−0.326982	+	0.566350i
$95$	−912.000	+	1579.63i	−0.984939	+	1.70596i
$96$	1152.00	−	665.108i	1.22474	−	0.707107i
$97$	165.500	+	286.654i	0.173237	+	0.300055i	0.939550	−	0.342413i	$-0.111244\pi$
$97$	165.500	+	286.654i	0.173237	+	0.300055i	−0.766313	+	0.642468i	$0.777911\pi$
$98$	−1332.00			−1.37298
$99$	148.500	−	257.210i	0.150756	−	0.261116i
$100$	1888.00			1.88800
$101$	−29.0000	−	50.2295i	−0.0285704	−	0.0494853i	0.851387	−	0.524539i	$-0.175762\pi$
$101$	−29.0000	−	50.2295i	−0.0285704	−	0.0494853i	−0.879957	+	0.475053i	$0.842429\pi$
$102$		−	2161.60i		−	2.09834i
$103$	123.500	−	213.908i	0.118144	−	0.204631i	−0.800888	−	0.598814i	$-0.795639\pi$
$103$	123.500	−	213.908i	0.118144	−	0.204631i	0.919032	+	0.394183i	$0.128972\pi$
$104$		0			0
$105$	−2223.00	−	1283.45i	−2.06612	−	1.19287i
$106$	−834.000	−	1444.53i	−0.764200	−	1.32363i
$107$	1158.00			1.04624			0.523122	−	0.852258i	$-0.324767\pi$
$107$	1158.00			1.04624			0.523122	+	0.852258i	$0.324767\pi$
$108$	972.000	+	561.184i	0.866025	+	0.500000i
$109$	−44.0000			−0.0386645			−0.0193323	−	0.999813i	$-0.506154\pi$
$109$	−44.0000			−0.0386645			−0.0193323	+	0.999813i	$0.506154\pi$
$110$	−418.000	−	723.997i	−0.362316	−	0.627549i
$111$	−337.500	−	194.856i	−0.288595	−	0.166621i
$112$	−832.000	+	1441.07i	−0.701934	+	1.21579i
$113$	−478.500	+	828.786i	−0.398350	+	0.689962i	−0.993522	−	0.113636i	$-0.963750\pi$
$113$	−478.500	+	828.786i	−0.398350	+	0.689962i	0.595173	+	0.803598i	$0.297084\pi$
$114$			1995.32i			1.63929i
$115$	380.000	+	658.179i	0.308132	+	0.533700i
$116$	144.000			0.115259
$117$	1512.00			1.19474
$118$	68.0000			0.0530501
$119$	1352.00	+	2341.73i	1.04149	+	1.80392i
$120$		0			0
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$	180.000	−	311.769i	0.133577	−	0.231363i
$123$	1332.00	−	769.031i	0.976442	−	0.563749i
$124$	−196.000	−	339.482i	−0.141946	−	0.245858i
$125$	−2109.00			−1.50908
$126$	−2808.00			−1.98537
$127$	434.000			0.303238			0.151619	−	0.988439i	$-0.451551\pi$
$127$	434.000			0.303238			0.151619	+	0.988439i	$0.451551\pi$
$128$		0			0
$129$			1932.97i			1.31929i
$130$	2128.00	−	3685.80i	1.43568	−	2.48666i
$131$	−90.0000	+	155.885i	−0.0600255	+	0.103967i	−0.894477	−	0.447115i	$-0.852452\pi$
$131$	−90.0000	+	155.885i	−0.0600255	+	0.103967i	0.834451	+	0.551082i	$0.185785\pi$
$132$	−396.000	−	228.631i	−0.261116	−	0.150756i
$133$	−1248.00	−	2161.60i	−0.813649	−	1.40928i
$134$	−4292.00			−2.76696
$135$	−2308.50	−	1332.81i	−1.47173	−	0.849706i
$136$		0			0
$137$	−258.500	−	447.735i	−0.161205	−	0.279216i	0.774096	−	0.633068i	$-0.218205\pi$
$137$	−258.500	−	447.735i	−0.161205	−	0.279216i	−0.935301	+	0.353852i	$0.884872\pi$
$138$	720.000	+	415.692i	0.444134	+	0.256421i
$139$	931.000	−	1612.54i	0.568104	−	0.983984i	−0.428650	−	0.903471i	$-0.641011\pi$
$139$	931.000	−	1612.54i	0.568104	−	0.983984i	0.996754	−	0.0805135i	$-0.0256560\pi$
$140$	−1976.00	+	3422.53i	−1.19287	+	2.06612i
$141$		−	774.227i		−	0.462423i
$142$	−570.000	−	987.269i	−0.336854	−	0.583449i
$143$	−616.000			−0.360227
$144$	−864.000	+	1496.49i	−0.500000	+	0.866025i
$145$	−342.000			−0.195873
$146$	−1924.00	−	3332.47i	−1.09063	−	1.88902i
$147$	1498.50	−	865.159i	0.840777	−	0.485423i
$148$	−300.000	+	519.615i	−0.166621	+	0.288595i
$149$	796.000	−	1378.71i	0.437657	−	0.758044i	−0.559852	−	0.828593i	$-0.689142\pi$
$149$	796.000	−	1378.71i	0.437657	−	0.758044i	0.997508	+	0.0705492i	$0.0224752\pi$
$150$	−4248.00	+	2452.58i	−2.31232	+	1.33502i
$151$	458.000	+	793.279i	0.246831	+	0.427524i	0.962645	−	0.270767i	$-0.0872773\pi$
$151$	458.000	+	793.279i	0.246831	+	0.427524i	−0.715814	+	0.698291i	$0.753944\pi$
$152$		0			0
$153$	1404.00	+	2431.80i	0.741874	+	1.28496i
$154$	1144.00			0.598611
$155$	465.500	+	806.270i	0.241225	+	0.417814i
$156$		−	2327.88i		−	1.19474i
$157$	1281.50	−	2219.62i	0.651432	−	1.12831i	−0.331343	−	0.943510i	$-0.607502\pi$
$157$	1281.50	−	2219.62i	0.651432	−	1.12831i	0.982776	−	0.184803i	$-0.0591648\pi$
$158$	1192.00	−	2064.60i	0.600193	−	1.03956i
$159$	1876.50	+	1083.40i	0.935951	+	0.540371i
$160$	2432.00	+	4212.35i	1.20167	+	2.08135i
$161$	−1040.00			−0.509090
$162$	−2916.00			−1.41421
$163$	−1841.00			−0.884652			−0.442326	−	0.896854i	$-0.645847\pi$
$163$	−1841.00			−0.884652			−0.442326	+	0.896854i	$0.645847\pi$
$164$	−1184.00	−	2050.75i	−0.563749	−	0.976442i
$165$	940.500	+	542.998i	0.443744	+	0.256196i
$166$	−996.000	+	1725.12i	−0.465690	+	0.806599i
$167$	−342.000	+	592.361i	−0.158472	+	0.274481i	−0.934318	−	0.356441i	$-0.883990\pi$
$167$	−342.000	+	592.361i	−0.158472	+	0.274481i	0.775846	+	0.630922i	$0.217323\pi$
$168$		0			0
$169$	−469.500	−	813.198i	−0.213701	−	0.370140i
$170$	7904.00			3.56594
$171$	−1296.00	−	2244.74i	−0.579577	−	1.00386i
$172$	2976.00			1.31929
$173$	−888.000	−	1538.06i	−0.390251	−	0.675934i	0.602232	−	0.798321i	$-0.294278\pi$
$173$	−888.000	−	1538.06i	−0.390251	−	0.675934i	−0.992482	+	0.122387i	$0.960945\pi$
$174$	−324.000	+	187.061i	−0.141163	+	0.0815005i
$175$	3068.00	−	5313.93i	1.32525	−	2.29540i
$176$	352.000	−	609.682i	0.150756	−	0.261116i
$177$	−76.5000	+	44.1673i	−0.0324864	+	0.0187560i
$178$	2460.00	+	4260.84i	1.03587	+	1.79418i
$179$	1857.00			0.775412			0.387706	−	0.921783i	$-0.373268\pi$
$179$	1857.00			0.775412			0.387706	+	0.921783i	$0.373268\pi$
$180$	−2052.00	+	3554.17i	−0.849706	+	1.47173i
$181$	−4577.00			−1.87959			−0.939795	−	0.341739i	$-0.888984\pi$
$181$	−4577.00			−1.87959			−0.939795	+	0.341739i	$0.888984\pi$
$182$	2912.00	+	5043.73i	1.18600	+	2.05421i
$183$			467.654i			0.188907i
$184$		0			0
$185$	712.500	−	1234.09i	0.283157	−	0.490442i
$186$	882.000	+	509.223i	0.347696	+	0.200742i
$187$	−572.000	−	990.733i	−0.223683	−	0.387431i
$188$	−1192.00			−0.462423
$189$	3159.00	−	1823.85i	1.21579	−	0.701934i
$190$	−7296.00			−2.78583
$191$	461.500	+	799.341i	0.174832	+	0.302818i	0.940103	−	0.340890i	$-0.110728\pi$
$191$	461.500	+	799.341i	0.174832	+	0.302818i	−0.765271	+	0.643708i	$0.777395\pi$
$192$	2304.00	+	1330.22i	0.866025	+	0.500000i
$193$	−242.000	+	419.156i	−0.0902567	+	0.156329i	−0.907619	−	0.419795i	$-0.862102\pi$
$193$	−242.000	+	419.156i	−0.0902567	+	0.156329i	0.817362	+	0.576124i	$0.195435\pi$
$194$	−662.000	+	1146.62i	−0.244994	+	0.424342i
$195$			5528.71i			2.03035i
$196$	−1332.00	−	2307.09i	−0.485423	−	0.840777i
$197$	−3562.00			−1.28823			−0.644117	−	0.764927i	$-0.722775\pi$
$197$	−3562.00			−1.28823			−0.644117	+	0.764927i	$0.722775\pi$
$198$	1188.00			0.426401
$199$	−2805.00			−0.999202			−0.499601	−	0.866256i	$-0.666520\pi$
$199$	−2805.00			−0.999202			−0.499601	+	0.866256i	$0.666520\pi$
$200$		0			0
$201$	4828.50	−	2787.74i	1.69441	−	0.978267i
$202$	116.000	−	200.918i	0.0404046	−	0.0699828i
$203$	234.000	−	405.300i	0.0809043	−	0.140130i
$204$	3744.00	−	2161.60i	1.28496	−	0.741874i
$205$	2812.00	+	4870.53i	0.958042	+	1.65938i
$206$	988.000			0.334161
$207$	−1080.00			−0.362634
$208$	3584.00			1.19474
$209$	528.000	+	914.523i	0.174749	+	0.302674i
$210$		−	10267.6i		−	3.37396i
$211$	−795.000	+	1376.98i	−0.259384	+	0.449267i	−0.966077	−	0.258254i	$-0.916853\pi$
$211$	−795.000	+	1376.98i	−0.259384	+	0.449267i	0.706693	+	0.707520i	$0.250186\pi$
$212$	1668.00	−	2889.06i	0.540371	−	0.935951i
$213$	1282.50	+	740.452i	0.412561	+	0.238192i
$214$	2316.00	+	4011.43i	0.739806	+	1.28138i
$215$	−7068.00			−2.24202
$216$		0			0
$217$	−1274.00			−0.398547
$218$	−88.0000	−	152.420i	−0.0273400	−	0.0473542i
$219$	4329.00	+	2499.35i	1.33574	+	0.771189i
$220$	836.000	−	1447.99i	0.256196	−	0.443744i
$221$	2912.00	−	5043.73i	0.886345	−	1.53520i
$222$		−	1558.85i		−	0.471274i
$223$	−92.0000	−	159.349i	−0.0276268	−	0.0478510i	0.851881	−	0.523735i	$-0.175462\pi$
$223$	−92.0000	−	159.349i	−0.0276268	−	0.0478510i	−0.879508	+	0.475884i	$0.842128\pi$
$224$	−6656.00			−1.98537
$225$	3186.00	−	5518.31i	0.944000	−	1.63506i
$226$	−3828.00			−1.12670
$227$	1182.00	+	2047.28i	0.345604	+	0.598604i	0.985463	−	0.169888i	$-0.0543407\pi$
$227$	1182.00	+	2047.28i	0.345604	+	0.598604i	−0.639859	+	0.768492i	$0.721007\pi$
$228$	−3456.00	+	1995.32i	−1.00386	+	0.579577i
$229$	−285.000	+	493.634i	−0.0822416	+	0.142447i	−0.904212	−	0.427083i	$-0.859541\pi$
$229$	−285.000	+	493.634i	−0.0822416	+	0.142447i	0.821971	+	0.569530i	$0.192875\pi$
$230$	−1520.00	+	2632.72i	−0.435764	+	0.754766i
$231$	−1287.00	+	743.050i	−0.366573	+	0.211641i
$232$		0			0
$233$	4662.00			1.31081			0.655403	−	0.755279i	$-0.272499\pi$
$233$	4662.00			1.31081			0.655403	+	0.755279i	$0.272499\pi$
$234$	3024.00	+	5237.72i	0.844808	+	1.46325i
$235$	2831.00			0.785847
$236$	68.0000	+	117.779i	0.0187560	+	0.0324864i
$237$			3096.91i			0.848800i
$238$	−5408.00	+	9366.93i	−1.47289	+	2.55113i
$239$	2247.00	−	3891.92i	0.608144	−	1.05334i	−0.383402	−	0.923581i	$-0.625248\pi$
$239$	2247.00	−	3891.92i	0.608144	−	1.05334i	0.991546	−	0.129754i	$-0.0414189\pi$
$240$	−5472.00	−	3159.26i	−1.47173	−	0.849706i
$241$	2440.00	+	4226.20i	0.652175	+	1.12960i	0.982594	+	0.185766i	$0.0594767\pi$
$241$	2440.00	+	4226.20i	0.652175	+	1.12960i	−0.330419	+	0.943834i	$0.607190\pi$
$242$	−484.000			−0.128565
$243$	3280.50	−	1894.00i	0.866025	−	0.500000i
$244$	720.000			0.188907
$245$	3163.50	+	5479.34i	0.824933	+	1.42883i
$246$	5328.00	+	3076.12i	1.38090	+	0.797262i
$247$	−2688.00	+	4655.75i	−0.692443	+	1.19935i
$248$		0			0
$249$		−	2587.68i		−	0.658586i
$250$	−4218.00	−	7305.79i	−1.06708	−	1.84823i
$251$	−4396.00			−1.10547			−0.552735	−	0.833357i	$-0.686416\pi$
$251$	−4396.00			−1.10547			−0.552735	+	0.833357i	$0.686416\pi$
$252$	−2808.00	−	4863.60i	−0.701934	−	1.21579i
$253$	440.000			0.109338
$254$	868.000	+	1503.42i	0.214422	+	0.371390i
$255$	−8892.00	+	5133.80i	−2.18368	+	1.26075i
$256$	−2048.00	+	3547.24i	−0.500000	+	0.866025i
$257$	−1897.00	+	3285.70i	−0.460434	+	0.797496i	−0.998983	−	0.0450991i	$-0.985640\pi$
$257$	−1897.00	+	3285.70i	−0.460434	+	0.797496i	0.538548	+	0.842595i	$0.318973\pi$
$258$	−6696.00	+	3865.94i	−1.61579	+	0.932879i
$259$	975.000	+	1688.75i	0.233913	+	0.405150i
$260$	8512.00			2.03035
$261$	243.000	−	420.888i	0.0576296	−	0.0998174i
$262$	−720.000			−0.169778
$263$	−3908.00	−	6768.85i	−0.916265	−	1.58702i	−0.805039	−	0.593222i	$-0.797856\pi$
$263$	−3908.00	−	6768.85i	−0.916265	−	1.58702i	−0.111226	−	0.993795i	$-0.535478\pi$
$264$		0			0
$265$	−3961.50	+	6861.52i	−0.918313	+	1.59057i
$266$	4992.00	−	8646.40i	1.15067	−	1.99303i
$267$	−5535.00	−	3195.63i	−1.26868	−	0.732470i
$268$	−4292.00	−	7433.96i	−0.978267	−	1.69441i
$269$	4775.00			1.08229			0.541147	−	0.840928i	$-0.317990\pi$
$269$	4775.00			1.08229			0.541147	+	0.840928i	$0.317990\pi$
$270$		−	10662.5i		−	2.40333i
$271$	3764.00			0.843715			0.421857	−	0.906662i	$-0.361378\pi$
$271$	3764.00			0.843715			0.421857	+	0.906662i	$0.361378\pi$
$272$	3328.00	+	5764.27i	0.741874	+	1.28496i
$273$	−6552.00	−	3782.80i	−1.45255	−	0.838628i
$274$	1034.00	−	1790.94i	0.227979	−	0.394871i
$275$	−1298.00	+	2248.20i	−0.284627	+	0.492988i
$276$			1662.77i			0.362634i
$277$	−1784.00	−	3089.98i	−0.386968	−	0.670248i	0.605072	−	0.796171i	$-0.293144\pi$
$277$	−1784.00	−	3089.98i	−0.386968	−	0.670248i	−0.992040	+	0.125922i	$0.959811\pi$
$278$	7448.00			1.60684
$279$	−1323.00			−0.283892
$280$		0			0
$281$	−12.0000	−	20.7846i	−0.00254754	−	0.00441248i	0.864749	−	0.502205i	$-0.167478\pi$
$281$	−12.0000	−	20.7846i	−0.00254754	−	0.00441248i	−0.867296	+	0.497792i	$0.834144\pi$
$282$	2682.00	−	1548.45i	0.566350	−	0.326982i
$283$	427.000	−	739.586i	0.0896909	−	0.155349i	−0.817690	−	0.575659i	$-0.804745\pi$
$283$	427.000	−	739.586i	0.0896909	−	0.155349i	0.907380	+	0.420310i	$0.138079\pi$
$284$	1140.00	−	1974.54i	0.238192	−	0.412561i
$285$	8208.00	−	4738.89i	1.70596	−	0.984939i
$286$	−1232.00	−	2133.89i	−0.254719	−	0.441187i
$287$	−7696.00			−1.58286
$288$	−6912.00			−1.41421
$289$	5903.00			1.20151
$290$	−684.000	−	1184.72i	−0.138503	−	0.239894i
$291$		−	1719.93i		−	0.346474i
$292$	3848.00	−	6664.93i	0.771189	−	1.33574i
$293$	−2061.00	+	3569.76i	−0.410938	+	0.711766i	−0.994993	−	0.0999486i	$-0.968132\pi$
$293$	−2061.00	+	3569.76i	−0.410938	+	0.711766i	0.584054	+	0.811715i	$0.301465\pi$
$294$	5994.00	+	3460.64i	1.18904	+	0.686491i
$295$	−161.500	−	279.726i	−0.0318742	−	0.0552078i
$296$		0			0
$297$	−1336.50	+	771.629i	−0.261116	+	0.150756i
$298$	6368.00			1.23788
$299$	1120.00	+	1939.90i	0.216626	+	0.375208i
$300$	−8496.00	−	4905.17i	−1.63506	−	0.944000i
$301$	4836.00	−	8376.20i	0.926055	−	1.60397i
$302$	−1832.00	+	3173.12i	−0.349072	+	0.604610i
$303$			301.377i			0.0571407i
$304$	−3072.00	−	5320.86i	−0.579577	−	1.00386i
$305$	−1710.00			−0.321031
$306$	−5616.00	+	9727.20i	−1.04917	+	1.81721i
$307$	2072.00			0.385196			0.192598	−	0.981278i	$-0.438309\pi$
$307$	2072.00			0.385196			0.192598	+	0.981278i	$0.438309\pi$
$308$	1144.00	+	1981.47i	0.211641	+	0.366573i
$309$	−1111.50	+	641.725i	−0.204631	+	0.118144i
$310$	−1862.00	+	3225.08i	−0.341144	+	0.590878i
$311$	4627.50	−	8015.07i	0.843735	−	1.46139i	−0.0429811	−	0.999076i	$-0.513686\pi$
$311$	4627.50	−	8015.07i	0.843735	−	1.46139i	0.886716	−	0.462315i	$-0.152981\pi$
$312$		0			0
$313$	−2491.00	−	4314.54i	−0.449839	−	0.779144i	0.548536	−	0.836127i	$-0.315185\pi$
$313$	−2491.00	−	4314.54i	−0.449839	−	0.779144i	−0.998375	+	0.0569827i	$0.981852\pi$
$314$	10252.0			1.84253
$315$	6669.00	+	11551.0i	1.19287	+	2.06612i
$316$	4768.00			0.848800
$317$	−2479.00	−	4293.75i	−0.439226	−	0.760761i	0.558404	−	0.829569i	$-0.311414\pi$
$317$	−2479.00	−	4293.75i	−0.439226	−	0.760761i	−0.997630	+	0.0688079i	$0.978080\pi$
$318$			8667.18i			1.52840i
$319$	−99.0000	+	171.473i	−0.0173760	+	0.0300961i
$320$	−4864.00	+	8424.70i	−0.849706	+	1.47173i
$321$	−5211.00	−	3008.57i	−0.906074	−	0.523122i
$322$	−2080.00	−	3602.67i	−0.359981	−	0.623505i
$323$	−9984.00			−1.71989
$324$	−2916.00	−	5050.66i	−0.500000	−	0.866025i
$325$	−13216.0			−2.25567
$326$	−3682.00	−	6377.41i	−0.625543	−	1.08347i
$327$	198.000	+	114.315i	0.0334845	+	0.0193323i
$328$		0			0
$329$	−1937.00	+	3354.98i	−0.324590	+	0.562207i
$330$			4343.98i			0.724632i
$331$	3410.50	+	5907.16i	0.566338	+	0.980927i	0.996924	+	0.0783771i	$0.0249738\pi$
$331$	3410.50	+	5907.16i	0.566338	+	0.980927i	−0.430585	+	0.902550i	$0.641693\pi$
$332$	−3984.00			−0.658586
$333$	1012.50	+	1753.70i	0.166621	+	0.288595i
$334$	−2736.00			−0.448225
$335$	10193.5	+	17655.7i	1.66248	+	2.87950i
$336$	7488.00	−	4323.20i	1.21579	−	0.701934i
$337$	2627.00	−	4550.10i	0.424634	−	0.735488i	−0.571752	−	0.820427i	$-0.693736\pi$
$337$	2627.00	−	4550.10i	0.424634	−	0.735488i	0.996386	+	0.0849382i	$0.0270693\pi$
$338$	1878.00	−	3252.79i	0.302218	−	0.523457i
$339$	4306.50	−	2486.36i	0.689962	−	0.398350i
$340$	7904.00	+	13690.1i	1.26075	+	2.18368i
$341$	539.000			0.0855967
$342$	5184.00	−	8978.95i	0.819645	−	1.41967i
$343$	260.000			0.0409291
$344$		0			0
$345$		−	3949.08i		−	0.616264i
$346$	3552.00	−	6152.24i	0.551898	−	0.955915i
$347$	−3595.00	+	6226.72i	−0.556166	+	0.963308i	0.441645	+	0.897190i	$0.354395\pi$
$347$	−3595.00	+	6226.72i	−0.556166	+	0.963308i	−0.997812	+	0.0661187i	$0.978938\pi$
$348$	−648.000	−	374.123i	−0.0998174	−	0.0576296i
$349$	−4080.00	−	7066.77i	−0.625780	−	1.08388i	−0.988389	−	0.151942i	$-0.951447\pi$
$349$	−4080.00	−	7066.77i	−0.625780	−	1.08388i	0.362609	−	0.931941i	$-0.381886\pi$
$350$	24544.0			3.74838
$351$	−6804.00	−	3928.29i	−1.03467	−	0.597369i
$352$	2816.00			0.426401
$353$	2481.00	+	4297.22i	0.374080	+	0.647926i	0.990189	−	0.139735i	$-0.0446251\pi$
$353$	2481.00	+	4297.22i	0.374080	+	0.647926i	−0.616109	+	0.787661i	$0.711292\pi$
$354$	−306.000	−	176.669i	−0.0459427	−	0.0265250i
$355$	−2707.50	+	4689.53i	−0.404786	+	0.701111i
$356$	−4920.00	+	8521.69i	−0.732470	+	1.26868i
$357$		−	14050.4i		−	2.08299i
$358$	3714.00	+	6432.84i	0.548299	+	0.949682i
$359$	3554.00			0.522487			0.261244	−	0.965273i	$-0.415867\pi$
$359$	3554.00			0.522487			0.261244	+	0.965273i	$0.415867\pi$
$360$		0			0
$361$	2357.00			0.343636
$362$	−9154.00	−	15855.2i	−1.32907	−	2.30202i
$363$	544.500	−	314.367i	0.0787296	−	0.0454545i
$364$	−5824.00	+	10087.5i	−0.838628	+	1.45255i
$365$	−9139.00	+	15829.2i	−1.31057	+	2.26997i
$366$	−1620.00	+	935.307i	−0.231363	+	0.133577i
$367$	2732.50	+	4732.83i	0.388652	+	0.673165i	0.992269	−	0.124110i	$-0.0396075\pi$
$367$	2732.50	+	4732.83i	0.388652	+	0.673165i	−0.603616	+	0.797275i	$0.706274\pi$
$368$	−2560.00			−0.362634
$369$	−7992.00			−1.12750
$370$	5700.00			0.800889
$371$	−5421.00	−	9389.45i	−0.758610	−	1.31395i
$372$			2036.89i			0.283892i
$373$	−4958.00	+	8587.51i	−0.688245	+	1.19208i	0.284160	+	0.958777i	$0.408285\pi$
$373$	−4958.00	+	8587.51i	−0.688245	+	1.19208i	−0.972405	+	0.233299i	$0.925048\pi$
$374$	2288.00	−	3962.93i	0.316336	−	0.547910i
$375$	9490.50	+	5479.34i	1.30690	+	0.754539i
$376$		0			0
$377$	−1008.00			−0.137705
$378$	12636.0	+	7295.40i	1.71938	+	0.992685i
$379$	−5708.00			−0.773615			−0.386808	−	0.922160i	$-0.626422\pi$
$379$	−5708.00			−0.773615			−0.386808	+	0.922160i	$0.626422\pi$
$380$	−7296.00	−	12637.0i	−0.984939	−	1.70596i
$381$	−1953.00	−	1127.57i	−0.262612	−	0.151619i
$382$	−1846.00	+	3197.37i	−0.247250	+	0.428250i
$383$	1748.50	−	3028.49i	0.233275	−	0.404043i	−0.725495	−	0.688227i	$-0.758389\pi$
$383$	1748.50	−	3028.49i	0.233275	−	0.404043i	0.958770	+	0.284184i	$0.0917226\pi$
$384$		0			0
$385$	−2717.00	−	4705.98i	−0.359665	−	0.622959i
$386$	−1936.00			−0.255284
$387$	5022.00	−	8698.36i	0.659645	−	1.14254i
$388$	−2648.00			−0.346474
$389$	3901.50	+	6757.60i	0.508519	+	0.880781i	0.999951	+	0.00986502i	$0.00314018\pi$
$389$	3901.50	+	6757.60i	0.508519	+	0.880781i	−0.491432	+	0.870916i	$0.663526\pi$
$390$	−19152.0	+	11057.4i	−2.48666	+	1.43568i
$391$	−2080.00	+	3602.67i	−0.269028	+	0.465971i
$392$		0			0
$393$	810.000	−	467.654i	0.103967	−	0.0600255i
$394$	−7124.00	−	12339.1i	−0.910919	−	1.57776i
$395$	−11324.0			−1.44246
$396$	1188.00	+	2057.68i	0.150756	+	0.261116i
$397$	12913.0			1.63246			0.816228	−	0.577730i	$-0.196061\pi$
$397$	12913.0			1.63246			0.816228	+	0.577730i	$0.196061\pi$
$398$	−5610.00	−	9716.81i	−0.706542	−	1.22377i
$399$			12969.6i			1.62730i
$400$	7552.00	−	13080.4i	0.944000	−	1.63506i
$401$	5525.50	−	9570.45i	0.688105	−	1.19183i	−0.284345	−	0.958722i	$-0.591776\pi$
$401$	5525.50	−	9570.45i	0.688105	−	1.19183i	0.972450	−	0.233112i	$-0.0748907\pi$
$402$	19314.0	+	11150.9i	2.39626	+	1.38348i
$403$	1372.00	+	2376.37i	0.169589	+	0.293736i
$404$	464.000			0.0571407
$405$	6925.50	+	11995.3i	0.849706	+	1.47173i
$406$	1872.00			0.228832
$407$	−412.500	−	714.471i	−0.0502380	−	0.0870148i
$408$		0			0
$409$	−90.0000	+	155.885i	−0.0108807	+	0.0188460i	−0.871414	−	0.490547i	$-0.836797\pi$
$409$	−90.0000	+	155.885i	−0.0108807	+	0.0188460i	0.860534	+	0.509393i	$0.170130\pi$
$410$	−11248.0	+	19482.1i	−1.35488	+	2.34671i
$411$			2686.41i			0.322411i
$412$	988.000	+	1711.27i	0.118144	+	0.204631i
$413$	442.000			0.0526620
$414$	−2160.00	−	3741.23i	−0.256421	−	0.444134i
$415$	9462.00			1.11921
$416$	7168.00	+	12415.3i	0.844808	+	1.46325i
$417$	−8379.00	+	4837.62i	−0.983984	+	0.568104i
$418$	−2112.00	+	3658.09i	−0.247132	+	0.428046i
$419$	5462.50	−	9461.33i	0.636899	−	1.10314i	−0.349211	−	0.937044i	$-0.613550\pi$
$419$	5462.50	−	9461.33i	0.636899	−	1.10314i	0.986109	−	0.166097i	$-0.0531164\pi$
$420$	17784.0	−	10267.6i	2.06612	−	1.19287i
$421$	7853.50	+	13602.7i	0.909160	+	1.57471i	0.815234	+	0.579131i	$0.196608\pi$
$421$	7853.50	+	13602.7i	0.909160	+	1.57471i	0.0939252	+	0.995579i	$0.470059\pi$
$422$	−6360.00			−0.733649
$423$	−2011.50	+	3484.02i	−0.231212	+	0.400470i
$424$		0			0
$425$	−12272.0	−	21255.7i	−1.40066	−	2.42601i
$426$			5923.61i			0.673709i
$427$	1170.00	−	2026.50i	0.132600	−	0.229670i
$428$	−4632.00	+	8022.86i	−0.523122	+	0.906074i
$429$	2772.00	+	1600.41i	0.311966	+	0.180114i
$430$	−14136.0	−	24484.3i	−1.58535	−	2.74590i
$431$	11346.0			1.26802			0.634011	−	0.773324i	$-0.281407\pi$
$431$	11346.0			1.26802			0.634011	+	0.773324i	$0.281407\pi$
$432$	7776.00	−	4489.48i	0.866025	−	0.500000i
$433$	−8582.00			−0.952482			−0.476241	−	0.879315i	$-0.658001\pi$
$433$	−8582.00			−0.952482			−0.476241	+	0.879315i	$0.658001\pi$
$434$	−2548.00	−	4413.27i	−0.281815	−	0.488119i
$435$	1539.00	+	888.542i	0.169631	+	0.0979364i
$436$	176.000	−	304.841i	0.0193323	−	0.0334845i
$437$	1920.00	−	3325.54i	0.210174	−	0.364032i
$438$			19994.8i			2.18125i
$439$	−7445.00	−	12895.1i	−0.809409	−	1.40194i	−0.913274	−	0.407346i	$-0.866454\pi$
$439$	−7445.00	−	12895.1i	−0.809409	−	1.40194i	0.103865	−	0.994591i	$-0.466879\pi$
$440$		0			0
$441$	−8991.00			−0.970845
$442$	23296.0			2.50696
$443$	−2933.50	−	5080.97i	−0.314616	−	0.544931i	0.664740	−	0.747075i	$-0.268542\pi$
$443$	−2933.50	−	5080.97i	−0.314616	−	0.544931i	−0.979356	+	0.202144i	$0.935209\pi$
$444$	2700.00	−	1558.85i	0.288595	−	0.166621i
$445$	11685.0	−	20239.0i	1.24477	−	2.15600i
$446$	368.000	−	637.395i	0.0390702	−	0.0676716i
$447$	−7164.00	+	4136.14i	−0.758044	+	0.437657i
$448$	−6656.00	−	11528.5i	−0.701934	−	1.21579i
$449$	16147.0			1.69716			0.848579	−	0.529069i	$-0.177459\pi$
$449$	16147.0			1.69716			0.848579	+	0.529069i	$0.177459\pi$
$450$	25488.0			2.67004
$451$	3256.00			0.339954
$452$	−3828.00	−	6630.29i	−0.398350	−	0.689962i
$453$		−	4759.68i		−	0.493662i
$454$	−4728.00	+	8189.14i	−0.488758	+	0.846553i
$455$	13832.0	−	23957.7i	1.42517	−	2.46847i
$456$		0			0
$457$	−927.000	−	1605.61i	−0.0948867	−	0.164349i	0.814675	−	0.579918i	$-0.196916\pi$
$457$	−927.000	−	1605.61i	−0.0948867	−	0.164349i	−0.909561	+	0.415570i	$0.863582\pi$
$458$	−2280.00			−0.232614
$459$		−	14590.8i		−	1.48375i
$460$	−6080.00			−0.616264
$461$	8535.00	+	14783.1i	0.862288	+	1.49353i	0.869715	+	0.493554i	$0.164302\pi$
$461$	8535.00	+	14783.1i	0.862288	+	1.49353i	−0.00742784	+	0.999972i	$0.502364\pi$
$462$	−5148.00	−	2972.20i	−0.518413	−	0.299306i
$463$	−7076.00	+	12256.0i	−0.710258	+	1.23020i	0.254502	+	0.967072i	$0.418089\pi$
$463$	−7076.00	+	12256.0i	−0.710258	+	1.23020i	−0.964760	+	0.263131i	$0.915245\pi$
$464$	576.000	−	997.661i	0.0576296	−	0.0998174i
$465$		−	4837.62i		−	0.482450i
$466$	9324.00	+	16149.6i	0.926880	+	1.60540i
$467$	−11475.0			−1.13704			−0.568522	−	0.822668i	$-0.692485\pi$
$467$	−11475.0			−1.13704			−0.568522	+	0.822668i	$0.692485\pi$
$468$	−6048.00	+	10475.4i	−0.597369	+	1.03467i
$469$	−27898.0			−2.74672
$470$	5662.00	+	9806.87i	0.555678	+	0.962462i
$471$	−11533.5	+	6658.87i	−1.12831	+	0.651432i
$472$		0			0
$473$	−2046.00	+	3543.78i	−0.198890	+	0.344488i
$474$	−10728.0	+	6193.81i	−1.03956	+	0.600193i
$475$	11328.0	+	19620.7i	1.09424	+	1.89528i
$476$	−21632.0			−2.08299
$477$	−5629.50	−	9750.58i	−0.540371	−	0.935951i
$478$	17976.0			1.72009
$479$	−9965.00	−	17259.9i	−0.950548	−	1.64640i	−0.744242	−	0.667910i	$-0.767189\pi$
$479$	−9965.00	−	17259.9i	−0.950548	−	1.64640i	−0.206306	−	0.978488i	$-0.566144\pi$
$480$		−	25274.1i		−	2.40333i
$481$	2100.00	−	3637.31i	0.199068	−	0.344796i
$482$	−9760.00	+	16904.8i	−0.922315	+	1.59750i
$483$	4680.00	+	2702.00i	0.440885	+	0.254545i
$484$	−484.000	−	838.313i	−0.0454545	−	0.0787296i
$485$	6289.00			0.588802
$486$	13122.0	+	7575.99i	1.22474	+	0.707107i
$487$	4805.00			0.447095			0.223548	−	0.974693i	$-0.428236\pi$
$487$	4805.00			0.447095			0.223548	+	0.974693i	$0.428236\pi$
$488$		0			0
$489$	8284.50	+	4783.06i	0.766131	+	0.442326i
$490$	−12654.0	+	21917.4i	−1.16663	+	2.02067i
$491$	4385.00	−	7595.04i	0.403039	−	0.698084i	−0.591052	−	0.806634i	$-0.701287\pi$
$491$	4385.00	−	7595.04i	0.403039	−	0.698084i	0.994091	+	0.108549i	$0.0346205\pi$
$492$			12304.5i			1.12750i
$493$	−936.000	−	1621.20i	−0.0855077	−	0.148104i
$494$	−21504.0			−1.95852
$495$	−2821.50	−	4886.98i	−0.256196	−	0.443744i
$496$	−3136.00			−0.283892
$497$	−3705.00	−	6417.25i	−0.334390	−	0.579181i
$498$	8964.00	−	5175.37i	0.806599	−	0.465690i
$499$	−3032.50	+	5252.44i	−0.272051	+	0.471206i	−0.969387	−	0.245539i	$-0.921035\pi$
$499$	−3032.50	+	5252.44i	−0.272051	+	0.471206i	0.697336	+	0.716744i	$0.254369\pi$
$500$	8436.00	−	14611.6i	0.754539	−	1.30690i
$501$	3078.00	−	1777.08i	0.274481	−	0.158472i
$502$	−8792.00	−	15228.2i	−0.781686	−	1.35392i
$503$	10538.0			0.934128			0.467064	−	0.884224i	$-0.345312\pi$
$503$	10538.0			0.934128			0.467064	+	0.884224i	$0.345312\pi$
$504$		0			0
$505$	−1102.00			−0.0971057
$506$	880.000	+	1524.20i	0.0773138	+	0.133911i
$507$			4879.19i			0.427401i
$508$	−1736.00	+	3006.84i	−0.151619	+	0.262612i
$509$	−4989.00	+	8641.20i	−0.434447	+	0.752484i	−0.997250	−	0.0741065i	$-0.976390\pi$
$509$	−4989.00	+	8641.20i	−0.434447	+	0.752484i	0.562803	+	0.826591i	$0.309723\pi$
$510$	−35568.0	−	20535.2i	−3.08819	−	1.78297i
$511$	−12506.0	−	21661.0i	−1.08265	−	1.87520i
$512$	−16384.0			−1.41421
$513$			13468.4i			1.15915i
$514$	−15176.0			−1.30230
$515$	−2346.50	−	4064.26i	−0.200775	−	0.347753i
$516$	−13392.0	−	7731.87i	−1.14254	−	0.659645i
$517$	819.500	−	1419.42i	0.0697129	−	0.120746i
$518$	−3900.00	+	6755.00i	−0.330803	+	0.572968i
$519$			9228.37i			0.780502i
$520$		0			0
$521$	19305.0			1.62335			0.811677	−	0.584107i	$-0.198555\pi$
$521$	19305.0			1.62335			0.811677	+	0.584107i	$0.198555\pi$
$522$	1944.00			0.163001
$523$	12188.0			1.01901			0.509507	−	0.860467i	$-0.329828\pi$
$523$	12188.0			1.01901			0.509507	+	0.860467i	$0.329828\pi$
$524$	−720.000	−	1247.08i	−0.0600255	−	0.103967i
$525$	−27612.0	+	15941.8i	−2.29540	+	1.32525i
$526$	15632.0	−	27075.4i	1.29579	−	2.24438i
$527$	−2548.00	+	4413.27i	−0.210612	+	0.364791i
$528$	−3168.00	+	1829.05i	−0.261116	+	0.150756i
$529$	5283.50	+	9151.29i	0.434248	+	0.752140i
$530$	−31692.0			−2.59738
$531$	459.000			0.0375121
$532$	19968.0			1.62730
$533$	8288.00	+	14355.2i	0.673533	+	1.16659i
$534$		−	25565.1i		−	2.07174i
$535$	11001.0	−	19054.3i	0.888999	−	1.53979i
$536$		0			0
$537$	−8356.50	−	4824.63i	−0.671526	−	0.387706i
$538$	9550.00	+	16541.1i	0.765297	+	1.32553i
$539$	3663.00			0.292721
$540$	18468.0	−	10662.5i	1.47173	−	0.849706i
$541$	−9218.00			−0.732556			−0.366278	−	0.930505i	$-0.619368\pi$
$541$	−9218.00			−0.732556			−0.366278	+	0.930505i	$0.619368\pi$
$542$	7528.00	+	13038.9i	0.596596	+	1.03334i
$543$	20596.5	+	11891.4i	1.62777	+	0.939795i
$544$	−13312.0	+	23057.1i	−1.04917	+	1.81721i
$545$	−418.000	+	723.997i	−0.0328535	+	0.0569039i
$546$		−	30262.4i		−	2.37200i
$547$	4061.00	+	7033.86i	0.317433	+	0.549810i	0.979952	−	0.199235i	$-0.0638458\pi$
$547$	4061.00	+	7033.86i	0.317433	+	0.549810i	−0.662519	+	0.749045i	$0.730512\pi$
$548$	4136.00			0.322411
$549$	1215.00	−	2104.44i	0.0944534	−	0.163598i
$550$	−10384.0			−0.805046
$551$	864.000	+	1496.49i	0.0668015	+	0.115704i
$552$		0			0
$553$	7748.00	−	13419.9i	0.595802	−	1.03196i
$554$	7136.00	−	12359.9i	0.547256	−	0.947874i
$555$	−6412.50	+	3702.26i	−0.490442	+	0.283157i
$556$	7448.00	+	12900.3i	0.568104	+	0.983984i
$557$	194.000			0.0147577			0.00737885	−	0.999973i	$-0.497651\pi$
$557$	194.000			0.0147577			0.00737885	+	0.999973i	$0.497651\pi$
$558$	−2646.00	−	4583.01i	−0.200742	−	0.347696i
$559$	−20832.0			−1.57621
$560$	15808.0	+	27380.3i	1.19287	+	2.06612i
$561$			5944.40i			0.447367i
$562$	48.0000	−	83.1384i	0.00360277	−	0.00624018i
$563$	1904.00	−	3297.82i	0.142529	−	0.246868i	−0.785919	−	0.618329i	$-0.787810\pi$
$563$	1904.00	−	3297.82i	0.142529	−	0.246868i	0.928448	+	0.371461i	$0.121143\pi$
$564$	5364.00	+	3096.91i	0.400470	+	0.231212i
$565$	9091.50	+	15746.9i	0.676960	+	1.17253i
$566$	3416.00			0.253684
$567$	−18954.0			−1.40387
$568$		0			0
$569$	4209.00	+	7290.20i	0.310106	+	0.537120i	0.978385	−	0.206791i	$-0.0663020\pi$
$569$	4209.00	+	7290.20i	0.310106	+	0.537120i	−0.668279	+	0.743911i	$0.732969\pi$
$570$	32832.0	+	18955.6i	2.41260	+	1.39291i
$571$	−661.000	+	1144.89i	−0.0484448	+	0.0839089i	−0.889231	−	0.457458i	$-0.848760\pi$
$571$	−661.000	+	1144.89i	−0.0484448	+	0.0839089i	0.840786	+	0.541367i	$0.182093\pi$
$572$	2464.00	−	4267.77i	0.180114	−	0.311966i
$573$		−	4796.05i		−	0.349665i
$574$	−15392.0	−	26659.7i	−1.11925	−	1.93860i
$575$	9440.00			0.684653
$576$	−6912.00	−	11971.9i	−0.500000	−	0.866025i
$577$	−20283.0			−1.46342			−0.731709	−	0.681617i	$-0.761277\pi$
$577$	−20283.0			−1.46342			−0.731709	+	0.681617i	$0.761277\pi$
$578$	11806.0	+	20448.6i	0.849593	+	1.47154i
$579$	2178.00	−	1257.47i	0.156329	−	0.0902567i
$580$	1368.00	−	2369.45i	0.0979364	−	0.169631i
$581$	−6474.00	+	11213.3i	−0.462284	+	0.800699i
$582$	5958.00	−	3439.85i	0.424342	−	0.244994i
$583$	2293.50	+	3972.46i	0.162928	+	0.282200i
$584$		0			0
$585$	14364.0	−	24879.2i	1.01518	−	1.75834i
$586$	−16488.0			−1.16231
$587$	6411.50	+	11105.0i	0.450819	+	0.780842i	0.998437	−	0.0558867i	$-0.0177985\pi$
$587$	6411.50	+	11105.0i	0.450819	+	0.780842i	−0.547618	+	0.836729i	$0.684465\pi$
$588$			13842.6i			0.970845i
$589$	2352.00	−	4073.78i	0.164537	−	0.284987i
$590$	646.000	−	1118.90i	0.0450769	−	0.0780756i
$591$	16029.0	+	9254.35i	1.11564	+	0.644117i
$592$	2400.00	+	4156.92i	0.166621	+	0.288595i
$593$	12730.0			0.881549			0.440774	−	0.897618i	$-0.354704\pi$
$593$	12730.0			0.881549			0.440774	+	0.897618i	$0.354704\pi$
$594$	−5346.00	−	3086.51i	−0.369274	−	0.213201i
$595$	51376.0			3.53985
$596$	6368.00	+	11029.7i	0.437657	+	0.758044i
$597$	12622.5	+	7287.60i	0.865334	+	0.499601i
$598$	−4480.00	+	7759.59i	−0.306356	+	0.530624i
$599$	−3208.00	+	5556.42i	−0.218824	+	0.379014i	−0.954449	−	0.298375i	$-0.903555\pi$
$599$	−3208.00	+	5556.42i	−0.218824	+	0.379014i	0.735625	+	0.677389i	$0.236889\pi$
$600$		0			0
$601$	−2674.00	−	4631.50i	−0.181489	−	0.314348i	0.760899	−	0.648870i	$-0.224758\pi$
$601$	−2674.00	−	4631.50i	−0.181489	−	0.314348i	−0.942388	+	0.334523i	$0.891425\pi$
$602$	38688.0			2.61928
$603$	−28971.0			−1.95653
$604$	−7328.00			−0.493662
$605$	1149.50	+	1990.99i	0.0772460	+	0.133794i
$606$	−1044.00	+	602.754i	−0.0699828	+	0.0404046i
$607$	872.000	−	1510.35i	0.0583087	−	0.100994i	−0.835398	−	0.549646i	$-0.814763\pi$
$607$	872.000	−	1510.35i	0.0583087	−	0.100994i	0.893706	+	0.448652i	$0.148096\pi$
$608$	12288.0	−	21283.4i	0.819645	−	1.41967i
$609$	−2106.00	+	1215.90i	−0.140130	+	0.0809043i
$610$	−3420.00	−	5923.61i	−0.227003	−	0.393181i
$611$	8344.00			0.552475
$612$	−22464.0			−1.48375
$613$	15404.0			1.01495			0.507473	−	0.861668i	$-0.330580\pi$
$613$	15404.0			1.01495			0.507473	+	0.861668i	$0.330580\pi$
$614$	4144.00	+	7177.62i	0.272375	+	0.471767i
$615$		−	29223.2i		−	1.91608i
$616$		0			0
$617$	−2380.50	+	4123.15i	−0.155325	+	0.269030i	−0.933177	−	0.359417i	$-0.882976\pi$
$617$	−2380.50	+	4123.15i	−0.155325	+	0.269030i	0.777853	+	0.628447i	$0.216309\pi$
$618$	−4446.00	−	2566.90i	−0.289392	−	0.167081i
$619$	−6596.50	−	11425.5i	−0.428329	−	0.741888i	0.568396	−	0.822755i	$-0.307564\pi$
$619$	−6596.50	−	11425.5i	−0.428329	−	0.741888i	−0.996725	+	0.0808675i	$0.974231\pi$
$620$	−7448.00			−0.482450
$621$	4860.00	+	2805.92i	0.314050	+	0.181317i
$622$	37020.0			2.38644
$623$	15990.0	+	27695.5i	1.02829	+	1.78105i
$624$	−16128.0	−	9311.51i	−1.03467	−	0.597369i
$625$	−5285.50	+	9154.75i	−0.338272	+	0.585904i
$626$	9964.00	−	17258.2i	0.636169	−	1.10188i
$627$		−	5487.14i		−	0.349498i
$628$	10252.0	+	17757.0i	0.651432	+	1.12831i
$629$	7800.00			0.494446
$630$	−26676.0	+	46204.2i	−1.68698	+	2.92193i
$631$	−23153.0			−1.46071			−0.730354	−	0.683069i	$-0.760645\pi$
$631$	−23153.0			−1.46071			−0.730354	+	0.683069i	$0.760645\pi$
$632$		0			0
$633$	7155.00	−	4130.94i	0.449267	−	0.259384i
$634$	9916.00	−	17175.0i	0.621159	−	1.07588i
$635$	4123.00	−	7141.25i	0.257663	−	0.446286i
$636$	−15012.0	+	8667.18i	−0.935951	+	0.540371i
$637$	9324.00	+	16149.6i	0.579953	+	1.00451i
$638$	−792.000			−0.0491467
$639$	−3847.50	−	6664.07i	−0.238192	−	0.412561i
$640$		0			0
$641$	−3081.00	−	5336.45i	−0.189847	−	0.328825i	0.755352	−	0.655319i	$-0.227466\pi$
$641$	−3081.00	−	5336.45i	−0.189847	−	0.328825i	−0.945199	+	0.326494i	$0.894133\pi$
$642$		−	24068.6i		−	1.47961i
$643$	−2374.00	+	4111.89i	−0.145601	+	0.252188i	−0.929597	−	0.368578i	$-0.879845\pi$
$643$	−2374.00	+	4111.89i	−0.145601	+	0.252188i	0.783996	+	0.620766i	$0.213178\pi$
$644$	4160.00	−	7205.33i	0.254545	−	0.440885i
$645$	31806.0	+	18363.2i	1.94164	+	1.12101i
$646$	−19968.0	−	34585.6i	−1.21615	−	2.10643i
$647$	21484.0			1.30545			0.652723	−	0.757597i	$-0.273627\pi$
$647$	21484.0			1.30545			0.652723	+	0.757597i	$0.273627\pi$
$648$		0			0
$649$	−187.000			−0.0113103
$650$	−26432.0	−	45781.6i	−1.59500	−	2.76262i
$651$	5733.00	+	3309.95i	0.345152	+	0.199274i
$652$	7364.00	−	12754.8i	0.442326	−	0.766131i
$653$	6846.50	−	11858.5i	0.410297	−	0.710656i	−0.584625	−	0.811304i	$-0.698758\pi$
$653$	6846.50	−	11858.5i	0.410297	−	0.710656i	0.994922	+	0.100648i	$0.0320915\pi$
$654$			914.523i			0.0546799i
$655$	1710.00	+	2961.81i	0.102008	+	0.176683i
$656$	−18944.0			−1.12750
$657$	−12987.0	−	22494.1i	−0.771189	−	1.33574i
$658$	−15496.0			−0.918081
$659$	−9754.00	−	16894.4i	−0.576573	−	0.998654i	−0.995869	−	0.0908046i	$-0.971056\pi$
$659$	−9754.00	−	16894.4i	−0.576573	−	0.998654i	0.419295	−	0.907850i	$-0.362277\pi$
$660$	−7524.00	+	4343.98i	−0.443744	+	0.256196i
$661$	−2958.50	+	5124.27i	−0.174088	+	0.301530i	−0.939845	−	0.341600i	$-0.889031\pi$
$661$	−2958.50	+	5124.27i	−0.174088	+	0.301530i	0.765757	+	0.643130i	$0.222364\pi$
$662$	−13642.0	+	23628.6i	−0.800924	+	1.38724i
$663$	−26208.0	+	15131.2i	−1.53520	+	0.886345i
$664$		0			0
$665$	−47424.0			−2.76545
$666$	−4050.00	+	7014.81i	−0.235637	+	0.408135i
$667$	720.000			0.0417969
$668$	−2736.00	−	4738.89i	−0.158472	−	0.274481i
$669$			956.092i			0.0552536i
$670$	−40774.0	+	70622.6i	−2.35110	+	4.07222i
$671$	−495.000	+	857.365i	−0.0284788	+	0.0493267i
$672$	29952.0	+	17292.8i	1.71938	+	0.992685i
$673$	−12382.0	−	21446.3i	−0.709199	−	1.22837i	−0.965155	−	0.261680i	$-0.915723\pi$
$673$	−12382.0	−	21446.3i	−0.709199	−	1.22837i	0.255955	−	0.966689i	$-0.417610\pi$
$674$	21016.0			1.20105
$675$	−28674.0	+	16554.9i	−1.63506	+	0.944000i
$676$	7512.00			0.427401
$677$	489.000	+	846.973i	0.0277604	+	0.0480824i	0.879572	−	0.475766i	$-0.157829\pi$
$677$	489.000	+	846.973i	0.0277604	+	0.0480824i	−0.851811	+	0.523849i	$0.824496\pi$
$678$	17226.0	+	9945.44i	0.975753	+	0.563351i
$679$	−4303.00	+	7453.01i	−0.243202	+	0.421238i
$680$		0			0
$681$		−	12283.7i		−	0.691208i
$682$	1078.00	+	1867.15i	0.0605260	+	0.104834i
$683$	−30125.0			−1.68770			−0.843851	−	0.536577i	$-0.819717\pi$
$683$	−30125.0			−1.68770			−0.843851	+	0.536577i	$0.819717\pi$
$684$	20736.0			1.15915
$685$	−9823.00			−0.547909
$686$	520.000	+	900.666i	0.0289412	+	0.0501277i
$687$	2565.00	−	1480.90i	0.142447	−	0.0822416i
$688$	11904.0	−	20618.3i	0.659645	−	1.14254i
$689$	−11676.0	+	20223.4i	−0.645603	+	1.11822i
$690$	13680.0	−	7898.15i	0.754766	−	0.435764i
$691$	17001.5	+	29447.5i	0.935988	+	1.62118i	0.772863	+	0.634573i	$0.218824\pi$
$691$	17001.5	+	29447.5i	0.935988	+	1.62118i	0.163125	+	0.986605i	$0.447843\pi$
$692$	14208.0			0.780502
$693$	7722.00			0.423282
$694$	−28760.0			−1.57308
$695$	−17689.0	−	30638.2i	−0.965442	−	1.67219i
$696$		0			0
$697$	−15392.0	+	26659.7i	−0.836461	+	1.44879i
$698$	16320.0	−	28267.1i	0.884987	−	1.53284i
$699$	−20979.0	−	12112.2i	−1.13519	−	0.655403i
$700$	24544.0	+	42511.5i	1.32525	+	2.29540i
$701$	−44.0000			−0.00237069			−0.00118535	−	0.999999i	$-0.500377\pi$
$701$	−44.0000			−0.00237069			−0.00118535	+	0.999999i	$0.500377\pi$
$702$		−	31426.3i		−	1.68962i
$703$	−7200.00			−0.386278
$704$	2816.00	+	4877.46i	0.150756	+	0.261116i
$705$	−12739.5	−	7355.15i	−0.680564	−	0.392924i
$706$	−9924.00	+	17188.9i	−0.529029	+	0.916306i
$707$	754.000	−	1305.97i	0.0401090	−	0.0694709i
$708$		−	706.677i		−	0.0375121i
$709$	14484.5	+	25087.9i	0.767245	+	1.32891i	0.939051	+	0.343777i	$0.111706\pi$
$709$	14484.5	+	25087.9i	0.767245	+	1.32891i	−0.171806	+	0.985131i	$0.554960\pi$
$710$	−21660.0			−1.14491
$711$	8046.00	−	13936.1i	0.424400	−	0.735083i
$712$		0			0
$713$	−980.000	−	1697.41i	−0.0514745	−	0.0891564i
$714$	48672.0	−	28100.8i	2.55113	−	1.47289i
$715$	−5852.00	+	10136.0i	−0.306087	+	0.530159i
$716$	−7428.00	+	12865.7i	−0.387706	+	0.671526i
$717$	−20223.0	+	11675.8i	−1.05334	+	0.608144i
$718$	7108.00	+	12311.4i	0.369454	+	0.639914i
$719$	29775.0			1.54440			0.772198	−	0.635382i	$-0.219158\pi$
$719$	29775.0			1.54440			0.772198	+	0.635382i	$0.219158\pi$
$720$	16416.0	+	28433.3i	0.849706	+	1.47173i
$721$	6422.00			0.331717
$722$	4714.00	+	8164.89i	0.242987	+	0.420867i
$723$		−	25357.2i		−	1.30435i
$724$	18308.0	−	31710.4i	0.939795	−	1.62777i
$725$	−2124.00	+	3678.88i	−0.108805	+	0.188455i
$726$	2178.00	+	1257.47i	0.111340	+	0.0642824i
$727$	−4762.50	−	8248.89i	−0.242959	−	0.420818i	0.718597	−	0.695427i	$-0.244785\pi$
$727$	−4762.50	−	8248.89i	−0.242959	−	0.420818i	−0.961556	+	0.274609i	$0.911451\pi$
$728$		0			0
$729$	−19683.0			−1.00000
$730$	−73112.0			−3.70684
$731$	−19344.0	−	33504.8i	−0.978746	−	1.69524i
$732$	−3240.00	−	1870.61i	−0.163598	−	0.0944534i
$733$	555.000	−	961.288i	0.0279664	−	0.0484393i	−0.851703	−	0.524024i	$-0.824430\pi$
$733$	555.000	−	961.288i	0.0279664	−	0.0484393i	0.879670	+	0.475585i	$0.157764\pi$
$734$	−10930.0	+	18931.3i	−0.549637	+	0.951999i
$735$		−	32876.1i		−	1.64987i
$736$	−5120.00	−	8868.10i	−0.256421	−	0.444134i
$737$	11803.0			0.589917
$738$	−15984.0	−	27685.1i	−0.797262	−	1.38090i
$739$	−4144.00			−0.206278			−0.103139	−	0.994667i	$-0.532889\pi$
$739$	−4144.00			−0.206278			−0.103139	+	0.994667i	$0.532889\pi$
$740$	5700.00	+	9872.69i	0.283157	+	0.490442i
$741$	24192.0	−	13967.3i	1.19935	−	0.692443i
$742$	21684.0	−	37557.8i	1.07284	−	1.85821i
$743$	−259.000	+	448.601i	−0.0127884	+	0.0221502i	−0.872349	−	0.488884i	$-0.837404\pi$
$743$	−259.000	+	448.601i	−0.0127884	+	0.0221502i	0.859560	+	0.511034i	$0.170737\pi$
$744$		0			0
$745$	−15124.0	−	26195.5i	−0.743759	−	1.28823i
$746$	−39664.0			−1.94665
$747$	−6723.00	+	11644.6i	−0.329293	+	0.570352i
$748$	9152.00			0.447367
$749$	15054.0	+	26074.3i	0.734394	+	1.27201i
$750$			43834.7i			2.13416i
$751$	15476.5	−	26806.1i	0.751991	−	1.30249i	−0.194865	−	0.980830i	$-0.562427\pi$
$751$	15476.5	−	26806.1i	0.751991	−	1.30249i	0.946856	−	0.321657i	$-0.104240\pi$
$752$	−4768.00	+	8258.42i	−0.231212	+	0.400470i
$753$	19782.0	+	11421.1i	0.957365	+	0.552735i
$754$	−2016.00	−	3491.81i	−0.0973719	−	0.168653i
$755$	17404.0			0.838936
$756$			29181.6i			1.40387i
$757$	−5335.00			−0.256148			−0.128074	−	0.991765i	$-0.540879\pi$
$757$	−5335.00			−0.256148			−0.128074	+	0.991765i	$0.540879\pi$
$758$	−11416.0	−	19773.1i	−0.547029	−	0.947482i
$759$	−1980.00	−	1143.15i	−0.0946897	−	0.0546691i
$760$		0			0
$761$	15435.0	−	26734.2i	0.735241	−	1.27347i	−0.219377	−	0.975640i	$-0.570402\pi$
$761$	15435.0	−	26734.2i	0.735241	−	1.27347i	0.954618	−	0.297834i	$-0.0962643\pi$
$762$		−	9020.52i		−	0.428844i
$763$	−572.000	−	990.733i	−0.0271400	−	0.0470078i
$764$	−7384.00			−0.349665
$765$	53352.0			2.52150
$766$	13988.0			0.659800
$767$	−476.000	−	824.456i	−0.0224086	−	0.0388128i
$768$	18432.0	−	10641.7i	0.866025	−	0.500000i
$769$	−265.000	+	458.993i	−0.0124267	+	0.0215237i	−0.872172	−	0.489200i	$-0.837289\pi$
$769$	−265.000	+	458.993i	−0.0124267	+	0.0215237i	0.859745	+	0.510723i	$0.170622\pi$
$770$	10868.0	−	18823.9i	0.508644	−	0.880996i
$771$	17073.0	−	9857.10i	0.797496	−	0.460434i
$772$	−1936.00	−	3353.25i	−0.0902567	−	0.156329i
$773$	−4614.00			−0.214688			−0.107344	−	0.994222i	$-0.534235\pi$
$773$	−4614.00			−0.214688			−0.107344	+	0.994222i	$0.534235\pi$
$774$	40176.0			1.86576
$775$	11564.0			0.535989
$776$		0			0
$777$		−	10132.5i		−	0.467827i
$778$	−15606.0	+	27030.4i	−0.719155	+	1.24561i
$779$	14208.0	−	24609.0i	0.653472	−	1.13185i
$780$	−38304.0	−	22114.8i	−1.75834	−	1.01518i
$781$	1567.50	+	2714.99i	0.0718176	+	0.124392i
$782$	−16640.0			−0.760927
$783$	−2187.00	+	1262.67i	−0.0998174	+	0.0576296i
$784$	−21312.0			−0.970845
$785$	−24348.5	−	42172.8i	−1.10705	−	1.91747i
$786$	3240.00	+	1870.61i	0.147032	+	0.0848888i
$787$	12340.0	−	21373.5i	0.558924	−	0.968085i	−0.438662	−	0.898652i	$-0.644548\pi$
$787$	12340.0	−	21373.5i	0.558924	−	0.968085i	0.997587	−	0.0694334i	$-0.0221191\pi$
$788$	14248.0	−	24678.3i	0.644117	−	1.11564i
$789$			40613.1i			1.83253i
$790$	−22648.0	−	39227.5i	−1.01997	−	1.76665i
$791$	−24882.0			−1.11846
$792$		0			0
$793$	−5040.00			−0.225694
$794$	25826.0	+	44731.9i	1.15432	+	1.99934i
$795$	35653.5	−	20584.6i	1.59057	−	0.918313i
$796$	11220.0	−	19433.6i	0.499601	−	0.865334i
$797$	779.500	−	1350.13i	0.0346440	−	0.0600053i	−0.848184	−	0.529702i	$-0.822304\pi$
$797$	779.500	−	1350.13i	0.0346440	−	0.0600053i	0.882828	+	0.469697i	$0.155637\pi$
$798$	−44928.0	+	25939.2i	−1.99303	+	1.15067i
$799$	7748.00	+	13419.9i	0.343059	+	0.594196i
$800$	60416.0			2.67004
$801$	16605.0	+	28760.7i	0.732470	+	1.26868i
$802$	44204.0			1.94626
$803$	5291.00	+	9164.28i	0.232522	+	0.402740i
$804$			44603.8i			1.95653i
$805$	−9880.00	+	17112.7i	−0.432577	+	0.749245i
$806$	−5488.00	+	9505.49i	−0.239834	+	0.415405i
$807$	−21487.5	−	12405.8i	−0.937293	−	0.541147i
$808$		0			0
$809$	−19290.0			−0.838319			−0.419160	−	0.907913i	$-0.637675\pi$
$809$	−19290.0			−0.838319			−0.419160	+	0.907913i	$0.637675\pi$
$810$	−27702.0	+	47981.3i	−1.20167	+	2.08135i
$811$	−914.000			−0.0395745			−0.0197872	−	0.999804i	$-0.506299\pi$
$811$	−914.000			−0.0395745			−0.0197872	+	0.999804i	$0.506299\pi$
$812$	1872.00	+	3242.40i	0.0809043	+	0.140130i
$813$	−16938.0	−	9779.16i	−0.730678	−	0.421857i
$814$	1650.00	−	2857.88i	0.0710473	−	0.123057i
$815$	−17489.5	+	30292.7i	−0.751694	+	1.30197i
$816$		−	34585.6i		−	1.48375i
$817$	17856.0	+	30927.5i	0.764630	+	1.32438i
$818$	−720.000			−0.0307753
$819$	19656.0	+	34045.2i	0.838628	+	1.45255i
$820$	−44992.0			−1.91608
$821$	20252.0	+	35077.5i	0.860901	+	1.49112i	0.871060	+	0.491176i	$0.163433\pi$
$821$	20252.0	+	35077.5i	0.860901	+	1.49112i	−0.0101595	+	0.999948i	$0.503234\pi$
$822$	−9306.00	+	5372.82i	−0.394871	+	0.227979i
$823$	11808.0	−	20452.1i	0.500123	−	0.866238i	−0.499877	−	0.866096i	$-0.666622\pi$
$823$	11808.0	−	20452.1i	0.500123	−	0.866238i	1.00000		0.000141720i	$-4.51109e-5\pi$
$824$		0			0
$825$	11682.0	−	6744.61i	0.492988	−	0.284627i
$826$	884.000	+	1531.13i	0.0372376	+	0.0644975i
$827$	−44792.0			−1.88340			−0.941699	−	0.336456i	$-0.890772\pi$
$827$	−44792.0			−1.88340			−0.941699	+	0.336456i	$0.890772\pi$
$828$	4320.00	−	7482.46i	0.181317	−	0.314050i
$829$	3265.00			0.136789			0.0683945	−	0.997658i	$-0.478212\pi$
$829$	3265.00			0.136789			0.0683945	+	0.997658i	$0.478212\pi$
$830$	18924.0	+	32777.3i	0.791400	+	1.37074i
$831$			18539.9i			0.773936i
$832$	−14336.0	+	24830.7i	−0.597369	+	1.03467i
$833$	−17316.0	+	29992.2i	−0.720245	+	1.24750i
$834$	−33516.0	−	19350.5i	−1.39156	−	0.803420i
$835$	6498.00	+	11254.9i	0.269308	+	0.466456i
$836$	−8448.00			−0.349498
$837$	5953.50	+	3437.25i	0.245858	+	0.141946i
$838$	43700.0			1.80142
$839$	−9472.00	−	16406.0i	−0.389761	−	0.675086i	0.602656	−	0.798001i	$-0.294109\pi$
$839$	−9472.00	−	16406.0i	−0.389761	−	0.675086i	−0.992417	+	0.122915i	$0.960776\pi$
$840$		0			0
$841$	12032.5	−	20840.9i	0.493358	−	0.854521i
$842$	−31414.0	+	54410.6i	−1.28575	+	2.22698i
$843$			124.708i			0.00509509i
$844$	−6360.00	−	11015.8i	−0.259384	−	0.449267i
$845$	−17841.0			−0.726330
$846$	−16092.0			−0.653965
$847$	−3146.00			−0.127624
$848$	−13344.0	−	23112.5i	−0.540371	−	0.935951i
$849$	−3843.00	+	2218.76i	−0.155349	+	0.0896909i
$850$	49088.0	−	85022.9i	1.98083	−	3.43090i
$851$	−1500.00	+	2598.08i	−0.0604223	+	0.104654i
$852$	−10260.0	+	5923.61i	−0.412561	+	0.238192i
$853$	−18313.0	−	31719.0i	−0.735082	−	1.27320i	−0.954687	−	0.297611i	$-0.903810\pi$
$853$	−18313.0	−	31719.0i	−0.735082	−	1.27320i	0.219605	−	0.975589i	$-0.429523\pi$
$854$	9360.00			0.375050
$855$	−49248.0			−1.96988
$856$		0			0
$857$	3181.00	+	5509.65i	0.126792	+	0.219610i	0.922432	−	0.386159i	$-0.126199\pi$
$857$	3181.00	+	5509.65i	0.126792	+	0.219610i	−0.795640	+	0.605770i	$0.792865\pi$
$858$			12803.3i			0.509438i
$859$	17203.5	−	29797.3i	0.683325	−	1.18355i	−0.290636	−	0.956834i	$-0.593867\pi$
$859$	17203.5	−	29797.3i	0.683325	−	1.18355i	0.973960	−	0.226719i	$-0.0727999\pi$
$860$	28272.0	−	48968.5i	1.12101	−	1.94164i
$861$	34632.0	+	19994.8i	1.37080	+	0.791429i
$862$	22692.0	+	39303.7i	0.896627	+	1.55300i
$863$	3912.00			0.154306			0.0771530	−	0.997019i	$-0.475417\pi$
$863$	3912.00			0.154306			0.0771530	+	0.997019i	$0.475417\pi$
$864$	31104.0	+	17957.9i	1.22474	+	0.707107i
$865$	−33744.0			−1.32639
$866$	−17164.0	−	29728.9i	−0.673506	−	1.16655i
$867$	−26563.5	−	15336.4i	−1.04053	−	0.600753i
$868$	5096.00	−	8826.53i	0.199274	−	0.345152i
$869$	−3278.00	+	5677.66i	−0.127961	+	0.221636i
$870$			7108.34i			0.277006i
$871$	30044.0	+	52037.7i	1.16877	+	2.02438i
$872$		0			0
$873$	−4468.50	+	7739.67i	−0.173237	+	0.300055i
$874$	15360.0			0.594462
$875$	−27417.0	−	47487.6i	−1.05927	−	1.83471i
$876$	−34632.0	+	19994.8i	−1.33574	+	0.771189i
$877$	−19665.0	+	34060.8i	−0.757172	+	1.31146i	0.187115	+	0.982338i	$0.440086\pi$
$877$	−19665.0	+	34060.8i	−0.757172	+	1.31146i	−0.944287	+	0.329122i	$0.893247\pi$
$878$	29780.0	−	51580.5i	1.14468	−	1.98264i
$879$	18549.0	−	10709.3i	0.711766	−	0.410938i
$880$	−6688.00	−	11584.0i	−0.256196	−	0.443744i
$881$	51865.0			1.98340			0.991700	−	0.128570i	$-0.0410386\pi$
$881$	51865.0			1.98340			0.991700	+	0.128570i	$0.0410386\pi$
$882$	−17982.0	−	31145.7i	−0.686491	−	1.18904i
$883$	−383.000			−0.0145968			−0.00729840	−	0.999973i	$-0.502323\pi$
$883$	−383.000			−0.0145968			−0.00729840	+	0.999973i	$0.502323\pi$
$884$	23296.0	+	40349.9i	0.886345	+	1.53520i
$885$			1678.36i			0.0637484i
$886$	11734.0	−	20323.9i	0.444934	−	0.770648i
$887$	−3560.00	+	6166.10i	−0.134761	+	0.233413i	−0.925506	−	0.378733i	$-0.876360\pi$
$887$	−3560.00	+	6166.10i	−0.134761	+	0.233413i	0.790745	+	0.612146i	$0.209693\pi$
$888$		0			0
$889$	5642.00	+	9772.23i	0.212853	+	0.368673i
$890$	93480.0			3.52074
$891$	8019.00			0.301511
$892$	1472.00			0.0552536
$893$	−7152.00	−	12387.6i	−0.268010	−	0.464206i
$894$	−28656.0	−	16544.5i	−1.07204	−	0.618940i
$895$	17641.5	−	30556.0i	0.658872	−	1.14120i
$896$		0			0
$897$		−	11639.4i		−	0.433253i
$898$	32294.0	+	55934.8i	1.20007	+	2.07859i
$899$	882.000			0.0327212
$900$	25488.0	+	44146.5i	0.944000	+	1.63506i
$901$	−43368.0			−1.60355
$902$	6512.00	+	11279.1i	0.240383	+	0.416356i
$903$	−43524.0	+	25128.6i	−1.60397	+	0.926055i
$904$		0			0
$905$	−43481.5	+	75312.2i	−1.59710	+	2.76626i
$906$	16488.0	−	9519.35i	0.604610	−	0.349072i
$907$	−22794.0	−	39480.4i	−0.834468	−	1.44534i	−0.894463	−	0.447142i	$-0.852442\pi$
$907$	−22794.0	−	39480.4i	−0.834468	−	1.44534i	0.0599951	−	0.998199i	$-0.480891\pi$
$908$	−18912.0			−0.691208
$909$	783.000	−	1356.20i	0.0285704	−	0.0494853i
$910$	110656.			4.03100
$911$	8971.50	+	15539.1i	0.326278	+	0.565130i	0.981770	−	0.190072i	$-0.0608722\pi$
$911$	8971.50	+	15539.1i	0.326278	+	0.565130i	−0.655492	+	0.755202i	$0.727539\pi$
$912$			31925.2i			1.15915i
$913$	2739.00	−	4744.09i	0.0992855	−	0.171968i
$914$	3708.00	−	6422.44i	0.134190	−	0.232424i
$915$	7695.00	+	4442.71i	0.278021	+	0.160515i
$916$	−2280.00	−	3949.08i	−0.0822416	−	0.142447i
$917$	−4680.00			−0.168536
$918$	50544.0	−	29181.6i	1.81721	−	1.04917i
$919$	46516.0			1.66966			0.834832	−	0.550505i	$-0.185565\pi$
$919$	46516.0			1.66966			0.834832	+	0.550505i	$0.185565\pi$
$920$		0			0
$921$	−9324.00	−	5383.21i	−0.333590	−	0.192598i
$922$	−34140.0	+	59132.2i	−1.21946	+	2.11216i
$923$	−7980.00	+	13821.8i	−0.284577	+	0.492902i
$924$		−	11888.8i		−	0.423282i
$925$	−8850.00	−	15328.6i	−0.314580	−	0.544868i
$926$	−56608.0			−2.00891
$927$	6669.00			0.236288
$928$	4608.00			0.163001
$929$	9763.50	+	16910.9i	0.344812	+	0.597231i	0.985320	−	0.170720i	$-0.0546094\pi$
$929$	9763.50	+	16910.9i	0.344812	+	0.597231i	−0.640508	+	0.767952i	$0.721276\pi$
$930$	16758.0	−	9675.24i	0.590878	−	0.341144i
$931$	15984.0	−	27685.1i	0.562679	−	0.974589i
$932$	−18648.0	+	32299.3i	−0.655403	+	1.13519i
$933$	−41647.5	+	24045.2i	−1.46139	+	0.843735i
$934$	−22950.0	−	39750.6i	−0.804012	−	1.39259i
$935$	−21736.0			−0.760260
$936$		0			0
$937$	−38194.0			−1.33164			−0.665818	−	0.746114i	$-0.731917\pi$
$937$	−38194.0			−1.33164			−0.665818	+	0.746114i	$0.731917\pi$
$938$	−55796.0	−	96641.5i	−1.94222	−	3.36403i
$939$			25887.2i			0.899678i
$940$	−11324.0	+	19613.7i	−0.392924	+	0.680564i
$941$	−291.000	+	504.027i	−0.0100811	+	0.0174610i	−0.871022	−	0.491244i	$-0.836542\pi$
$941$	−291.000	+	504.027i	−0.0100811	+	0.0174610i	0.860941	+	0.508705i	$0.169876\pi$
$942$	−46134.0	−	26635.5i	−1.59568	−	0.921264i
$943$	−5920.00	−	10253.7i	−0.204434	−	0.354091i
$944$	1088.00			0.0375121
$945$		−	69306.3i		−	2.38575i
$946$	−16368.0			−0.562547
$947$	−8836.50	−	15305.3i	−0.303218	−	0.525189i	0.673645	−	0.739055i	$-0.264728\pi$
$947$	−8836.50	−	15305.3i	−0.303218	−	0.525189i	−0.976863	+	0.213866i	$0.931394\pi$
$948$	−21456.0	−	12387.6i	−0.735083	−	0.424400i
$949$	−26936.0	+	46654.5i	−0.921369	+	1.59586i
$950$	−45312.0	+	78482.7i	−1.54749	+	2.68033i
$951$			25762.5i			0.878451i
$952$		0			0
$953$	−17674.0			−0.600752			−0.300376	−	0.953821i	$-0.597112\pi$
$953$	−17674.0			−0.600752			−0.300376	+	0.953821i	$0.597112\pi$
$954$	22518.0	−	39002.3i	0.764200	−	1.32363i
$955$	17537.0			0.594224
$956$	17976.0	+	31135.3i	0.608144	+	1.05334i
$957$	891.000	−	514.419i	0.0300961	−	0.0173760i
$958$	39860.0	−	69039.5i	1.34428	−	2.32836i
$959$	6721.00	−	11641.1i	0.226311	−	0.391982i
$960$	43776.0	−	25274.1i	1.47173	−	0.849706i
$961$	13695.0	+	23720.4i	0.459703	+	0.796228i
$962$	16800.0			0.563050
$963$	15633.0	+	27077.2i	0.523122	+	0.906074i
$964$	−39040.0			−1.30435
$965$	4598.00	+	7963.97i	0.153383	+	0.265668i
$966$			21616.0i			0.719962i
$967$	21340.0	−	36962.0i	0.709667	−	1.22918i	−0.255313	−	0.966858i	$-0.582179\pi$
$967$	21340.0	−	36962.0i	0.709667	−	1.22918i	0.964981	−	0.262321i	$-0.0844880\pi$
$968$		0			0
$969$	44928.0	+	25939.2i	1.48947	+	0.859945i
$970$	12578.0	+	21785.7i	0.416346	+	0.721132i
$971$	−22580.0			−0.746268			−0.373134	−	0.927777i	$-0.621717\pi$
$971$	−22580.0			−0.746268			−0.373134	+	0.927777i	$0.621717\pi$
$972$			30304.0i			1.00000i
$973$	48412.0			1.59508
$974$	9610.00	+	16645.0i	0.316144	+	0.547577i
$975$	59472.0	+	34336.2i	1.95346	+	1.12783i
$976$	2880.00	−	4988.31i	0.0944534	−	0.163598i
$977$	13563.0	−	23491.8i	0.444134	−	0.769262i	−0.553858	−	0.832611i	$-0.686845\pi$
$977$	13563.0	−	23491.8i	0.444134	−	0.769262i	0.997991	+	0.0633490i	$0.0201781\pi$
$978$			38264.5i			1.25109i
$979$	−6765.00	−	11717.3i	−0.220848	−	0.382520i
$980$	−50616.0			−1.64987
$981$	−594.000	−	1028.84i	−0.0193323	−	0.0334845i
$982$	35080.0			1.13997
$983$	19591.5	+	33933.5i	0.635678	+	1.10103i	0.986371	+	0.164537i	$0.0526129\pi$
$983$	19591.5	+	33933.5i	0.635678	+	1.10103i	−0.350693	+	0.936491i	$0.614054\pi$
$984$		0			0
$985$	−33839.0	+	58610.9i	−1.09462	+	1.89594i
$986$	3744.00	−	6484.80i	0.120926	−	0.209450i
$987$	17433.0	−	10064.9i	0.562207	−	0.324590i
$988$	−21504.0	−	37246.0i	−0.692443	−	1.19935i
$989$	14880.0			0.478419
$990$	11286.0	−	19547.9i	0.362316	−	0.627549i
$991$	−23192.0			−0.743409			−0.371704	−	0.928351i	$-0.621227\pi$
$991$	−23192.0			−0.743409			−0.371704	+	0.928351i	$0.621227\pi$
$992$	−6272.00	−	10863.4i	−0.200742	−	0.347696i
$993$		−	35443.0i		−	1.13268i
$994$	14820.0	−	25669.0i	0.472899	−	0.819086i
$995$	−26647.5	+	46154.8i	−0.849028	+	1.47056i
$996$	17928.0	+	10350.7i	0.570352	+	0.329293i
$997$	1838.00	+	3183.51i	0.0583852	+	0.101126i	0.893741	−	0.448584i	$-0.148072\pi$
$997$	1838.00	+	3183.51i	0.0583852	+	0.101126i	−0.835355	+	0.549710i	$0.814738\pi$
$998$	−24260.0			−0.769476
$999$		−	10522.2i		−	0.333241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.e.a.67.1	yes	2
3.2	odd	2		297.4.e.a.199.1		2
9.2	odd	6		297.4.e.a.100.1		2
9.4	even	3		891.4.a.a.1.1		1
9.5	odd	6		891.4.a.d.1.1		1
9.7	even	3	inner	99.4.e.a.34.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.4.e.a.34.1	✓	2	9.7	even	3	inner
99.4.e.a.67.1	yes	2	1.1	even	1	trivial
297.4.e.a.100.1		2	9.2	odd	6
297.4.e.a.199.1		2	3.2	odd	2
891.4.a.a.1.1		1	9.4	even	3
891.4.a.d.1.1		1	9.5	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(9.50000 - 16.4545i) q^{5} -20.7846i q^{6} +(13.0000 + 22.5167i) q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(9.50000 - 16.4545i) q^{5} -20.7846i q^{6} +(13.0000 + 22.5167i) q^{7} +(13.5000 + 23.3827i) q^{9} +76.0000 q^{10} +(-5.50000 - 9.52628i) q^{11} +(36.0000 - 20.7846i) q^{12} +(28.0000 - 48.4974i) q^{13} +(-52.0000 + 90.0666i) q^{14} +(-85.5000 + 49.3634i) q^{15} +(32.0000 + 55.4256i) q^{16} +104.000 q^{17} +(-54.0000 + 93.5307i) q^{18} -96.0000 q^{19} +(76.0000 + 131.636i) q^{20} -135.100i q^{21} +(22.0000 - 38.1051i) q^{22} +(-20.0000 + 34.6410i) q^{23} +(-118.000 - 204.382i) q^{25} +224.000 q^{26} -140.296i q^{27} -208.000 q^{28} +(-9.00000 - 15.5885i) q^{29} +(-342.000 - 197.454i) q^{30} +(-24.5000 + 42.4352i) q^{31} +(-128.000 + 221.703i) q^{32} +57.1577i q^{33} +(208.000 + 360.267i) q^{34} +494.000 q^{35} -216.000 q^{36} +75.0000 q^{37} +(-192.000 - 332.554i) q^{38} +(-252.000 + 145.492i) q^{39} +(-148.000 + 256.344i) q^{41} +(468.000 - 270.200i) q^{42} +(-186.000 - 322.161i) q^{43} +88.0000 q^{44} +513.000 q^{45} -160.000 q^{46} +(74.5000 + 129.038i) q^{47} -332.554i q^{48} +(-166.500 + 288.386i) q^{49} +(472.000 - 817.528i) q^{50} +(-468.000 - 270.200i) q^{51} +(224.000 + 387.979i) q^{52} -417.000 q^{53} +(486.000 - 280.592i) q^{54} -209.000 q^{55} +(432.000 + 249.415i) q^{57} +(36.0000 - 62.3538i) q^{58} +(8.50000 - 14.7224i) q^{59} -789.815i q^{60} +(-45.0000 - 77.9423i) q^{61} -196.000 q^{62} +(-351.000 + 607.950i) q^{63} -512.000 q^{64} +(-532.000 - 921.451i) q^{65} +(-198.000 + 114.315i) q^{66} +(-536.500 + 929.245i) q^{67} +(-416.000 + 720.533i) q^{68} +(180.000 - 103.923i) q^{69} +(988.000 + 1711.27i) q^{70} -285.000 q^{71} -962.000 q^{73} +(150.000 + 259.808i) q^{74} +1226.29i q^{75} +(384.000 - 665.108i) q^{76} +(143.000 - 247.683i) q^{77} +(-1008.00 - 581.969i) q^{78} +(-298.000 - 516.151i) q^{79} +1216.00 q^{80} +(-364.500 + 631.333i) q^{81} -1184.00 q^{82} +(249.000 + 431.281i) q^{83} +(936.000 + 540.400i) q^{84} +(988.000 - 1711.27i) q^{85} +(744.000 - 1288.65i) q^{86} +93.5307i q^{87} +1230.00 q^{89} +(1026.00 + 1777.08i) q^{90} +1456.00 q^{91} +(-160.000 - 277.128i) q^{92} +(220.500 - 127.306i) q^{93} +(-298.000 + 516.151i) q^{94} +(-912.000 + 1579.63i) q^{95} +(1152.00 - 665.108i) q^{96} +(165.500 + 286.654i) q^{97} -1332.00 q^{98} +(148.500 - 257.210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 9 q^{3} - 8 q^{4} + 19 q^{5} + 26 q^{7} + 27 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 9 * q^3 - 8 * q^4 + 19 * q^5 + 26 * q^7 + 27 * q^9	\( 2 q + 4 q^{2} - 9 q^{3} - 8 q^{4} + 19 q^{5} + 26 q^{7} + 27 q^{9} + 152 q^{10} - 11 q^{11} + 72 q^{12} + 56 q^{13} - 104 q^{14} - 171 q^{15} + 64 q^{16} + 208 q^{17} - 108 q^{18} - 192 q^{19} + 152 q^{20} + 44 q^{22} - 40 q^{23} - 236 q^{25} + 448 q^{26} - 416 q^{28} - 18 q^{29} - 684 q^{30} - 49 q^{31} - 256 q^{32} + 416 q^{34} + 988 q^{35} - 432 q^{36} + 150 q^{37} - 384 q^{38} - 504 q^{39} - 296 q^{41} + 936 q^{42} - 372 q^{43} + 176 q^{44} + 1026 q^{45} - 320 q^{46} + 149 q^{47} - 333 q^{49} + 944 q^{50} - 936 q^{51} + 448 q^{52} - 834 q^{53} + 972 q^{54} - 418 q^{55} + 864 q^{57} + 72 q^{58} + 17 q^{59} - 90 q^{61} - 392 q^{62} - 702 q^{63} - 1024 q^{64} - 1064 q^{65} - 396 q^{66} - 1073 q^{67} - 832 q^{68} + 360 q^{69} + 1976 q^{70} - 570 q^{71} - 1924 q^{73} + 300 q^{74} + 768 q^{76} + 286 q^{77} - 2016 q^{78} - 596 q^{79} + 2432 q^{80} - 729 q^{81} - 2368 q^{82} + 498 q^{83} + 1872 q^{84} + 1976 q^{85} + 1488 q^{86} + 2460 q^{89} + 2052 q^{90} + 2912 q^{91} - 320 q^{92} + 441 q^{93} - 596 q^{94} - 1824 q^{95} + 2304 q^{96} + 331 q^{97} - 2664 q^{98} + 297 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 9 * q^3 - 8 * q^4 + 19 * q^5 + 26 * q^7 + 27 * q^9 + 152 * q^10 - 11 * q^11 + 72 * q^12 + 56 * q^13 - 104 * q^14 - 171 * q^15 + 64 * q^16 + 208 * q^17 - 108 * q^18 - 192 * q^19 + 152 * q^20 + 44 * q^22 - 40 * q^23 - 236 * q^25 + 448 * q^26 - 416 * q^28 - 18 * q^29 - 684 * q^30 - 49 * q^31 - 256 * q^32 + 416 * q^34 + 988 * q^35 - 432 * q^36 + 150 * q^37 - 384 * q^38 - 504 * q^39 - 296 * q^41 + 936 * q^42 - 372 * q^43 + 176 * q^44 + 1026 * q^45 - 320 * q^46 + 149 * q^47 - 333 * q^49 + 944 * q^50 - 936 * q^51 + 448 * q^52 - 834 * q^53 + 972 * q^54 - 418 * q^55 + 864 * q^57 + 72 * q^58 + 17 * q^59 - 90 * q^61 - 392 * q^62 - 702 * q^63 - 1024 * q^64 - 1064 * q^65 - 396 * q^66 - 1073 * q^67 - 832 * q^68 + 360 * q^69 + 1976 * q^70 - 570 * q^71 - 1924 * q^73 + 300 * q^74 + 768 * q^76 + 286 * q^77 - 2016 * q^78 - 596 * q^79 + 2432 * q^80 - 729 * q^81 - 2368 * q^82 + 498 * q^83 + 1872 * q^84 + 1976 * q^85 + 1488 * q^86 + 2460 * q^89 + 2052 * q^90 + 2912 * q^91 - 320 * q^92 + 441 * q^93 - 596 * q^94 - 1824 * q^95 + 2304 * q^96 + 331 * q^97 - 2664 * q^98 + 297 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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