LMFDB - Embedded newform 99.4.e.a.34.1

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			34.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	99.34
Dual form			99.4.e.a.67.1

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	2.00000	−	3.46410i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	−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	0.881471	+	0.472238i	$0.156554\pi$
$5$	9.50000	+	16.4545i	0.849706	+	1.47173i	−0.0317651	+	0.999495i	$0.510113\pi$
$6$			20.7846i			1.41421i
$7$	13.0000	−	22.5167i	0.701934	−	1.21579i	−0.265853	−	0.964014i	$-0.585653\pi$
$7$	13.0000	−	22.5167i	0.701934	−	1.21579i	0.967787	−	0.251772i	$-0.0810132\pi$
$8$		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	0.993208	+	0.116354i	$0.0371207\pi$
$13$	28.0000	+	48.4974i	0.597369	+	1.03467i	−0.395838	+	0.918320i	$0.629546\pi$
$14$	−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	0.761012	−	0.648737i	$-0.224703\pi$
$23$	−20.0000	−	34.6410i	−0.181317	−	0.314050i	−0.942329	+	0.334687i	$0.891369\pi$
$24$		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	−0.893401	−	0.449260i	$-0.851688\pi$
$29$	−9.00000	+	15.5885i	−0.0576296	+	0.0998174i	0.835771	+	0.549078i	$0.185021\pi$
$30$	−342.000	+	197.454i	−2.08135	+	1.20167i
$31$	−24.5000	−	42.4352i	−0.141946	−	0.245858i	0.786283	−	0.617866i	$-0.212003\pi$
$31$	−24.5000	−	42.4352i	−0.141946	−	0.245858i	−0.928229	+	0.372008i	$0.878669\pi$
$32$	−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	−0.997165	−	0.0752481i	$-0.976025\pi$
$41$	−148.000	−	256.344i	−0.563749	−	0.976442i	0.433416	−	0.901194i	$-0.357308\pi$
$42$	468.000	+	270.200i	1.71938	+	0.992685i
$43$	−186.000	+	322.161i	−0.659645	+	1.14254i	0.321063	+	0.947058i	$0.395960\pi$
$43$	−186.000	+	322.161i	−0.659645	+	1.14254i	−0.980708	+	0.195481i	$0.937373\pi$
$44$	88.0000			0.301511
$45$	513.000			1.69941
$46$	−160.000			−0.512842
$47$	74.5000	−	129.038i	0.231212	−	0.400470i	−0.726953	−	0.686687i	$-0.759064\pi$
$47$	74.5000	−	129.038i	0.231212	−	0.400470i	0.958165	+	0.286217i	$0.0923977\pi$
$48$			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	0.875251	−	0.483669i	$-0.160696\pi$
$59$	8.50000	+	14.7224i	0.0187560	+	0.0324864i	−0.856495	+	0.516155i	$0.827363\pi$
$60$			789.815i			1.69941i
$61$	−45.0000	+	77.9423i	−0.0944534	+	0.163598i	−0.909380	−	0.415966i	$-0.863444\pi$
$61$	−45.0000	+	77.9423i	−0.0944534	+	0.163598i	0.814927	+	0.579564i	$0.196777\pi$
$62$	−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	−0.668702	−	0.743530i	$-0.733150\pi$
$67$	−536.500	−	929.245i	−0.978267	−	1.69441i	−0.309565	−	0.950878i	$-0.600183\pi$
$68$	−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	−0.996364	−	0.0851960i	$-0.972848\pi$
$79$	−298.000	+	516.151i	−0.424400	+	0.735083i	0.571964	+	0.820279i	$0.306182\pi$
$80$	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	−0.653079	−	0.757290i	$-0.726523\pi$
$83$	249.000	−	431.281i	0.329293	−	0.570352i	0.982372	+	0.186938i	$0.0598564\pi$
$84$	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	−0.766313	−	0.642468i	$-0.777911\pi$
$97$	165.500	−	286.654i	0.173237	−	0.300055i	0.939550	+	0.342413i	$0.111244\pi$
$98$	−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	−0.879957	−	0.475053i	$-0.842429\pi$
$101$	−29.0000	+	50.2295i	−0.0285704	+	0.0494853i	0.851387	+	0.524539i	$0.175762\pi$
$102$			2161.60i			2.09834i
$103$	123.500	+	213.908i	0.118144	+	0.204631i	0.919032	−	0.394183i	$-0.128972\pi$
$103$	123.500	+	213.908i	0.118144	+	0.204631i	−0.800888	+	0.598814i	$0.795639\pi$
$104$		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	0.595173	−	0.803598i	$-0.297084\pi$
$113$	−478.500	−	828.786i	−0.398350	−	0.689962i	−0.993522	+	0.113636i	$0.963750\pi$
$114$		−	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	0.834451	−	0.551082i	$-0.185785\pi$
$131$	−90.0000	−	155.885i	−0.0600255	−	0.103967i	−0.894477	+	0.447115i	$0.852452\pi$
$132$	−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	−0.935301	−	0.353852i	$-0.884872\pi$
$137$	−258.500	+	447.735i	−0.161205	+	0.279216i	0.774096	+	0.633068i	$0.218205\pi$
$138$	720.000	−	415.692i	0.444134	−	0.256421i
$139$	931.000	+	1612.54i	0.568104	+	0.983984i	0.996754	+	0.0805135i	$0.0256560\pi$
$139$	931.000	+	1612.54i	0.568104	+	0.983984i	−0.428650	+	0.903471i	$0.641011\pi$
$140$	−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	0.997508	−	0.0705492i	$-0.0224752\pi$
$149$	796.000	+	1378.71i	0.437657	+	0.758044i	−0.559852	+	0.828593i	$0.689142\pi$
$150$	−4248.00	−	2452.58i	−2.31232	−	1.33502i
$151$	458.000	−	793.279i	0.246831	−	0.427524i	−0.715814	−	0.698291i	$-0.753944\pi$
$151$	458.000	−	793.279i	0.246831	−	0.427524i	0.962645	+	0.270767i	$0.0872773\pi$
$152$		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	0.982776	+	0.184803i	$0.0591648\pi$
$157$	1281.50	+	2219.62i	0.651432	+	1.12831i	−0.331343	+	0.943510i	$0.607502\pi$
$158$	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	0.775846	−	0.630922i	$-0.217323\pi$
$167$	−342.000	−	592.361i	−0.158472	−	0.274481i	−0.934318	+	0.356441i	$0.883990\pi$
$168$		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	−0.992482	−	0.122387i	$-0.960945\pi$
$173$	−888.000	+	1538.06i	−0.390251	+	0.675934i	0.602232	+	0.798321i	$0.294278\pi$
$174$	−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	−0.765271	−	0.643708i	$-0.777395\pi$
$191$	461.500	−	799.341i	0.174832	−	0.302818i	0.940103	+	0.340890i	$0.110728\pi$
$192$	2304.00	−	1330.22i	0.866025	−	0.500000i
$193$	−242.000	−	419.156i	−0.0902567	−	0.156329i	0.817362	−	0.576124i	$-0.195435\pi$
$193$	−242.000	−	419.156i	−0.0902567	−	0.156329i	−0.907619	+	0.419795i	$0.862102\pi$
$194$	−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	0.706693	−	0.707520i	$-0.250186\pi$
$211$	−795.000	−	1376.98i	−0.259384	−	0.449267i	−0.966077	+	0.258254i	$0.916853\pi$
$212$	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	−0.879508	−	0.475884i	$-0.842128\pi$
$223$	−92.0000	+	159.349i	−0.0276268	+	0.0478510i	0.851881	+	0.523735i	$0.175462\pi$
$224$	−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	−0.639859	−	0.768492i	$-0.721007\pi$
$227$	1182.00	−	2047.28i	0.345604	−	0.598604i	0.985463	+	0.169888i	$0.0543407\pi$
$228$	−3456.00	−	1995.32i	−1.00386	−	0.579577i
$229$	−285.000	−	493.634i	−0.0822416	−	0.142447i	0.821971	−	0.569530i	$-0.192875\pi$
$229$	−285.000	−	493.634i	−0.0822416	−	0.142447i	−0.904212	+	0.427083i	$0.859541\pi$
$230$	−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	0.991546	+	0.129754i	$0.0414189\pi$
$239$	2247.00	+	3891.92i	0.608144	+	1.05334i	−0.383402	+	0.923581i	$0.625248\pi$
$240$	−5472.00	+	3159.26i	−1.47173	+	0.849706i
$241$	2440.00	−	4226.20i	0.652175	−	1.12960i	−0.330419	−	0.943834i	$-0.607190\pi$
$241$	2440.00	−	4226.20i	0.652175	−	1.12960i	0.982594	−	0.185766i	$-0.0594767\pi$
$242$	−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	0.538548	−	0.842595i	$-0.318973\pi$
$257$	−1897.00	−	3285.70i	−0.460434	−	0.797496i	−0.998983	+	0.0450991i	$0.985640\pi$
$258$	−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	−0.111226	+	0.993795i	$0.535478\pi$
$263$	−3908.00	+	6768.85i	−0.916265	+	1.58702i	−0.805039	+	0.593222i	$0.797856\pi$
$264$		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	−0.992040	−	0.125922i	$-0.959811\pi$
$277$	−1784.00	+	3089.98i	−0.386968	+	0.670248i	0.605072	+	0.796171i	$0.293144\pi$
$278$	7448.00			1.60684
$279$	−1323.00			−0.283892
$280$		0			0
$281$	−12.0000	+	20.7846i	−0.00254754	+	0.00441248i	−0.867296	−	0.497792i	$-0.834144\pi$
$281$	−12.0000	+	20.7846i	−0.00254754	+	0.00441248i	0.864749	+	0.502205i	$0.167478\pi$
$282$	2682.00	+	1548.45i	0.566350	+	0.326982i
$283$	427.000	+	739.586i	0.0896909	+	0.155349i	0.907380	−	0.420310i	$-0.138079\pi$
$283$	427.000	+	739.586i	0.0896909	+	0.155349i	−0.817690	+	0.575659i	$0.804745\pi$
$284$	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	0.584054	−	0.811715i	$-0.301465\pi$
$293$	−2061.00	−	3569.76i	−0.410938	−	0.711766i	−0.994993	+	0.0999486i	$0.968132\pi$
$294$	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	0.886716	+	0.462315i	$0.152981\pi$
$311$	4627.50	+	8015.07i	0.843735	+	1.46139i	−0.0429811	+	0.999076i	$0.513686\pi$
$312$		0			0
$313$	−2491.00	+	4314.54i	−0.449839	+	0.779144i	−0.998375	−	0.0569827i	$-0.981852\pi$
$313$	−2491.00	+	4314.54i	−0.449839	+	0.779144i	0.548536	+	0.836127i	$0.315185\pi$
$314$	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	−0.997630	−	0.0688079i	$-0.978080\pi$
$317$	−2479.00	+	4293.75i	−0.439226	+	0.760761i	0.558404	+	0.829569i	$0.311414\pi$
$318$		−	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	−0.430585	−	0.902550i	$-0.641693\pi$
$331$	3410.50	−	5907.16i	0.566338	−	0.980927i	0.996924	−	0.0783771i	$-0.0249738\pi$
$332$	−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	0.996386	−	0.0849382i	$-0.0270693\pi$
$337$	2627.00	+	4550.10i	0.424634	+	0.735488i	−0.571752	+	0.820427i	$0.693736\pi$
$338$	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	−0.997812	−	0.0661187i	$-0.978938\pi$
$347$	−3595.00	−	6226.72i	−0.556166	−	0.963308i	0.441645	−	0.897190i	$-0.354395\pi$
$348$	−648.000	+	374.123i	−0.0998174	+	0.0576296i
$349$	−4080.00	+	7066.77i	−0.625780	+	1.08388i	0.362609	+	0.931941i	$0.381886\pi$
$349$	−4080.00	+	7066.77i	−0.625780	+	1.08388i	−0.988389	+	0.151942i	$0.951447\pi$
$350$	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	−0.616109	−	0.787661i	$-0.711292\pi$
$353$	2481.00	−	4297.22i	0.374080	−	0.647926i	0.990189	+	0.139735i	$0.0446251\pi$
$354$	−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	−0.603616	−	0.797275i	$-0.706274\pi$
$367$	2732.50	−	4732.83i	0.388652	−	0.673165i	0.992269	+	0.124110i	$0.0396075\pi$
$368$	−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	−0.972405	−	0.233299i	$-0.925048\pi$
$373$	−4958.00	−	8587.51i	−0.688245	−	1.19208i	0.284160	−	0.958777i	$-0.408285\pi$
$374$	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	0.958770	−	0.284184i	$-0.0917226\pi$
$383$	1748.50	+	3028.49i	0.233275	+	0.404043i	−0.725495	+	0.688227i	$0.758389\pi$
$384$		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	−0.491432	−	0.870916i	$-0.663526\pi$
$389$	3901.50	−	6757.60i	0.508519	−	0.880781i	0.999951	−	0.00986502i	$-0.00314018\pi$
$390$	−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	0.972450	+	0.233112i	$0.0748907\pi$
$401$	5525.50	+	9570.45i	0.688105	+	1.19183i	−0.284345	+	0.958722i	$0.591776\pi$
$402$	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	0.860534	−	0.509393i	$-0.170130\pi$
$409$	−90.0000	−	155.885i	−0.0108807	−	0.0188460i	−0.871414	+	0.490547i	$0.836797\pi$
$410$	−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	0.986109	+	0.166097i	$0.0531164\pi$
$419$	5462.50	+	9461.33i	0.636899	+	1.10314i	−0.349211	+	0.937044i	$0.613550\pi$
$420$	17784.0	+	10267.6i	2.06612	+	1.19287i
$421$	7853.50	−	13602.7i	0.909160	−	1.57471i	0.0939252	−	0.995579i	$-0.470059\pi$
$421$	7853.50	−	13602.7i	0.909160	−	1.57471i	0.815234	−	0.579131i	$-0.196608\pi$
$422$	−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	0.103865	+	0.994591i	$0.466879\pi$
$439$	−7445.00	+	12895.1i	−0.809409	+	1.40194i	−0.913274	+	0.407346i	$0.866454\pi$
$440$		0			0
$441$	−8991.00			−0.970845
$442$	23296.0			2.50696
$443$	−2933.50	+	5080.97i	−0.314616	+	0.544931i	−0.979356	−	0.202144i	$-0.935209\pi$
$443$	−2933.50	+	5080.97i	−0.314616	+	0.544931i	0.664740	+	0.747075i	$0.268542\pi$
$444$	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	−0.909561	−	0.415570i	$-0.863582\pi$
$457$	−927.000	+	1605.61i	−0.0948867	+	0.164349i	0.814675	+	0.579918i	$0.196916\pi$
$458$	−2280.00			−0.232614
$459$			14590.8i			1.48375i
$460$	−6080.00			−0.616264
$461$	8535.00	−	14783.1i	0.862288	−	1.49353i	−0.00742784	−	0.999972i	$-0.502364\pi$
$461$	8535.00	−	14783.1i	0.862288	−	1.49353i	0.869715	−	0.493554i	$-0.164302\pi$
$462$	−5148.00	+	2972.20i	−0.518413	+	0.299306i
$463$	−7076.00	−	12256.0i	−0.710258	−	1.23020i	−0.964760	−	0.263131i	$-0.915245\pi$
$463$	−7076.00	−	12256.0i	−0.710258	−	1.23020i	0.254502	−	0.967072i	$-0.418089\pi$
$464$	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	−0.206306	+	0.978488i	$0.566144\pi$
$479$	−9965.00	+	17259.9i	−0.950548	+	1.64640i	−0.744242	+	0.667910i	$0.767189\pi$
$480$			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	0.994091	−	0.108549i	$-0.0346205\pi$
$491$	4385.00	+	7595.04i	0.403039	+	0.698084i	−0.591052	+	0.806634i	$0.701287\pi$
$492$		−	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	0.697336	−	0.716744i	$-0.254369\pi$
$499$	−3032.50	−	5252.44i	−0.272051	−	0.471206i	−0.969387	+	0.245539i	$0.921035\pi$
$500$	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	0.562803	−	0.826591i	$-0.309723\pi$
$509$	−4989.00	−	8641.20i	−0.434447	−	0.752484i	−0.997250	+	0.0741065i	$0.976390\pi$
$510$	−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	−0.662519	−	0.749045i	$-0.730512\pi$
$547$	4061.00	−	7033.86i	0.317433	−	0.549810i	0.979952	+	0.199235i	$0.0638458\pi$
$548$	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	0.928448	−	0.371461i	$-0.121143\pi$
$563$	1904.00	+	3297.82i	0.142529	+	0.246868i	−0.785919	+	0.618329i	$0.787810\pi$
$564$	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	−0.668279	−	0.743911i	$-0.732969\pi$
$569$	4209.00	−	7290.20i	0.310106	−	0.537120i	0.978385	+	0.206791i	$0.0663020\pi$
$570$	32832.0	−	18955.6i	2.41260	−	1.39291i
$571$	−661.000	−	1144.89i	−0.0484448	−	0.0839089i	0.840786	−	0.541367i	$-0.182093\pi$
$571$	−661.000	−	1144.89i	−0.0484448	−	0.0839089i	−0.889231	+	0.457458i	$0.848760\pi$
$572$	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	−0.547618	−	0.836729i	$-0.684465\pi$
$587$	6411.50	−	11105.0i	0.450819	−	0.780842i	0.998437	+	0.0558867i	$0.0177985\pi$
$588$		−	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	0.735625	−	0.677389i	$-0.236889\pi$
$599$	−3208.00	−	5556.42i	−0.218824	−	0.379014i	−0.954449	+	0.298375i	$0.903555\pi$
$600$		0			0
$601$	−2674.00	+	4631.50i	−0.181489	+	0.314348i	−0.942388	−	0.334523i	$-0.891425\pi$
$601$	−2674.00	+	4631.50i	−0.181489	+	0.314348i	0.760899	+	0.648870i	$0.224758\pi$
$602$	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	0.893706	−	0.448652i	$-0.148096\pi$
$607$	872.000	+	1510.35i	0.0583087	+	0.100994i	−0.835398	+	0.549646i	$0.814763\pi$
$608$	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	0.777853	−	0.628447i	$-0.216309\pi$
$617$	−2380.50	−	4123.15i	−0.155325	−	0.269030i	−0.933177	+	0.359417i	$0.882976\pi$
$618$	−4446.00	+	2566.90i	−0.289392	+	0.167081i
$619$	−6596.50	+	11425.5i	−0.428329	+	0.741888i	−0.996725	−	0.0808675i	$-0.974231\pi$
$619$	−6596.50	+	11425.5i	−0.428329	+	0.741888i	0.568396	+	0.822755i	$0.307564\pi$
$620$	−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	−0.945199	−	0.326494i	$-0.894133\pi$
$641$	−3081.00	+	5336.45i	−0.189847	+	0.328825i	0.755352	+	0.655319i	$0.227466\pi$
$642$			24068.6i			1.47961i
$643$	−2374.00	−	4111.89i	−0.145601	−	0.252188i	0.783996	−	0.620766i	$-0.213178\pi$
$643$	−2374.00	−	4111.89i	−0.145601	−	0.252188i	−0.929597	+	0.368578i	$0.879845\pi$
$644$	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	0.994922	−	0.100648i	$-0.0320915\pi$
$653$	6846.50	+	11858.5i	0.410297	+	0.710656i	−0.584625	+	0.811304i	$0.698758\pi$
$654$		−	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	0.419295	+	0.907850i	$0.362277\pi$
$659$	−9754.00	+	16894.4i	−0.576573	+	0.998654i	−0.995869	+	0.0908046i	$0.971056\pi$
$660$	−7524.00	−	4343.98i	−0.443744	−	0.256196i
$661$	−2958.50	−	5124.27i	−0.174088	−	0.301530i	0.765757	−	0.643130i	$-0.222364\pi$
$661$	−2958.50	−	5124.27i	−0.174088	−	0.301530i	−0.939845	+	0.341600i	$0.889031\pi$
$662$	−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	0.255955	+	0.966689i	$0.417610\pi$
$673$	−12382.0	+	21446.3i	−0.709199	+	1.22837i	−0.965155	+	0.261680i	$0.915723\pi$
$674$	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	−0.851811	−	0.523849i	$-0.824496\pi$
$677$	489.000	−	846.973i	0.0277604	−	0.0480824i	0.879572	+	0.475766i	$0.157829\pi$
$678$	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	0.163125	−	0.986605i	$-0.447843\pi$
$691$	17001.5	−	29447.5i	0.935988	−	1.62118i	0.772863	−	0.634573i	$-0.218824\pi$
$692$	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	−0.171806	−	0.985131i	$-0.554960\pi$
$709$	14484.5	−	25087.9i	0.767245	−	1.32891i	0.939051	−	0.343777i	$-0.111706\pi$
$710$	−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	−0.961556	−	0.274609i	$-0.911451\pi$
$727$	−4762.50	+	8248.89i	−0.242959	+	0.420818i	0.718597	+	0.695427i	$0.244785\pi$
$728$		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	0.879670	−	0.475585i	$-0.157764\pi$
$733$	555.000	+	961.288i	0.0279664	+	0.0484393i	−0.851703	+	0.524024i	$0.824430\pi$
$734$	−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	0.859560	−	0.511034i	$-0.170737\pi$
$743$	−259.000	−	448.601i	−0.0127884	−	0.0221502i	−0.872349	+	0.488884i	$0.837404\pi$
$744$		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	0.946856	+	0.321657i	$0.104240\pi$
$751$	15476.5	+	26806.1i	0.751991	+	1.30249i	−0.194865	+	0.980830i	$0.562427\pi$
$752$	−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	0.954618	+	0.297834i	$0.0962643\pi$
$761$	15435.0	+	26734.2i	0.735241	+	1.27347i	−0.219377	+	0.975640i	$0.570402\pi$
$762$			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	0.859745	−	0.510723i	$-0.170622\pi$
$769$	−265.000	−	458.993i	−0.0124267	−	0.0215237i	−0.872172	+	0.489200i	$0.837289\pi$
$770$	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	0.997587	+	0.0694334i	$0.0221191\pi$
$787$	12340.0	+	21373.5i	0.558924	+	0.968085i	−0.438662	+	0.898652i	$0.644548\pi$
$788$	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	0.882828	−	0.469697i	$-0.155637\pi$
$797$	779.500	+	1350.13i	0.0346440	+	0.0600053i	−0.848184	+	0.529702i	$0.822304\pi$
$798$	−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	−0.0101595	−	0.999948i	$-0.503234\pi$
$821$	20252.0	−	35077.5i	0.860901	−	1.49112i	0.871060	−	0.491176i	$-0.163433\pi$
$822$	−9306.00	−	5372.82i	−0.394871	−	0.227979i
$823$	11808.0	+	20452.1i	0.500123	+	0.866238i	1.00000		0.000141720i	$4.51109e-5\pi$
$823$	11808.0	+	20452.1i	0.500123	+	0.866238i	−0.499877	+	0.866096i	$0.666622\pi$
$824$		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	−0.992417	−	0.122915i	$-0.960776\pi$
$839$	−9472.00	+	16406.0i	−0.389761	+	0.675086i	0.602656	+	0.798001i	$0.294109\pi$
$840$		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	0.219605	+	0.975589i	$0.429523\pi$
$853$	−18313.0	+	31719.0i	−0.735082	+	1.27320i	−0.954687	+	0.297611i	$0.903810\pi$
$854$	9360.00			0.375050
$855$	−49248.0			−1.96988
$856$		0			0
$857$	3181.00	−	5509.65i	0.126792	−	0.219610i	−0.795640	−	0.605770i	$-0.792865\pi$
$857$	3181.00	−	5509.65i	0.126792	−	0.219610i	0.922432	+	0.386159i	$0.126199\pi$
$858$		−	12803.3i		−	0.509438i
$859$	17203.5	+	29797.3i	0.683325	+	1.18355i	0.973960	+	0.226719i	$0.0727999\pi$
$859$	17203.5	+	29797.3i	0.683325	+	1.18355i	−0.290636	+	0.956834i	$0.593867\pi$
$860$	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	−0.944287	−	0.329122i	$-0.893247\pi$
$877$	−19665.0	−	34060.8i	−0.757172	−	1.31146i	0.187115	−	0.982338i	$-0.440086\pi$
$878$	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	0.790745	−	0.612146i	$-0.209693\pi$
$887$	−3560.00	−	6166.10i	−0.134761	−	0.233413i	−0.925506	+	0.378733i	$0.876360\pi$
$888$		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	0.0599951	+	0.998199i	$0.480891\pi$
$907$	−22794.0	+	39480.4i	−0.834468	+	1.44534i	−0.894463	+	0.447142i	$0.852442\pi$
$908$	−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	−0.655492	−	0.755202i	$-0.727539\pi$
$911$	8971.50	−	15539.1i	0.326278	−	0.565130i	0.981770	+	0.190072i	$0.0608722\pi$
$912$		−	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	−0.640508	−	0.767952i	$-0.721276\pi$
$929$	9763.50	−	16910.9i	0.344812	−	0.597231i	0.985320	+	0.170720i	$0.0546094\pi$
$930$	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	0.860941	−	0.508705i	$-0.169876\pi$
$941$	−291.000	−	504.027i	−0.0100811	−	0.0174610i	−0.871022	+	0.491244i	$0.836542\pi$
$942$	−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	−0.976863	−	0.213866i	$-0.931394\pi$
$947$	−8836.50	+	15305.3i	−0.303218	+	0.525189i	0.673645	+	0.739055i	$0.264728\pi$
$948$	−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	0.964981	+	0.262321i	$0.0844880\pi$
$967$	21340.0	+	36962.0i	0.709667	+	1.22918i	−0.255313	+	0.966858i	$0.582179\pi$
$968$		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	0.997991	−	0.0633490i	$-0.0201781\pi$
$977$	13563.0	+	23491.8i	0.444134	+	0.769262i	−0.553858	+	0.832611i	$0.686845\pi$
$978$		−	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	−0.350693	−	0.936491i	$-0.614054\pi$
$983$	19591.5	−	33933.5i	0.635678	−	1.10103i	0.986371	−	0.164537i	$-0.0526129\pi$
$984$		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	−0.835355	−	0.549710i	$-0.814738\pi$
$997$	1838.00	−	3183.51i	0.0583852	−	0.101126i	0.893741	+	0.448584i	$0.148072\pi$
$998$	−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.34.1	✓	2
3.2	odd	2		297.4.e.a.100.1		2
9.2	odd	6		891.4.a.d.1.1		1
9.4	even	3	inner	99.4.e.a.67.1	yes	2
9.5	odd	6		297.4.e.a.199.1		2
9.7	even	3		891.4.a.a.1.1		1

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