LMFDB - Embedded newform 105.4.d.b.64.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 $ x^10 + 37x^8 + 398x^6 + 1149x^4 + 1040x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.9
Root			$1.37042i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.4.d.b.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.88936i q^{2} -3.00000i q^{3} -15.9059 q^{4} +(-9.63020 - 5.67972i) q^{5} +14.6681 q^{6} -7.00000i q^{7} -38.6546i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.88936i q^{2} -3.00000i q^{3} -15.9059 q^{4} +(-9.63020 - 5.67972i) q^{5} +14.6681 q^{6} -7.00000i q^{7} -38.6546i q^{8} -9.00000 q^{9} +(27.7702 - 47.0855i) q^{10} +54.9009 q^{11} +47.7176i q^{12} -49.7580i q^{13} +34.2255 q^{14} +(-17.0392 + 28.8906i) q^{15} +61.7496 q^{16} -133.661i q^{17} -44.0043i q^{18} -138.986 q^{19} +(153.177 + 90.3409i) q^{20} -21.0000 q^{21} +268.430i q^{22} +7.32751i q^{23} -115.964 q^{24} +(60.4815 + 109.394i) q^{25} +243.285 q^{26} +27.0000i q^{27} +111.341i q^{28} -87.2408 q^{29} +(-141.257 - 83.3106i) q^{30} -209.479 q^{31} -7.32107i q^{32} -164.703i q^{33} +653.519 q^{34} +(-39.7580 + 67.4114i) q^{35} +143.153 q^{36} +67.9041i q^{37} -679.555i q^{38} -149.274 q^{39} +(-219.547 + 372.252i) q^{40} +77.6804 q^{41} -102.677i q^{42} -197.692i q^{43} -873.246 q^{44} +(86.6718 + 51.1175i) q^{45} -35.8269 q^{46} -4.97613i q^{47} -185.249i q^{48} -49.0000 q^{49} +(-534.865 + 295.716i) q^{50} -400.984 q^{51} +791.444i q^{52} -53.0843i q^{53} -132.013 q^{54} +(-528.706 - 311.822i) q^{55} -270.582 q^{56} +416.959i q^{57} -426.552i q^{58} +683.950 q^{59} +(271.023 - 459.530i) q^{60} -26.8658 q^{61} -1024.22i q^{62} +63.0000i q^{63} +529.792 q^{64} +(-282.612 + 479.180i) q^{65} +805.291 q^{66} -149.300i q^{67} +2126.00i q^{68} +21.9825 q^{69} +(-329.599 - 194.391i) q^{70} +6.15571 q^{71} +347.892i q^{72} +294.545i q^{73} -332.008 q^{74} +(328.181 - 181.445i) q^{75} +2210.70 q^{76} -384.306i q^{77} -729.855i q^{78} +938.669 q^{79} +(-594.661 - 350.720i) q^{80} +81.0000 q^{81} +379.807i q^{82} +784.907i q^{83} +334.023 q^{84} +(-759.160 + 1287.19i) q^{85} +966.590 q^{86} +261.722i q^{87} -2122.17i q^{88} -275.928 q^{89} +(-249.932 + 423.770i) q^{90} -348.306 q^{91} -116.550i q^{92} +628.437i q^{93} +24.3301 q^{94} +(1338.47 + 789.404i) q^{95} -21.9632 q^{96} -1165.27i q^{97} -239.579i q^{98} -494.108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9}+O(q^{10}) $ 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9	$ 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9} + 92 q^{10} + 132 q^{11} - 14 q^{14} + 310 q^{16} - 348 q^{19} + 366 q^{20} - 210 q^{21} + 198 q^{24} - 374 q^{25} + 892 q^{26} - 740 q^{29} - 378 q^{30} + 684 q^{31} - 224 q^{34} + 486 q^{36} - 12 q^{39} - 2156 q^{40} + 1604 q^{41} - 580 q^{44} + 126 q^{45} + 1280 q^{46} - 490 q^{49} - 2504 q^{50} - 648 q^{51} + 54 q^{54} - 452 q^{55} + 462 q^{56} - 1408 q^{59} - 852 q^{60} + 1300 q^{61} - 150 q^{64} - 3296 q^{65} + 3036 q^{66} - 696 q^{69} - 882 q^{70} + 2940 q^{71} + 2624 q^{74} - 408 q^{75} + 8740 q^{76} + 1640 q^{79} - 4126 q^{80} + 810 q^{81} + 1134 q^{84} - 1704 q^{85} + 1664 q^{86} - 572 q^{89} - 828 q^{90} - 28 q^{91} - 5080 q^{94} + 1268 q^{95} + 330 q^{96} - 1188 q^{99}+O(q^{100}) $ 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9 + 92 * q^10 + 132 * q^11 - 14 * q^14 + 310 * q^16 - 348 * q^19 + 366 * q^20 - 210 * q^21 + 198 * q^24 - 374 * q^25 + 892 * q^26 - 740 * q^29 - 378 * q^30 + 684 * q^31 - 224 * q^34 + 486 * q^36 - 12 * q^39 - 2156 * q^40 + 1604 * q^41 - 580 * q^44 + 126 * q^45 + 1280 * q^46 - 490 * q^49 - 2504 * q^50 - 648 * q^51 + 54 * q^54 - 452 * q^55 + 462 * q^56 - 1408 * q^59 - 852 * q^60 + 1300 * q^61 - 150 * q^64 - 3296 * q^65 + 3036 * q^66 - 696 * q^69 - 882 * q^70 + 2940 * q^71 + 2624 * q^74 - 408 * q^75 + 8740 * q^76 + 1640 * q^79 - 4126 * q^80 + 810 * q^81 + 1134 * q^84 - 1704 * q^85 + 1664 * q^86 - 572 * q^89 - 828 * q^90 - 28 * q^91 - 5080 * q^94 + 1268 * q^95 + 330 * q^96 - 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			4.88936i			1.72865i	0.502933	+	0.864325i	$0.332254\pi$
$2$			4.88936i			1.72865i	−0.502933	+	0.864325i	$0.667746\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−15.9059			−1.98823
$5$	−9.63020	−	5.67972i	−0.861351	−	0.508010i
$5$	−9.63020	−	5.67972i	−0.861351	−	0.508010i
$6$	14.6681			0.998037
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$		−	38.6546i		−	1.70831i
$9$	−9.00000			−0.333333
$10$	27.7702	−	47.0855i	0.878171	−	1.48898i
$11$	54.9009			1.50484			0.752420	−	0.658684i	$-0.228887\pi$
$11$	54.9009			1.50484			0.752420	+	0.658684i	$0.228887\pi$
$12$			47.7176i			1.14791i
$13$		−	49.7580i		−	1.06157i	−0.847507	−	0.530784i	$-0.821897\pi$
$13$		−	49.7580i		−	1.06157i	0.847507	−	0.530784i	$-0.178103\pi$
$14$	34.2255			0.653368
$15$	−17.0392	+	28.8906i	−0.293300	+	0.497301i
$16$	61.7496			0.964837
$17$		−	133.661i		−	1.90692i	−0.301517	−	0.953461i	$-0.597493\pi$
$17$		−	133.661i		−	1.90692i	0.301517	−	0.953461i	$-0.402507\pi$
$18$		−	44.0043i		−	0.576217i
$19$	−138.986			−1.67819			−0.839097	−	0.543983i	$-0.816916\pi$
$19$	−138.986			−1.67819			−0.839097	+	0.543983i	$0.816916\pi$
$20$	153.177	+	90.3409i	1.71257	+	1.01004i
$21$	−21.0000			−0.218218
$22$			268.430i			2.60134i
$23$			7.32751i			0.0664301i	0.999448	+	0.0332150i	$0.0105746\pi$
$23$			7.32751i			0.0664301i	−0.999448	+	0.0332150i	$0.989425\pi$
$24$	−115.964			−0.986293
$25$	60.4815	+	109.394i	0.483852	+	0.875150i
$26$	243.285			1.83508
$27$			27.0000i			0.192450i
$28$			111.341i			0.751481i
$29$	−87.2408			−0.558628			−0.279314	−	0.960200i	$-0.590107\pi$
$29$	−87.2408			−0.558628			−0.279314	+	0.960200i	$0.590107\pi$
$30$	−141.257	−	83.3106i	−0.859660	−	0.507012i
$31$	−209.479			−1.21366			−0.606831	−	0.794831i	$-0.707560\pi$
$31$	−209.479			−1.21366			−0.606831	+	0.794831i	$0.707560\pi$
$32$		−	7.32107i		−	0.0404436i
$33$		−	164.703i		−	0.868820i
$34$	653.519			3.29640
$35$	−39.7580	+	67.4114i	−0.192010	+	0.325560i
$36$	143.153			0.662744
$37$			67.9041i			0.301713i	0.988556	+	0.150856i	$0.0482031\pi$
$37$			67.9041i			0.301713i	−0.988556	+	0.150856i	$0.951797\pi$
$38$		−	679.555i		−	2.90101i
$39$	−149.274			−0.612897
$40$	−219.547	+	372.252i	−0.867838	+	1.47145i
$41$	77.6804			0.295894			0.147947	−	0.988995i	$-0.452734\pi$
$41$	77.6804			0.295894			0.147947	+	0.988995i	$0.452734\pi$
$42$		−	102.677i		−	0.377222i
$43$		−	197.692i		−	0.701112i	−0.936542	−	0.350556i	$-0.885993\pi$
$43$		−	197.692i		−	0.701112i	0.936542	−	0.350556i	$-0.114007\pi$
$44$	−873.246			−2.99197
$45$	86.6718	+	51.1175i	0.287117	+	0.169337i
$46$	−35.8269			−0.114834
$47$		−	4.97613i		−	0.0154435i	−0.999970	−	0.00772173i	$-0.997542\pi$
$47$		−	4.97613i		−	0.0154435i	0.999970	−	0.00772173i	$-0.00245793\pi$
$48$		−	185.249i		−	0.557049i
$49$	−49.0000			−0.142857
$50$	−534.865	+	295.716i	−1.51283	+	0.836412i
$51$	−400.984			−1.10096
$52$			791.444i			2.11065i
$53$		−	53.0843i		−	0.137579i	−0.997631	−	0.0687895i	$-0.978086\pi$
$53$		−	53.0843i		−	0.137579i	0.997631	−	0.0687895i	$-0.0219137\pi$
$54$	−132.013			−0.332679
$55$	−528.706	−	311.822i	−1.29620	−	0.764473i
$56$	−270.582			−0.645680
$57$			416.959i			0.968905i
$58$		−	426.552i		−	0.965673i
$59$	683.950			1.50920			0.754599	−	0.656186i	$-0.227831\pi$
$59$	683.950			1.50920			0.754599	+	0.656186i	$0.227831\pi$
$60$	271.023	−	459.530i	0.583148	−	0.988751i
$61$	−26.8658			−0.0563904			−0.0281952	−	0.999602i	$-0.508976\pi$
$61$	−26.8658			−0.0563904			−0.0281952	+	0.999602i	$0.508976\pi$
$62$		−	1024.22i		−	2.09800i
$63$			63.0000i			0.125988i
$64$	529.792			1.03475
$65$	−282.612	+	479.180i	−0.539287	+	0.914383i
$66$	805.291			1.50189
$67$		−	149.300i		−	0.272237i	−0.990693	−	0.136119i	$-0.956537\pi$
$67$		−	149.300i		−	0.272237i	0.990693	−	0.136119i	$-0.0434628\pi$
$68$			2126.00i			3.79140i
$69$	21.9825			0.0383534
$70$	−329.599	−	194.391i	−0.562780	−	0.331918i
$71$	6.15571			0.0102894			0.00514470	−	0.999987i	$-0.498362\pi$
$71$	6.15571			0.0102894			0.00514470	+	0.999987i	$0.498362\pi$
$72$			347.892i			0.569436i
$73$			294.545i			0.472245i	0.971723	+	0.236123i	$0.0758767\pi$
$73$			294.545i			0.472245i	−0.971723	+	0.236123i	$0.924123\pi$
$74$	−332.008			−0.521556
$75$	328.181	−	181.445i	0.505268	−	0.279352i
$76$	2210.70			3.33664
$77$		−	384.306i		−	0.568776i
$78$		−	729.855i		−	1.05948i
$79$	938.669			1.33682			0.668409	−	0.743794i	$-0.266976\pi$
$79$	938.669			1.33682			0.668409	+	0.743794i	$0.266976\pi$
$80$	−594.661	−	350.720i	−0.831063	−	0.490146i
$81$	81.0000			0.111111
$82$			379.807i			0.511496i
$83$			784.907i			1.03801i	0.854772	+	0.519004i	$0.173697\pi$
$83$			784.907i			1.03801i	−0.854772	+	0.519004i	$0.826303\pi$
$84$	334.023			0.433868
$85$	−759.160	+	1287.19i	−0.968735	+	1.64253i
$86$	966.590			1.21198
$87$			261.722i			0.322524i
$88$		−	2122.17i		−	2.57073i
$89$	−275.928			−0.328633			−0.164316	−	0.986408i	$-0.552542\pi$
$89$	−275.928			−0.328633			−0.164316	+	0.986408i	$0.552542\pi$
$90$	−249.932	+	423.770i	−0.292724	+	0.496325i
$91$	−348.306			−0.401235
$92$		−	116.550i		−	0.132078i
$93$			628.437i			0.700708i
$94$	24.3301			0.0266963
$95$	1338.47	+	789.404i	1.44551	+	0.852538i
$96$	−21.9632			−0.0233501
$97$		−	1165.27i		−	1.21975i	−0.792499	−	0.609873i	$-0.791220\pi$
$97$		−	1165.27i		−	1.21975i	0.792499	−	0.609873i	$-0.208780\pi$
$98$		−	239.579i		−	0.246950i
$99$	−494.108			−0.501613
$100$	−962.011	−	1740.00i	−0.962011	−	1.74000i
$101$	−0.162999			−0.000160584			−8.02919e−5	−	1.00000i	$-0.500026\pi$
$101$	−0.162999			−0.000160584			−8.02919e−5		1.00000i	$0.500026\pi$
$102$		−	1960.56i		−	1.90318i
$103$			1300.78i			1.24437i	0.782871	+	0.622184i	$0.213755\pi$
$103$			1300.78i			1.24437i	−0.782871	+	0.622184i	$0.786245\pi$
$104$	−1923.38			−1.81349
$105$	202.234	+	119.274i	0.187962	+	0.110857i
$106$	259.548			0.237826
$107$		−	1531.63i		−	1.38382i	−0.721985	−	0.691908i	$-0.756770\pi$
$107$		−	1531.63i		−	1.38382i	0.721985	−	0.691908i	$-0.243230\pi$
$108$		−	429.458i		−	0.382636i
$109$	−1971.39			−1.73234			−0.866171	−	0.499748i	$-0.833426\pi$
$109$	−1971.39			−1.73234			−0.866171	+	0.499748i	$0.833426\pi$
$110$	1524.61	−	2585.04i	1.32151	−	2.24067i
$111$	203.712			0.174194
$112$		−	432.247i		−	0.364674i
$113$		−	262.817i		−	0.218794i	−0.993998	−	0.109397i	$-0.965108\pi$
$113$		−	262.817i		−	0.218794i	0.993998	−	0.109397i	$-0.0348920\pi$
$114$	−2038.66			−1.67490
$115$	41.6182	−	70.5654i	0.0337471	−	0.0572196i
$116$	1387.64			1.11068
$117$			447.822i			0.353856i
$118$			3344.08i			2.60888i
$119$	−935.630			−0.720749
$120$	1116.76	+	658.642i	0.849545	+	0.501046i
$121$	1683.11			1.26454
$122$		−	131.357i		−	0.0974793i
$123$		−	233.041i		−	0.170834i
$124$	3331.94			2.41304
$125$	38.8765	−	1397.00i	0.0278177	−	0.999613i
$126$	−308.030			−0.217789
$127$		−	569.649i		−	0.398017i	−0.979998	−	0.199009i	$-0.936228\pi$
$127$		−	569.649i		−	0.398017i	0.979998	−	0.199009i	$-0.0637722\pi$
$128$			2531.78i			1.74828i
$129$	−593.077			−0.404787
$130$	−2342.88	−	1381.79i	−1.58065	−	0.932239i
$131$	984.808			0.656817			0.328409	−	0.944536i	$-0.393488\pi$
$131$	984.808			0.656817			0.328409	+	0.944536i	$0.393488\pi$
$132$			2619.74i			1.72742i
$133$			972.905i			0.634297i
$134$	729.982			0.470603
$135$	153.352	−	260.015i	0.0977665	−	0.165767i
$136$	−5166.63			−3.25761
$137$			1377.35i			0.858942i	0.903081	+	0.429471i	$0.141300\pi$
$137$			1377.35i			0.858942i	−0.903081	+	0.429471i	$0.858700\pi$
$138$			107.481i			0.0662997i
$139$	−839.673			−0.512375			−0.256188	−	0.966627i	$-0.582466\pi$
$139$	−839.673			−0.512375			−0.256188	+	0.966627i	$0.582466\pi$
$140$	632.386	−	1072.24i	0.381760	−	0.647289i
$141$	−14.9284			−0.00891629
$142$			30.0975i			0.0177868i
$143$		−	2731.76i		−	1.59749i
$144$	−555.746			−0.321612
$145$	840.147	+	495.504i	0.481175	+	0.283788i
$146$	−1440.14			−0.816347
$147$			147.000i			0.0824786i
$148$		−	1080.07i		−	0.599875i
$149$	1470.33			0.808416			0.404208	−	0.914667i	$-0.367547\pi$
$149$	1470.33			0.808416			0.404208	+	0.914667i	$0.367547\pi$
$150$	887.148	+	1604.60i	0.482902	+	0.873432i
$151$	−1695.79			−0.913916			−0.456958	−	0.889488i	$-0.651061\pi$
$151$	−1695.79			−0.913916			−0.456958	+	0.889488i	$0.651061\pi$
$152$			5372.47i			2.86687i
$153$			1202.95i			0.635641i
$154$	1879.01			0.983215
$155$	2017.32	+	1189.78i	1.04539	+	0.616552i
$156$	2374.33			1.21858
$157$		−	959.433i		−	0.487714i	−0.969811	−	0.243857i	$-0.921587\pi$
$157$		−	959.433i		−	0.487714i	0.969811	−	0.243857i	$-0.0784127\pi$
$158$			4589.49i			2.31089i
$159$	−159.253			−0.0794312
$160$	−41.5816	+	70.5033i	−0.0205457	+	0.0348361i
$161$	51.2926			0.0251082
$162$			396.038i			0.192072i
$163$		−	3865.27i		−	1.85737i	−0.370869	−	0.928685i	$-0.620940\pi$
$163$		−	3865.27i		−	1.85737i	0.370869	−	0.928685i	$-0.379060\pi$
$164$	−1235.57			−0.588305
$165$	−935.465	+	1586.12i	−0.441369	+	0.748359i
$166$	−3837.69			−1.79435
$167$			465.084i			0.215505i	0.994178	+	0.107752i	$0.0343653\pi$
$167$			465.084i			0.215505i	−0.994178	+	0.107752i	$0.965635\pi$
$168$			811.747i			0.372784i
$169$	−278.860			−0.126927
$170$	−6293.52	−	3711.81i	−2.83936	−	1.67460i
$171$	1250.88			0.559398
$172$			3144.47i			1.39397i
$173$			2048.04i			0.900057i	0.893014	+	0.450028i	$0.148586\pi$
$173$			2048.04i			0.900057i	−0.893014	+	0.450028i	$0.851414\pi$
$174$	−1279.66			−0.557531
$175$	765.756	−	423.371i	0.330775	−	0.182879i
$176$	3390.10			1.45192
$177$		−	2051.85i		−	0.871336i
$178$		−	1349.11i		−	0.568091i
$179$	911.856			0.380756			0.190378	−	0.981711i	$-0.439029\pi$
$179$	911.856			0.380756			0.190378	+	0.981711i	$0.439029\pi$
$180$	−1378.59	−	813.068i	−0.570856	−	0.336681i
$181$	−2029.81			−0.833562			−0.416781	−	0.909007i	$-0.636842\pi$
$181$	−2029.81			−0.833562			−0.416781	+	0.909007i	$0.636842\pi$
$182$		−	1702.99i		−	0.693595i
$183$			80.5975i			0.0325570i
$184$	283.242			0.113483
$185$	385.677	−	653.930i	0.153273	−	0.259881i
$186$	−3072.66			−1.21128
$187$		−	7338.13i		−	2.86961i
$188$			79.1496i			0.0307052i
$189$	189.000			0.0727393
$190$	−3859.68	+	6544.25i	−1.47374	+	2.49879i
$191$	4984.11			1.88815			0.944077	−	0.329725i	$-0.106956\pi$
$191$	4984.11			1.88815			0.944077	+	0.329725i	$0.106956\pi$
$192$		−	1589.38i		−	0.597413i
$193$		−	3393.44i		−	1.26562i	−0.774306	−	0.632811i	$-0.781901\pi$
$193$		−	3393.44i		−	1.26562i	0.774306	−	0.632811i	$-0.218099\pi$
$194$	5697.43			2.10852
$195$	1437.54	+	847.835i	0.527919	+	0.311358i
$196$	779.387			0.284033
$197$		−	762.475i		−	0.275757i	−0.990449	−	0.137878i	$-0.955972\pi$
$197$		−	762.475i		−	0.275757i	0.990449	−	0.137878i	$-0.0440283\pi$
$198$		−	2415.87i		−	0.867114i
$199$	1272.32			0.453227			0.226613	−	0.973985i	$-0.427235\pi$
$199$	1272.32			0.453227			0.226613	+	0.973985i	$0.427235\pi$
$200$	4228.57	−	2337.89i	1.49503	−	0.826569i
$201$	−447.900			−0.157176
$202$		−	0.796959i		−	0.000277593i
$203$			610.686i			0.211142i
$204$	6378.00			2.18897
$205$	−748.077	−	441.203i	−0.254868	−	0.150317i
$206$	−6360.00			−2.15108
$207$		−	65.9476i		−	0.0221434i
$208$		−	3072.53i		−	1.02424i
$209$	−7630.47			−2.52541
$210$	−583.174	+	988.796i	−0.191633	+	0.324921i
$211$	2010.72			0.656035			0.328017	−	0.944672i	$-0.393620\pi$
$211$	2010.72			0.656035			0.328017	+	0.944672i	$0.393620\pi$
$212$			844.351i			0.273539i
$213$		−	18.4671i		−	0.00594059i
$214$	7488.70			2.39214
$215$	−1122.84	+	1903.82i	−0.356172	+	0.603904i
$216$	1043.67			0.328764
$217$			1466.35i			0.458721i
$218$		−	9638.85i		−	2.99461i
$219$	883.635			0.272651
$220$	8409.53	+	4959.79i	2.57714	+	1.51995i
$221$	−6650.73			−2.02433
$222$			996.024i			0.301120i
$223$			1516.44i			0.455374i	0.973734	+	0.227687i	$0.0731163\pi$
$223$			1516.44i			0.455374i	−0.973734	+	0.227687i	$0.926884\pi$
$224$	−51.2475			−0.0152862
$225$	−544.334	−	984.543i	−0.161284	−	0.291717i
$226$	1285.01			0.378219
$227$		−	4101.17i		−	1.19914i	−0.800323	−	0.599568i	$-0.795339\pi$
$227$		−	4101.17i		−	1.19914i	0.800323	−	0.599568i	$-0.204661\pi$
$228$		−	6632.10i		−	1.92641i
$229$	1029.24			0.297004			0.148502	−	0.988912i	$-0.452555\pi$
$229$	1029.24			0.297004			0.148502	+	0.988912i	$0.452555\pi$
$230$	345.020	+	203.487i	0.0989128	+	0.0583370i
$231$	−1152.92			−0.328383
$232$			3372.26i			0.954309i
$233$			5578.41i			1.56847i	0.620463	+	0.784236i	$0.286945\pi$
$233$			5578.41i			1.56847i	−0.620463	+	0.784236i	$0.713055\pi$
$234$	−2189.56			−0.611694
$235$	−28.2630	+	47.9211i	−0.00784543	+	0.0133022i
$236$	−10878.8			−3.00064
$237$		−	2816.01i		−	0.771812i
$238$		−	4574.64i		−	1.24592i
$239$	−5389.67			−1.45870			−0.729348	−	0.684142i	$-0.760177\pi$
$239$	−5389.67			−1.45870			−0.729348	+	0.684142i	$0.760177\pi$
$240$	−1052.16	+	1783.98i	−0.282986	+	0.479815i
$241$	3976.27			1.06280			0.531399	−	0.847122i	$-0.321667\pi$
$241$	3976.27			1.06280			0.531399	+	0.847122i	$0.321667\pi$
$242$			8229.31i			2.18595i
$243$		−	243.000i		−	0.0641500i
$244$	427.324			0.112117
$245$	471.880	+	278.306i	0.123050	+	0.0725728i
$246$	1139.42			0.295313
$247$			6915.69i			1.78152i
$248$			8097.33i			2.07331i
$249$	2354.72			0.599294
$250$	6830.45	+	190.081i	1.72798	+	0.0480871i
$251$	7095.76			1.78438			0.892192	−	0.451655i	$-0.149166\pi$
$251$	7095.76			1.78438			0.892192	+	0.451655i	$0.149166\pi$
$252$		−	1002.07i		−	0.250494i
$253$			402.287i			0.0999666i
$254$	2785.22			0.688033
$255$	3861.56	+	2277.48i	0.948315	+	0.559299i
$256$	−8140.43			−1.98741
$257$			2526.56i			0.613239i	0.951832	+	0.306619i	$0.0991979\pi$
$257$			2526.56i			0.613239i	−0.951832	+	0.306619i	$0.900802\pi$
$258$		−	2899.77i		−	0.699735i
$259$	475.329			0.114037
$260$	4495.18	−	7621.77i	1.07223	−	1.81801i
$261$	785.167			0.186209
$262$			4815.08i			1.13541i
$263$		−	3842.34i		−	0.900871i	−0.892809	−	0.450435i	$-0.851269\pi$
$263$		−	3842.34i		−	0.900871i	0.892809	−	0.450435i	$-0.148731\pi$
$264$	−6366.52			−1.48421
$265$	−301.504	+	511.212i	−0.0698914	+	0.118504i
$266$	−4756.88			−1.09648
$267$			827.784i			0.189736i
$268$			2374.75i			0.541271i
$269$	8411.04			1.90643			0.953216	−	0.302291i	$-0.0977514\pi$
$269$	8411.04			1.90643			0.953216	+	0.302291i	$0.0977514\pi$
$270$	1271.31	+	749.796i	0.286553	+	0.169004i
$271$	5659.73			1.26865			0.634325	−	0.773067i	$-0.281278\pi$
$271$	5659.73			1.26865			0.634325	+	0.773067i	$0.281278\pi$
$272$		−	8253.54i		−	1.83987i
$273$			1044.92i			0.231653i
$274$	−6734.37			−1.48481
$275$	3320.49	+	6005.81i	0.728120	+	1.31696i
$276$	−349.651			−0.0762555
$277$			881.409i			0.191187i	0.995420	+	0.0955934i	$0.0304749\pi$
$277$			881.409i			0.191187i	−0.995420	+	0.0955934i	$0.969525\pi$
$278$		−	4105.47i		−	0.885718i
$279$	1885.31			0.404554
$280$	2605.76	+	1536.83i	0.556157	+	0.328012i
$281$	−3853.71			−0.818124			−0.409062	−	0.912506i	$-0.634144\pi$
$281$	−3853.71			−0.818124			−0.409062	+	0.912506i	$0.634144\pi$
$282$		−	72.9902i		−	0.0154131i
$283$		−	1891.60i		−	0.397328i	−0.980068	−	0.198664i	$-0.936340\pi$
$283$		−	1891.60i		−	0.397328i	0.980068	−	0.198664i	$-0.0636603\pi$
$284$	−97.9118			−0.0204577
$285$	2368.21	−	4015.40i	0.492213	−	0.834568i
$286$	13356.6			2.76150
$287$		−	543.763i		−	0.111837i
$288$			65.8896i			0.0134812i
$289$	−12952.4			−2.63635
$290$	−2422.70	+	4107.78i	−0.490571	+	0.831784i
$291$	−3495.81			−0.704221
$292$		−	4684.99i		−	0.938933i
$293$		−	4076.18i		−	0.812742i	−0.913708	−	0.406371i	$-0.866794\pi$
$293$		−	4076.18i		−	0.812742i	0.913708	−	0.406371i	$-0.133206\pi$
$294$	−718.736			−0.142577
$295$	−6586.58	−	3884.65i	−1.29995	−	0.766687i
$296$	2624.81			0.515419
$297$			1482.32i			0.289607i
$298$			7188.97i			1.39747i
$299$	364.602			0.0705201
$300$	−5220.00	+	2886.03i	−1.00459	+	0.555417i
$301$	−1383.85			−0.264995
$302$		−	8291.33i		−	1.57984i
$303$			0.488996i			9.27131e-5i
$304$	−8582.35			−1.61918
$305$	258.723	+	152.590i	0.0485720	+	0.0286469i
$306$	−5881.67			−1.09880
$307$		−	6201.87i		−	1.15296i	−0.817110	−	0.576481i	$-0.804425\pi$
$307$		−	6201.87i		−	1.15296i	0.817110	−	0.576481i	$-0.195575\pi$
$308$			6112.72i			1.13086i
$309$	3902.35			0.718437
$310$	−5817.28	+	9863.43i	−1.06580	+	1.80711i
$311$	−6601.95			−1.20374			−0.601868	−	0.798595i	$-0.705577\pi$
$311$	−6601.95			−1.20374			−0.601868	+	0.798595i	$0.705577\pi$
$312$			5770.13i			1.04702i
$313$			2291.01i			0.413724i	0.978370	+	0.206862i	$0.0663251\pi$
$313$			2291.01i			0.413724i	−0.978370	+	0.206862i	$0.933675\pi$
$314$	4691.02			0.843087
$315$	357.822	−	606.703i	0.0640032	−	0.108520i
$316$	−14930.3			−2.65790
$317$		−	3124.07i		−	0.553517i	−0.960939	−	0.276759i	$-0.910740\pi$
$317$		−	3124.07i		−	0.553517i	0.960939	−	0.276759i	$-0.0892603\pi$
$318$		−	778.644i		−	0.137309i
$319$	−4789.60			−0.840646
$320$	−5102.00	−	3009.07i	−0.891283	−	0.525663i
$321$	−4594.89			−0.798947
$322$			250.788i			0.0434033i
$323$			18577.1i			3.20018i
$324$	−1288.37			−0.220915
$325$	5443.21	−	3009.44i	0.929031	−	0.513642i
$326$	18898.7			3.21074
$327$			5914.18i			1.00017i
$328$		−	3002.70i		−	0.505478i
$329$	−34.8329			−0.00583708
$330$	−7755.11	−	4573.83i	−1.29365	−	0.762972i
$331$	9825.49			1.63159			0.815797	−	0.578338i	$-0.196298\pi$
$331$	9825.49			1.63159			0.815797	+	0.578338i	$0.196298\pi$
$332$		−	12484.6i		−	2.06380i
$333$		−	611.137i		−	0.100571i
$334$	−2273.96			−0.372532
$335$	−847.983	+	1437.79i	−0.138299	+	0.234492i
$336$	−1296.74			−0.210545
$337$			8526.35i			1.37822i	0.724657	+	0.689110i	$0.241998\pi$
$337$			8526.35i			1.37822i	−0.724657	+	0.689110i	$0.758002\pi$
$338$		−	1363.45i		−	0.219413i
$339$	−788.451			−0.126321
$340$	12075.1	−	20473.8i	1.92607	−	3.26573i
$341$	−11500.6			−1.82637
$342$			6115.99i			0.967003i
$343$			343.000i			0.0539949i
$344$	−7641.73			−1.19772
$345$	−211.696	−	124.855i	−0.0330358	−	0.0194839i
$346$	−10013.6			−1.55588
$347$		−	4164.54i		−	0.644277i	−0.946693	−	0.322138i	$-0.895598\pi$
$347$		−	4164.54i		−	0.644277i	0.946693	−	0.322138i	$-0.104402\pi$
$348$		−	4162.92i		−	0.641253i
$349$	−2584.60			−0.396420			−0.198210	−	0.980160i	$-0.563513\pi$
$349$	−2584.60			−0.396420			−0.198210	+	0.980160i	$0.563513\pi$
$350$	2070.01	+	3744.06i	0.316134	+	0.571795i
$351$	1343.47			0.204299
$352$		−	401.933i		−	0.0608611i
$353$			4199.25i			0.633154i	0.948567	+	0.316577i	$0.102534\pi$
$353$			4199.25i			0.633154i	−0.948567	+	0.316577i	$0.897466\pi$
$354$	10032.2			1.50624
$355$	−59.2807	−	34.9627i	−0.00886280	−	0.00522712i
$356$	4388.87			0.653398
$357$			2806.89i			0.416124i
$358$			4458.39i			0.658194i
$359$	990.277			0.145584			0.0727922	−	0.997347i	$-0.476809\pi$
$359$	990.277			0.145584			0.0727922	+	0.997347i	$0.476809\pi$
$360$	1975.93	−	3350.27i	0.289279	−	0.490485i
$361$	12458.2			1.81633
$362$		−	9924.48i		−	1.44094i
$363$		−	5049.32i		−	0.730084i
$364$	5540.11			0.797749
$365$	1672.93	−	2836.53i	0.239905	−	0.406769i
$366$	−394.070			−0.0562797
$367$		−	4179.24i		−	0.594427i	−0.954811	−	0.297213i	$-0.903943\pi$
$367$		−	4179.24i		−	0.594427i	0.954811	−	0.297213i	$-0.0960573\pi$
$368$			452.471i			0.0640942i
$369$	−699.123			−0.0986312
$370$	3197.30	+	1885.71i	0.449243	+	0.264955i
$371$	−371.590			−0.0519999
$372$		−	9995.83i		−	1.39317i
$373$		−	7365.36i		−	1.02242i	−0.859455	−	0.511212i	$-0.829197\pi$
$373$		−	7365.36i		−	1.02242i	0.859455	−	0.511212i	$-0.170803\pi$
$374$	35878.8			4.96056
$375$	−4191.00	−	116.629i	−0.577127	−	0.0160606i
$376$	−192.350			−0.0263822
$377$			4340.93i			0.593022i
$378$			924.089i			0.125741i
$379$	6214.13			0.842213			0.421106	−	0.907011i	$-0.361642\pi$
$379$	6214.13			0.842213			0.421106	+	0.907011i	$0.361642\pi$
$380$	−21289.5	−	12556.2i	−2.87402	−	1.69504i
$381$	−1708.95			−0.229795
$382$			24369.1i			3.26396i
$383$		−	1755.04i		−	0.234148i	−0.993123	−	0.117074i	$-0.962649\pi$
$383$		−	1755.04i		−	0.234148i	0.993123	−	0.117074i	$-0.0373514\pi$
$384$	7595.33			1.00937
$385$	−2182.75	+	3700.94i	−0.288944	+	0.489916i
$386$	16591.7			2.18782
$387$			1779.23i			0.233704i
$388$			18534.6i			2.42514i
$389$	−8805.69			−1.14773			−0.573864	−	0.818950i	$-0.694556\pi$
$389$	−8805.69			−1.14773			−0.573864	+	0.818950i	$0.694556\pi$
$390$	−4145.37	+	7028.65i	−0.538228	+	0.912588i
$391$	979.406			0.126677
$392$			1894.08i			0.244044i
$393$		−	2954.42i		−	0.379214i
$394$	3728.01			0.476687
$395$	−9039.57	−	5331.38i	−1.15147	−	0.679116i
$396$	7859.21			0.997324
$397$			13717.2i			1.73413i	0.498199	+	0.867063i	$0.333995\pi$
$397$			13717.2i			1.73413i	−0.498199	+	0.867063i	$0.666005\pi$
$398$			6220.82i			0.783471i
$399$	2918.71			0.366212
$400$	3734.71	+	6755.01i	0.466838	+	0.844377i
$401$	307.220			0.0382590			0.0191295	−	0.999817i	$-0.493911\pi$
$401$	307.220			0.0382590			0.0191295	+	0.999817i	$0.493911\pi$
$402$		−	2189.95i		−	0.271703i
$403$			10423.3i			1.28839i
$404$	2.59263			0.000319278
$405$	−780.046	−	460.057i	−0.0957057	−	0.0564455i
$406$	−2985.86			−0.364990
$407$			3728.00i			0.454029i
$408$			15499.9i			1.88078i
$409$	−12390.7			−1.49799			−0.748997	−	0.662573i	$-0.769464\pi$
$409$	−12390.7			−1.49799			−0.748997	+	0.662573i	$0.769464\pi$
$410$	2157.20	−	3657.62i	0.259845	−	0.440578i
$411$	4132.05			0.495910
$412$		−	20690.1i		−	2.47409i
$413$		−	4787.65i		−	0.570423i
$414$	322.442			0.0382781
$415$	4458.05	−	7558.81i	0.527318	−	0.894090i
$416$	−364.282			−0.0429336
$417$			2519.02i			0.295820i
$418$		−	37308.2i		−	4.36555i
$419$	−2664.10			−0.310620			−0.155310	−	0.987866i	$-0.549638\pi$
$419$	−2664.10			−0.310620			−0.155310	+	0.987866i	$0.549638\pi$
$420$	−3216.71	−	1897.16i	−0.373713	−	0.220409i
$421$	−6851.11			−0.793118			−0.396559	−	0.918009i	$-0.629796\pi$
$421$	−6851.11			−0.793118			−0.396559	+	0.918009i	$0.629796\pi$
$422$			9831.12i			1.13406i
$423$			44.7851i			0.00514782i
$424$	−2051.95			−0.235027
$425$	14621.7	−	8084.05i	1.66884	−	0.922668i
$426$	90.2924			0.0102692
$427$			188.061i			0.0213136i
$428$			24361.9i			2.75135i
$429$	−8195.27			−0.922311
$430$	−9308.45	−	5489.96i	−1.04394	−	0.615696i
$431$	−7651.38			−0.855114			−0.427557	−	0.903988i	$-0.640626\pi$
$431$	−7651.38			−0.855114			−0.427557	+	0.903988i	$0.640626\pi$
$432$			1667.24i			0.185683i
$433$			691.572i			0.0767548i	0.999263	+	0.0383774i	$0.0122189\pi$
$433$			691.572i			0.0767548i	−0.999263	+	0.0383774i	$0.987781\pi$
$434$	−7169.53			−0.792969
$435$	1486.51	−	2520.44i	0.163845	−	0.277807i
$436$	31356.7			3.44430
$437$		−	1018.42i		−	0.111483i
$438$			4320.41i			0.471318i
$439$	−10621.7			−1.15478			−0.577389	−	0.816469i	$-0.695928\pi$
$439$	−10621.7			−1.15478			−0.577389	+	0.816469i	$0.695928\pi$
$440$	−12053.3	+	20436.9i	−1.30596	+	2.21430i
$441$	441.000			0.0476190
$442$		−	32517.8i		−	3.49936i
$443$		−	3133.67i		−	0.336084i	−0.985780	−	0.168042i	$-0.946256\pi$
$443$		−	3133.67i		−	0.336084i	0.985780	−	0.168042i	$-0.0537444\pi$
$444$	−3240.22			−0.346338
$445$	2657.24	+	1567.19i	0.283068	+	0.166949i
$446$	−7414.43			−0.787182
$447$		−	4410.99i		−	0.466739i
$448$		−	3708.54i		−	0.391099i
$449$	9144.92			0.961192			0.480596	−	0.876942i	$-0.340420\pi$
$449$	9144.92			0.961192			0.480596	+	0.876942i	$0.340420\pi$
$450$	4813.79	−	2661.45i	0.504276	−	0.278804i
$451$	4264.72			0.445272
$452$			4180.33i			0.435014i
$453$			5087.37i			0.527650i
$454$	20052.1			2.07289
$455$	3354.26	+	1978.28i	0.345604	+	0.203831i
$456$	16117.4			1.65519
$457$			8142.60i			0.833468i	0.909029	+	0.416734i	$0.136825\pi$
$457$			8142.60i			0.833468i	−0.909029	+	0.416734i	$0.863175\pi$
$458$			5032.32i			0.513417i
$459$	3608.86			0.366987
$460$	−661.974	+	1122.40i	−0.0670971	+	0.113766i
$461$	−9287.29			−0.938291			−0.469145	−	0.883121i	$-0.655438\pi$
$461$	−9287.29			−0.938291			−0.469145	+	0.883121i	$0.655438\pi$
$462$		−	5637.04i		−	0.567659i
$463$		−	2440.53i		−	0.244970i	−0.992470	−	0.122485i	$-0.960914\pi$
$463$		−	2440.53i		−	0.244970i	0.992470	−	0.122485i	$-0.0390864\pi$
$464$	−5387.08			−0.538985
$465$	3569.35	−	6051.97i	0.355967	−	0.603556i
$466$	−27274.9			−2.71134
$467$		−	12066.3i		−	1.19564i	−0.801632	−	0.597818i	$-0.796034\pi$
$467$		−	12066.3i		−	1.19564i	0.801632	−	0.597818i	$-0.203966\pi$
$468$		−	7123.00i		−	0.703548i
$469$	−1045.10			−0.102896
$470$	−234.304	−	138.188i	−0.0229949	−	0.0135620i
$471$	−2878.30			−0.281582
$472$		−	26437.8i		−	2.57818i
$473$		−	10853.5i		−	1.05506i
$474$	13768.5			1.33419
$475$	−8406.11	−	15204.2i	−0.811998	−	1.46867i
$476$	14882.0			1.43302
$477$			477.758i			0.0458596i
$478$		−	26352.0i		−	2.52158i
$479$	−395.211			−0.0376987			−0.0188493	−	0.999822i	$-0.506000\pi$
$479$	−395.211			−0.0376987			−0.0188493	+	0.999822i	$0.506000\pi$
$480$	211.510	+	124.745i	0.0201126	+	0.0118621i
$481$	3378.77			0.320289
$482$			19441.4i			1.83721i
$483$		−	153.878i		−	0.0144962i
$484$	−26771.2			−2.51420
$485$	−6618.42	+	11221.8i	−0.619643	+	1.05063i
$486$	1188.11			0.110893
$487$		−	9609.06i		−	0.894102i	−0.894508	−	0.447051i	$-0.852474\pi$
$487$		−	9609.06i		−	0.894102i	0.894508	−	0.447051i	$-0.147526\pi$
$488$			1038.49i			0.0963323i
$489$	−11595.8			−1.07235
$490$	−1360.74	+	2307.19i	−0.125453	+	0.212711i
$491$	10941.0			1.00562			0.502810	−	0.864397i	$-0.332299\pi$
$491$	10941.0			1.00562			0.502810	+	0.864397i	$0.332299\pi$
$492$			3706.72i			0.339658i
$493$			11660.7i			1.06526i
$494$	−33813.3			−3.07962
$495$	4758.36	+	2806.39i	0.432065	+	0.254824i
$496$	−12935.2			−1.17099
$497$		−	43.0899i		−	0.00388903i
$498$			11513.1i			1.03597i
$499$	−9269.90			−0.831618			−0.415809	−	0.909452i	$-0.636502\pi$
$499$	−9269.90			−0.831618			−0.415809	+	0.909452i	$0.636502\pi$
$500$	−618.363	+	22220.5i	−0.0553081	+	1.98746i
$501$	1395.25			0.124422
$502$			34693.8i			3.08458i
$503$		−	15085.4i		−	1.33723i	−0.743609	−	0.668615i	$-0.766888\pi$
$503$		−	15085.4i		−	1.33723i	0.743609	−	0.668615i	$-0.233112\pi$
$504$	2435.24			0.215227
$505$	1.56971	+	0.925787i	0.000138319	+	8.15781e-5i
$506$	−1966.93			−0.172807
$507$			836.579i			0.0732816i
$508$			9060.76i			0.791351i
$509$	−8650.44			−0.753289			−0.376645	−	0.926358i	$-0.622922\pi$
$509$	−8650.44			−0.753289			−0.376645	+	0.926358i	$0.622922\pi$
$510$	−11135.4	+	18880.6i	−0.966833	+	1.63931i
$511$	2061.82			0.178492
$512$		−	19547.3i		−	1.68726i
$513$		−	3752.63i		−	0.322968i
$514$	−12353.3			−1.06008
$515$	7388.09	−	12526.8i	0.632151	−	1.07184i
$516$	9433.40			0.804811
$517$		−	273.194i		−	0.0232399i
$518$			2324.06i			0.197130i
$519$	6144.13			0.519648
$520$	18522.5	+	10924.2i	1.56205	+	0.921269i
$521$	10661.6			0.896535			0.448268	−	0.893899i	$-0.352041\pi$
$521$	10661.6			0.896535			0.448268	+	0.893899i	$0.352041\pi$
$522$			3838.97i			0.321891i
$523$		−	3449.22i		−	0.288382i	−0.989550	−	0.144191i	$-0.953942\pi$
$523$		−	3449.22i		−	0.288382i	0.989550	−	0.144191i	$-0.0460580\pi$
$524$	−15664.2			−1.30591
$525$	−1270.11	−	2297.27i	−0.105585	−	0.190973i
$526$	18786.6			1.55729
$527$			27999.3i			2.31436i
$528$		−	10170.3i		−	0.838269i
$529$	12113.3			0.995587
$530$	−2499.50	−	1474.16i	−0.204852	−	0.120818i
$531$	−6155.55			−0.503066
$532$		−	15474.9i		−	1.26113i
$533$		−	3865.22i		−	0.314111i
$534$	−4047.34			−0.327988
$535$	−8699.24	+	14749.9i	−0.702992	+	1.19195i
$536$	−5771.14			−0.465066
$537$		−	2735.57i		−	0.219829i
$538$			41124.6i			3.29555i
$539$	−2690.14			−0.214977
$540$	−2439.20	+	4135.77i	−0.194383	+	0.329584i
$541$	13403.2			1.06516			0.532578	−	0.846381i	$-0.321223\pi$
$541$	13403.2			1.06516			0.532578	+	0.846381i	$0.321223\pi$
$542$			27672.5i			2.19305i
$543$			6089.43i			0.481257i
$544$	−978.544			−0.0771227
$545$	18984.9	+	11197.0i	1.49215	+	0.880046i
$546$	−5108.98			−0.400447
$547$			3670.29i			0.286893i	0.989658	+	0.143446i	$0.0458184\pi$
$547$			3670.29i			0.286893i	−0.989658	+	0.143446i	$0.954182\pi$
$548$		−	21907.9i		−	1.70778i
$549$	241.792			0.0187968
$550$	−29364.6	+	16235.1i	−2.27656	+	1.25867i
$551$	12125.3			0.937486
$552$		−	849.727i		−	0.0655195i
$553$		−	6570.69i		−	0.505269i
$554$	−4309.53			−0.330495
$555$	−1961.79	−	1157.03i	−0.150042	−	0.0884922i
$556$	13355.7			1.01872
$557$		−	521.169i		−	0.0396456i	−0.999804	−	0.0198228i	$-0.993690\pi$
$557$		−	521.169i		−	0.0396456i	0.999804	−	0.0198228i	$-0.00631021\pi$
$558$			9217.97i			0.699333i
$559$	−9836.78			−0.744278
$560$	−2455.04	+	4162.62i	−0.185258	+	0.314112i
$561$	−22014.4			−1.65677
$562$		−	18842.2i		−	1.41425i
$563$		−	17970.2i		−	1.34521i	−0.740000	−	0.672606i	$-0.765175\pi$
$563$		−	17970.2i		−	1.34521i	0.740000	−	0.672606i	$-0.234825\pi$
$564$	237.449			0.0177277
$565$	−1492.73	+	2530.98i	−0.111150	+	0.188459i
$566$	9248.71			0.686842
$567$		−	567.000i		−	0.0419961i
$568$		−	237.947i		−	0.0175775i
$569$	21808.6			1.60679			0.803396	−	0.595445i	$-0.203024\pi$
$569$	21808.6			1.60679			0.803396	+	0.595445i	$0.203024\pi$
$570$	19632.7	+	11579.0i	1.44268	+	0.850865i
$571$	6604.75			0.484064			0.242032	−	0.970268i	$-0.422186\pi$
$571$	6604.75			0.484064			0.242032	+	0.970268i	$0.422186\pi$
$572$			43451.0i			3.17618i
$573$		−	14952.3i		−	1.09013i
$574$	2658.65			0.193327
$575$	−801.584	+	443.179i	−0.0581363	+	0.0321423i
$576$	−4768.13			−0.344916
$577$			25886.9i			1.86774i	0.357618	+	0.933868i	$0.383589\pi$
$577$			25886.9i			1.86774i	−0.357618	+	0.933868i	$0.616411\pi$
$578$		−	63328.9i		−	4.55733i
$579$	−10180.3			−0.730707
$580$	−13363.3	−	7881.41i	−0.956688	−	0.564238i
$581$	5494.35			0.392330
$582$		−	17092.3i		−	1.21735i
$583$		−	2914.37i		−	0.207034i
$584$	11385.5			0.806741
$585$	2543.50	−	4312.62i	0.179762	−	0.304794i
$586$	19929.9			1.40495
$587$			4949.88i			0.348046i	0.984742	+	0.174023i	$0.0556768\pi$
$587$			4949.88i			0.348046i	−0.984742	+	0.174023i	$0.944323\pi$
$588$		−	2338.16i		−	0.163987i
$589$	29114.7			2.03676
$590$	18993.4	−	32204.2i	1.32533	−	2.24716i
$591$	−2287.42			−0.159208
$592$			4193.05i			0.291104i
$593$			31.3988i			0.00217436i	0.999999	+	0.00108718i	$0.000346059\pi$
$593$			31.3988i			0.00217436i	−0.999999	+	0.00108718i	$0.999654\pi$
$594$	−7247.62			−0.500628
$595$	9010.31	+	5314.12i	0.620818	+	0.366147i
$596$	−23386.8			−1.60732
$597$		−	3816.95i		−	0.261671i
$598$			1782.67i			0.121905i
$599$	11870.4			0.809704			0.404852	−	0.914382i	$-0.367323\pi$
$599$	11870.4			0.809704			0.404852	+	0.914382i	$0.367323\pi$
$600$	−7013.67	−	12685.7i	−0.477220	−	0.863154i
$601$	−967.320			−0.0656536			−0.0328268	−	0.999461i	$-0.510451\pi$
$601$	−967.320			−0.0656536			−0.0328268	+	0.999461i	$0.510451\pi$
$602$		−	6766.13i		−	0.458084i
$603$			1343.70i			0.0907458i
$604$	26973.0			1.81708
$605$	−16208.6	−	9559.57i	−1.08922	−	0.642400i
$606$	−2.39088			−0.000160269
$607$			9518.28i			0.636466i	0.948013	+	0.318233i	$0.103089\pi$
$607$			9518.28i			0.636466i	−0.948013	+	0.318233i	$0.896911\pi$
$608$			1017.53i			0.0678721i
$609$	1832.06			0.121903
$610$	−746.070	+	1264.99i	−0.0495205	+	0.0839640i
$611$	−247.602			−0.0163943
$612$		−	19134.0i		−	1.26380i
$613$		−	3607.19i		−	0.237672i	−0.992914	−	0.118836i	$-0.962084\pi$
$613$		−	3607.19i		−	0.237672i	0.992914	−	0.118836i	$-0.0379163\pi$
$614$	30323.2			1.99307
$615$	−1323.61	+	2244.23i	−0.0867854	+	0.147148i
$616$	−14855.2			−0.971645
$617$		−	22473.2i		−	1.46635i	−0.680042	−	0.733173i	$-0.738038\pi$
$617$		−	22473.2i		−	1.46635i	0.680042	−	0.733173i	$-0.261962\pi$
$618$			19080.0i			1.24193i
$619$	−19200.1			−1.24672			−0.623358	−	0.781936i	$-0.714232\pi$
$619$	−19200.1			−1.24672			−0.623358	+	0.781936i	$0.714232\pi$
$620$	−32087.3	−	18924.5i	−2.07848	−	1.22585i
$621$	−197.843			−0.0127845
$622$		−	32279.3i		−	2.08084i
$623$			1931.50i			0.124211i
$624$	−9217.60			−0.591345
$625$	−8308.97	+	13232.6i	−0.531774	+	0.846886i
$626$	−11201.6			−0.715184
$627$			22891.4i			1.45805i
$628$			15260.6i			0.969689i
$629$	9076.17			0.575343
$630$	2966.39	+	1749.52i	0.187593	+	0.110639i
$631$	−6980.64			−0.440404			−0.220202	−	0.975454i	$-0.570672\pi$
$631$	−6980.64			−0.440404			−0.220202	+	0.975454i	$0.570672\pi$
$632$		−	36283.9i		−	2.28370i
$633$		−	6032.15i		−	0.378762i
$634$	15274.7			0.956838
$635$	−3235.45	+	5485.83i	−0.202197	+	0.342833i
$636$	2533.05			0.157928
$637$			2438.14i			0.151653i
$638$		−	23418.1i		−	1.45318i
$639$	−55.4014			−0.00342980
$640$	14379.8	−	24381.5i	0.888142	−	1.50588i
$641$	−1083.82			−0.0667837			−0.0333919	−	0.999442i	$-0.510631\pi$
$641$	−1083.82			−0.0667837			−0.0333919	+	0.999442i	$0.510631\pi$
$642$		−	22466.1i		−	1.38110i
$643$			4151.42i			0.254613i	0.991863	+	0.127307i	$0.0406332\pi$
$643$			4151.42i			0.254613i	−0.991863	+	0.127307i	$0.959367\pi$
$644$	−815.853			−0.0499210
$645$	5711.45	+	3368.51i	0.348664	+	0.205636i
$646$	−90830.3			−5.53200
$647$		−	3014.99i		−	0.183202i	−0.995796	−	0.0916008i	$-0.970802\pi$
$647$		−	3014.99i		−	0.183202i	0.995796	−	0.0916008i	$-0.0291984\pi$
$648$		−	3131.02i		−	0.189812i
$649$	37549.4			2.27110
$650$	14714.2	+	26613.8i	0.887908	+	1.60597i
$651$	4399.06			0.264843
$652$			61480.5i			3.69288i
$653$			21130.7i			1.26632i	0.774019	+	0.633162i	$0.218243\pi$
$653$			21130.7i			1.26632i	−0.774019	+	0.633162i	$0.781757\pi$
$654$	−28916.6			−1.72894
$655$	−9483.90	−	5593.44i	−0.565751	−	0.333670i
$656$	4796.73			0.285489
$657$		−	2650.91i		−	0.157415i
$658$		−	170.311i		−	0.0100903i
$659$	9961.24			0.588824			0.294412	−	0.955679i	$-0.404876\pi$
$659$	9961.24			0.588824			0.294412	+	0.955679i	$0.404876\pi$
$660$	14879.4	−	25228.6i	0.877544	−	1.48791i
$661$	1581.43			0.0930569			0.0465285	−	0.998917i	$-0.485184\pi$
$661$	1581.43			0.0930569			0.0465285	+	0.998917i	$0.485184\pi$
$662$			48040.4i			2.82046i
$663$			19952.2i			1.16875i
$664$	30340.3			1.77324
$665$	5525.83	−	9369.27i	0.322229	−	0.546353i
$666$	2988.07			0.173852
$667$		−	639.258i		−	0.0371097i
$668$		−	7397.56i		−	0.428473i
$669$	4549.32			0.262910
$670$	−7029.87	−	4146.09i	−0.405355	−	0.239071i
$671$	−1474.96			−0.0848586
$672$			153.742i			0.00882551i
$673$		−	11101.6i		−	0.635865i	−0.948113	−	0.317932i	$-0.897012\pi$
$673$		−	11101.6i		−	0.635865i	0.948113	−	0.317932i	$-0.102988\pi$
$674$	−41688.4			−2.38246
$675$	−2953.63	+	1633.00i	−0.168423	+	0.0931174i
$676$	4435.50			0.252361
$677$		−	18249.8i		−	1.03603i	−0.855370	−	0.518017i	$-0.826670\pi$
$677$		−	18249.8i		−	1.03603i	0.855370	−	0.518017i	$-0.173330\pi$
$678$		−	3855.02i		−	0.218365i
$679$	−8156.90			−0.461021
$680$	49755.7	+	29345.0i	2.80595	+	1.65490i
$681$	−12303.5			−0.692322
$682$		−	56230.5i		−	3.15715i
$683$			14144.2i			0.792403i	0.918164	+	0.396202i	$0.129672\pi$
$683$			14144.2i			0.792403i	−0.918164	+	0.396202i	$0.870328\pi$
$684$	−19896.3			−1.11221
$685$	7822.97	−	13264.2i	0.436351	−	0.739851i
$686$	−1677.05			−0.0933384
$687$		−	3087.71i		−	0.171475i
$688$		−	12207.4i		−	0.676458i
$689$	−2641.37			−0.146049
$690$	610.460	−	1035.06i	0.0336809	−	0.0571073i
$691$	19621.7			1.08024			0.540120	−	0.841588i	$-0.318379\pi$
$691$	19621.7			1.08024			0.540120	+	0.841588i	$0.318379\pi$
$692$		−	32575.9i		−	1.78952i
$693$			3458.75i			0.189592i
$694$	20361.9			1.11373
$695$	8086.22	+	4769.11i	0.441335	+	0.260292i
$696$	10116.8			0.550971
$697$		−	10382.9i		−	0.564246i
$698$		−	12637.1i		−	0.685272i
$699$	16735.2			0.905557
$700$	−12180.0	+	6734.08i	−0.657659	+	0.363606i
$701$	21609.1			1.16428			0.582142	−	0.813087i	$-0.302215\pi$
$701$	21609.1			1.16428			0.582142	+	0.813087i	$0.302215\pi$
$702$			6568.69i			0.353161i
$703$		−	9437.75i		−	0.506332i
$704$	29086.0			1.55713
$705$	143.763	+	84.7890i	0.00768005	+	0.00452956i
$706$	−20531.6			−1.09450
$707$			1.14099i			6.06950e-5i
$708$			32636.4i			1.73242i
$709$	12557.2			0.665158			0.332579	−	0.943075i	$-0.392081\pi$
$709$	12557.2			0.665158			0.332579	+	0.943075i	$0.392081\pi$
$710$	170.945	−	289.845i	0.00903586	−	0.0153207i
$711$	−8448.02			−0.445606
$712$			10665.9i			0.561406i
$713$		−	1534.96i		−	0.0806237i
$714$	−13723.9			−0.719334
$715$	−15515.6	+	26307.4i	−0.811540	+	1.37600i
$716$	−14503.9			−0.757031
$717$			16169.0i			0.842179i
$718$			4841.82i			0.251665i
$719$	−36151.9			−1.87516			−0.937580	−	0.347771i	$-0.886939\pi$
$719$	−36151.9			−1.87516			−0.937580	+	0.347771i	$0.886939\pi$
$720$	5351.95	+	3156.48i	0.277021	+	0.163382i
$721$	9105.48			0.470327
$722$			60912.8i			3.13980i
$723$		−	11928.8i		−	0.613606i
$724$	32285.9			1.65731
$725$	−5276.46	−	9543.60i	−0.270293	−	0.488883i
$726$	24687.9			1.26206
$727$			12007.2i			0.612550i	0.951943	+	0.306275i	$0.0990828\pi$
$727$			12007.2i			0.612550i	−0.951943	+	0.306275i	$0.900917\pi$
$728$			13463.6i			0.685434i
$729$	−729.000			−0.0370370
$730$	13868.8	+	8179.58i	0.703162	+	0.414712i
$731$	−26423.9			−1.33697
$732$		−	1281.97i		−	0.0647310i
$733$			15920.2i			0.802220i	0.916030	+	0.401110i	$0.131375\pi$
$733$			15920.2i			0.802220i	−0.916030	+	0.401110i	$0.868625\pi$
$734$	20433.8			1.02756
$735$	834.919	−	1415.64i	0.0418999	−	0.0710431i
$736$	53.6452			0.00268667
$737$		−	8196.70i		−	0.409674i
$738$		−	3418.27i		−	0.170499i
$739$	26581.1			1.32314			0.661571	−	0.749882i	$-0.269890\pi$
$739$	26581.1			1.32314			0.661571	+	0.749882i	$0.269890\pi$
$740$	−6134.52	+	10401.3i	−0.304742	+	0.516703i
$741$	20747.1			1.02856
$742$		−	1816.84i		−	0.0898897i
$743$			6601.38i			0.325950i	0.986630	+	0.162975i	$0.0521090\pi$
$743$			6601.38i			0.325950i	−0.986630	+	0.162975i	$0.947891\pi$
$744$	24292.0			1.19703
$745$	−14159.6	−	8351.06i	−0.696330	−	0.410683i
$746$	36011.9			1.76741
$747$		−	7064.16i		−	0.346003i
$748$			116719.i			5.70546i
$749$	−10721.4			−0.523034
$750$	570.243	−	20491.3i	0.0277631	−	0.997651i
$751$	−29809.6			−1.44842			−0.724212	−	0.689578i	$-0.757796\pi$
$751$	−29809.6			−1.44842			−0.724212	+	0.689578i	$0.757796\pi$
$752$		−	307.274i		−	0.0149004i
$753$		−	21287.3i		−	1.03022i
$754$	−21224.4			−1.02513
$755$	16330.8	+	9631.61i	0.787203	+	0.464278i
$756$	−3006.21			−0.144623
$757$		−	8179.09i		−	0.392700i	−0.980534	−	0.196350i	$-0.937091\pi$
$757$		−	8179.09i		−	0.392700i	0.980534	−	0.196350i	$-0.0629089\pi$
$758$			30383.2i			1.45589i
$759$	1206.86			0.0577158
$760$	30514.1	−	51737.9i	1.45640	−	2.46938i
$761$	−31616.8			−1.50605			−0.753027	−	0.657990i	$-0.771407\pi$
$761$	−31616.8			−1.50605			−0.753027	+	0.657990i	$0.771407\pi$
$762$		−	8355.66i		−	0.397236i
$763$			13799.8i			0.654763i
$764$	−79276.5			−3.75409
$765$	6832.44	−	11584.7i	0.322912	−	0.547510i
$766$	8581.05			0.404760
$767$		−	34032.0i		−	1.60212i
$768$			24421.3i			1.14743i
$769$	−24651.3			−1.15598			−0.577991	−	0.816043i	$-0.696163\pi$
$769$	−24651.3			−1.15598			−0.577991	+	0.816043i	$0.696163\pi$
$770$	−18095.3	−	10672.3i	−0.846893	−	0.499483i
$771$	7579.67			0.354054
$772$			53975.6i			2.51635i
$773$			7888.63i			0.367056i	0.983015	+	0.183528i	$0.0587518\pi$
$773$			7888.63i			0.367056i	−0.983015	+	0.183528i	$0.941248\pi$
$774$	−8699.31			−0.403992
$775$	−12669.6	−	22915.7i	−0.587233	−	1.06214i
$776$	−45043.1			−2.08370
$777$		−	1425.99i		−	0.0658391i
$778$		−	43054.2i		−	1.98402i
$779$	−10796.5			−0.496566
$780$	−22865.3	−	13485.5i	−1.04963	−	0.619051i
$781$	337.954			0.0154839
$782$			4788.67i			0.218980i
$783$		−	2355.50i		−	0.107508i
$784$	−3025.73			−0.137834
$785$	−5449.31	+	9239.53i	−0.247763	+	0.420093i
$786$	14445.2			0.655528
$787$		−	8592.94i		−	0.389206i	−0.980882	−	0.194603i	$-0.937658\pi$
$787$		−	8592.94i		−	0.389206i	0.980882	−	0.194603i	$-0.0623419\pi$
$788$			12127.8i			0.548268i
$789$	−11527.0			−0.520118
$790$	26067.1	−	44197.8i	1.17395	−	1.99049i
$791$	−1839.72			−0.0826964
$792$			19099.6i			0.856910i
$793$			1336.79i			0.0598623i
$794$	−67068.5			−2.99770
$795$	1533.64	+	904.511i	0.0684182	+	0.0403518i
$796$	−20237.3			−0.901120
$797$		−	37498.1i		−	1.66656i	−0.552848	−	0.833282i	$-0.686459\pi$
$797$		−	37498.1i		−	1.66656i	0.552848	−	0.833282i	$-0.313541\pi$
$798$			14270.7i			0.633052i
$799$	−665.116			−0.0294495
$800$	800.878	−	442.789i	0.0353942	−	0.0195687i
$801$	2483.35			0.109544
$802$			1502.11i			0.0661364i
$803$			16170.8i			0.710653i
$804$	7124.24			0.312503
$805$	−493.958	−	291.328i	−0.0216270	−	0.0127552i
$806$	−50963.1			−2.22717
$807$		−	25233.1i		−	1.10068i
$808$			6.30065i			0.000274327i
$809$	−33834.0			−1.47039			−0.735193	−	0.677858i	$-0.762908\pi$
$809$	−33834.0			−1.47039			−0.735193	+	0.677858i	$0.762908\pi$
$810$	2249.39	−	3813.93i	0.0975746	−	0.165442i
$811$	16234.0			0.702899			0.351450	−	0.936207i	$-0.385689\pi$
$811$	16234.0			0.702899			0.351450	+	0.936207i	$0.385689\pi$
$812$		−	9713.48i		−	0.419799i
$813$		−	16979.2i		−	0.732455i
$814$	−18227.5			−0.784858
$815$	−21953.7	+	37223.3i	−0.943562	+	1.59985i
$816$	−24760.6			−1.06225
$817$			27476.6i			1.17660i
$818$		−	60582.5i		−	2.58951i
$819$	3134.75			0.133745
$820$	11898.8	+	7017.71i	0.506737	+	0.298865i
$821$	−26551.4			−1.12868			−0.564342	−	0.825541i	$-0.690870\pi$
$821$	−26551.4			−1.12868			−0.564342	+	0.825541i	$0.690870\pi$
$822$			20203.1i			0.857255i
$823$		−	651.954i		−	0.0276132i	−0.999905	−	0.0138066i	$-0.995605\pi$
$823$		−	651.954i		−	0.0276132i	0.999905	−	0.0138066i	$-0.00439492\pi$
$824$	50281.3			2.12577
$825$	18017.4	−	9961.47i	0.760347	−	0.420380i
$826$	23408.6			0.986063
$827$			13248.0i			0.557046i	0.960430	+	0.278523i	$0.0898448\pi$
$827$			13248.0i			0.557046i	−0.960430	+	0.278523i	$0.910155\pi$
$828$			1048.95i			0.0440262i
$829$	36828.9			1.54297			0.771484	−	0.636248i	$-0.219515\pi$
$829$	36828.9			1.54297			0.771484	+	0.636248i	$0.219515\pi$
$830$	36957.7	+	21797.0i	1.54557	+	0.911549i
$831$	2644.23			0.110382
$832$		−	26361.4i		−	1.09846i
$833$			6549.41i			0.272417i
$834$	−12316.4			−0.511369
$835$	2641.55	−	4478.85i	0.109478	−	0.185625i
$836$	121369.			5.02111
$837$		−	5655.93i		−	0.233569i
$838$		−	13025.7i		−	0.536953i
$839$	10641.5			0.437884			0.218942	−	0.975738i	$-0.429739\pi$
$839$	10641.5			0.437884			0.218942	+	0.975738i	$0.429739\pi$
$840$	4610.50	−	7817.29i	0.189378	−	0.321098i
$841$	−16778.0			−0.687935
$842$		−	33497.6i		−	1.37102i
$843$			11561.1i			0.472344i
$844$	−31982.2			−1.30435
$845$	2685.47	+	1583.84i	0.109329	+	0.0644804i
$846$	−218.971			−0.00889878
$847$		−	11781.7i		−	0.477952i
$848$		−	3277.93i		−	0.132741i
$849$	−5674.80			−0.229398
$850$	39525.9	+	71490.9i	1.59497	+	2.88484i
$851$	−497.568			−0.0200428
$852$			293.735i			0.0118113i
$853$		−	2819.13i		−	0.113160i	−0.998398	−	0.0565799i	$-0.981980\pi$
$853$		−	2819.13i		−	0.113160i	0.998398	−	0.0565799i	$-0.0180196\pi$
$854$	−919.497			−0.0368437
$855$	−12046.2	−	7104.64i	−0.481838	−	0.284179i
$856$	−59204.6			−2.36399
$857$		−	38853.9i		−	1.54869i	−0.632766	−	0.774343i	$-0.718081\pi$
$857$		−	38853.9i		−	1.54869i	0.632766	−	0.774343i	$-0.281919\pi$
$858$		−	40069.7i		−	1.59435i
$859$	−8959.42			−0.355869			−0.177935	−	0.984042i	$-0.556942\pi$
$859$	−8959.42			−0.355869			−0.177935	+	0.984042i	$0.556942\pi$
$860$	17859.7	−	30281.9i	0.708152	−	1.20070i
$861$	−1631.29			−0.0645693
$862$		−	37410.4i		−	1.47819i
$863$			32649.8i			1.28785i	0.765090	+	0.643924i	$0.222695\pi$
$863$			32649.8i			1.28785i	−0.765090	+	0.643924i	$0.777305\pi$
$864$	197.669			0.00778337
$865$	11632.3	−	19723.1i	0.457238	−	0.775265i
$866$	−3381.35			−0.132682
$867$			38857.2i			1.52210i
$868$		−	23323.6i		−	0.912045i
$869$	51533.8			2.01170
$870$	12323.3	+	7268.09i	0.480230	+	0.283231i
$871$	−7428.87			−0.288999
$872$			76203.5i			2.95937i
$873$			10487.4i			0.406582i
$874$	4979.45			0.192714
$875$	−9779.01	−	272.135i	−0.377818	−	0.0105141i
$876$	−14055.0			−0.542093
$877$		−	20229.3i		−	0.778899i	−0.921048	−	0.389450i	$-0.872665\pi$
$877$		−	20229.3i		−	0.778899i	0.921048	−	0.389450i	$-0.127335\pi$
$878$		−	51933.5i		−	1.99621i
$879$	−12228.6			−0.469237
$880$	−32647.4	−	19254.8i	−1.25062	−	0.737592i
$881$	4356.08			0.166584			0.0832918	−	0.996525i	$-0.473457\pi$
$881$	4356.08			0.166584			0.0832918	+	0.996525i	$0.473457\pi$
$882$			2156.21i			0.0823167i
$883$		−	43349.9i		−	1.65214i	−0.563567	−	0.826070i	$-0.690571\pi$
$883$		−	43349.9i		−	1.65214i	0.563567	−	0.826070i	$-0.309429\pi$
$884$	105786.			4.02484
$885$	−11653.9	+	19759.7i	−0.442647	+	0.750526i
$886$	15321.6			0.580971
$887$		−	9754.67i		−	0.369256i	−0.982809	−	0.184628i	$-0.940892\pi$
$887$		−	9754.67i		−	0.369256i	0.982809	−	0.184628i	$-0.0591080\pi$
$888$		−	7874.43i		−	0.297577i
$889$	−3987.54			−0.150436
$890$	−7662.58	+	12992.2i	−0.288596	+	0.489326i
$891$	4446.97			0.167204
$892$		−	24120.3i		−	0.905389i
$893$			691.614i			0.0259171i
$894$	21566.9			0.806829
$895$	−8781.35	−	5179.09i	−0.327965	−	0.193428i
$896$	17722.4			0.660786
$897$		−	1093.81i		−	0.0407148i
$898$			44712.8i			1.66157i
$899$	18275.1			0.677986
$900$	8658.10	+	15660.0i	0.320670	+	0.580000i
$901$	−7095.32			−0.262352
$902$			20851.8i			0.769720i
$903$			4151.54i			0.152995i
$904$	−10159.1			−0.373768
$905$	19547.5	+	11528.8i	0.717989	+	0.423457i
$906$	−24874.0			−0.912122
$907$		−	7155.16i		−	0.261944i	−0.991386	−	0.130972i	$-0.958190\pi$
$907$		−	7155.16i		−	0.261944i	0.991386	−	0.130972i	$-0.0418098\pi$
$908$			65232.6i			2.38416i
$909$	1.46699			5.35279e−5
$910$	−9672.53	+	16400.2i	−0.352353	+	0.597429i
$911$	−47255.4			−1.71860			−0.859298	−	0.511475i	$-0.829099\pi$
$911$	−47255.4			−1.71860			−0.859298	+	0.511475i	$0.829099\pi$
$912$			25747.0i			0.934835i
$913$			43092.1i			1.56204i
$914$	−39812.1			−1.44077
$915$	457.771	−	776.170i	0.0165393	−	0.0280430i
$916$	−16370.9			−0.590514
$917$		−	6893.66i		−	0.248254i
$918$			17645.0i			0.634393i
$919$	−30942.1			−1.11065			−0.555324	−	0.831634i	$-0.687406\pi$
$919$	−30942.1			−1.11065			−0.555324	+	0.831634i	$0.687406\pi$
$920$	−2727.68	−	1608.74i	−0.0977488	−	0.0576505i
$921$	−18605.6			−0.665663
$922$		−	45408.9i		−	1.62198i
$923$		−	306.296i		−	0.0109229i
$924$	18338.2			0.652902
$925$	−7428.29	+	4106.95i	−0.264044	+	0.145984i
$926$	11932.6			0.423468
$927$		−	11707.0i		−	0.414790i
$928$			638.696i			0.0225929i
$929$	−12147.4			−0.429004			−0.214502	−	0.976724i	$-0.568813\pi$
$929$	−12147.4			−0.429004			−0.214502	+	0.976724i	$0.568813\pi$
$930$	29590.3	+	17451.8i	1.04334	+	0.615342i
$931$	6810.33			0.239742
$932$		−	88729.4i		−	3.11849i
$933$			19805.8i			0.694978i
$934$	58996.6			2.06684
$935$	−41678.5	+	70667.7i	−1.45779	+	2.47174i
$936$	17310.4			0.604496
$937$		−	13388.6i		−	0.466794i	−0.972381	−	0.233397i	$-0.925016\pi$
$937$		−	13388.6i		−	0.466794i	0.972381	−	0.233397i	$-0.0749842\pi$
$938$		−	5109.87i		−	0.177871i
$939$	6873.03			0.238864
$940$	449.548	−	762.226i	0.0155985	−	0.0264480i
$941$	−8035.36			−0.278369			−0.139184	−	0.990266i	$-0.544448\pi$
$941$	−8035.36			−0.278369			−0.139184	+	0.990266i	$0.544448\pi$
$942$		−	14073.0i		−	0.486757i
$943$			569.204i			0.0196562i
$944$	42233.6			1.45613
$945$	−1820.11	−	1073.47i	−0.0626541	−	0.0369523i
$946$	53066.6			1.82383
$947$			17647.7i			0.605567i	0.953059	+	0.302784i	$0.0979160\pi$
$947$			17647.7i			0.605567i	−0.953059	+	0.302784i	$0.902084\pi$
$948$			44791.0i			1.53454i
$949$	14656.0			0.501321
$950$	74339.0	−	41100.5i	2.53882	−	1.40366i
$951$	−9372.20			−0.319573
$952$			36166.4i			1.23126i
$953$		−	35629.1i		−	1.21106i	−0.795823	−	0.605529i	$-0.792961\pi$
$953$		−	35629.1i		−	1.21106i	0.795823	−	0.605529i	$-0.207039\pi$
$954$	−2335.93			−0.0792753
$955$	−47998.0	−	28308.3i	−1.62636	−	0.959200i
$956$	85727.3			2.90023
$957$			14368.8i			0.485347i
$958$		−	1932.33i		−	0.0651679i
$959$	9641.45			0.324649
$960$	−9027.21	+	15306.0i	−0.303492	+	0.514582i
$961$	14090.4			0.472977
$962$			16520.1i			0.553667i
$963$			13784.7i			0.461272i
$964$	−63246.0			−2.11309
$965$	−19273.8	+	32679.5i	−0.642948	+	1.09015i
$966$	752.364			0.0250589
$967$			35954.1i			1.19566i	0.801622	+	0.597831i	$0.203971\pi$
$967$			35954.1i			1.19566i	−0.801622	+	0.597831i	$0.796029\pi$
$968$		−	65059.8i		−	2.16023i
$969$	55731.4			1.84763
$970$	−54867.4	−	32359.8i	−1.81617	−	1.07115i
$971$	59266.0			1.95874			0.979370	−	0.202074i	$-0.0647680\pi$
$971$	59266.0			1.95874			0.979370	+	0.202074i	$0.0647680\pi$
$972$			3865.12i			0.127545i
$973$			5877.71i			0.193660i
$974$	46982.2			1.54559
$975$	−9028.32	−	16329.6i	−0.296552	−	0.536376i
$976$	−1658.95			−0.0544076
$977$			35518.9i			1.16310i	0.813510	+	0.581551i	$0.197554\pi$
$977$			35518.9i			1.16310i	−0.813510	+	0.581551i	$0.802446\pi$
$978$		−	56696.1i		−	1.85372i
$979$	−15148.7			−0.494540
$980$	−7505.66	−	4426.70i	−0.244652	−	0.144292i
$981$	17742.5			0.577447
$982$			53494.4i			1.73837i
$983$			37683.6i			1.22271i	0.791358	+	0.611353i	$0.209374\pi$
$983$			37683.6i			1.22271i	−0.791358	+	0.611353i	$0.790626\pi$
$984$	−9008.11			−0.291838
$985$	−4330.64	+	7342.78i	−0.140087	+	0.237523i
$986$	−57013.6			−1.84146
$987$			104.499i			0.00337004i
$988$		−	110000.i		−	3.54207i
$989$	1448.59			0.0465749
$990$	−13721.5	+	23265.3i	−0.440502	+	0.746890i
$991$	21371.1			0.685041			0.342521	−	0.939510i	$-0.388719\pi$
$991$	21371.1			0.685041			0.342521	+	0.939510i	$0.388719\pi$
$992$			1533.61i			0.0490848i
$993$		−	29476.5i		−	0.942002i
$994$	210.682			0.00672278
$995$	−12252.7	−	7226.40i	−0.390387	−	0.230244i
$996$	−37453.8			−1.19154
$997$			42934.0i			1.36383i	0.731434	+	0.681913i	$0.238852\pi$
$997$			42934.0i			1.36383i	−0.731434	+	0.681913i	$0.761148\pi$
$998$		−	45323.9i		−	1.43758i
$999$	−1833.41			−0.0580646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.d.b.64.9	yes	10
3.2	odd	2		315.4.d.b.64.2		10
5.2	odd	4		525.4.a.x.1.1		5
5.3	odd	4		525.4.a.w.1.5		5
5.4	even	2	inner	105.4.d.b.64.2	✓	10
15.2	even	4		1575.4.a.bo.1.5		5
15.8	even	4		1575.4.a.bp.1.1		5
15.14	odd	2		315.4.d.b.64.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.2	✓	10	5.4	even	2	inner
105.4.d.b.64.9	yes	10	1.1	even	1	trivial
315.4.d.b.64.2		10	3.2	odd	2
315.4.d.b.64.9		10	15.14	odd	2
525.4.a.w.1.5		5	5.3	odd	4
525.4.a.x.1.1		5	5.2	odd	4
1575.4.a.bo.1.5		5	15.2	even	4
1575.4.a.bp.1.1		5	15.8	even	4

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.88936i q^{2} -3.00000i q^{3} -15.9059 q^{4} +(-9.63020 - 5.67972i) q^{5} +14.6681 q^{6} -7.00000i q^{7} -38.6546i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.88936i q^{2} -3.00000i q^{3} -15.9059 q^{4} +(-9.63020 - 5.67972i) q^{5} +14.6681 q^{6} -7.00000i q^{7} -38.6546i q^{8} -9.00000 q^{9} +(27.7702 - 47.0855i) q^{10} +54.9009 q^{11} +47.7176i q^{12} -49.7580i q^{13} +34.2255 q^{14} +(-17.0392 + 28.8906i) q^{15} +61.7496 q^{16} -133.661i q^{17} -44.0043i q^{18} -138.986 q^{19} +(153.177 + 90.3409i) q^{20} -21.0000 q^{21} +268.430i q^{22} +7.32751i q^{23} -115.964 q^{24} +(60.4815 + 109.394i) q^{25} +243.285 q^{26} +27.0000i q^{27} +111.341i q^{28} -87.2408 q^{29} +(-141.257 - 83.3106i) q^{30} -209.479 q^{31} -7.32107i q^{32} -164.703i q^{33} +653.519 q^{34} +(-39.7580 + 67.4114i) q^{35} +143.153 q^{36} +67.9041i q^{37} -679.555i q^{38} -149.274 q^{39} +(-219.547 + 372.252i) q^{40} +77.6804 q^{41} -102.677i q^{42} -197.692i q^{43} -873.246 q^{44} +(86.6718 + 51.1175i) q^{45} -35.8269 q^{46} -4.97613i q^{47} -185.249i q^{48} -49.0000 q^{49} +(-534.865 + 295.716i) q^{50} -400.984 q^{51} +791.444i q^{52} -53.0843i q^{53} -132.013 q^{54} +(-528.706 - 311.822i) q^{55} -270.582 q^{56} +416.959i q^{57} -426.552i q^{58} +683.950 q^{59} +(271.023 - 459.530i) q^{60} -26.8658 q^{61} -1024.22i q^{62} +63.0000i q^{63} +529.792 q^{64} +(-282.612 + 479.180i) q^{65} +805.291 q^{66} -149.300i q^{67} +2126.00i q^{68} +21.9825 q^{69} +(-329.599 - 194.391i) q^{70} +6.15571 q^{71} +347.892i q^{72} +294.545i q^{73} -332.008 q^{74} +(328.181 - 181.445i) q^{75} +2210.70 q^{76} -384.306i q^{77} -729.855i q^{78} +938.669 q^{79} +(-594.661 - 350.720i) q^{80} +81.0000 q^{81} +379.807i q^{82} +784.907i q^{83} +334.023 q^{84} +(-759.160 + 1287.19i) q^{85} +966.590 q^{86} +261.722i q^{87} -2122.17i q^{88} -275.928 q^{89} +(-249.932 + 423.770i) q^{90} -348.306 q^{91} -116.550i q^{92} +628.437i q^{93} +24.3301 q^{94} +(1338.47 + 789.404i) q^{95} -21.9632 q^{96} -1165.27i q^{97} -239.579i q^{98} -494.108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9}+O(q^{10}) \) 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9	\( 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9} + 92 q^{10} + 132 q^{11} - 14 q^{14} + 310 q^{16} - 348 q^{19} + 366 q^{20} - 210 q^{21} + 198 q^{24} - 374 q^{25} + 892 q^{26} - 740 q^{29} - 378 q^{30} + 684 q^{31} - 224 q^{34} + 486 q^{36} - 12 q^{39} - 2156 q^{40} + 1604 q^{41} - 580 q^{44} + 126 q^{45} + 1280 q^{46} - 490 q^{49} - 2504 q^{50} - 648 q^{51} + 54 q^{54} - 452 q^{55} + 462 q^{56} - 1408 q^{59} - 852 q^{60} + 1300 q^{61} - 150 q^{64} - 3296 q^{65} + 3036 q^{66} - 696 q^{69} - 882 q^{70} + 2940 q^{71} + 2624 q^{74} - 408 q^{75} + 8740 q^{76} + 1640 q^{79} - 4126 q^{80} + 810 q^{81} + 1134 q^{84} - 1704 q^{85} + 1664 q^{86} - 572 q^{89} - 828 q^{90} - 28 q^{91} - 5080 q^{94} + 1268 q^{95} + 330 q^{96} - 1188 q^{99}+O(q^{100}) \) 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9 + 92 * q^10 + 132 * q^11 - 14 * q^14 + 310 * q^16 - 348 * q^19 + 366 * q^20 - 210 * q^21 + 198 * q^24 - 374 * q^25 + 892 * q^26 - 740 * q^29 - 378 * q^30 + 684 * q^31 - 224 * q^34 + 486 * q^36 - 12 * q^39 - 2156 * q^40 + 1604 * q^41 - 580 * q^44 + 126 * q^45 + 1280 * q^46 - 490 * q^49 - 2504 * q^50 - 648 * q^51 + 54 * q^54 - 452 * q^55 + 462 * q^56 - 1408 * q^59 - 852 * q^60 + 1300 * q^61 - 150 * q^64 - 3296 * q^65 + 3036 * q^66 - 696 * q^69 - 882 * q^70 + 2940 * q^71 + 2624 * q^74 - 408 * q^75 + 8740 * q^76 + 1640 * q^79 - 4126 * q^80 + 810 * q^81 + 1134 * q^84 - 1704 * q^85 + 1664 * q^86 - 572 * q^89 - 828 * q^90 - 28 * q^91 - 5080 * q^94 + 1268 * q^95 + 330 * q^96 - 1188 * q^99

Introduction

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