LMFDB - Embedded newform 22.5.b.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,5,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	22.b (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:	$2.27413918784$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{553})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 271x^{2} + 272x + 19602 $ x^4 - 2x^3 - 271x^2 + 272*x + 19602
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.1
Root			$-11.2580 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.5.b.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -11.2580 q^{3} -8.00000 q^{4} -19.2580 q^{5} +31.8424i q^{6} -33.9411i q^{7} +22.6274i q^{8} +45.7420 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -11.2580 q^{3} -8.00000 q^{4} -19.2580 q^{5} +31.8424i q^{6} -33.9411i q^{7} +22.6274i q^{8} +45.7420 q^{9} +54.4698i q^{10} +(2.03190 - 120.983i) q^{11} +90.0638 q^{12} -72.2602i q^{13} -96.0000 q^{14} +216.806 q^{15} +64.0000 q^{16} +517.873i q^{17} -129.378i q^{18} -411.672i q^{19} +154.064 q^{20} +382.108i q^{21} +(-342.191 - 5.74709i) q^{22} -967.641 q^{23} -254.739i q^{24} -254.130 q^{25} -204.383 q^{26} +396.933 q^{27} +271.529i q^{28} -640.503i q^{29} -613.219i q^{30} +716.487 q^{31} -181.019i q^{32} +(-22.8751 + 1362.02i) q^{33} +1464.77 q^{34} +653.637i q^{35} -365.936 q^{36} +1209.64 q^{37} -1164.38 q^{38} +813.504i q^{39} -435.758i q^{40} -966.781i q^{41} +1080.77 q^{42} -2720.75i q^{43} +(-16.2552 + 967.864i) q^{44} -880.899 q^{45} +2736.90i q^{46} -177.085 q^{47} -720.510 q^{48} +1249.00 q^{49} +718.789i q^{50} -5830.20i q^{51} +578.082i q^{52} -4023.28 q^{53} -1122.70i q^{54} +(-39.1304 + 2329.89i) q^{55} +768.000 q^{56} +4634.59i q^{57} -1811.62 q^{58} -1988.02 q^{59} -1734.45 q^{60} +2396.69i q^{61} -2026.53i q^{62} -1552.54i q^{63} -512.000 q^{64} +1391.59i q^{65} +(3852.38 + 64.7006i) q^{66} -2007.13 q^{67} -4142.98i q^{68} +10893.7 q^{69} +1848.77 q^{70} +4255.04 q^{71} +1035.02i q^{72} -1288.68i q^{73} -3421.37i q^{74} +2860.99 q^{75} +3293.37i q^{76} +(-4106.30 - 68.9651i) q^{77} +2300.94 q^{78} -1480.23i q^{79} -1232.51 q^{80} -8173.77 q^{81} -2734.47 q^{82} +10124.2i q^{83} -3056.87i q^{84} -9973.18i q^{85} -7695.45 q^{86} +7210.77i q^{87} +(2737.53 + 45.9767i) q^{88} +5133.72 q^{89} +2491.56i q^{90} -2452.59 q^{91} +7741.13 q^{92} -8066.19 q^{93} +500.871i q^{94} +7927.96i q^{95} +2037.91i q^{96} +2239.34 q^{97} -3532.71i q^{98} +(92.9434 - 5534.00i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 32 q^{4} - 30 q^{5} + 230 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 32 * q^4 - 30 * q^5 + 230 * q^9	$ 4 q + 2 q^{3} - 32 q^{4} - 30 q^{5} + 230 q^{9} - 180 q^{11} - 16 q^{12} - 384 q^{14} + 538 q^{15} + 256 q^{16} + 240 q^{20} - 240 q^{22} - 1566 q^{23} - 1722 q^{25} + 1440 q^{26} + 506 q^{27} + 4418 q^{31} - 2302 q^{33} + 1344 q^{34} - 1840 q^{36} - 382 q^{37} - 2400 q^{38} - 192 q^{42} + 1440 q^{44} - 1172 q^{45} + 5688 q^{47} + 128 q^{48} + 4996 q^{49} - 8568 q^{53} - 862 q^{55} + 3072 q^{56} - 9504 q^{58} - 3390 q^{59} - 4304 q^{60} - 2048 q^{64} + 13152 q^{66} - 8734 q^{67} + 26314 q^{69} + 2880 q^{70} + 3522 q^{71} - 9156 q^{75} - 2880 q^{77} + 27264 q^{78} - 1920 q^{80} - 31096 q^{81} - 19968 q^{82} - 10464 q^{86} + 1920 q^{88} - 8766 q^{89} + 17280 q^{91} + 12528 q^{92} + 20458 q^{93} + 17282 q^{97} - 12562 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 32 * q^4 - 30 * q^5 + 230 * q^9 - 180 * q^11 - 16 * q^12 - 384 * q^14 + 538 * q^15 + 256 * q^16 + 240 * q^20 - 240 * q^22 - 1566 * q^23 - 1722 * q^25 + 1440 * q^26 + 506 * q^27 + 4418 * q^31 - 2302 * q^33 + 1344 * q^34 - 1840 * q^36 - 382 * q^37 - 2400 * q^38 - 192 * q^42 + 1440 * q^44 - 1172 * q^45 + 5688 * q^47 + 128 * q^48 + 4996 * q^49 - 8568 * q^53 - 862 * q^55 + 3072 * q^56 - 9504 * q^58 - 3390 * q^59 - 4304 * q^60 - 2048 * q^64 + 13152 * q^66 - 8734 * q^67 + 26314 * q^69 + 2880 * q^70 + 3522 * q^71 - 9156 * q^75 - 2880 * q^77 + 27264 * q^78 - 1920 * q^80 - 31096 * q^81 - 19968 * q^82 - 10464 * q^86 + 1920 * q^88 - 8766 * q^89 + 17280 * q^91 + 12528 * q^92 + 20458 * q^93 + 17282 * q^97 - 12562 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$-1$

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−11.2580			−1.25089			−0.625443	−	0.780270i	$-0.715082\pi$
$3$	−11.2580			−1.25089			−0.625443	+	0.780270i	$0.715082\pi$
$4$	−8.00000			−0.500000
$5$	−19.2580			−0.770319			−0.385160	−	0.922850i	$-0.625854\pi$
$5$	−19.2580			−0.770319			−0.385160	+	0.922850i	$0.625854\pi$
$6$			31.8424i			0.884510i
$7$		−	33.9411i		−	0.692676i	−0.938110	−	0.346338i	$-0.887425\pi$
$7$		−	33.9411i		−	0.692676i	0.938110	−	0.346338i	$-0.112575\pi$
$8$			22.6274i			0.353553i
$9$	45.7420			0.564716
$10$			54.4698i			0.544698i
$11$	2.03190	−	120.983i	0.0167926	−	0.999859i
$11$	2.03190	−	120.983i	0.0167926	−	0.999859i
$12$	90.0638			0.625443
$13$		−	72.2602i		−	0.427575i	−0.976880	−	0.213788i	$-0.931420\pi$
$13$		−	72.2602i		−	0.427575i	0.976880	−	0.213788i	$-0.0685801\pi$
$14$	−96.0000			−0.489796
$15$	216.806			0.963581
$16$	64.0000			0.250000
$17$			517.873i			1.79195i	0.444107	+	0.895974i	$0.353521\pi$
$17$			517.873i			1.79195i	−0.444107	+	0.895974i	$0.646479\pi$
$18$		−	129.378i		−	0.399315i
$19$		−	411.672i		−	1.14036i	−0.821518	−	0.570182i	$-0.806873\pi$
$19$		−	411.672i		−	1.14036i	0.821518	−	0.570182i	$-0.193127\pi$
$20$	154.064			0.385160
$21$			382.108i			0.866459i
$22$	−342.191	−	5.74709i	−0.707007	−	0.0118742i
$23$	−967.641			−1.82919			−0.914594	−	0.404373i	$-0.867490\pi$
$23$	−967.641			−1.82919			−0.914594	+	0.404373i	$0.867490\pi$
$24$		−	254.739i		−	0.442255i
$25$	−254.130			−0.406609
$26$	−204.383			−0.302341
$27$	396.933			0.544490
$28$			271.529i			0.346338i
$29$		−	640.503i		−	0.761597i	−0.924658	−	0.380799i	$-0.875649\pi$
$29$		−	640.503i		−	0.761597i	0.924658	−	0.380799i	$-0.124351\pi$
$30$		−	613.219i		−	0.681355i
$31$	716.487			0.745564			0.372782	−	0.927919i	$-0.378404\pi$
$31$	716.487			0.745564			0.372782	+	0.927919i	$0.378404\pi$
$32$		−	181.019i		−	0.176777i
$33$	−22.8751	+	1362.02i	−0.0210056	+	1.25071i
$34$	1464.77			1.26710
$35$			653.637i			0.533582i
$36$	−365.936			−0.282358
$37$	1209.64			0.883590			0.441795	−	0.897116i	$-0.354342\pi$
$37$	1209.64			0.883590			0.441795	+	0.897116i	$0.354342\pi$
$38$	−1164.38			−0.806359
$39$			813.504i			0.534848i
$40$		−	435.758i		−	0.272349i
$41$		−	966.781i		−	0.575122i	−0.957762	−	0.287561i	$-0.907156\pi$
$41$		−	966.781i		−	0.575122i	0.957762	−	0.287561i	$-0.0928445\pi$
$42$	1080.77			0.612679
$43$		−	2720.75i		−	1.47147i	−0.677269	−	0.735736i	$-0.736837\pi$
$43$		−	2720.75i		−	1.47147i	0.677269	−	0.735736i	$-0.263163\pi$
$44$	−16.2552	+	967.864i	−0.00839630	+	0.499929i
$45$	−880.899			−0.435012
$46$			2736.90i			1.29343i
$47$	−177.085			−0.0801651			−0.0400826	−	0.999196i	$-0.512762\pi$
$47$	−177.085			−0.0801651			−0.0400826	+	0.999196i	$0.512762\pi$
$48$	−720.510			−0.312722
$49$	1249.00			0.520200
$50$			718.789i			0.287516i
$51$		−	5830.20i		−	2.24152i
$52$			578.082i			0.213788i
$53$	−4023.28			−1.43228			−0.716140	−	0.697956i	$-0.754093\pi$
$53$	−4023.28			−1.43228			−0.716140	+	0.697956i	$0.754093\pi$
$54$		−	1122.70i		−	0.385013i
$55$	−39.1304	+	2329.89i	−0.0129357	+	0.770210i
$56$	768.000			0.244898
$57$			4634.59i			1.42647i
$58$	−1811.62			−0.538531
$59$	−1988.02			−0.571107			−0.285554	−	0.958363i	$-0.592177\pi$
$59$	−1988.02			−0.571107			−0.285554	+	0.958363i	$0.592177\pi$
$60$	−1734.45			−0.481791
$61$			2396.69i			0.644097i	0.946723	+	0.322049i	$0.104371\pi$
$61$			2396.69i			0.644097i	−0.946723	+	0.322049i	$0.895629\pi$
$62$		−	2026.53i		−	0.527193i
$63$		−	1552.54i		−	0.391165i
$64$	−512.000			−0.125000
$65$			1391.59i			0.329370i
$66$	3852.38	+	64.7006i	0.884385	+	0.0148532i
$67$	−2007.13			−0.447122			−0.223561	−	0.974690i	$-0.571768\pi$
$67$	−2007.13			−0.447122			−0.223561	+	0.974690i	$0.571768\pi$
$68$		−	4142.98i		−	0.895974i
$69$	10893.7			2.28811
$70$	1848.77			0.377299
$71$	4255.04			0.844086			0.422043	−	0.906576i	$-0.361313\pi$
$71$	4255.04			0.844086			0.422043	+	0.906576i	$0.361313\pi$
$72$			1035.02i			0.199657i
$73$		−	1288.68i		−	0.241824i	−0.992663	−	0.120912i	$-0.961418\pi$
$73$		−	1288.68i		−	0.241824i	0.992663	−	0.120912i	$-0.0385819\pi$
$74$		−	3421.37i		−	0.624793i
$75$	2860.99			0.508621
$76$			3293.37i			0.570182i
$77$	−4106.30	−	68.9651i	−0.692578	−	0.0116318i
$78$	2300.94			0.378195
$79$		−	1480.23i		−	0.237178i	−0.992943	−	0.118589i	$-0.962163\pi$
$79$		−	1480.23i		−	0.237178i	0.992943	−	0.118589i	$-0.0378371\pi$
$80$	−1232.51			−0.192580
$81$	−8173.77			−1.24581
$82$	−2734.47			−0.406673
$83$			10124.2i			1.46963i	0.678270	+	0.734813i	$0.262730\pi$
$83$			10124.2i			1.46963i	−0.678270	+	0.734813i	$0.737270\pi$
$84$		−	3056.87i		−	0.433229i
$85$		−	9973.18i		−	1.38037i
$86$	−7695.45			−1.04049
$87$			7210.77i			0.952672i
$88$	2737.53	+	45.9767i	0.353504	+	0.00593708i
$89$	5133.72			0.648115			0.324058	−	0.946037i	$-0.394953\pi$
$89$	5133.72			0.648115			0.324058	+	0.946037i	$0.394953\pi$
$90$			2491.56i			0.307600i
$91$	−2452.59			−0.296171
$92$	7741.13			0.914594
$93$	−8066.19			−0.932615
$94$			500.871i			0.0566853i
$95$			7927.96i			0.878444i
$96$			2037.91i			0.221128i
$97$	2239.34			0.238000			0.119000	−	0.992894i	$-0.462031\pi$
$97$	2239.34			0.238000			0.119000	+	0.992894i	$0.462031\pi$
$98$		−	3532.71i		−	0.367837i
$99$	92.9434	−	5534.00i	0.00948305	−	0.564637i
$100$	2033.04			0.203304
$101$		−	15580.0i		−	1.52730i	−0.645629	−	0.763651i	$-0.723405\pi$
$101$		−	15580.0i		−	1.52730i	0.645629	−	0.763651i	$-0.276595\pi$
$102$	−16490.3			−1.58500
$103$	−9119.47			−0.859597			−0.429799	−	0.902925i	$-0.641415\pi$
$103$	−9119.47			−0.859597			−0.429799	+	0.902925i	$0.641415\pi$
$104$	1635.06			0.151171
$105$		−	7358.63i		−	0.667450i
$106$			11379.5i			1.01278i
$107$			11204.9i			0.978684i	0.872092	+	0.489342i	$0.162763\pi$
$107$			11204.9i			0.978684i	−0.872092	+	0.489342i	$0.837237\pi$
$108$	−3175.47			−0.272245
$109$		−	10286.3i		−	0.865776i	−0.901448	−	0.432888i	$-0.857495\pi$
$109$		−	10286.3i		−	0.865776i	0.901448	−	0.432888i	$-0.142505\pi$
$110$	6589.91	+	110.677i	0.544621	+	0.00914689i
$111$	−13618.0			−1.10527
$112$		−	2172.23i		−	0.173169i
$113$	17026.9			1.33345			0.666727	−	0.745302i	$-0.267695\pi$
$113$	17026.9			1.33345			0.666727	+	0.745302i	$0.267695\pi$
$114$	13108.6			1.00866
$115$	18634.8			1.40906
$116$			5124.03i			0.380799i
$117$		−	3305.33i		−	0.241459i
$118$			5622.98i			0.403834i
$119$	17577.2			1.24124
$120$			4905.76i			0.340677i
$121$	−14632.7	−	491.651i	−0.999436	−	0.0335805i
$122$	6778.85			0.455446
$123$			10884.0i			0.719413i
$124$	−5731.89			−0.372782
$125$	16930.3			1.08354
$126$	−4391.23			−0.276596
$127$		−	27813.0i		−	1.72441i	−0.506558	−	0.862206i	$-0.669082\pi$
$127$		−	27813.0i		−	1.72441i	0.506558	−	0.862206i	$-0.330918\pi$
$128$			1448.15i			0.0883883i
$129$			30630.1i			1.84064i
$130$	3936.00			0.232899
$131$		−	6310.74i		−	0.367738i	−0.982951	−	0.183869i	$-0.941138\pi$
$131$		−	6310.74i		−	0.367738i	0.982951	−	0.183869i	$-0.0588621\pi$
$132$	183.001	−	10896.2i	0.0105028	−	0.625355i
$133$	−13972.6			−0.789903
$134$			5677.02i			0.316163i
$135$	−7644.13			−0.419431
$136$	−11718.1			−0.633549
$137$	−14207.1			−0.756944			−0.378472	−	0.925613i	$-0.623550\pi$
$137$	−14207.1			−0.756944			−0.378472	+	0.925613i	$0.623550\pi$
$138$		−	30812.0i		−	1.61794i
$139$			27772.6i			1.43743i	0.695306	+	0.718714i	$0.255269\pi$
$139$			27772.6i			1.43743i	−0.695306	+	0.718714i	$0.744731\pi$
$140$		−	5229.10i		−	0.266791i
$141$	1993.62			0.100277
$142$		−	12035.1i		−	0.596859i
$143$	−8742.26	−	146.826i	−0.427515	−	0.00718010i
$144$	2927.49			0.141179
$145$			12334.8i			0.586673i
$146$	−3644.94			−0.170995
$147$	−14061.2			−0.650711
$148$	−9677.08			−0.441795
$149$		−	23436.8i		−	1.05567i	−0.849348	−	0.527833i	$-0.823005\pi$
$149$		−	23436.8i		−	1.05567i	0.849348	−	0.527833i	$-0.176995\pi$
$150$		−	8092.11i		−	0.359649i
$151$		−	6556.14i		−	0.287538i	−0.989611	−	0.143769i	$-0.954078\pi$
$151$		−	6556.14i		−	0.287538i	0.989611	−	0.143769i	$-0.0459222\pi$
$152$	9315.06			0.403180
$153$			23688.6i			1.01194i
$154$	−195.063	+	11614.4i	−0.00822494	+	0.489727i
$155$	−13798.1			−0.574322
$156$		−	6508.03i		−	0.267424i
$157$	2315.17			0.0939254			0.0469627	−	0.998897i	$-0.485046\pi$
$157$	2315.17			0.0939254			0.0469627	+	0.998897i	$0.485046\pi$
$158$	−4186.72			−0.167710
$159$	45293.9			1.79162
$160$			3486.07i			0.136174i
$161$			32842.8i			1.26704i
$162$			23118.9i			0.880922i
$163$	−21728.0			−0.817796			−0.408898	−	0.912580i	$-0.634087\pi$
$163$	−21728.0			−0.817796			−0.408898	+	0.912580i	$0.634087\pi$
$164$			7734.25i			0.287561i
$165$	440.529	−	26229.8i	0.0161810	−	0.963446i
$166$	28635.7			1.03918
$167$		−	26470.6i		−	0.949143i	−0.880217	−	0.474571i	$-0.842603\pi$
$167$		−	26470.6i		−	0.949143i	0.880217	−	0.474571i	$-0.157397\pi$
$168$	−8646.13			−0.306339
$169$	23339.5			0.817179
$170$	−28208.4			−0.976070
$171$		−	18830.7i		−	0.643982i
$172$			21766.0i			0.735736i
$173$			6136.89i			0.205048i	0.994731	+	0.102524i	$0.0326919\pi$
$173$			6136.89i			0.205048i	−0.994731	+	0.102524i	$0.967308\pi$
$174$	20395.1			0.673641
$175$			8625.47i			0.281648i
$176$	130.042	−	7742.91i	0.00419815	−	0.249965i
$177$	22381.1			0.714390
$178$		−	14520.4i		−	0.458287i
$179$	−8164.31			−0.254808			−0.127404	−	0.991851i	$-0.540665\pi$
$179$	−8164.31			−0.254808			−0.127404	+	0.991851i	$0.540665\pi$
$180$	7047.19			0.217506
$181$	−10130.6			−0.309228			−0.154614	−	0.987975i	$-0.549413\pi$
$181$	−10130.6			−0.309228			−0.154614	+	0.987975i	$0.549413\pi$
$182$			6936.98i			0.209425i
$183$		−	26981.8i		−	0.805692i
$184$		−	21895.2i		−	0.646716i
$185$	−23295.1			−0.680647
$186$			22814.6i			0.659459i
$187$	62653.8	+	1052.27i	1.79170	+	0.0300915i
$188$	1416.68			0.0400826
$189$		−	13472.4i		−	0.377155i
$190$	22423.7			0.621154
$191$	13853.6			0.379749			0.189875	−	0.981808i	$-0.439192\pi$
$191$	13853.6			0.379749			0.189875	+	0.981808i	$0.439192\pi$
$192$	5764.08			0.156361
$193$			55752.8i			1.49676i	0.663270	+	0.748380i	$0.269168\pi$
$193$			55752.8i			1.49676i	−0.663270	+	0.748380i	$0.730832\pi$
$194$		−	6333.81i		−	0.168291i
$195$		−	15666.4i		−	0.412004i
$196$	−9992.00			−0.260100
$197$		−	38577.9i		−	0.994046i	−0.867737	−	0.497023i	$-0.834426\pi$
$197$		−	38577.9i		−	0.994046i	0.867737	−	0.497023i	$-0.165574\pi$
$198$	−15652.5	−	262.884i	−0.399258	−	0.00670553i
$199$	−43741.2			−1.10455			−0.552275	−	0.833662i	$-0.686240\pi$
$199$	−43741.2			−1.10455			−0.552275	+	0.833662i	$0.686240\pi$
$200$		−	5750.31i		−	0.143758i
$201$	22596.2			0.559299
$202$	−44066.9			−1.07997
$203$	−21739.4			−0.527540
$204$			46641.6i			1.12076i
$205$			18618.2i			0.443028i
$206$			25793.7i			0.607827i
$207$	−44261.8			−1.03297
$208$		−	4624.66i		−	0.106894i
$209$	−49805.2	−	836.477i	−1.14020	−	0.0191497i
$210$	−20813.4			−0.471958
$211$		−	40460.8i		−	0.908803i	−0.890797	−	0.454402i	$-0.849853\pi$
$211$		−	40460.8i		−	0.908803i	0.890797	−	0.454402i	$-0.150147\pi$
$212$	32186.2			0.716140
$213$	−47903.1			−1.05586
$214$	31692.4			0.692034
$215$			52396.2i			1.13350i
$216$			8981.58i			0.192506i
$217$		−	24318.4i		−	0.516434i
$218$	−29094.0			−0.612196
$219$			14507.9i			0.302494i
$220$	313.043	−	18639.1i	0.00646783	−	0.385105i
$221$	37421.6			0.766193
$222$			38517.6i			0.781545i
$223$	12067.6			0.242667			0.121334	−	0.992612i	$-0.461283\pi$
$223$	12067.6			0.242667			0.121334	+	0.992612i	$0.461283\pi$
$224$	−6144.00			−0.122449
$225$	−11624.4			−0.229619
$226$		−	48159.3i		−	0.942894i
$227$		−	38616.4i		−	0.749411i	−0.927144	−	0.374705i	$-0.877744\pi$
$227$		−	38616.4i		−	0.749411i	0.927144	−	0.374705i	$-0.122256\pi$
$228$		−	37076.7i		−	0.713233i
$229$	74080.9			1.41265			0.706326	−	0.707887i	$-0.250351\pi$
$229$	74080.9			1.41265			0.706326	+	0.707887i	$0.250351\pi$
$230$		−	52707.2i		−	0.996355i
$231$	46228.6	+	776.408i	0.866337	+	0.0145501i
$232$	14492.9			0.269265
$233$			51719.5i			0.952670i	0.879264	+	0.476335i	$0.158035\pi$
$233$			51719.5i			0.952670i	−0.879264	+	0.476335i	$0.841965\pi$
$234$	−9348.89			−0.170737
$235$	3410.29			0.0617527
$236$	15904.2			0.285554
$237$			16664.4i			0.296683i
$238$		−	49715.8i		−	0.877689i
$239$			16911.3i			0.296062i	0.988983	+	0.148031i	$0.0472935\pi$
$239$			16911.3i			0.296062i	−0.988983	+	0.148031i	$0.952706\pi$
$240$	13875.6			0.240895
$241$			59892.0i			1.03118i	0.856835	+	0.515590i	$0.172427\pi$
$241$			59892.0i			1.03118i	−0.856835	+	0.515590i	$0.827573\pi$
$242$	−1390.60	+	41387.6i	−0.0237450	+	0.706708i
$243$	59868.5			1.01388
$244$		−	19173.5i		−	0.322049i
$245$	−24053.2			−0.400720
$246$	30784.6			0.508702
$247$	−29747.5			−0.487592
$248$			16212.2i			0.263597i
$249$		−	113979.i		−	1.83833i
$250$		−	47886.0i		−	0.766177i
$251$	−19186.2			−0.304538			−0.152269	−	0.988339i	$-0.548658\pi$
$251$	−19186.2			−0.304538			−0.152269	+	0.988339i	$0.548658\pi$
$252$			12420.3i			0.195583i
$253$	−1966.15	+	117068.i	−0.0307168	+	1.82893i
$254$	−78667.1			−1.21934
$255$			112278.i			1.72669i
$256$	4096.00			0.0625000
$257$	30625.1			0.463672			0.231836	−	0.972755i	$-0.425527\pi$
$257$	30625.1			0.463672			0.231836	+	0.972755i	$0.425527\pi$
$258$	86635.1			1.30153
$259$		−	41056.4i		−	0.612042i
$260$		−	11132.7i		−	0.164685i
$261$		−	29297.9i		−	0.430086i
$262$	−17849.5			−0.260030
$263$		−	73815.1i		−	1.06717i	−0.845746	−	0.533585i	$-0.820844\pi$
$263$		−	73815.1i		−	1.06717i	0.845746	−	0.533585i	$-0.179156\pi$
$264$	−30819.1	−	517.605i	−0.442193	−	0.00742661i
$265$	77480.2			1.10331
$266$			39520.5i			0.558546i
$267$	−57795.3			−0.810718
$268$	16057.0			0.223561
$269$	−87292.0			−1.20634			−0.603170	−	0.797612i	$-0.706096\pi$
$269$	−87292.0			−1.20634			−0.603170	+	0.797612i	$0.706096\pi$
$270$			21620.9i			0.296583i
$271$		−	4518.78i		−	0.0615294i	−0.999527	−	0.0307647i	$-0.990206\pi$
$271$		−	4518.78i		−	0.0615294i	0.999527	−	0.0307647i	$-0.00979425\pi$
$272$			33143.9i			0.447987i
$273$	27611.2			0.370477
$274$			40183.7i			0.535240i
$275$	−516.369	+	30745.4i	−0.00682801	+	0.406551i
$276$	−87149.4			−1.14405
$277$			4641.04i			0.0604861i	0.999543	+	0.0302431i	$0.00962813\pi$
$277$			4641.04i			0.0604861i	−0.999543	+	0.0302431i	$0.990372\pi$
$278$	78552.6			1.01642
$279$	32773.6			0.421032
$280$	−14790.1			−0.188650
$281$		−	58621.1i		−	0.742406i	−0.928552	−	0.371203i	$-0.878945\pi$
$281$		−	58621.1i		−	0.742406i	0.928552	−	0.371203i	$-0.121055\pi$
$282$		−	5638.80i		−	0.0709069i
$283$		−	90326.0i		−	1.12782i	−0.825836	−	0.563910i	$-0.809296\pi$
$283$		−	90326.0i		−	1.12782i	0.825836	−	0.563910i	$-0.190704\pi$
$284$	−34040.3			−0.422043
$285$		−	89252.8i		−	1.09883i
$286$	−415.286	+	24726.8i	−0.00507710	+	0.302299i
$287$	−32813.6			−0.398373
$288$		−	8280.19i		−	0.0998287i
$289$	−184671.			−2.21108
$290$	34888.1			0.414840
$291$	−25210.4			−0.297710
$292$			10309.4i			0.120912i
$293$		−	77687.4i		−	0.904931i	−0.891782	−	0.452465i	$-0.850545\pi$
$293$		−	77687.4i		−	0.904931i	0.891782	−	0.452465i	$-0.149455\pi$
$294$			39771.1i			0.460122i
$295$	38285.3			0.439935
$296$			27370.9i			0.312396i
$297$	806.531	−	48022.2i	0.00914341	−	0.544414i
$298$	−66289.4			−0.746469
$299$			69922.0i			0.782116i
$300$	−22887.9			−0.254311
$301$	−92345.3			−1.01925
$302$	−18543.6			−0.203320
$303$			175399.i			1.91048i
$304$		−	26347.0i		−	0.285091i
$305$		−	46155.3i		−	0.496160i
$306$	67001.3			0.715551
$307$			60487.2i			0.641781i	0.947116	+	0.320890i	$0.103982\pi$
$307$			60487.2i			0.641781i	−0.947116	+	0.320890i	$0.896018\pi$
$308$	32850.4	+	551.721i	0.346289	+	0.00581591i
$309$	102667.			1.07526
$310$			39026.9i			0.406107i
$311$	32106.2			0.331947			0.165973	−	0.986130i	$-0.446923\pi$
$311$	32106.2			0.331947			0.165973	+	0.986130i	$0.446923\pi$
$312$	−18407.5			−0.189097
$313$	111475.			1.13786			0.568932	−	0.822384i	$-0.307357\pi$
$313$	111475.			1.13786			0.568932	+	0.822384i	$0.307357\pi$
$314$		−	6548.28i		−	0.0664153i
$315$			29898.7i			0.301322i
$316$			11841.8i			0.118589i
$317$	139267.			1.38589			0.692945	−	0.720990i	$-0.256313\pi$
$317$	139267.			1.38589			0.692945	+	0.720990i	$0.256313\pi$
$318$		−	128111.i		−	1.26687i
$319$	−77490.0	−	1301.44i	−0.761490	−	0.0127892i
$320$	9860.08			0.0962899
$321$		−	126145.i		−	1.22422i
$322$	92893.5			0.895929
$323$	213194.			2.04347
$324$	65390.2			0.622906
$325$			18363.5i			0.173856i
$326$			61456.1i			0.578269i
$327$			115803.i			1.08299i
$328$	21875.7			0.203336
$329$			6010.46i			0.0555285i
$330$	−74189.1	−	1246.00i	−0.681259	−	0.0114417i
$331$	−60223.2			−0.549677			−0.274839	−	0.961490i	$-0.588624\pi$
$331$	−60223.2			−0.549677			−0.274839	+	0.961490i	$0.588624\pi$
$332$		−	80994.0i		−	0.734813i
$333$	55331.2			0.498978
$334$	−74870.3			−0.671145
$335$	38653.3			0.344427
$336$			24454.9i			0.216615i
$337$			85639.9i			0.754078i	0.926197	+	0.377039i	$0.123058\pi$
$337$			85639.9i			0.754078i	−0.926197	+	0.377039i	$0.876942\pi$
$338$		−	66014.0i		−	0.577833i
$339$	−191688.			−1.66800
$340$			79785.5i			0.690186i
$341$	1455.83	−	86682.7i	0.0125200	−	0.745459i
$342$	−53261.2			−0.455364
$343$		−	123885.i		−	1.05301i
$344$	61563.6			0.520244
$345$	−209790.			−1.76257
$346$	17357.8			0.144991
$347$			99499.7i			0.826348i	0.910652	+	0.413174i	$0.135580\pi$
$347$			99499.7i			0.826348i	−0.910652	+	0.413174i	$0.864420\pi$
$348$		−	57686.2i		−	0.476336i
$349$		−	47515.3i		−	0.390106i	−0.980793	−	0.195053i	$-0.937512\pi$
$349$		−	47515.3i		−	0.390106i	0.980793	−	0.195053i	$-0.0624878\pi$
$350$	24396.5			0.199155
$351$		−	28682.5i		−	0.232811i
$352$	−21900.3	−	367.814i	−0.176752	−	0.00296854i
$353$	167482.			1.34406			0.672030	−	0.740524i	$-0.265423\pi$
$353$	167482.			1.34406			0.672030	+	0.740524i	$0.265423\pi$
$354$		−	63303.4i		−	0.505150i
$355$	−81943.4			−0.650216
$356$	−41069.8			−0.324058
$357$	−197884.			−1.55265
$358$			23092.2i			0.180177i
$359$		−	5063.91i		−	0.0392914i	−0.999807	−	0.0196457i	$-0.993746\pi$
$359$		−	5063.91i		−	0.0392914i	0.999807	−	0.0196457i	$-0.00625382\pi$
$360$		−	19932.5i		−	0.153800i
$361$	−39152.4			−0.300431
$362$			28653.7i			0.218657i
$363$	164735.	+	5535.00i	1.25018	+	0.0420053i
$364$	19620.8			0.148086
$365$			24817.4i			0.186282i
$366$	−76316.1			−0.569711
$367$	264021.			1.96023			0.980115	−	0.198429i	$-0.0635841\pi$
$367$	264021.			1.96023			0.980115	+	0.198429i	$0.0635841\pi$
$368$	−61929.0			−0.457297
$369$		−	44222.5i		−	0.324781i
$370$			65888.6i			0.481290i
$371$			136555.i			0.992106i
$372$	64529.5			0.466308
$373$			270510.i			1.94431i	0.234339	+	0.972155i	$0.424707\pi$
$373$			270510.i			1.94431i	−0.234339	+	0.972155i	$0.575293\pi$
$374$	2976.26	−	177212.i	0.0212779	−	1.26692i
$375$	−190601.			−1.35538
$376$		−	4006.97i		−	0.0283426i
$377$	−46282.9			−0.325640
$378$	−38105.6			−0.266689
$379$	−38850.0			−0.270466			−0.135233	−	0.990814i	$-0.543178\pi$
$379$	−38850.0			−0.270466			−0.135233	+	0.990814i	$0.543178\pi$
$380$		−	63423.7i		−	0.439222i
$381$			313118.i			2.15704i
$382$		−	39184.0i		−	0.268523i
$383$	−243070.			−1.65704			−0.828522	−	0.559956i	$-0.810818\pi$
$383$	−243070.			−1.65704			−0.828522	+	0.559956i	$0.810818\pi$
$384$		−	16303.3i		−	0.110564i
$385$	79079.0	+	1328.13i	0.533506	+	0.00896022i
$386$	157693.			1.05837
$387$		−	124453.i		−	0.830964i
$388$	−17914.7			−0.119000
$389$	−142544.			−0.941995			−0.470998	−	0.882135i	$-0.656106\pi$
$389$	−142544.			−0.941995			−0.470998	+	0.882135i	$0.656106\pi$
$390$	−44311.4			−0.291331
$391$		−	501115.i		−	3.27781i
$392$			28261.6i			0.183918i
$393$			71046.2i			0.459998i
$394$	−109115.			−0.702897
$395$			28506.2i			0.182703i
$396$	−743.547	+	44272.0i	−0.00474153	+	0.282318i
$397$	−73860.0			−0.468628			−0.234314	−	0.972161i	$-0.575284\pi$
$397$	−73860.0			−0.468628			−0.234314	+	0.972161i	$0.575284\pi$
$398$			123719.i			0.781034i
$399$	157303.			0.988079
$400$	−16264.3			−0.101652
$401$	225776.			1.40407			0.702034	−	0.712143i	$-0.252275\pi$
$401$	225776.			1.40407			0.702034	+	0.712143i	$0.252275\pi$
$402$		−	63911.8i		−	0.395484i
$403$		−	51773.5i		−	0.318785i
$404$			124640.i			0.763651i
$405$	157410.			0.959673
$406$			61488.3i			0.373027i
$407$	2457.86	−	146345.i	0.0148378	−	0.883466i
$408$	131922.			0.792498
$409$			97972.9i			0.585679i	0.956162	+	0.292839i	$0.0946001\pi$
$409$			97972.9i			0.585679i	−0.956162	+	0.292839i	$0.905400\pi$
$410$	52660.3			0.313268
$411$	159943.			0.946851
$412$	72955.7			0.429799
$413$			67475.8i			0.395592i
$414$			125191.i			0.730422i
$415$		−	194973.i		−	1.13208i
$416$	−13080.5			−0.0755854
$417$		−	312663.i		−	1.79806i
$418$	−2365.91	+	140870.i	−0.0135409	+	0.806246i
$419$	−64572.5			−0.367807			−0.183903	−	0.982944i	$-0.558873\pi$
$419$	−64572.5			−0.367807			−0.183903	+	0.982944i	$0.558873\pi$
$420$			58869.1i			0.333725i
$421$	203272.			1.14687			0.573434	−	0.819252i	$-0.305611\pi$
$421$	203272.			1.14687			0.573434	+	0.819252i	$0.305611\pi$
$422$	−114441.			−0.642621
$423$	−8100.21			−0.0452706
$424$		−	91036.3i		−	0.506388i
$425$		−	131607.i		−	0.728621i
$426$			135491.i			0.746603i
$427$	81346.2			0.446151
$428$		−	89639.6i		−	0.489342i
$429$	98420.1	+	1652.96i	0.534773	+	0.00898149i
$430$	148199.			0.801507
$431$			11113.4i			0.0598266i	0.999552	+	0.0299133i	$0.00952311\pi$
$431$			11113.4i			0.0598266i	−0.999552	+	0.0299133i	$0.990477\pi$
$432$	25403.7			0.136123
$433$	−288512.			−1.53882			−0.769409	−	0.638756i	$-0.779449\pi$
$433$	−288512.			−1.53882			−0.769409	+	0.638756i	$0.779449\pi$
$434$	−68782.7			−0.365174
$435$		−	138865.i		−	0.733861i
$436$			82290.2i			0.432888i
$437$			398350.i			2.08594i
$438$	41034.6			0.213896
$439$			107467.i			0.557630i	0.960345	+	0.278815i	$0.0899417\pi$
$439$			107467.i			0.557630i	−0.960345	+	0.278815i	$0.910058\pi$
$440$	−52719.3	−	885.419i	−0.272311	−	0.00457345i
$441$	57131.8			0.293765
$442$		−	105844.i		−	0.541780i
$443$	−130812.			−0.666563			−0.333281	−	0.942827i	$-0.608156\pi$
$443$	−130812.			−0.666563			−0.333281	+	0.942827i	$0.608156\pi$
$444$	108944.			0.552636
$445$	−98865.0			−0.499255
$446$		−	34132.3i		−	0.171592i
$447$			263851.i			1.32052i
$448$			17377.9i			0.0865845i
$449$	−158898.			−0.788181			−0.394090	−	0.919072i	$-0.628940\pi$
$449$	−158898.			−0.788181			−0.394090	+	0.919072i	$0.628940\pi$
$450$			32878.9i			0.162365i
$451$	−116964.	−	1964.41i	−0.575041	−	0.00965780i
$452$	−136215.			−0.666727
$453$			73808.9i			0.359677i
$454$	−109224.			−0.529913
$455$	47232.0			0.228146
$456$	−104869.			−0.504332
$457$		−	291561.i		−	1.39604i	−0.716079	−	0.698019i	$-0.754065\pi$
$457$		−	291561.i		−	1.39604i	0.716079	−	0.698019i	$-0.245935\pi$
$458$		−	209532.i		−	0.998896i
$459$			205561.i			0.975698i
$460$	−149078.			−0.704529
$461$		−	62731.9i		−	0.295180i	−0.989049	−	0.147590i	$-0.952848\pi$
$461$		−	62731.9i		−	0.295180i	0.989049	−	0.147590i	$-0.0471515\pi$
$462$	2196.01	−	130754.i	0.0102885	−	0.612593i
$463$	−170883.			−0.797146			−0.398573	−	0.917137i	$-0.630494\pi$
$463$	−170883.			−0.797146			−0.398573	+	0.917137i	$0.630494\pi$
$464$		−	40992.2i		−	0.190399i
$465$	155339.			0.718411
$466$	146285.			0.673639
$467$	94559.0			0.433580			0.216790	−	0.976218i	$-0.430441\pi$
$467$	94559.0			0.433580			0.216790	+	0.976218i	$0.430441\pi$
$468$			26442.6i			0.120729i
$469$			68124.3i			0.309711i
$470$		−	9645.77i		−	0.0436658i
$471$	−26064.1			−0.117490
$472$		−	44983.8i		−	0.201917i
$473$	−329164.	−	5528.30i	−1.47126	−	0.0247098i
$474$	47134.0			0.209786
$475$			104618.i			0.463682i
$476$	−140618.			−0.620620
$477$	−184033.			−0.808832
$478$	47832.5			0.209347
$479$			154781.i			0.674600i	0.941397	+	0.337300i	$0.109514\pi$
$479$			154781.i			0.674600i	−0.941397	+	0.337300i	$0.890486\pi$
$480$		−	39246.0i		−	0.170339i
$481$		−	87408.6i		−	0.377802i
$482$	169400.			0.729155
$483$		−	369744.i		−	1.58492i
$484$	117062.	+	3933.21i	0.499718	+	0.0167902i
$485$	−43125.1			−0.183336
$486$		−	169334.i		−	0.716920i
$487$	205330.			0.865754			0.432877	−	0.901453i	$-0.357498\pi$
$487$	205330.			0.865754			0.432877	+	0.901453i	$0.357498\pi$
$488$	−54230.8			−0.227723
$489$	244614.			1.02297
$490$			68032.8i			0.283352i
$491$			180799.i			0.749950i	0.927035	+	0.374975i	$0.122349\pi$
$491$			180799.i			0.749950i	−0.927035	+	0.374975i	$0.877651\pi$
$492$		−	87071.9i		−	0.359706i
$493$	331699.			1.36474
$494$			84138.6i			0.344779i
$495$	−1789.90	+	106574.i	−0.00730498	+	0.434950i
$496$	45855.2			0.186391
$497$		−	144421.i		−	0.584678i
$498$	−322380.			−1.29990
$499$	198403.			0.796797			0.398399	−	0.917212i	$-0.369566\pi$
$499$	198403.			0.796797			0.398399	+	0.917212i	$0.369566\pi$
$500$	−135442.			−0.541769
$501$			298006.i			1.18727i
$502$			54266.8i			0.215341i
$503$		−	278604.i		−	1.10116i	−0.834781	−	0.550582i	$-0.814406\pi$
$503$		−	278604.i		−	1.10116i	0.834781	−	0.550582i	$-0.185594\pi$
$504$	35129.9			0.138298
$505$			300040.i			1.17651i
$506$	331118.	+	5561.12i	1.29325	+	0.0217201i
$507$	−262755.			−1.02220
$508$			222504.i			0.862206i
$509$	−195175.			−0.753336			−0.376668	−	0.926348i	$-0.622930\pi$
$509$	−195175.			−0.753336			−0.376668	+	0.926348i	$0.622930\pi$
$510$	317570.			1.22095
$511$	−43739.2			−0.167506
$512$		−	11585.2i		−	0.0441942i
$513$		−	163406.i		−	0.620917i
$514$		−	86620.8i		−	0.327866i
$515$	175622.			0.662164
$516$		−	245041.i		−	0.920322i
$517$	−359.819	+	21424.2i	−0.00134618	+	0.0801538i
$518$	−116125.			−0.432779
$519$		−	69089.0i		−	0.256492i
$520$	−31488.0			−0.116450
$521$	−2617.52			−0.00964304			−0.00482152	−	0.999988i	$-0.501535\pi$
$521$	−2617.52			−0.00964304			−0.00482152	+	0.999988i	$0.501535\pi$
$522$	−82867.0			−0.304117
$523$			309803.i			1.13261i	0.824194	+	0.566307i	$0.191628\pi$
$523$			309803.i			1.13261i	−0.824194	+	0.566307i	$0.808372\pi$
$524$			50486.0i			0.183869i
$525$		−	97105.3i		−	0.352310i
$526$	−208781.			−0.754603
$527$			371049.i			1.33601i
$528$	−1464.01	+	87169.5i	−0.00525141	+	0.312677i
$529$	656488.			2.34593
$530$		−	219147.i		−	0.780160i
$531$	−90936.2			−0.322513
$532$	111781.			0.394952
$533$	−69859.8			−0.245908
$534$			163470.i			0.573264i
$535$		−	215785.i		−	0.753899i
$536$		−	45416.2i		−	0.158081i
$537$	91913.7			0.318736
$538$			246899.i			0.853012i
$539$	2537.85	−	151108.i	0.00873551	−	0.520127i
$540$	61153.1			0.209716
$541$		−	197545.i		−	0.674948i	−0.941335	−	0.337474i	$-0.890427\pi$
$541$		−	197545.i		−	0.674948i	0.941335	−	0.337474i	$-0.109573\pi$
$542$	−12781.0			−0.0435079
$543$	114050.			0.386809
$544$	93745.0			0.316775
$545$			198093.i			0.666923i
$546$		−	78096.4i		−	0.261966i
$547$		−	440541.i		−	1.47235i	−0.676790	−	0.736176i	$-0.736630\pi$
$547$		−	440541.i		−	1.47235i	0.676790	−	0.736176i	$-0.263370\pi$
$548$	113657.			0.378472
$549$			109629.i			0.363732i
$550$	86961.2	+	1460.51i	0.287475	+	0.00482813i
$551$	−263677.			−0.868498
$552$			246496.i			0.808968i
$553$	−50240.6			−0.164288
$554$	13126.8			0.0427701
$555$	262256.			0.851411
$556$		−	222180.i		−	0.718714i
$557$		−	422793.i		−	1.36275i	−0.731933	−	0.681376i	$-0.761382\pi$
$557$		−	422793.i		−	1.36275i	0.731933	−	0.681376i	$-0.238618\pi$
$558$		−	92697.6i		−	0.297715i
$559$	−196602.			−0.629165
$560$			41832.8i			0.133395i
$561$	−705355.	−	11846.4i	−2.24121	−	0.0376410i
$562$	−165805.			−0.524960
$563$		−	52520.6i		−	0.165696i	−0.996562	−	0.0828482i	$-0.973598\pi$
$563$		−	52520.6i		−	0.165696i	0.996562	−	0.0828482i	$-0.0264017\pi$
$564$	−15948.9			−0.0501387
$565$	−327903.			−1.02718
$566$	−255481.			−0.797490
$567$			277427.i			0.862944i
$568$			96280.5i			0.298430i
$569$		−	140197.i		−	0.433025i	−0.976280	−	0.216513i	$-0.930532\pi$
$569$		−	140197.i		−	0.433025i	0.976280	−	0.216513i	$-0.0694683\pi$
$570$	−252445.			−0.776993
$571$			207548.i			0.636569i	0.947995	+	0.318284i	$0.103107\pi$
$571$			207548.i			0.636569i	−0.947995	+	0.318284i	$0.896893\pi$
$572$	69938.1	+	1174.61i	0.213758	+	0.00359005i
$573$	−155964.			−0.475023
$574$			92810.9i			0.281693i
$575$	245907.			0.743764
$576$	−23419.9			−0.0705895
$577$	−273572.			−0.821712			−0.410856	−	0.911700i	$-0.634770\pi$
$577$	−273572.			−0.821712			−0.410856	+	0.911700i	$0.634770\pi$
$578$			522329.i			1.56347i
$579$		−	627664.i		−	1.87228i
$580$		−	98678.4i		−	0.293336i
$581$	343628.			1.01797
$582$			71305.8i			0.210513i
$583$	−8174.91	+	486748.i	−0.0240517	+	1.43208i
$584$	29159.5			0.0854977
$585$			63654.0i			0.186000i
$586$	−219733.			−0.639883
$587$	−576701.			−1.67369			−0.836843	−	0.547442i	$-0.815602\pi$
$587$	−576701.			−1.67369			−0.836843	+	0.547442i	$0.815602\pi$
$588$	112490.			0.325355
$589$		−	294957.i		−	0.850214i
$590$		−	108287.i		−	0.311081i
$591$			434309.i			1.24344i
$592$	77416.7			0.220898
$593$		−	671956.i		−	1.91087i	−0.295202	−	0.955435i	$-0.595387\pi$
$593$		−	671956.i		−	1.91087i	0.295202	−	0.955435i	$-0.404613\pi$
$594$	−135827.	−	2281.21i	−0.384959	−	0.00646536i
$595$	−338501.			−0.956150
$596$			187495.i			0.527833i
$597$	492438.			1.38167
$598$	197769.			0.553040
$599$	582984.			1.62481			0.812406	−	0.583092i	$-0.198157\pi$
$599$	582984.			1.62481			0.812406	+	0.583092i	$0.198157\pi$
$600$			64736.9i			0.179825i
$601$			377092.i			1.04399i	0.852947	+	0.521997i	$0.174813\pi$
$601$			377092.i			1.04399i	−0.852947	+	0.521997i	$0.825187\pi$
$602$			261192.i			0.720721i
$603$	−91810.2			−0.252497
$604$			52449.2i			0.143769i
$605$	281797.	+	9468.21i	0.769885	+	0.0258677i
$606$	496104.			1.35091
$607$			465535.i			1.26350i	0.775173	+	0.631750i	$0.217663\pi$
$607$			465535.i			1.26350i	−0.775173	+	0.631750i	$0.782337\pi$
$608$	−74520.5			−0.201590
$609$	244742.			0.659893
$610$	−130547.			−0.350838
$611$			12796.2i			0.0342766i
$612$		−	189508.i		−	0.505971i
$613$		−	623300.i		−	1.65873i	−0.558705	−	0.829366i	$-0.688702\pi$
$613$		−	623300.i		−	1.65873i	0.558705	−	0.829366i	$-0.311298\pi$
$614$	171084.			0.453807
$615$		−	209604.i		−	0.554177i
$616$	1560.50	−	92914.9i	0.00411247	−	0.244863i
$617$	197189.			0.517980			0.258990	−	0.965880i	$-0.416610\pi$
$617$	197189.			0.517980			0.258990	+	0.965880i	$0.416610\pi$
$618$		−	290385.i		−	0.760322i
$619$	214900.			0.560861			0.280431	−	0.959874i	$-0.409523\pi$
$619$	214900.			0.560861			0.280431	+	0.959874i	$0.409523\pi$
$620$	110385.			0.287161
$621$	−384089.			−0.995976
$622$		−	90810.1i		−	0.234722i
$623$		−	174244.i		−	0.448934i
$624$			52064.3i			0.133712i
$625$	−167211.			−0.428061
$626$		−	315300.i		−	0.804592i
$627$	560706.	+	9417.04i	1.42626	+	0.0239541i
$628$	−18521.3			−0.0469627
$629$			626437.i			1.58335i
$630$	84566.3			0.213067
$631$	−40334.6			−0.101302			−0.0506511	−	0.998716i	$-0.516130\pi$
$631$	−40334.6			−0.101302			−0.0506511	+	0.998716i	$0.516130\pi$
$632$	33493.8			0.0838551
$633$			455507.i			1.13681i
$634$		−	393906.i		−	0.979973i
$635$			535623.i			1.32835i
$636$	−362352.			−0.895810
$637$		−	90253.1i		−	0.222425i
$638$	−3681.03	+	219175.i	−0.00904333	+	0.538455i
$639$	194634.			0.476669
$640$		−	27888.5i		−	0.0680872i
$641$	−19965.1			−0.0485909			−0.0242954	−	0.999705i	$-0.507734\pi$
$641$	−19965.1			−0.0485909			−0.0242954	+	0.999705i	$0.507734\pi$
$642$	−356792.			−0.865656
$643$	21885.5			0.0529340			0.0264670	−	0.999650i	$-0.491574\pi$
$643$	21885.5			0.0529340			0.0264670	+	0.999650i	$0.491574\pi$
$644$		−	262743.i		−	0.633518i
$645$		−	589875.i		−	1.41788i
$646$		−	603002.i		−	1.44495i
$647$	−345969.			−0.826472			−0.413236	−	0.910624i	$-0.635602\pi$
$647$	−345969.			−0.826472			−0.413236	+	0.910624i	$0.635602\pi$
$648$		−	184951.i		−	0.440461i
$649$	−4039.47	+	240517.i	−0.00959037	+	0.571027i
$650$	51939.9			0.122935
$651$			273776.i			0.646000i
$652$	173824.			0.408898
$653$	380939.			0.893366			0.446683	−	0.894692i	$-0.352605\pi$
$653$	380939.			0.893366			0.446683	+	0.894692i	$0.352605\pi$
$654$	327539.			0.765787
$655$			121532.i			0.283275i
$656$		−	61874.0i		−	0.143781i
$657$		−	58946.8i		−	0.136562i
$658$	17000.1			0.0392645
$659$		−	149577.i		−	0.344424i	−0.985060	−	0.172212i	$-0.944909\pi$
$659$		−	149577.i		−	0.344424i	0.985060	−	0.172212i	$-0.0550914\pi$
$660$	−3524.23	+	209838.i	−0.00809052	+	0.481723i
$661$	−637662.			−1.45945			−0.729723	−	0.683743i	$-0.760351\pi$
$661$	−637662.			−1.45945			−0.729723	+	0.683743i	$0.760351\pi$
$662$			170337.i			0.388681i
$663$	−421292.			−0.958420
$664$	−229086.			−0.519591
$665$	269084.			0.608477
$666$		−	156500.i		−	0.352831i
$667$			619777.i			1.39311i
$668$			211765.i			0.474571i
$669$	−135857.			−0.303549
$670$		−	109328.i		−	0.243546i
$671$	289958.	+	4869.84i	0.644006	+	0.0108161i
$672$	69169.0			0.153170
$673$		−	165463.i		−	0.365318i	−0.983176	−	0.182659i	$-0.941530\pi$
$673$		−	165463.i		−	0.365318i	0.983176	−	0.182659i	$-0.0584704\pi$
$674$	242226.			0.533214
$675$	−100873.			−0.221394
$676$	−186716.			−0.408590
$677$		−	420292.i		−	0.917009i	−0.888692	−	0.458504i	$-0.848385\pi$
$677$		−	420292.i		−	0.917009i	0.888692	−	0.458504i	$-0.151615\pi$
$678$			542176.i			1.17945i
$679$		−	76005.7i		−	0.164857i
$680$	225667.			0.488035
$681$			434742.i			0.937428i
$682$	−245176.	−	4117.72i	−0.527119	−	0.00885294i
$683$	265281.			0.568677			0.284338	−	0.958724i	$-0.408226\pi$
$683$	265281.			0.568677			0.284338	+	0.958724i	$0.408226\pi$
$684$			150646.i			0.321991i
$685$	273600.			0.583089
$686$	−350400.			−0.744588
$687$	−834001.			−1.76707
$688$		−	174128.i		−	0.367868i
$689$			290723.i			0.612408i
$690$			593376.i			1.24633i
$691$	−72314.2			−0.151449			−0.0757247	−	0.997129i	$-0.524127\pi$
$691$	−72314.2			−0.151449			−0.0757247	+	0.997129i	$0.524127\pi$
$692$		−	49095.1i		−	0.102524i
$693$	−187830.	−	3154.60i	−0.391110	−	0.00656868i
$694$	281428.			0.584316
$695$		−	534843.i		−	1.10728i
$696$	−163161.			−0.336820
$697$	500669.			1.03059
$698$	−134393.			−0.275846
$699$		−	582257.i		−	1.19168i
$700$		−	69003.8i		−	0.140824i
$701$			142549.i			0.290088i	0.989425	+	0.145044i	$0.0463324\pi$
$701$			142549.i			0.290088i	−0.989425	+	0.145044i	$0.953668\pi$
$702$	−81126.4			−0.164622
$703$		−	497972.i		−	1.00761i
$704$	−1040.33	+	61943.3i	−0.00209907	+	0.124982i
$705$	−38393.0			−0.0772456
$706$		−	473711.i		−	0.950394i
$707$	−528803.			−1.05793
$708$	−179049.			−0.357195
$709$	−588664.			−1.17105			−0.585525	−	0.810654i	$-0.699112\pi$
$709$	−588664.			−1.17105			−0.585525	+	0.810654i	$0.699112\pi$
$710$			231771.i			0.459772i
$711$		−	67708.7i		−	0.133938i
$712$			116163.i			0.229143i
$713$	−693302.			−1.36378
$714$			559699.i			1.09789i
$715$	168358.	+	2827.57i	0.329323	+	0.00553097i
$716$	65314.5			0.127404
$717$		−	190387.i		−	0.370340i
$718$	−14322.9			−0.0277832
$719$	−133520.			−0.258280			−0.129140	−	0.991626i	$-0.541222\pi$
$719$	−133520.			−0.258280			−0.129140	+	0.991626i	$0.541222\pi$
$720$	−56377.5			−0.108753
$721$			309525.i			0.595422i
$722$			110740.i			0.212437i
$723$		−	674263.i		−	1.28989i
$724$	81044.9			0.154614
$725$			162771.i			0.309672i
$726$	15655.3	−	465941.i	0.0297023	−	0.884011i
$727$	224313.			0.424410			0.212205	−	0.977225i	$-0.431936\pi$
$727$	224313.			0.424410			0.212205	+	0.977225i	$0.431936\pi$
$728$		−	55495.9i		−	0.104712i
$729$	−11922.8			−0.0224348
$730$	70194.1			0.131721
$731$	1.40900e6			2.63680
$732$			215855.i			0.402846i
$733$			297252.i			0.553243i	0.960979	+	0.276622i	$0.0892149\pi$
$733$			297252.i			0.553243i	−0.960979	+	0.276622i	$0.910785\pi$
$734$		−	746765.i		−	1.38609i
$735$	270790.			0.501255
$736$			175162.i			0.323358i
$737$	−4078.30	+	242829.i	−0.00750834	+	0.447059i
$738$	−125080.			−0.229655
$739$		−	268988.i		−	0.492543i	−0.969201	−	0.246272i	$-0.920794\pi$
$739$		−	268988.i		−	0.492543i	0.969201	−	0.246272i	$-0.0792056\pi$
$740$	186361.			0.340323
$741$	334896.			0.609922
$742$	386235.			0.701525
$743$		−	133653.i		−	0.242104i	−0.992646	−	0.121052i	$-0.961373\pi$
$743$		−	133653.i		−	0.242104i	0.992646	−	0.121052i	$-0.0386267\pi$
$744$		−	182517.i		−	0.329729i
$745$			451346.i			0.813200i
$746$	765117.			1.37483
$747$			463104.i			0.829921i
$748$	−501230.	−	8418.14i	−0.895848	−	0.0150457i
$749$	380309.			0.677911
$750$			539100.i			0.958400i
$751$	201267.			0.356856			0.178428	−	0.983953i	$-0.442899\pi$
$751$	201267.			0.356856			0.178428	+	0.983953i	$0.442899\pi$
$752$	−11333.4			−0.0200413
$753$	215998.			0.380942
$754$			130908.i			0.230262i
$755$			126258.i			0.221496i
$756$			107779.i			0.188578i
$757$	835429.			1.45787			0.728934	−	0.684584i	$-0.240016\pi$
$757$	835429.			1.45787			0.728934	+	0.684584i	$0.240016\pi$
$758$			109884.i			0.191248i
$759$	22134.9	−	1.31795e6i	0.0384233	−	2.28778i
$760$	−179389.			−0.310577
$761$		−	345963.i		−	0.597393i	−0.954348	−	0.298696i	$-0.903448\pi$
$761$		−	345963.i		−	0.597393i	0.954348	−	0.298696i	$-0.0965518\pi$
$762$	885633.			1.52526
$763$	−349128.			−0.599702
$764$	−110829.			−0.189875
$765$		−	456194.i		−	0.779518i
$766$			687506.i			1.17171i
$767$			143655.i			0.244191i
$768$	−46112.7			−0.0781804
$769$			1.05669e6i			1.78688i	0.449183	+	0.893440i	$0.351715\pi$
$769$			1.05669e6i			1.78688i	−0.449183	+	0.893440i	$0.648285\pi$
$770$	3756.51	−	223669.i	0.00633583	−	0.377246i
$771$	−344776.			−0.580001
$772$		−	446022.i		−	0.748380i
$773$	−224559.			−0.375813			−0.187907	−	0.982187i	$-0.560170\pi$
$773$	−224559.			−0.375813			−0.187907	+	0.982187i	$0.560170\pi$
$774$	−352005.			−0.587580
$775$	−182081.			−0.303153
$776$			50670.4i			0.0841456i
$777$			462212.i			0.765595i
$778$			403174.i			0.666091i
$779$	−397996.			−0.655849
$780$			125332.i			0.206002i
$781$	8645.83	−	514787.i	0.0141744	−	0.843967i
$782$	−1.41737e6			−2.31776
$783$		−	254237.i		−	0.414682i
$784$	79936.0			0.130050
$785$	−44585.4			−0.0723525
$786$	200949.			0.325268
$787$			227376.i			0.367109i	0.983010	+	0.183554i	$0.0587603\pi$
$787$			227376.i			0.367109i	−0.983010	+	0.183554i	$0.941240\pi$
$788$			308623.i			0.497023i
$789$			831008.i			1.33491i
$790$	80627.7			0.129190
$791$		−	577911.i		−	0.923651i
$792$	125220.	+	2103.07i	0.199629	+	0.00335277i
$793$	173185.			0.275400
$794$			208908.i			0.331370i
$795$	−872270.			−1.38012
$796$	349930.			0.552275
$797$	−972019.			−1.53023			−0.765117	−	0.643891i	$-0.777319\pi$
$797$	−972019.			−1.53023			−0.765117	+	0.643891i	$0.777319\pi$
$798$		−	444920.i		−	0.698677i
$799$		−	91707.4i		−	0.143652i
$800$			46002.5i			0.0718789i
$801$	234827.			0.366001
$802$		−	638590.i		−	0.992826i
$803$	−155908.	−	2618.47i	−0.241790	−	0.00406085i
$804$	−180770.			−0.279649
$805$		−	632486.i		−	0.976021i
$806$	−146438.			−0.225415
$807$	982732.			1.50900
$808$	352535.			0.539983
$809$			56475.6i			0.0862906i	0.999069	+	0.0431453i	$0.0137378\pi$
$809$			56475.6i			0.0862906i	−0.999069	+	0.0431453i	$0.986262\pi$
$810$		−	445224.i		−	0.678591i
$811$			224590.i			0.341467i	0.985317	+	0.170733i	$0.0546137\pi$
$811$			224590.i			0.341467i	−0.985317	+	0.170733i	$0.945386\pi$
$812$	173915.			0.263770
$813$			50872.3i			0.0769663i
$814$	−413927.	−	6951.89i	−0.624705	−	0.0104919i
$815$	418438.			0.629964
$816$		−	373133.i		−	0.560381i
$817$	−1.12006e6			−1.67801
$818$	277109.			0.414137
$819$	−112187.			−0.167253
$820$		−	148946.i		−	0.221514i
$821$			719097.i			1.06684i	0.845849	+	0.533422i	$0.179094\pi$
$821$			719097.i			1.06684i	−0.845849	+	0.533422i	$0.820906\pi$
$822$		−	452387.i		−	0.669525i
$823$	52447.6			0.0774330			0.0387165	−	0.999250i	$-0.487673\pi$
$823$	52447.6			0.0774330			0.0387165	+	0.999250i	$0.487673\pi$
$824$		−	206350.i		−	0.303913i
$825$	5813.26	−	346131.i	0.00854107	−	0.508549i
$826$	190850.			0.279726
$827$		−	121409.i		−	0.177517i	−0.996053	−	0.0887586i	$-0.971710\pi$
$827$		−	121409.i		−	0.177517i	0.996053	−	0.0887586i	$-0.0282900\pi$
$828$	354095.			0.516486
$829$	555136.			0.807774			0.403887	−	0.914809i	$-0.367659\pi$
$829$	555136.			0.807774			0.403887	+	0.914809i	$0.367659\pi$
$830$	−551466.			−0.800502
$831$		−	52248.7i		−	0.0756612i
$832$			36997.2i			0.0534469i
$833$			646823.i			0.932171i
$834$	−884344.			−1.27142
$835$			509771.i			0.731143i
$836$	398442.	+	6691.82i	0.570102	+	0.00957484i
$837$	284398.			0.405952
$838$			182639.i			0.260079i
$839$	−728123.			−1.03438			−0.517191	−	0.855870i	$-0.673022\pi$
$839$	−728123.			−1.03438			−0.517191	+	0.855870i	$0.673022\pi$
$840$	166507.			0.235979
$841$	297036.			0.419969
$842$		−	574940.i		−	0.810958i
$843$			659955.i			0.928665i
$844$			323687.i			0.454402i
$845$	−449471.			−0.629489
$846$			22910.9i			0.0320111i
$847$	−16687.2	+	496652.i	−0.0232604	+	0.692285i
$848$	−257490.			−0.358070
$849$			1.01689e6i			1.41078i
$850$	−372241.			−0.515213
$851$	−1.17049e6			−1.61625
$852$	383225.			0.527928
$853$		−	560810.i		−	0.770757i	−0.922759	−	0.385379i	$-0.874071\pi$
$853$		−	560810.i		−	0.770757i	0.922759	−	0.385379i	$-0.125929\pi$
$854$		−	230082.i		−	0.315476i
$855$			362641.i			0.496072i
$856$	−253539.			−0.346017
$857$		−	1.02077e6i		−	1.38984i	−0.719086	−	0.694921i	$-0.755439\pi$
$857$		−	1.02077e6i		−	1.38984i	0.719086	−	0.694921i	$-0.244561\pi$
$858$	4675.28	−	278374.i	0.00635087	−	0.378141i
$859$	350246.			0.474665			0.237332	−	0.971428i	$-0.423727\pi$
$859$	350246.			0.474665			0.237332	+	0.971428i	$0.423727\pi$
$860$		−	419169.i		−	0.566751i
$861$	369415.			0.498320
$862$	31433.6			0.0423038
$863$	−516997.			−0.694170			−0.347085	−	0.937834i	$-0.612829\pi$
$863$	−516997.			−0.694170			−0.347085	+	0.937834i	$0.612829\pi$
$864$		−	71852.6i		−	0.0962532i
$865$		−	118184.i		−	0.157953i
$866$			816034.i			1.08811i
$867$	2.07903e6			2.76581
$868$			194547.i			0.258217i
$869$	−179082.	−	3007.68i	−0.237145	−	0.00398284i
$870$	−392769.			−0.518918
$871$			145036.i			0.191178i
$872$	232752.			0.306098
$873$	102432.			0.134402
$874$	1.12670e6			1.47498
$875$		−	574632.i		−	0.750540i
$876$		−	116063.i		−	0.151247i
$877$		−	657406.i		−	0.854741i	−0.904077	−	0.427371i	$-0.859440\pi$
$877$		−	657406.i		−	0.854741i	0.904077	−	0.427371i	$-0.140560\pi$
$878$	303963.			0.394304
$879$			874603.i			1.13197i
$880$	−2504.34	+	149113.i	−0.00323391	+	0.192553i
$881$	869395.			1.12012			0.560061	−	0.828452i	$-0.310778\pi$
$881$	869395.			1.12012			0.560061	+	0.828452i	$0.310778\pi$
$882$		−	161593.i		−	0.207724i
$883$	955758.			1.22582			0.612910	−	0.790153i	$-0.289999\pi$
$883$	955758.			1.22582			0.612910	+	0.790153i	$0.289999\pi$
$884$	−299373.			−0.383096
$885$	−431015.			−0.550308
$886$			369993.i			0.471331i
$887$			436265.i			0.554503i	0.960797	+	0.277251i	$0.0894235\pi$
$887$			436265.i			0.554503i	−0.960797	+	0.277251i	$0.910577\pi$
$888$		−	308141.i		−	0.390772i
$889$	−944006.			−1.19446
$890$			279633.i			0.353027i
$891$	−16608.3	+	988887.i	−0.0209204	+	1.24564i
$892$	−96540.7			−0.121334
$893$			72900.7i			0.0914174i
$894$	746284.			0.933747
$895$	157228.			0.196284
$896$	49152.0			0.0612245
$897$		−	787180.i		−	0.978338i
$898$			449432.i			0.557328i
$899$		−	458912.i		−	0.567819i
$900$	92995.5			0.114809
$901$		−	2.08355e6i		−	2.56657i
$902$	−5556.18	+	330824.i	−0.00682909	+	0.406616i
$903$	1.03962e6			1.27497
$904$			385274.i			0.471447i
$905$	195095.			0.238204
$906$	208763.			0.254330
$907$	−707203.			−0.859666			−0.429833	−	0.902909i	$-0.641427\pi$
$907$	−707203.			−0.859666			−0.429833	+	0.902909i	$0.641427\pi$
$908$			308931.i			0.374705i
$909$		−	712661.i		−	0.862493i
$910$		−	133592.i		−	0.161324i
$911$	132785.			0.159998			0.0799989	−	0.996795i	$-0.474508\pi$
$911$	132785.			0.159998			0.0799989	+	0.996795i	$0.474508\pi$
$912$			296614.i			0.356616i
$913$	1.22486e6	+	20571.5i	1.46942	+	0.0246788i
$914$	−824660.			−0.987149
$915$			519615.i			0.620640i
$916$	−592647.			−0.706326
$917$	−214194.			−0.254723
$918$	581414.			0.689923
$919$		−	964589.i		−	1.14212i	−0.820909	−	0.571059i	$-0.806533\pi$
$919$		−	964589.i		−	1.14212i	0.820909	−	0.571059i	$-0.193467\pi$
$920$			421657.i			0.498178i
$921$		−	680963.i		−	0.802795i
$922$	−177432.			−0.208723
$923$		−	307470.i		−	0.360911i
$924$	−369829.	−	6211.26i	−0.433168	−	0.00727505i
$925$	−307405.			−0.359275
$926$			483331.i			0.563667i
$927$	−417143.			−0.485429
$928$	−115943.			−0.134633
$929$	634849.			0.735596			0.367798	−	0.929906i	$-0.380112\pi$
$929$	634849.			0.735596			0.367798	+	0.929906i	$0.380112\pi$
$930$		−	439364.i		−	0.507994i
$931$		−	514178.i		−	0.593217i
$932$		−	413756.i		−	0.476335i
$933$	−361451.			−0.415228
$934$		−	267453.i		−	0.306587i
$935$	−1.20659e6	−	20264.6i	−1.38018	−	0.0231800i
$936$	74791.1			0.0853686
$937$			3331.90i			0.00379501i	0.999998	+	0.00189750i	$0.000603995\pi$
$937$			3331.90i			0.00379501i	−0.999998	+	0.00189750i	$0.999396\pi$
$938$	192685.			0.218998
$939$	−1.25499e6			−1.42334
$940$	−27282.3			−0.0308764
$941$			1.13619e6i			1.28313i	0.767069	+	0.641564i	$0.221714\pi$
$941$			1.13619e6i			1.28313i	−0.767069	+	0.641564i	$0.778286\pi$
$942$			73720.4i			0.0830780i
$943$			935496.i			1.05201i
$944$	−127234.			−0.142777
$945$			259451.i			0.290530i
$946$	−15636.4	+	931018.i	−0.0174725	+	1.04034i
$947$	156679.			0.174707			0.0873536	−	0.996177i	$-0.472159\pi$
$947$	156679.			0.174707			0.0873536	+	0.996177i	$0.472159\pi$
$948$		−	133315.i		−	0.148341i
$949$	−93120.3			−0.103398
$950$	295905.			0.327873
$951$	−1.56786e6			−1.73359
$952$			397726.i			0.438844i
$953$			343607.i			0.378334i	0.981945	+	0.189167i	$0.0605788\pi$
$953$			343607.i			0.378334i	−0.981945	+	0.189167i	$0.939421\pi$
$954$			520523.i			0.571931i
$955$	−266793.			−0.292528
$956$		−	135291.i		−	0.148031i
$957$	872380.	+	14651.6i	0.952537	+	0.0159978i
$958$	437786.			0.477014
$959$			482205.i			0.524317i
$960$	−111005.			−0.120448
$961$	−410168.			−0.444135
$962$	−247229.			−0.267146
$963$			512537.i			0.552679i
$964$		−	479136.i		−	0.515590i
$965$		−	1.07369e6i		−	1.15298i
$966$	−1.04579e6			−1.12071
$967$			395609.i			0.423071i	0.977370	+	0.211536i	$0.0678464\pi$
$967$			395609.i			0.423071i	−0.977370	+	0.211536i	$0.932154\pi$
$968$	11124.8	−	331101.i	0.0118725	−	0.353354i
$969$	−2.40013e6			−2.55615
$970$			121976.i			0.129638i
$971$	1.28188e6			1.35960			0.679799	−	0.733398i	$-0.262067\pi$
$971$	1.28188e6			1.35960			0.679799	+	0.733398i	$0.262067\pi$
$972$	−478948.			−0.506939
$973$	942632.			0.995672
$974$		−	580761.i		−	0.612181i
$975$		−	206736.i		−	0.217474i
$976$			153388.i			0.161024i
$977$	−1.02959e6			−1.07863			−0.539316	−	0.842103i	$-0.681317\pi$
$977$	−1.02959e6			−1.07863			−0.539316	+	0.842103i	$0.681317\pi$
$978$		−	691872.i		−	0.723349i
$979$	10431.2	−	621092.i	0.0108835	−	0.648024i
$980$	192426.			0.200360
$981$		−	470515.i		−	0.488918i
$982$	511376.			0.530295
$983$	1.35529e6			1.40257			0.701284	−	0.712882i	$-0.252610\pi$
$983$	1.35529e6			1.40257			0.701284	+	0.712882i	$0.252610\pi$
$984$	−246277.			−0.254351
$985$			742933.i			0.765732i
$986$		−	938187.i		−	0.965019i
$987$		−	67665.6i		−	0.0694598i
$988$	237980.			0.243796
$989$			2.63271e6i			2.69160i
$990$	301436.	+	5062.61i	0.307556	+	0.00516540i
$991$	−47967.0			−0.0488422			−0.0244211	−	0.999702i	$-0.507774\pi$
$991$	−47967.0			−0.0488422			−0.0244211	+	0.999702i	$0.507774\pi$
$992$		−	129698.i		−	0.131798i
$993$	677991.			0.687584
$994$	−408484.			−0.413430
$995$	842368.			0.850855
$996$			911828.i			0.919167i
$997$		−	1.71845e6i		−	1.72881i	−0.502798	−	0.864404i	$-0.667696\pi$
$997$		−	1.71845e6i		−	1.72881i	0.502798	−	0.864404i	$-0.332304\pi$
$998$		−	561169.i		−	0.563421i
$999$	480145.			0.481106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.b.a.21.1	✓	4
3.2	odd	2		198.5.d.a.109.4		4
4.3	odd	2		176.5.h.e.65.4		4
5.2	odd	4		550.5.c.a.549.7		8
5.3	odd	4		550.5.c.a.549.2		8
5.4	even	2		550.5.d.a.351.4		4
8.3	odd	2		704.5.h.j.65.2		4
8.5	even	2		704.5.h.i.65.3		4
11.10	odd	2	inner	22.5.b.a.21.3	yes	4
33.32	even	2		198.5.d.a.109.2		4
44.43	even	2		176.5.h.e.65.3		4
55.32	even	4		550.5.c.a.549.3		8
55.43	even	4		550.5.c.a.549.6		8
55.54	odd	2		550.5.d.a.351.2		4
88.21	odd	2		704.5.h.i.65.4		4
88.43	even	2		704.5.h.j.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.b.a.21.1	✓	4	1.1	even	1	trivial
22.5.b.a.21.3	yes	4	11.10	odd	2	inner
176.5.h.e.65.3		4	44.43	even	2
176.5.h.e.65.4		4	4.3	odd	2
198.5.d.a.109.2		4	33.32	even	2
198.5.d.a.109.4		4	3.2	odd	2
550.5.c.a.549.2		8	5.3	odd	4
550.5.c.a.549.3		8	55.32	even	4
550.5.c.a.549.6		8	55.43	even	4
550.5.c.a.549.7		8	5.2	odd	4
550.5.d.a.351.2		4	55.54	odd	2
550.5.d.a.351.4		4	5.4	even	2
704.5.h.i.65.3		4	8.5	even	2
704.5.h.i.65.4		4	88.21	odd	2
704.5.h.j.65.1		4	88.43	even	2
704.5.h.j.65.2		4	8.3	odd	2

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -11.2580 q^{3} -8.00000 q^{4} -19.2580 q^{5} +31.8424i q^{6} -33.9411i q^{7} +22.6274i q^{8} +45.7420 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -11.2580 q^{3} -8.00000 q^{4} -19.2580 q^{5} +31.8424i q^{6} -33.9411i q^{7} +22.6274i q^{8} +45.7420 q^{9} +54.4698i q^{10} +(2.03190 - 120.983i) q^{11} +90.0638 q^{12} -72.2602i q^{13} -96.0000 q^{14} +216.806 q^{15} +64.0000 q^{16} +517.873i q^{17} -129.378i q^{18} -411.672i q^{19} +154.064 q^{20} +382.108i q^{21} +(-342.191 - 5.74709i) q^{22} -967.641 q^{23} -254.739i q^{24} -254.130 q^{25} -204.383 q^{26} +396.933 q^{27} +271.529i q^{28} -640.503i q^{29} -613.219i q^{30} +716.487 q^{31} -181.019i q^{32} +(-22.8751 + 1362.02i) q^{33} +1464.77 q^{34} +653.637i q^{35} -365.936 q^{36} +1209.64 q^{37} -1164.38 q^{38} +813.504i q^{39} -435.758i q^{40} -966.781i q^{41} +1080.77 q^{42} -2720.75i q^{43} +(-16.2552 + 967.864i) q^{44} -880.899 q^{45} +2736.90i q^{46} -177.085 q^{47} -720.510 q^{48} +1249.00 q^{49} +718.789i q^{50} -5830.20i q^{51} +578.082i q^{52} -4023.28 q^{53} -1122.70i q^{54} +(-39.1304 + 2329.89i) q^{55} +768.000 q^{56} +4634.59i q^{57} -1811.62 q^{58} -1988.02 q^{59} -1734.45 q^{60} +2396.69i q^{61} -2026.53i q^{62} -1552.54i q^{63} -512.000 q^{64} +1391.59i q^{65} +(3852.38 + 64.7006i) q^{66} -2007.13 q^{67} -4142.98i q^{68} +10893.7 q^{69} +1848.77 q^{70} +4255.04 q^{71} +1035.02i q^{72} -1288.68i q^{73} -3421.37i q^{74} +2860.99 q^{75} +3293.37i q^{76} +(-4106.30 - 68.9651i) q^{77} +2300.94 q^{78} -1480.23i q^{79} -1232.51 q^{80} -8173.77 q^{81} -2734.47 q^{82} +10124.2i q^{83} -3056.87i q^{84} -9973.18i q^{85} -7695.45 q^{86} +7210.77i q^{87} +(2737.53 + 45.9767i) q^{88} +5133.72 q^{89} +2491.56i q^{90} -2452.59 q^{91} +7741.13 q^{92} -8066.19 q^{93} +500.871i q^{94} +7927.96i q^{95} +2037.91i q^{96} +2239.34 q^{97} -3532.71i q^{98} +(92.9434 - 5534.00i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 32 q^{4} - 30 q^{5} + 230 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 32 * q^4 - 30 * q^5 + 230 * q^9	\( 4 q + 2 q^{3} - 32 q^{4} - 30 q^{5} + 230 q^{9} - 180 q^{11} - 16 q^{12} - 384 q^{14} + 538 q^{15} + 256 q^{16} + 240 q^{20} - 240 q^{22} - 1566 q^{23} - 1722 q^{25} + 1440 q^{26} + 506 q^{27} + 4418 q^{31} - 2302 q^{33} + 1344 q^{34} - 1840 q^{36} - 382 q^{37} - 2400 q^{38} - 192 q^{42} + 1440 q^{44} - 1172 q^{45} + 5688 q^{47} + 128 q^{48} + 4996 q^{49} - 8568 q^{53} - 862 q^{55} + 3072 q^{56} - 9504 q^{58} - 3390 q^{59} - 4304 q^{60} - 2048 q^{64} + 13152 q^{66} - 8734 q^{67} + 26314 q^{69} + 2880 q^{70} + 3522 q^{71} - 9156 q^{75} - 2880 q^{77} + 27264 q^{78} - 1920 q^{80} - 31096 q^{81} - 19968 q^{82} - 10464 q^{86} + 1920 q^{88} - 8766 q^{89} + 17280 q^{91} + 12528 q^{92} + 20458 q^{93} + 17282 q^{97} - 12562 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 32 * q^4 - 30 * q^5 + 230 * q^9 - 180 * q^11 - 16 * q^12 - 384 * q^14 + 538 * q^15 + 256 * q^16 + 240 * q^20 - 240 * q^22 - 1566 * q^23 - 1722 * q^25 + 1440 * q^26 + 506 * q^27 + 4418 * q^31 - 2302 * q^33 + 1344 * q^34 - 1840 * q^36 - 382 * q^37 - 2400 * q^38 - 192 * q^42 + 1440 * q^44 - 1172 * q^45 + 5688 * q^47 + 128 * q^48 + 4996 * q^49 - 8568 * q^53 - 862 * q^55 + 3072 * q^56 - 9504 * q^58 - 3390 * q^59 - 4304 * q^60 - 2048 * q^64 + 13152 * q^66 - 8734 * q^67 + 26314 * q^69 + 2880 * q^70 + 3522 * q^71 - 9156 * q^75 - 2880 * q^77 + 27264 * q^78 - 1920 * q^80 - 31096 * q^81 - 19968 * q^82 - 10464 * q^86 + 1920 * q^88 - 8766 * q^89 + 17280 * q^91 + 12528 * q^92 + 20458 * q^93 + 17282 * q^97 - 12562 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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