LMFDB - Embedded newform 550.5.c.a.549.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,5,Mod(549,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("550.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	550.c (of order $2$, degree $1$, not 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:	$56.8534796961$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6128870652706816.40
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 38641x^{4} + 362673936 $ x^8 + 38641*x^4 + 362673936
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			549.6
Root			$7.96059 + 7.96059i$ of defining polynomial
Character	$\chi$	$=$	550.549
Dual form			550.5.c.a.549.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{2} -11.2580i q^{3} +8.00000 q^{4} -31.8424i q^{6} +33.9411 q^{7} +22.6274 q^{8} -45.7420 q^{9} +O(q^{10})$	\(q+2.82843 q^{2} -11.2580i q^{3} +8.00000 q^{4} -31.8424i q^{6} +33.9411 q^{7} +22.6274 q^{8} -45.7420 q^{9} +(2.03190 + 120.983i) q^{11} -90.0638i q^{12} -72.2602 q^{13} +96.0000 q^{14} +64.0000 q^{16} -517.873 q^{17} -129.378 q^{18} -411.672i q^{19} -382.108i q^{21} +(5.74709 + 342.191i) q^{22} -967.641i q^{23} -254.739i q^{24} -204.383 q^{26} -396.933i q^{27} +271.529 q^{28} -640.503i q^{29} +716.487 q^{31} +181.019 q^{32} +(1362.02 - 22.8751i) q^{33} -1464.77 q^{34} -365.936 q^{36} -1209.64i q^{37} -1164.38i q^{38} +813.504i q^{39} +966.781i q^{41} -1080.77i q^{42} -2720.75 q^{43} +(16.2552 + 967.864i) q^{44} -2736.90i q^{46} +177.085i q^{47} -720.510i q^{48} -1249.00 q^{49} +5830.20i q^{51} -578.082 q^{52} -4023.28i q^{53} -1122.70i q^{54} +768.000 q^{56} -4634.59 q^{57} -1811.62i q^{58} +1988.02 q^{59} -2396.69i q^{61} +2026.53 q^{62} -1552.54 q^{63} +512.000 q^{64} +(3852.38 - 64.7006i) q^{66} +2007.13i q^{67} -4142.98 q^{68} -10893.7 q^{69} +4255.04 q^{71} -1035.02 q^{72} -1288.68 q^{73} -3421.37i q^{74} -3293.37i q^{76} +(68.9651 + 4106.30i) q^{77} +2300.94i q^{78} -1480.23i q^{79} -8173.77 q^{81} +2734.47i q^{82} +10124.2 q^{83} -3056.87i q^{84} -7695.45 q^{86} -7210.77 q^{87} +(45.9767 + 2737.53i) q^{88} -5133.72 q^{89} -2452.59 q^{91} -7741.13i q^{92} -8066.19i q^{93} +500.871i q^{94} -2037.91i q^{96} -2239.34i q^{97} -3532.71 q^{98} +(-92.9434 - 5534.00i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{4} - 460 q^{9}+O(q^{10}) $ 8 * q + 64 * q^4 - 460 * q^9	$ 8 q + 64 q^{4} - 460 q^{9} - 360 q^{11} + 768 q^{14} + 512 q^{16} + 2880 q^{26} + 8836 q^{31} - 2688 q^{34} - 3680 q^{36} - 2880 q^{44} - 9992 q^{49} + 6144 q^{56} + 6780 q^{59} + 4096 q^{64} + 26304 q^{66} - 52628 q^{69} + 7044 q^{71} - 62192 q^{81} - 20928 q^{86} + 17532 q^{89} + 34560 q^{91} + 25124 q^{99}+O(q^{100}) $ 8 * q + 64 * q^4 - 460 * q^9 - 360 * q^11 + 768 * q^14 + 512 * q^16 + 2880 * q^26 + 8836 * q^31 - 2688 * q^34 - 3680 * q^36 - 2880 * q^44 - 9992 * q^49 + 6144 * q^56 + 6780 * q^59 + 4096 * q^64 + 26304 * q^66 - 52628 * q^69 + 7044 * q^71 - 62192 * q^81 - 20928 * q^86 + 17532 * q^89 + 34560 * q^91 + 25124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$-1$

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 $

$2$	2.82843			0.707107
$2$	2.82843			0.707107
$3$		−	11.2580i		−	1.25089i	−0.780270	−	0.625443i	$-0.784918\pi$
$3$		−	11.2580i		−	1.25089i	0.780270	−	0.625443i	$-0.215082\pi$
$4$	8.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	31.8424i		−	0.884510i
$7$	33.9411			0.692676			0.346338	−	0.938110i	$-0.387425\pi$
$7$	33.9411			0.692676			0.346338	+	0.938110i	$0.387425\pi$
$8$	22.6274			0.353553
$9$	−45.7420			−0.564716
$10$		0			0
$11$	2.03190	+	120.983i	0.0167926	+	0.999859i
$11$	2.03190	+	120.983i	0.0167926	+	0.999859i
$12$		−	90.0638i		−	0.625443i
$13$	−72.2602			−0.427575			−0.213788	−	0.976880i	$-0.568580\pi$
$13$	−72.2602			−0.427575			−0.213788	+	0.976880i	$0.568580\pi$
$14$	96.0000			0.489796
$15$		0			0
$16$	64.0000			0.250000
$17$	−517.873			−1.79195			−0.895974	−	0.444107i	$-0.853521\pi$
$17$	−517.873			−1.79195			−0.895974	+	0.444107i	$0.853521\pi$
$18$	−129.378			−0.399315
$19$		−	411.672i		−	1.14036i	−0.821518	−	0.570182i	$-0.806873\pi$
$19$		−	411.672i		−	1.14036i	0.821518	−	0.570182i	$-0.193127\pi$
$20$		0			0
$21$		−	382.108i		−	0.866459i
$22$	5.74709	+	342.191i	0.0118742	+	0.707007i
$23$		−	967.641i		−	1.82919i	−0.404373	−	0.914594i	$-0.632510\pi$
$23$		−	967.641i		−	1.82919i	0.404373	−	0.914594i	$-0.367490\pi$
$24$		−	254.739i		−	0.442255i
$25$		0			0
$26$	−204.383			−0.302341
$27$		−	396.933i		−	0.544490i
$28$	271.529			0.346338
$29$		−	640.503i		−	0.761597i	−0.924658	−	0.380799i	$-0.875649\pi$
$29$		−	640.503i		−	0.761597i	0.924658	−	0.380799i	$-0.124351\pi$
$30$		0			0
$31$	716.487			0.745564			0.372782	−	0.927919i	$-0.378404\pi$
$31$	716.487			0.745564			0.372782	+	0.927919i	$0.378404\pi$
$32$	181.019			0.176777
$33$	1362.02	−	22.8751i	1.25071	−	0.0210056i
$34$	−1464.77			−1.26710
$35$		0			0
$36$	−365.936			−0.282358
$37$		−	1209.64i		−	0.883590i	−0.897116	−	0.441795i	$-0.854342\pi$
$37$		−	1209.64i		−	0.883590i	0.897116	−	0.441795i	$-0.145658\pi$
$38$		−	1164.38i		−	0.806359i
$39$			813.504i			0.534848i
$40$		0			0
$41$			966.781i			0.575122i	0.957762	+	0.287561i	$0.0928445\pi$
$41$			966.781i			0.575122i	−0.957762	+	0.287561i	$0.907156\pi$
$42$		−	1080.77i		−	0.612679i
$43$	−2720.75			−1.47147			−0.735736	−	0.677269i	$-0.763163\pi$
$43$	−2720.75			−1.47147			−0.735736	+	0.677269i	$0.763163\pi$
$44$	16.2552	+	967.864i	0.00839630	+	0.499929i
$45$		0			0
$46$		−	2736.90i		−	1.29343i
$47$			177.085i			0.0801651i	0.999196	+	0.0400826i	$0.0127621\pi$
$47$			177.085i			0.0801651i	−0.999196	+	0.0400826i	$0.987238\pi$
$48$		−	720.510i		−	0.312722i
$49$	−1249.00			−0.520200
$50$		0			0
$51$			5830.20i			2.24152i
$52$	−578.082			−0.213788
$53$		−	4023.28i		−	1.43228i	−0.697956	−	0.716140i	$-0.745907\pi$
$53$		−	4023.28i		−	1.43228i	0.697956	−	0.716140i	$-0.254093\pi$
$54$		−	1122.70i		−	0.385013i
$55$		0			0
$56$	768.000			0.244898
$57$	−4634.59			−1.42647
$58$		−	1811.62i		−	0.538531i
$59$	1988.02			0.571107			0.285554	−	0.958363i	$-0.407823\pi$
$59$	1988.02			0.571107			0.285554	+	0.958363i	$0.407823\pi$
$60$		0			0
$61$		−	2396.69i		−	0.644097i	−0.946723	−	0.322049i	$-0.895629\pi$
$61$		−	2396.69i		−	0.644097i	0.946723	−	0.322049i	$-0.104371\pi$
$62$	2026.53			0.527193
$63$	−1552.54			−0.391165
$64$	512.000			0.125000
$65$		0			0
$66$	3852.38	−	64.7006i	0.884385	−	0.0148532i
$67$			2007.13i			0.447122i	0.974690	+	0.223561i	$0.0717682\pi$
$67$			2007.13i			0.447122i	−0.974690	+	0.223561i	$0.928232\pi$
$68$	−4142.98			−0.895974
$69$	−10893.7			−2.28811
$70$		0			0
$71$	4255.04			0.844086			0.422043	−	0.906576i	$-0.361313\pi$
$71$	4255.04			0.844086			0.422043	+	0.906576i	$0.361313\pi$
$72$	−1035.02			−0.199657
$73$	−1288.68			−0.241824			−0.120912	−	0.992663i	$-0.538582\pi$
$73$	−1288.68			−0.241824			−0.120912	+	0.992663i	$0.538582\pi$
$74$		−	3421.37i		−	0.624793i
$75$		0			0
$76$		−	3293.37i		−	0.570182i
$77$	68.9651	+	4106.30i	0.0116318	+	0.692578i
$78$			2300.94i			0.378195i
$79$		−	1480.23i		−	0.237178i	−0.992943	−	0.118589i	$-0.962163\pi$
$79$		−	1480.23i		−	0.237178i	0.992943	−	0.118589i	$-0.0378371\pi$
$80$		0			0
$81$	−8173.77			−1.24581
$82$			2734.47i			0.406673i
$83$	10124.2			1.46963			0.734813	−	0.678270i	$-0.237270\pi$
$83$	10124.2			1.46963			0.734813	+	0.678270i	$0.237270\pi$
$84$		−	3056.87i		−	0.433229i
$85$		0			0
$86$	−7695.45			−1.04049
$87$	−7210.77			−0.952672
$88$	45.9767	+	2737.53i	0.00593708	+	0.353504i
$89$	−5133.72			−0.648115			−0.324058	−	0.946037i	$-0.605047\pi$
$89$	−5133.72			−0.648115			−0.324058	+	0.946037i	$0.605047\pi$
$90$		0			0
$91$	−2452.59			−0.296171
$92$		−	7741.13i		−	0.914594i
$93$		−	8066.19i		−	0.932615i
$94$			500.871i			0.0566853i
$95$		0			0
$96$		−	2037.91i		−	0.221128i
$97$		−	2239.34i		−	0.238000i	−0.992894	−	0.119000i	$-0.962031\pi$
$97$		−	2239.34i		−	0.238000i	0.992894	−	0.119000i	$-0.0379688\pi$
$98$	−3532.71			−0.367837
$99$	−92.9434	−	5534.00i	−0.00948305	−	0.564637i
$100$		0			0
$101$			15580.0i			1.52730i	0.645629	+	0.763651i	$0.276595\pi$
$101$			15580.0i			1.52730i	−0.645629	+	0.763651i	$0.723405\pi$
$102$			16490.3i			1.58500i
$103$		−	9119.47i		−	0.859597i	−0.902925	−	0.429799i	$-0.858585\pi$
$103$		−	9119.47i		−	0.859597i	0.902925	−	0.429799i	$-0.141415\pi$
$104$	−1635.06			−0.151171
$105$		0			0
$106$		−	11379.5i		−	1.01278i
$107$	−11204.9			−0.978684			−0.489342	−	0.872092i	$-0.662763\pi$
$107$	−11204.9			−0.978684			−0.489342	+	0.872092i	$0.662763\pi$
$108$		−	3175.47i		−	0.272245i
$109$		−	10286.3i		−	0.865776i	−0.901448	−	0.432888i	$-0.857495\pi$
$109$		−	10286.3i		−	0.865776i	0.901448	−	0.432888i	$-0.142505\pi$
$110$		0			0
$111$	−13618.0			−1.10527
$112$	2172.23			0.173169
$113$			17026.9i			1.33345i	0.745302	+	0.666727i	$0.232305\pi$
$113$			17026.9i			1.33345i	−0.745302	+	0.666727i	$0.767695\pi$
$114$	−13108.6			−1.00866
$115$		0			0
$116$		−	5124.03i		−	0.380799i
$117$	3305.33			0.241459
$118$	5622.98			0.403834
$119$	−17577.2			−1.24124
$120$		0			0
$121$	−14632.7	+	491.651i	−0.999436	+	0.0335805i
$122$		−	6778.85i		−	0.455446i
$123$	10884.0			0.719413
$124$	5731.89			0.372782
$125$		0			0
$126$	−4391.23			−0.276596
$127$	27813.0			1.72441			0.862206	−	0.506558i	$-0.169082\pi$
$127$	27813.0			1.72441			0.862206	+	0.506558i	$0.169082\pi$
$128$	1448.15			0.0883883
$129$			30630.1i			1.84064i
$130$		0			0
$131$			6310.74i			0.367738i	0.982951	+	0.183869i	$0.0588621\pi$
$131$			6310.74i			0.367738i	−0.982951	+	0.183869i	$0.941138\pi$
$132$	10896.2	−	183.001i	0.625355	−	0.0105028i
$133$		−	13972.6i		−	0.789903i
$134$			5677.02i			0.316163i
$135$		0			0
$136$	−11718.1			−0.633549
$137$			14207.1i			0.756944i	0.925613	+	0.378472i	$0.123550\pi$
$137$			14207.1i			0.756944i	−0.925613	+	0.378472i	$0.876450\pi$
$138$	−30812.0			−1.61794
$139$			27772.6i			1.43743i	0.695306	+	0.718714i	$0.255269\pi$
$139$			27772.6i			1.43743i	−0.695306	+	0.718714i	$0.744731\pi$
$140$		0			0
$141$	1993.62			0.100277
$142$	12035.1			0.596859
$143$	−146.826	−	8742.26i	−0.00718010	−	0.427515i
$144$	−2927.49			−0.141179
$145$		0			0
$146$	−3644.94			−0.170995
$147$			14061.2i			0.650711i
$148$		−	9677.08i		−	0.441795i
$149$		−	23436.8i		−	1.05567i	−0.849348	−	0.527833i	$-0.823005\pi$
$149$		−	23436.8i		−	1.05567i	0.849348	−	0.527833i	$-0.176995\pi$
$150$		0			0
$151$			6556.14i			0.287538i	0.989611	+	0.143769i	$0.0459222\pi$
$151$			6556.14i			0.287538i	−0.989611	+	0.143769i	$0.954078\pi$
$152$		−	9315.06i		−	0.403180i
$153$	23688.6			1.01194
$154$	195.063	+	11614.4i	0.00822494	+	0.489727i
$155$		0			0
$156$			6508.03i			0.267424i
$157$		−	2315.17i		−	0.0939254i	−0.998897	−	0.0469627i	$-0.985046\pi$
$157$		−	2315.17i		−	0.0939254i	0.998897	−	0.0469627i	$-0.0149542\pi$
$158$		−	4186.72i		−	0.167710i
$159$	−45293.9			−1.79162
$160$		0			0
$161$		−	32842.8i		−	1.26704i
$162$	−23118.9			−0.880922
$163$		−	21728.0i		−	0.817796i	−0.912580	−	0.408898i	$-0.865913\pi$
$163$		−	21728.0i		−	0.817796i	0.912580	−	0.408898i	$-0.134087\pi$
$164$			7734.25i			0.287561i
$165$		0			0
$166$	28635.7			1.03918
$167$	26470.6			0.949143			0.474571	−	0.880217i	$-0.342603\pi$
$167$	26470.6			0.949143			0.474571	+	0.880217i	$0.342603\pi$
$168$		−	8646.13i		−	0.306339i
$169$	−23339.5			−0.817179
$170$		0			0
$171$			18830.7i			0.643982i
$172$	−21766.0			−0.735736
$173$	6136.89			0.205048			0.102524	−	0.994731i	$-0.467308\pi$
$173$	6136.89			0.205048			0.102524	+	0.994731i	$0.467308\pi$
$174$	−20395.1			−0.673641
$175$		0			0
$176$	130.042	+	7742.91i	0.00419815	+	0.249965i
$177$		−	22381.1i		−	0.714390i
$178$	−14520.4			−0.458287
$179$	8164.31			0.254808			0.127404	−	0.991851i	$-0.459335\pi$
$179$	8164.31			0.254808			0.127404	+	0.991851i	$0.459335\pi$
$180$		0			0
$181$	−10130.6			−0.309228			−0.154614	−	0.987975i	$-0.549413\pi$
$181$	−10130.6			−0.309228			−0.154614	+	0.987975i	$0.549413\pi$
$182$	−6936.98			−0.209425
$183$	−26981.8			−0.805692
$184$		−	21895.2i		−	0.646716i
$185$		0			0
$186$		−	22814.6i		−	0.659459i
$187$	−1052.27	−	62653.8i	−0.0300915	−	1.79170i
$188$			1416.68i			0.0400826i
$189$		−	13472.4i		−	0.377155i
$190$		0			0
$191$	13853.6			0.379749			0.189875	−	0.981808i	$-0.439192\pi$
$191$	13853.6			0.379749			0.189875	+	0.981808i	$0.439192\pi$
$192$		−	5764.08i		−	0.156361i
$193$	55752.8			1.49676			0.748380	−	0.663270i	$-0.230832\pi$
$193$	55752.8			1.49676			0.748380	+	0.663270i	$0.230832\pi$
$194$		−	6333.81i		−	0.168291i
$195$		0			0
$196$	−9992.00			−0.260100
$197$	38577.9			0.994046			0.497023	−	0.867737i	$-0.334426\pi$
$197$	38577.9			0.994046			0.497023	+	0.867737i	$0.334426\pi$
$198$	−262.884	−	15652.5i	−0.00670553	−	0.399258i
$199$	43741.2			1.10455			0.552275	−	0.833662i	$-0.313760\pi$
$199$	43741.2			1.10455			0.552275	+	0.833662i	$0.313760\pi$
$200$		0			0
$201$	22596.2			0.559299
$202$			44066.9i			1.07997i
$203$		−	21739.4i		−	0.527540i
$204$			46641.6i			1.12076i
$205$		0			0
$206$		−	25793.7i		−	0.607827i
$207$			44261.8i			1.03297i
$208$	−4624.66			−0.106894
$209$	49805.2	−	836.477i	1.14020	−	0.0191497i
$210$		0			0
$211$			40460.8i			0.908803i	0.890797	+	0.454402i	$0.150147\pi$
$211$			40460.8i			0.908803i	−0.890797	+	0.454402i	$0.849853\pi$
$212$		−	32186.2i		−	0.716140i
$213$		−	47903.1i		−	1.05586i
$214$	−31692.4			−0.692034
$215$		0			0
$216$		−	8981.58i		−	0.192506i
$217$	24318.4			0.516434
$218$		−	29094.0i		−	0.612196i
$219$			14507.9i			0.302494i
$220$		0			0
$221$	37421.6			0.766193
$222$	−38517.6			−0.781545
$223$			12067.6i			0.242667i	0.992612	+	0.121334i	$0.0387171\pi$
$223$			12067.6i			0.242667i	−0.992612	+	0.121334i	$0.961283\pi$
$224$	6144.00			0.122449
$225$		0			0
$226$			48159.3i			0.942894i
$227$	38616.4			0.749411			0.374705	−	0.927144i	$-0.377744\pi$
$227$	38616.4			0.749411			0.374705	+	0.927144i	$0.377744\pi$
$228$	−37076.7			−0.713233
$229$	−74080.9			−1.41265			−0.706326	−	0.707887i	$-0.749649\pi$
$229$	−74080.9			−1.41265			−0.706326	+	0.707887i	$0.749649\pi$
$230$		0			0
$231$	46228.6	−	776.408i	0.866337	−	0.0145501i
$232$		−	14492.9i		−	0.269265i
$233$	51719.5			0.952670			0.476335	−	0.879264i	$-0.341965\pi$
$233$	51719.5			0.952670			0.476335	+	0.879264i	$0.341965\pi$
$234$	9348.89			0.170737
$235$		0			0
$236$	15904.2			0.285554
$237$	−16664.4			−0.296683
$238$	−49715.8			−0.877689
$239$			16911.3i			0.296062i	0.988983	+	0.148031i	$0.0472935\pi$
$239$			16911.3i			0.296062i	−0.988983	+	0.148031i	$0.952706\pi$
$240$		0			0
$241$		−	59892.0i		−	1.03118i	−0.856835	−	0.515590i	$-0.827573\pi$
$241$		−	59892.0i		−	1.03118i	0.856835	−	0.515590i	$-0.172427\pi$
$242$	−41387.6	+	1390.60i	−0.706708	+	0.0237450i
$243$			59868.5i			1.01388i
$244$		−	19173.5i		−	0.322049i
$245$		0			0
$246$	30784.6			0.508702
$247$			29747.5i			0.487592i
$248$	16212.2			0.263597
$249$		−	113979.i		−	1.83833i
$250$		0			0
$251$	−19186.2			−0.304538			−0.152269	−	0.988339i	$-0.548658\pi$
$251$	−19186.2			−0.304538			−0.152269	+	0.988339i	$0.548658\pi$
$252$	−12420.3			−0.195583
$253$	117068.	−	1966.15i	1.82893	−	0.0307168i
$254$	78667.1			1.21934
$255$		0			0
$256$	4096.00			0.0625000
$257$		−	30625.1i		−	0.463672i	−0.972755	−	0.231836i	$-0.925527\pi$
$257$		−	30625.1i		−	0.463672i	0.972755	−	0.231836i	$-0.0744733\pi$
$258$			86635.1i			1.30153i
$259$		−	41056.4i		−	0.612042i
$260$		0			0
$261$			29297.9i			0.430086i
$262$			17849.5i			0.260030i
$263$	−73815.1			−1.06717			−0.533585	−	0.845746i	$-0.679156\pi$
$263$	−73815.1			−1.06717			−0.533585	+	0.845746i	$0.679156\pi$
$264$	30819.1	−	517.605i	0.442193	−	0.00742661i
$265$		0			0
$266$		−	39520.5i		−	0.558546i
$267$			57795.3i			0.810718i
$268$			16057.0i			0.223561i
$269$	87292.0			1.20634			0.603170	−	0.797612i	$-0.293904\pi$
$269$	87292.0			1.20634			0.603170	+	0.797612i	$0.293904\pi$
$270$		0			0
$271$			4518.78i			0.0615294i	0.999527	+	0.0307647i	$0.00979425\pi$
$271$			4518.78i			0.0615294i	−0.999527	+	0.0307647i	$0.990206\pi$
$272$	−33143.9			−0.447987
$273$			27611.2i			0.370477i
$274$			40183.7i			0.535240i
$275$		0			0
$276$	−87149.4			−1.14405
$277$	−4641.04			−0.0604861			−0.0302431	−	0.999543i	$-0.509628\pi$
$277$	−4641.04			−0.0604861			−0.0302431	+	0.999543i	$0.509628\pi$
$278$			78552.6i			1.01642i
$279$	−32773.6			−0.421032
$280$		0			0
$281$			58621.1i			0.742406i	0.928552	+	0.371203i	$0.121055\pi$
$281$			58621.1i			0.742406i	−0.928552	+	0.371203i	$0.878945\pi$
$282$	5638.80			0.0709069
$283$	−90326.0			−1.12782			−0.563910	−	0.825836i	$-0.690704\pi$
$283$	−90326.0			−1.12782			−0.563910	+	0.825836i	$0.690704\pi$
$284$	34040.3			0.422043
$285$		0			0
$286$	−415.286	−	24726.8i	−0.00507710	−	0.302299i
$287$			32813.6i			0.398373i
$288$	−8280.19			−0.0998287
$289$	184671.			2.21108
$290$		0			0
$291$	−25210.4			−0.297710
$292$	−10309.4			−0.120912
$293$	−77687.4			−0.904931			−0.452465	−	0.891782i	$-0.649455\pi$
$293$	−77687.4			−0.904931			−0.452465	+	0.891782i	$0.649455\pi$
$294$			39771.1i			0.460122i
$295$		0			0
$296$		−	27370.9i		−	0.312396i
$297$	48022.2	−	806.531i	0.544414	−	0.00914341i
$298$		−	66289.4i		−	0.746469i
$299$			69922.0i			0.782116i
$300$		0			0
$301$	−92345.3			−1.01925
$302$			18543.6i			0.203320i
$303$	175399.			1.91048
$304$		−	26347.0i		−	0.285091i
$305$		0			0
$306$	67001.3			0.715551
$307$	−60487.2			−0.641781			−0.320890	−	0.947116i	$-0.603982\pi$
$307$	−60487.2			−0.641781			−0.320890	+	0.947116i	$0.603982\pi$
$308$	551.721	+	32850.4i	0.00581591	+	0.346289i
$309$	−102667.			−1.07526
$310$		0			0
$311$	32106.2			0.331947			0.165973	−	0.986130i	$-0.446923\pi$
$311$	32106.2			0.331947			0.165973	+	0.986130i	$0.446923\pi$
$312$			18407.5i			0.189097i
$313$			111475.i			1.13786i	0.822384	+	0.568932i	$0.192643\pi$
$313$			111475.i			1.13786i	−0.822384	+	0.568932i	$0.807357\pi$
$314$		−	6548.28i		−	0.0664153i
$315$		0			0
$316$		−	11841.8i		−	0.118589i
$317$		−	139267.i		−	1.38589i	−0.720990	−	0.692945i	$-0.756313\pi$
$317$		−	139267.i		−	1.38589i	0.720990	−	0.692945i	$-0.243687\pi$
$318$	−128111.			−1.26687
$319$	77490.0	−	1301.44i	0.761490	−	0.0127892i
$320$		0			0
$321$			126145.i			1.22422i
$322$		−	92893.5i		−	0.895929i
$323$			213194.i			2.04347i
$324$	−65390.2			−0.622906
$325$		0			0
$326$		−	61456.1i		−	0.578269i
$327$	−115803.			−1.08299
$328$			21875.7i			0.203336i
$329$			6010.46i			0.0555285i
$330$		0			0
$331$	−60223.2			−0.549677			−0.274839	−	0.961490i	$-0.588624\pi$
$331$	−60223.2			−0.549677			−0.274839	+	0.961490i	$0.588624\pi$
$332$	80994.0			0.734813
$333$			55331.2i			0.498978i
$334$	74870.3			0.671145
$335$		0			0
$336$		−	24454.9i		−	0.216615i
$337$	−85639.9			−0.754078			−0.377039	−	0.926197i	$-0.623058\pi$
$337$	−85639.9			−0.754078			−0.377039	+	0.926197i	$0.623058\pi$
$338$	−66014.0			−0.577833
$339$	191688.			1.66800
$340$		0			0
$341$	1455.83	+	86682.7i	0.0125200	+	0.745459i
$342$			53261.2i			0.455364i
$343$	−123885.			−1.05301
$344$	−61563.6			−0.520244
$345$		0			0
$346$	17357.8			0.144991
$347$	−99499.7			−0.826348			−0.413174	−	0.910652i	$-0.635580\pi$
$347$	−99499.7			−0.826348			−0.413174	+	0.910652i	$0.635580\pi$
$348$	−57686.2			−0.476336
$349$		−	47515.3i		−	0.390106i	−0.980793	−	0.195053i	$-0.937512\pi$
$349$		−	47515.3i		−	0.390106i	0.980793	−	0.195053i	$-0.0624878\pi$
$350$		0			0
$351$			28682.5i			0.232811i
$352$	367.814	+	21900.3i	0.00296854	+	0.176752i
$353$			167482.i			1.34406i	0.740524	+	0.672030i	$0.234577\pi$
$353$			167482.i			1.34406i	−0.740524	+	0.672030i	$0.765423\pi$
$354$		−	63303.4i		−	0.505150i
$355$		0			0
$356$	−41069.8			−0.324058
$357$			197884.i			1.55265i
$358$	23092.2			0.180177
$359$		−	5063.91i		−	0.0392914i	−0.999807	−	0.0196457i	$-0.993746\pi$
$359$		−	5063.91i		−	0.0392914i	0.999807	−	0.0196457i	$-0.00625382\pi$
$360$		0			0
$361$	−39152.4			−0.300431
$362$	−28653.7			−0.218657
$363$	5535.00	+	164735.i	0.0420053	+	1.25018i
$364$	−19620.8			−0.148086
$365$		0			0
$366$	−76316.1			−0.569711
$367$		−	264021.i		−	1.96023i	−0.198429	−	0.980115i	$-0.563584\pi$
$367$		−	264021.i		−	1.96023i	0.198429	−	0.980115i	$-0.436416\pi$
$368$		−	61929.0i		−	0.457297i
$369$		−	44222.5i		−	0.324781i
$370$		0			0
$371$		−	136555.i		−	0.992106i
$372$		−	64529.5i		−	0.466308i
$373$	270510.			1.94431			0.972155	−	0.234339i	$-0.0752926\pi$
$373$	270510.			1.94431			0.972155	+	0.234339i	$0.0752926\pi$
$374$	−2976.26	−	177212.i	−0.0212779	−	1.26692i
$375$		0			0
$376$			4006.97i			0.0283426i
$377$			46282.9i			0.325640i
$378$		−	38105.6i		−	0.266689i
$379$	38850.0			0.270466			0.135233	−	0.990814i	$-0.456822\pi$
$379$	38850.0			0.270466			0.135233	+	0.990814i	$0.456822\pi$
$380$		0			0
$381$		−	313118.i		−	2.15704i
$382$	39184.0			0.268523
$383$		−	243070.i		−	1.65704i	−0.559956	−	0.828522i	$-0.689182\pi$
$383$		−	243070.i		−	1.65704i	0.559956	−	0.828522i	$-0.310818\pi$
$384$		−	16303.3i		−	0.110564i
$385$		0			0
$386$	157693.			1.05837
$387$	124453.			0.830964
$388$		−	17914.7i		−	0.119000i
$389$	142544.			0.941995			0.470998	−	0.882135i	$-0.343894\pi$
$389$	142544.			0.941995			0.470998	+	0.882135i	$0.343894\pi$
$390$		0			0
$391$			501115.i			3.27781i
$392$	−28261.6			−0.183918
$393$	71046.2			0.459998
$394$	109115.			0.702897
$395$		0			0
$396$	−743.547	−	44272.0i	−0.00474153	−	0.282318i
$397$			73860.0i			0.468628i	0.972161	+	0.234314i	$0.0752844\pi$
$397$			73860.0i			0.468628i	−0.972161	+	0.234314i	$0.924716\pi$
$398$	123719.			0.781034
$399$	−157303.			−0.988079
$400$		0			0
$401$	225776.			1.40407			0.702034	−	0.712143i	$-0.252275\pi$
$401$	225776.			1.40407			0.702034	+	0.712143i	$0.252275\pi$
$402$	63911.8			0.395484
$403$	−51773.5			−0.318785
$404$			124640.i			0.763651i
$405$		0			0
$406$		−	61488.3i		−	0.373027i
$407$	146345.	−	2457.86i	0.883466	−	0.0148378i
$408$			131922.i			0.792498i
$409$			97972.9i			0.585679i	0.956162	+	0.292839i	$0.0946001\pi$
$409$			97972.9i			0.585679i	−0.956162	+	0.292839i	$0.905400\pi$
$410$		0			0
$411$	159943.			0.946851
$412$		−	72955.7i		−	0.429799i
$413$	67475.8			0.395592
$414$			125191.i			0.730422i
$415$		0			0
$416$	−13080.5			−0.0755854
$417$	312663.			1.79806
$418$	140870.	−	2365.91i	0.806246	−	0.0135409i
$419$	64572.5			0.367807			0.183903	−	0.982944i	$-0.441127\pi$
$419$	64572.5			0.367807			0.183903	+	0.982944i	$0.441127\pi$
$420$		0			0
$421$	203272.			1.14687			0.573434	−	0.819252i	$-0.305611\pi$
$421$	203272.			1.14687			0.573434	+	0.819252i	$0.305611\pi$
$422$			114441.i			0.642621i
$423$		−	8100.21i		−	0.0452706i
$424$		−	91036.3i		−	0.506388i
$425$		0			0
$426$		−	135491.i		−	0.746603i
$427$		−	81346.2i		−	0.446151i
$428$	−89639.6			−0.489342
$429$	−98420.1	+	1652.96i	−0.534773	+	0.00898149i
$430$		0			0
$431$		−	11113.4i		−	0.0598266i	−0.999552	−	0.0299133i	$-0.990477\pi$
$431$		−	11113.4i		−	0.0598266i	0.999552	−	0.0299133i	$-0.00952311\pi$
$432$		−	25403.7i		−	0.136123i
$433$		−	288512.i		−	1.53882i	−0.638756	−	0.769409i	$-0.720551\pi$
$433$		−	288512.i		−	1.53882i	0.638756	−	0.769409i	$-0.279449\pi$
$434$	68782.7			0.365174
$435$		0			0
$436$		−	82290.2i		−	0.432888i
$437$	−398350.			−2.08594
$438$			41034.6i			0.213896i
$439$			107467.i			0.557630i	0.960345	+	0.278815i	$0.0899417\pi$
$439$			107467.i			0.557630i	−0.960345	+	0.278815i	$0.910058\pi$
$440$		0			0
$441$	57131.8			0.293765
$442$	105844.			0.541780
$443$		−	130812.i		−	0.666563i	−0.942827	−	0.333281i	$-0.891844\pi$
$443$		−	130812.i		−	0.666563i	0.942827	−	0.333281i	$-0.108156\pi$
$444$	−108944.			−0.552636
$445$		0			0
$446$			34132.3i			0.171592i
$447$	−263851.			−1.32052
$448$	17377.9			0.0865845
$449$	158898.			0.788181			0.394090	−	0.919072i	$-0.371060\pi$
$449$	158898.			0.788181			0.394090	+	0.919072i	$0.371060\pi$
$450$		0			0
$451$	−116964.	+	1964.41i	−0.575041	+	0.00965780i
$452$			136215.i			0.666727i
$453$	73808.9			0.359677
$454$	109224.			0.529913
$455$		0			0
$456$	−104869.			−0.504332
$457$	291561.			1.39604			0.698019	−	0.716079i	$-0.254065\pi$
$457$	291561.			1.39604			0.698019	+	0.716079i	$0.254065\pi$
$458$	−209532.			−0.998896
$459$			205561.i			0.975698i
$460$		0			0
$461$			62731.9i			0.295180i	0.989049	+	0.147590i	$0.0471515\pi$
$461$			62731.9i			0.295180i	−0.989049	+	0.147590i	$0.952848\pi$
$462$	130754.	−	2196.01i	0.612593	−	0.0102885i
$463$		−	170883.i		−	0.797146i	−0.917137	−	0.398573i	$-0.869506\pi$
$463$		−	170883.i		−	0.797146i	0.917137	−	0.398573i	$-0.130494\pi$
$464$		−	40992.2i		−	0.190399i
$465$		0			0
$466$	146285.			0.673639
$467$		−	94559.0i		−	0.433580i	−0.976218	−	0.216790i	$-0.930441\pi$
$467$		−	94559.0i		−	0.433580i	0.976218	−	0.216790i	$-0.0695587\pi$
$468$	26442.6			0.120729
$469$			68124.3i			0.309711i
$470$		0			0
$471$	−26064.1			−0.117490
$472$	44983.8			0.201917
$473$	−5528.30	−	329164.i	−0.0247098	−	1.47126i
$474$	−47134.0			−0.209786
$475$		0			0
$476$	−140618.			−0.620620
$477$			184033.i			0.808832i
$478$			47832.5i			0.209347i
$479$			154781.i			0.674600i	0.941397	+	0.337300i	$0.109514\pi$
$479$			154781.i			0.674600i	−0.941397	+	0.337300i	$0.890486\pi$
$480$		0			0
$481$			87408.6i			0.377802i
$482$		−	169400.i		−	0.729155i
$483$	−369744.			−1.58492
$484$	−117062.	+	3933.21i	−0.499718	+	0.0167902i
$485$		0			0
$486$			169334.i			0.716920i
$487$		−	205330.i		−	0.865754i	−0.901453	−	0.432877i	$-0.857498\pi$
$487$		−	205330.i		−	0.865754i	0.901453	−	0.432877i	$-0.142502\pi$
$488$		−	54230.8i		−	0.227723i
$489$	−244614.			−1.02297
$490$		0			0
$491$		−	180799.i		−	0.749950i	−0.927035	−	0.374975i	$-0.877651\pi$
$491$		−	180799.i		−	0.749950i	0.927035	−	0.374975i	$-0.122349\pi$
$492$	87071.9			0.359706
$493$			331699.i			1.36474i
$494$			84138.6i			0.344779i
$495$		0			0
$496$	45855.2			0.186391
$497$	144421.			0.584678
$498$		−	322380.i		−	1.29990i
$499$	−198403.			−0.796797			−0.398399	−	0.917212i	$-0.630434\pi$
$499$	−198403.			−0.796797			−0.398399	+	0.917212i	$0.630434\pi$
$500$		0			0
$501$		−	298006.i		−	1.18727i
$502$	−54266.8			−0.215341
$503$	−278604.			−1.10116			−0.550582	−	0.834781i	$-0.685594\pi$
$503$	−278604.			−1.10116			−0.550582	+	0.834781i	$0.685594\pi$
$504$	−35129.9			−0.138298
$505$		0			0
$506$	331118.	−	5561.12i	1.29325	−	0.0217201i
$507$			262755.i			1.02220i
$508$	222504.			0.862206
$509$	195175.			0.753336			0.376668	−	0.926348i	$-0.377070\pi$
$509$	195175.			0.753336			0.376668	+	0.926348i	$0.377070\pi$
$510$		0			0
$511$	−43739.2			−0.167506
$512$	11585.2			0.0441942
$513$	−163406.			−0.620917
$514$		−	86620.8i		−	0.327866i
$515$		0			0
$516$			245041.i			0.920322i
$517$	−21424.2	+	359.819i	−0.0801538	+	0.00134618i
$518$		−	116125.i		−	0.432779i
$519$		−	69089.0i		−	0.256492i
$520$		0			0
$521$	−2617.52			−0.00964304			−0.00482152	−	0.999988i	$-0.501535\pi$
$521$	−2617.52			−0.00964304			−0.00482152	+	0.999988i	$0.501535\pi$
$522$			82867.0i			0.304117i
$523$	309803.			1.13261			0.566307	−	0.824194i	$-0.308372\pi$
$523$	309803.			1.13261			0.566307	+	0.824194i	$0.308372\pi$
$524$			50486.0i			0.183869i
$525$		0			0
$526$	−208781.			−0.754603
$527$	−371049.			−1.33601
$528$	87169.5	−	1464.01i	0.312677	−	0.00525141i
$529$	−656488.			−2.34593
$530$		0			0
$531$	−90936.2			−0.322513
$532$		−	111781.i		−	0.394952i
$533$		−	69859.8i		−	0.245908i
$534$			163470.i			0.573264i
$535$		0			0
$536$			45416.2i			0.158081i
$537$		−	91913.7i		−	0.318736i
$538$	246899.			0.853012
$539$	−2537.85	−	151108.i	−0.00873551	−	0.520127i
$540$		0			0
$541$			197545.i			0.674948i	0.941335	+	0.337474i	$0.109573\pi$
$541$			197545.i			0.674948i	−0.941335	+	0.337474i	$0.890427\pi$
$542$			12781.0i			0.0435079i
$543$			114050.i			0.386809i
$544$	−93745.0			−0.316775
$545$		0			0
$546$			78096.4i			0.261966i
$547$	440541.			1.47235			0.736176	−	0.676790i	$-0.236630\pi$
$547$	440541.			1.47235			0.736176	+	0.676790i	$0.236630\pi$
$548$			113657.i			0.378472i
$549$			109629.i			0.363732i
$550$		0			0
$551$	−263677.			−0.868498
$552$	−246496.			−0.808968
$553$		−	50240.6i		−	0.164288i
$554$	−13126.8			−0.0427701
$555$		0			0
$556$			222180.i			0.718714i
$557$	422793.			1.36275			0.681376	−	0.731933i	$-0.261382\pi$
$557$	422793.			1.36275			0.681376	+	0.731933i	$0.261382\pi$
$558$	−92697.6			−0.297715
$559$	196602.			0.629165
$560$		0			0
$561$	−705355.	+	11846.4i	−2.24121	+	0.0376410i
$562$			165805.i			0.524960i
$563$	−52520.6			−0.165696			−0.0828482	−	0.996562i	$-0.526402\pi$
$563$	−52520.6			−0.165696			−0.0828482	+	0.996562i	$0.526402\pi$
$564$	15948.9			0.0501387
$565$		0			0
$566$	−255481.			−0.797490
$567$	−277427.			−0.862944
$568$	96280.5			0.298430
$569$		−	140197.i		−	0.433025i	−0.976280	−	0.216513i	$-0.930532\pi$
$569$		−	140197.i		−	0.433025i	0.976280	−	0.216513i	$-0.0694683\pi$
$570$		0			0
$571$		−	207548.i		−	0.636569i	−0.947995	−	0.318284i	$-0.896893\pi$
$571$		−	207548.i		−	0.636569i	0.947995	−	0.318284i	$-0.103107\pi$
$572$	−1174.61	−	69938.1i	−0.00359005	−	0.213758i
$573$		−	155964.i		−	0.475023i
$574$			92810.9i			0.281693i
$575$		0			0
$576$	−23419.9			−0.0705895
$577$			273572.i			0.821712i	0.911700	+	0.410856i	$0.134770\pi$
$577$			273572.i			0.821712i	−0.911700	+	0.410856i	$0.865230\pi$
$578$	522329.			1.56347
$579$		−	627664.i		−	1.87228i
$580$		0			0
$581$	343628.			1.01797
$582$	−71305.8			−0.210513
$583$	486748.	−	8174.91i	1.43208	−	0.0240517i
$584$	−29159.5			−0.0854977
$585$		0			0
$586$	−219733.			−0.639883
$587$			576701.i			1.67369i	0.547442	+	0.836843i	$0.315602\pi$
$587$			576701.i			1.67369i	−0.547442	+	0.836843i	$0.684398\pi$
$588$			112490.i			0.325355i
$589$		−	294957.i		−	0.850214i
$590$		0			0
$591$		−	434309.i		−	1.24344i
$592$		−	77416.7i		−	0.220898i
$593$	−671956.			−1.91087			−0.955435	−	0.295202i	$-0.904613\pi$
$593$	−671956.			−1.91087			−0.955435	+	0.295202i	$0.904613\pi$
$594$	135827.	−	2281.21i	0.384959	−	0.00646536i
$595$		0			0
$596$		−	187495.i		−	0.527833i
$597$		−	492438.i		−	1.38167i
$598$			197769.i			0.553040i
$599$	−582984.			−1.62481			−0.812406	−	0.583092i	$-0.801843\pi$
$599$	−582984.			−1.62481			−0.812406	+	0.583092i	$0.801843\pi$
$600$		0			0
$601$		−	377092.i		−	1.04399i	−0.852947	−	0.521997i	$-0.825187\pi$
$601$		−	377092.i		−	1.04399i	0.852947	−	0.521997i	$-0.174813\pi$
$602$	−261192.			−0.720721
$603$		−	91810.2i		−	0.252497i
$604$			52449.2i			0.143769i
$605$		0			0
$606$	496104.			1.35091
$607$	−465535.			−1.26350			−0.631750	−	0.775173i	$-0.717663\pi$
$607$	−465535.			−1.26350			−0.631750	+	0.775173i	$0.717663\pi$
$608$		−	74520.5i		−	0.201590i
$609$	−244742.			−0.659893
$610$		0			0
$611$		−	12796.2i		−	0.0342766i
$612$	189508.			0.505971
$613$	−623300.			−1.65873			−0.829366	−	0.558705i	$-0.811298\pi$
$613$	−623300.			−1.65873			−0.829366	+	0.558705i	$0.811298\pi$
$614$	−171084.			−0.453807
$615$		0			0
$616$	1560.50	+	92914.9i	0.00411247	+	0.244863i
$617$		−	197189.i		−	0.517980i	−0.965880	−	0.258990i	$-0.916610\pi$
$617$		−	197189.i		−	0.517980i	0.965880	−	0.258990i	$-0.0833897\pi$
$618$	−290385.			−0.760322
$619$	−214900.			−0.560861			−0.280431	−	0.959874i	$-0.590477\pi$
$619$	−214900.			−0.560861			−0.280431	+	0.959874i	$0.590477\pi$
$620$		0			0
$621$	−384089.			−0.995976
$622$	90810.1			0.234722
$623$	−174244.			−0.448934
$624$			52064.3i			0.133712i
$625$		0			0
$626$			315300.i			0.804592i
$627$	−9417.04	−	560706.i	−0.0239541	−	1.42626i
$628$		−	18521.3i		−	0.0469627i
$629$			626437.i			1.58335i
$630$		0			0
$631$	−40334.6			−0.101302			−0.0506511	−	0.998716i	$-0.516130\pi$
$631$	−40334.6			−0.101302			−0.0506511	+	0.998716i	$0.516130\pi$
$632$		−	33493.8i		−	0.0838551i
$633$	455507.			1.13681
$634$		−	393906.i		−	0.979973i
$635$		0			0
$636$	−362352.			−0.895810
$637$	90253.1			0.222425
$638$	219175.	−	3681.03i	0.538455	−	0.00904333i
$639$	−194634.			−0.476669
$640$		0			0
$641$	−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.i			0.865656i
$643$			21885.5i			0.0529340i	0.999650	+	0.0264670i	$0.00842568\pi$
$643$			21885.5i			0.0529340i	−0.999650	+	0.0264670i	$0.991574\pi$
$644$		−	262743.i		−	0.633518i
$645$		0			0
$646$			603002.i			1.44495i
$647$			345969.i			0.826472i	0.910624	+	0.413236i	$0.135602\pi$
$647$			345969.i			0.826472i	−0.910624	+	0.413236i	$0.864398\pi$
$648$	−184951.			−0.440461
$649$	4039.47	+	240517.i	0.00959037	+	0.571027i
$650$		0			0
$651$		−	273776.i		−	0.646000i
$652$		−	173824.i		−	0.408898i
$653$			380939.i			0.893366i	0.894692	+	0.446683i	$0.147395\pi$
$653$			380939.i			0.893366i	−0.894692	+	0.446683i	$0.852605\pi$
$654$	−327539.			−0.765787
$655$		0			0
$656$			61874.0i			0.143781i
$657$	58946.8			0.136562
$658$			17000.1i			0.0392645i
$659$		−	149577.i		−	0.344424i	−0.985060	−	0.172212i	$-0.944909\pi$
$659$		−	149577.i		−	0.344424i	0.985060	−	0.172212i	$-0.0550914\pi$
$660$		0			0
$661$	−637662.			−1.45945			−0.729723	−	0.683743i	$-0.760351\pi$
$661$	−637662.			−1.45945			−0.729723	+	0.683743i	$0.760351\pi$
$662$	−170337.			−0.388681
$663$		−	421292.i		−	0.958420i
$664$	229086.			0.519591
$665$		0			0
$666$			156500.i			0.352831i
$667$	−619777.			−1.39311
$668$	211765.			0.474571
$669$	135857.			0.303549
$670$		0			0
$671$	289958.	−	4869.84i	0.644006	−	0.0108161i
$672$		−	69169.0i		−	0.153170i
$673$	−165463.			−0.365318			−0.182659	−	0.983176i	$-0.558470\pi$
$673$	−165463.			−0.365318			−0.182659	+	0.983176i	$0.558470\pi$
$674$	−242226.			−0.533214
$675$		0			0
$676$	−186716.			−0.408590
$677$	420292.			0.917009			0.458504	−	0.888692i	$-0.348385\pi$
$677$	420292.			0.917009			0.458504	+	0.888692i	$0.348385\pi$
$678$	542176.			1.17945
$679$		−	76005.7i		−	0.164857i
$680$		0			0
$681$		−	434742.i		−	0.937428i
$682$	4117.72	+	245176.i	0.00885294	+	0.527119i
$683$			265281.i			0.568677i	0.958724	+	0.284338i	$0.0917739\pi$
$683$			265281.i			0.568677i	−0.958724	+	0.284338i	$0.908226\pi$
$684$			150646.i			0.321991i
$685$		0			0
$686$	−350400.			−0.744588
$687$			834001.i			1.76707i
$688$	−174128.			−0.367868
$689$			290723.i			0.612408i
$690$		0			0
$691$	−72314.2			−0.151449			−0.0757247	−	0.997129i	$-0.524127\pi$
$691$	−72314.2			−0.151449			−0.0757247	+	0.997129i	$0.524127\pi$
$692$	49095.1			0.102524
$693$	−3154.60	−	187830.i	−0.00656868	−	0.391110i
$694$	−281428.			−0.584316
$695$		0			0
$696$	−163161.			−0.336820
$697$		−	500669.i		−	1.03059i
$698$		−	134393.i		−	0.275846i
$699$		−	582257.i		−	1.19168i
$700$		0			0
$701$		−	142549.i		−	0.290088i	−0.989425	−	0.145044i	$-0.953668\pi$
$701$		−	142549.i		−	0.290088i	0.989425	−	0.145044i	$-0.0463324\pi$
$702$			81126.4i			0.164622i
$703$	−497972.			−1.00761
$704$	1040.33	+	61943.3i	0.00209907	+	0.124982i
$705$		0			0
$706$			473711.i			0.950394i
$707$			528803.i			1.05793i
$708$		−	179049.i		−	0.357195i
$709$	588664.			1.17105			0.585525	−	0.810654i	$-0.300888\pi$
$709$	588664.			1.17105			0.585525	+	0.810654i	$0.300888\pi$
$710$		0			0
$711$			67708.7i			0.133938i
$712$	−116163.			−0.229143
$713$		−	693302.i		−	1.36378i
$714$			559699.i			1.09789i
$715$		0			0
$716$	65314.5			0.127404
$717$	190387.			0.370340
$718$		−	14322.9i		−	0.0277832i
$719$	133520.			0.258280			0.129140	−	0.991626i	$-0.458778\pi$
$719$	133520.			0.258280			0.129140	+	0.991626i	$0.458778\pi$
$720$		0			0
$721$		−	309525.i		−	0.595422i
$722$	−110740.			−0.212437
$723$	−674263.			−1.28989
$724$	−81044.9			−0.154614
$725$		0			0
$726$	15655.3	+	465941.i	0.0297023	+	0.884011i
$727$		−	224313.i		−	0.424410i	−0.977225	−	0.212205i	$-0.931936\pi$
$727$		−	224313.i		−	0.424410i	0.977225	−	0.212205i	$-0.0680645\pi$
$728$	−55495.9			−0.104712
$729$	11922.8			0.0224348
$730$		0			0
$731$	1.40900e6			2.63680
$732$	−215855.			−0.402846
$733$	297252.			0.553243			0.276622	−	0.960979i	$-0.410785\pi$
$733$	297252.			0.553243			0.276622	+	0.960979i	$0.410785\pi$
$734$		−	746765.i		−	1.38609i
$735$		0			0
$736$		−	175162.i		−	0.323358i
$737$	−242829.	+	4078.30i	−0.447059	+	0.00750834i
$738$		−	125080.i		−	0.229655i
$739$		−	268988.i		−	0.492543i	−0.969201	−	0.246272i	$-0.920794\pi$
$739$		−	268988.i		−	0.492543i	0.969201	−	0.246272i	$-0.0792056\pi$
$740$		0			0
$741$	334896.			0.609922
$742$		−	386235.i		−	0.701525i
$743$	−133653.			−0.242104			−0.121052	−	0.992646i	$-0.538627\pi$
$743$	−133653.			−0.242104			−0.121052	+	0.992646i	$0.538627\pi$
$744$		−	182517.i		−	0.329729i
$745$		0			0
$746$	765117.			1.37483
$747$	−463104.			−0.829921
$748$	−8418.14	−	501230.i	−0.0150457	−	0.895848i
$749$	−380309.			−0.677911
$750$		0			0
$751$	201267.			0.356856			0.178428	−	0.983953i	$-0.442899\pi$
$751$	201267.			0.356856			0.178428	+	0.983953i	$0.442899\pi$
$752$			11333.4i			0.0200413i
$753$			215998.i			0.380942i
$754$			130908.i			0.230262i
$755$		0			0
$756$		−	107779.i		−	0.188578i
$757$		−	835429.i		−	1.45787i	−0.684584	−	0.728934i	$-0.740016\pi$
$757$		−	835429.i		−	1.45787i	0.684584	−	0.728934i	$-0.259984\pi$
$758$	109884.			0.191248
$759$	−22134.9	−	1.31795e6i	−0.0384233	−	2.28778i
$760$		0			0
$761$			345963.i			0.597393i	0.954348	+	0.298696i	$0.0965518\pi$
$761$			345963.i			0.597393i	−0.954348	+	0.298696i	$0.903448\pi$
$762$		−	885633.i		−	1.52526i
$763$		−	349128.i		−	0.599702i
$764$	110829.			0.189875
$765$		0			0
$766$		−	687506.i		−	1.17171i
$767$	−143655.			−0.244191
$768$		−	46112.7i		−	0.0781804i
$769$			1.05669e6i			1.78688i	0.449183	+	0.893440i	$0.351715\pi$
$769$			1.05669e6i			1.78688i	−0.449183	+	0.893440i	$0.648285\pi$
$770$		0			0
$771$	−344776.			−0.580001
$772$	446022.			0.748380
$773$		−	224559.i		−	0.375813i	−0.982187	−	0.187907i	$-0.939830\pi$
$773$		−	224559.i		−	0.375813i	0.982187	−	0.187907i	$-0.0601702\pi$
$774$	352005.			0.587580
$775$		0			0
$776$		−	50670.4i		−	0.0841456i
$777$	−462212.			−0.765595
$778$	403174.			0.666091
$779$	397996.			0.655849
$780$		0			0
$781$	8645.83	+	514787.i	0.0141744	+	0.843967i
$782$			1.41737e6i			2.31776i
$783$	−254237.			−0.414682
$784$	−79936.0			−0.130050
$785$		0			0
$786$	200949.			0.325268
$787$	−227376.			−0.367109			−0.183554	−	0.983010i	$-0.558760\pi$
$787$	−227376.			−0.367109			−0.183554	+	0.983010i	$0.558760\pi$
$788$	308623.			0.497023
$789$			831008.i			1.33491i
$790$		0			0
$791$			577911.i			0.923651i
$792$	−2103.07	−	125220.i	−0.00335277	−	0.199629i
$793$			173185.i			0.275400i
$794$			208908.i			0.331370i
$795$		0			0
$796$	349930.			0.552275
$797$			972019.i			1.53023i	0.643891	+	0.765117i	$0.277319\pi$
$797$			972019.i			1.53023i	−0.643891	+	0.765117i	$0.722681\pi$
$798$	−444920.			−0.698677
$799$		−	91707.4i		−	0.143652i
$800$		0			0
$801$	234827.			0.366001
$802$	638590.			0.992826
$803$	−2618.47	−	155908.i	−0.00406085	−	0.241790i
$804$	180770.			0.279649
$805$		0			0
$806$	−146438.			−0.225415
$807$		−	982732.i		−	1.50900i
$808$			352535.i			0.539983i
$809$			56475.6i			0.0862906i	0.999069	+	0.0431453i	$0.0137378\pi$
$809$			56475.6i			0.0862906i	−0.999069	+	0.0431453i	$0.986262\pi$
$810$		0			0
$811$		−	224590.i		−	0.341467i	−0.985317	−	0.170733i	$-0.945386\pi$
$811$		−	224590.i		−	0.341467i	0.985317	−	0.170733i	$-0.0546137\pi$
$812$		−	173915.i		−	0.263770i
$813$	50872.3			0.0769663
$814$	413927.	−	6951.89i	0.624705	−	0.0104919i
$815$		0			0
$816$			373133.i			0.560381i
$817$			1.12006e6i			1.67801i
$818$			277109.i			0.414137i
$819$	112187.			0.167253
$820$		0			0
$821$		−	719097.i		−	1.06684i	−0.845849	−	0.533422i	$-0.820906\pi$
$821$		−	719097.i		−	1.06684i	0.845849	−	0.533422i	$-0.179094\pi$
$822$	452387.			0.669525
$823$			52447.6i			0.0774330i	0.999250	+	0.0387165i	$0.0123269\pi$
$823$			52447.6i			0.0774330i	−0.999250	+	0.0387165i	$0.987673\pi$
$824$		−	206350.i		−	0.303913i
$825$		0			0
$826$	190850.			0.279726
$827$	121409.			0.177517			0.0887586	−	0.996053i	$-0.471710\pi$
$827$	121409.			0.177517			0.0887586	+	0.996053i	$0.471710\pi$
$828$			354095.i			0.516486i
$829$	−555136.			−0.807774			−0.403887	−	0.914809i	$-0.632341\pi$
$829$	−555136.			−0.807774			−0.403887	+	0.914809i	$0.632341\pi$
$830$		0			0
$831$			52248.7i			0.0756612i
$832$	−36997.2			−0.0534469
$833$	646823.			0.932171
$834$	884344.			1.27142
$835$		0			0
$836$	398442.	−	6691.82i	0.570102	−	0.00957484i
$837$		−	284398.i		−	0.405952i
$838$	182639.			0.260079
$839$	728123.			1.03438			0.517191	−	0.855870i	$-0.326978\pi$
$839$	728123.			1.03438			0.517191	+	0.855870i	$0.326978\pi$
$840$		0			0
$841$	297036.			0.419969
$842$	574940.			0.810958
$843$	659955.			0.928665
$844$			323687.i			0.454402i
$845$		0			0
$846$		−	22910.9i		−	0.0320111i
$847$	−496652.	+	16687.2i	−0.692285	+	0.0232604i
$848$		−	257490.i		−	0.358070i
$849$			1.01689e6i			1.41078i
$850$		0			0
$851$	−1.17049e6			−1.61625
$852$		−	383225.i		−	0.527928i
$853$	−560810.			−0.770757			−0.385379	−	0.922759i	$-0.625929\pi$
$853$	−560810.			−0.770757			−0.385379	+	0.922759i	$0.625929\pi$
$854$		−	230082.i		−	0.315476i
$855$		0			0
$856$	−253539.			−0.346017
$857$	1.02077e6			1.38984			0.694921	−	0.719086i	$-0.255439\pi$
$857$	1.02077e6			1.38984			0.694921	+	0.719086i	$0.255439\pi$
$858$	−278374.	+	4675.28i	−0.378141	+	0.00635087i
$859$	−350246.			−0.474665			−0.237332	−	0.971428i	$-0.576273\pi$
$859$	−350246.			−0.474665			−0.237332	+	0.971428i	$0.576273\pi$
$860$		0			0
$861$	369415.			0.498320
$862$		−	31433.6i		−	0.0423038i
$863$		−	516997.i		−	0.694170i	−0.937834	−	0.347085i	$-0.887171\pi$
$863$		−	516997.i		−	0.694170i	0.937834	−	0.347085i	$-0.112829\pi$
$864$		−	71852.6i		−	0.0962532i
$865$		0			0
$866$		−	816034.i		−	1.08811i
$867$		−	2.07903e6i		−	2.76581i
$868$	194547.			0.258217
$869$	179082.	−	3007.68i	0.237145	−	0.00398284i
$870$		0			0
$871$		−	145036.i		−	0.191178i
$872$		−	232752.i		−	0.306098i
$873$			102432.i			0.134402i
$874$	−1.12670e6			−1.47498
$875$		0			0
$876$			116063.i			0.151247i
$877$	657406.			0.854741			0.427371	−	0.904077i	$-0.359440\pi$
$877$	657406.			0.854741			0.427371	+	0.904077i	$0.359440\pi$
$878$			303963.i			0.394304i
$879$			874603.i			1.13197i
$880$		0			0
$881$	869395.			1.12012			0.560061	−	0.828452i	$-0.310778\pi$
$881$	869395.			1.12012			0.560061	+	0.828452i	$0.310778\pi$
$882$	161593.			0.207724
$883$			955758.i			1.22582i	0.790153	+	0.612910i	$0.210001\pi$
$883$			955758.i			1.22582i	−0.790153	+	0.612910i	$0.789999\pi$
$884$	299373.			0.383096
$885$		0			0
$886$		−	369993.i		−	0.471331i
$887$	−436265.			−0.554503			−0.277251	−	0.960797i	$-0.589423\pi$
$887$	−436265.			−0.554503			−0.277251	+	0.960797i	$0.589423\pi$
$888$	−308141.			−0.390772
$889$	944006.			1.19446
$890$		0			0
$891$	−16608.3	−	988887.i	−0.0209204	−	1.24564i
$892$			96540.7i			0.121334i
$893$	72900.7			0.0914174
$894$	−746284.			−0.933747
$895$		0			0
$896$	49152.0			0.0612245
$897$	787180.			0.978338
$898$	449432.			0.557328
$899$		−	458912.i		−	0.567819i
$900$		0			0
$901$			2.08355e6i			2.56657i
$902$	−330824.	+	5556.18i	−0.406616	+	0.00682909i
$903$			1.03962e6i			1.27497i
$904$			385274.i			0.471447i
$905$		0			0
$906$	208763.			0.254330
$907$			707203.i			0.859666i	0.902909	+	0.429833i	$0.141427\pi$
$907$			707203.i			0.859666i	−0.902909	+	0.429833i	$0.858573\pi$
$908$	308931.			0.374705
$909$		−	712661.i		−	0.862493i
$910$		0			0
$911$	132785.			0.159998			0.0799989	−	0.996795i	$-0.474508\pi$
$911$	132785.			0.159998			0.0799989	+	0.996795i	$0.474508\pi$
$912$	−296614.			−0.356616
$913$	20571.5	+	1.22486e6i	0.0246788	+	1.46942i
$914$	824660.			0.987149
$915$		0			0
$916$	−592647.			−0.706326
$917$			214194.i			0.254723i
$918$			581414.i			0.689923i
$919$		−	964589.i		−	1.14212i	−0.820909	−	0.571059i	$-0.806533\pi$
$919$		−	964589.i		−	1.14212i	0.820909	−	0.571059i	$-0.193467\pi$
$920$		0			0
$921$			680963.i			0.802795i
$922$			177432.i			0.208723i
$923$	−307470.			−0.360911
$924$	369829.	−	6211.26i	0.433168	−	0.00727505i
$925$		0			0
$926$		−	483331.i		−	0.563667i
$927$			417143.i			0.485429i
$928$		−	115943.i		−	0.134633i
$929$	−634849.			−0.735596			−0.367798	−	0.929906i	$-0.619888\pi$
$929$	−634849.			−0.735596			−0.367798	+	0.929906i	$0.619888\pi$
$930$		0			0
$931$			514178.i			0.593217i
$932$	413756.			0.476335
$933$		−	361451.i		−	0.415228i
$934$		−	267453.i		−	0.306587i
$935$		0			0
$936$	74791.1			0.0853686
$937$	−3331.90			−0.00379501			−0.00189750	−	0.999998i	$-0.500604\pi$
$937$	−3331.90			−0.00379501			−0.00189750	+	0.999998i	$0.500604\pi$
$938$			192685.i			0.218998i
$939$	1.25499e6			1.42334
$940$		0			0
$941$		−	1.13619e6i		−	1.28313i	−0.767069	−	0.641564i	$-0.778286\pi$
$941$		−	1.13619e6i		−	1.28313i	0.767069	−	0.641564i	$-0.221714\pi$
$942$	−73720.4			−0.0830780
$943$	935496.			1.05201
$944$	127234.			0.142777
$945$		0			0
$946$	−15636.4	−	931018.i	−0.0174725	−	1.04034i
$947$		−	156679.i		−	0.174707i	−0.996177	−	0.0873536i	$-0.972159\pi$
$947$		−	156679.i		−	0.174707i	0.996177	−	0.0873536i	$-0.0278410\pi$
$948$	−133315.			−0.148341
$949$	93120.3			0.103398
$950$		0			0
$951$	−1.56786e6			−1.73359
$952$	−397726.			−0.438844
$953$	343607.			0.378334			0.189167	−	0.981945i	$-0.439421\pi$
$953$	343607.			0.378334			0.189167	+	0.981945i	$0.439421\pi$
$954$			520523.i			0.571931i
$955$		0			0
$956$			135291.i			0.148031i
$957$	−14651.6	−	872380.i	−0.0159978	−	0.952537i
$958$			437786.i			0.477014i
$959$			482205.i			0.524317i
$960$		0			0
$961$	−410168.			−0.444135
$962$			247229.i			0.267146i
$963$	512537.			0.552679
$964$		−	479136.i		−	0.515590i
$965$		0			0
$966$	−1.04579e6			−1.12071
$967$	−395609.			−0.423071			−0.211536	−	0.977370i	$-0.567846\pi$
$967$	−395609.			−0.423071			−0.211536	+	0.977370i	$0.567846\pi$
$968$	−331101.	+	11124.8i	−0.353354	+	0.0118725i
$969$	2.40013e6			2.55615
$970$		0			0
$971$	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.i			0.506939i
$973$			942632.i			0.995672i
$974$		−	580761.i		−	0.612181i
$975$		0			0
$976$		−	153388.i		−	0.161024i
$977$			1.02959e6i			1.07863i	0.842103	+	0.539316i	$0.181317\pi$
$977$			1.02959e6i			1.07863i	−0.842103	+	0.539316i	$0.818683\pi$
$978$	−691872.			−0.723349
$979$	−10431.2	−	621092.i	−0.0108835	−	0.648024i
$980$		0			0
$981$			470515.i			0.488918i
$982$		−	511376.i		−	0.530295i
$983$			1.35529e6i			1.40257i	0.712882	+	0.701284i	$0.247390\pi$
$983$			1.35529e6i			1.40257i	−0.712882	+	0.701284i	$0.752610\pi$
$984$	246277.			0.254351
$985$		0			0
$986$			938187.i			0.965019i
$987$	67665.6			0.0694598
$988$			237980.i			0.243796i
$989$			2.63271e6i			2.69160i
$990$		0			0
$991$	−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.			0.131798
$993$			677991.i			0.687584i
$994$	408484.			0.413430
$995$		0			0
$996$		−	911828.i		−	0.919167i
$997$	1.71845e6			1.72881			0.864404	−	0.502798i	$-0.167696\pi$
$997$	1.71845e6			1.72881			0.864404	+	0.502798i	$0.167696\pi$
$998$	−561169.			−0.563421
$999$	−480145.			−0.481106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.5.c.a.549.6		8
5.2	odd	4		22.5.b.a.21.3	yes	4
5.3	odd	4		550.5.d.a.351.2		4
5.4	even	2	inner	550.5.c.a.549.3		8
11.10	odd	2	inner	550.5.c.a.549.2		8
15.2	even	4		198.5.d.a.109.2		4
20.7	even	4		176.5.h.e.65.3		4
40.27	even	4		704.5.h.j.65.1		4
40.37	odd	4		704.5.h.i.65.4		4
55.32	even	4		22.5.b.a.21.1	✓	4
55.43	even	4		550.5.d.a.351.4		4
55.54	odd	2	inner	550.5.c.a.549.7		8
165.32	odd	4		198.5.d.a.109.4		4
220.87	odd	4		176.5.h.e.65.4		4
440.197	even	4		704.5.h.i.65.3		4
440.307	odd	4		704.5.h.j.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.b.a.21.1	✓	4	55.32	even	4
22.5.b.a.21.3	yes	4	5.2	odd	4
176.5.h.e.65.3		4	20.7	even	4
176.5.h.e.65.4		4	220.87	odd	4
198.5.d.a.109.2		4	15.2	even	4
198.5.d.a.109.4		4	165.32	odd	4
550.5.c.a.549.2		8	11.10	odd	2	inner
550.5.c.a.549.3		8	5.4	even	2	inner
550.5.c.a.549.6		8	1.1	even	1	trivial
550.5.c.a.549.7		8	55.54	odd	2	inner
550.5.d.a.351.2		4	5.3	odd	4
550.5.d.a.351.4		4	55.43	even	4
704.5.h.i.65.3		4	440.197	even	4
704.5.h.i.65.4		4	40.37	odd	4
704.5.h.j.65.1		4	40.27	even	4
704.5.h.j.65.2		4	440.307	odd	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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	550.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} -11.2580i q^{3} +8.00000 q^{4} -31.8424i q^{6} +33.9411 q^{7} +22.6274 q^{8} -45.7420 q^{9} +O(q^{10})\)	\(q+2.82843 q^{2} -11.2580i q^{3} +8.00000 q^{4} -31.8424i q^{6} +33.9411 q^{7} +22.6274 q^{8} -45.7420 q^{9} +(2.03190 + 120.983i) q^{11} -90.0638i q^{12} -72.2602 q^{13} +96.0000 q^{14} +64.0000 q^{16} -517.873 q^{17} -129.378 q^{18} -411.672i q^{19} -382.108i q^{21} +(5.74709 + 342.191i) q^{22} -967.641i q^{23} -254.739i q^{24} -204.383 q^{26} -396.933i q^{27} +271.529 q^{28} -640.503i q^{29} +716.487 q^{31} +181.019 q^{32} +(1362.02 - 22.8751i) q^{33} -1464.77 q^{34} -365.936 q^{36} -1209.64i q^{37} -1164.38i q^{38} +813.504i q^{39} +966.781i q^{41} -1080.77i q^{42} -2720.75 q^{43} +(16.2552 + 967.864i) q^{44} -2736.90i q^{46} +177.085i q^{47} -720.510i q^{48} -1249.00 q^{49} +5830.20i q^{51} -578.082 q^{52} -4023.28i q^{53} -1122.70i q^{54} +768.000 q^{56} -4634.59 q^{57} -1811.62i q^{58} +1988.02 q^{59} -2396.69i q^{61} +2026.53 q^{62} -1552.54 q^{63} +512.000 q^{64} +(3852.38 - 64.7006i) q^{66} +2007.13i q^{67} -4142.98 q^{68} -10893.7 q^{69} +4255.04 q^{71} -1035.02 q^{72} -1288.68 q^{73} -3421.37i q^{74} -3293.37i q^{76} +(68.9651 + 4106.30i) q^{77} +2300.94i q^{78} -1480.23i q^{79} -8173.77 q^{81} +2734.47i q^{82} +10124.2 q^{83} -3056.87i q^{84} -7695.45 q^{86} -7210.77 q^{87} +(45.9767 + 2737.53i) q^{88} -5133.72 q^{89} -2452.59 q^{91} -7741.13i q^{92} -8066.19i q^{93} +500.871i q^{94} -2037.91i q^{96} -2239.34i q^{97} -3532.71 q^{98} +(-92.9434 - 5534.00i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{4} - 460 q^{9}+O(q^{10}) \) 8 * q + 64 * q^4 - 460 * q^9	\( 8 q + 64 q^{4} - 460 q^{9} - 360 q^{11} + 768 q^{14} + 512 q^{16} + 2880 q^{26} + 8836 q^{31} - 2688 q^{34} - 3680 q^{36} - 2880 q^{44} - 9992 q^{49} + 6144 q^{56} + 6780 q^{59} + 4096 q^{64} + 26304 q^{66} - 52628 q^{69} + 7044 q^{71} - 62192 q^{81} - 20928 q^{86} + 17532 q^{89} + 34560 q^{91} + 25124 q^{99}+O(q^{100}) \) 8 * q + 64 * q^4 - 460 * q^9 - 360 * q^11 + 768 * q^14 + 512 * q^16 + 2880 * q^26 + 8836 * q^31 - 2688 * q^34 - 3680 * q^36 - 2880 * q^44 - 9992 * q^49 + 6144 * q^56 + 6780 * q^59 + 4096 * q^64 + 26304 * q^66 - 52628 * q^69 + 7044 * q^71 - 62192 * q^81 - 20928 * q^86 + 17532 * q^89 + 34560 * q^91 + 25124 * q^99

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