LMFDB - Embedded newform 825.3.h.a.274.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,3,Mod(274,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("825.274");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	825.h (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:	$22.4796218097$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1579585536.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 $ x^8 - 2x^7 - 4x^6 + 28x^5 - 38x^4 + 8x^3 + 200x^2 - 352*x + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.6
Root			$1.11361 + 1.42401i$ of defining polynomial
Character	$\chi$	$=$	825.274
Dual form			825.3.h.a.274.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.35285 q^{2} +1.73205i q^{3} +1.53590 q^{4} +4.07525i q^{6} -6.42810 q^{7} -5.79766 q^{8} -3.00000 q^{9} +(3.26795 - 10.5034i) q^{11} +2.66025i q^{12} +7.68899 q^{13} -15.1244 q^{14} -19.7846 q^{16} +8.15051 q^{17} -7.05855 q^{18} -30.4181i q^{19} -11.1338i q^{21} +(7.68899 - 24.7128i) q^{22} -31.6603i q^{23} -10.0418i q^{24} +18.0910 q^{26} -5.19615i q^{27} -9.87291 q^{28} +6.88962i q^{29} +51.1769 q^{31} -23.3596 q^{32} +(18.1923 + 5.66025i) q^{33} +19.1769 q^{34} -4.60770 q^{36} +19.4641i q^{37} -71.5692i q^{38} +13.3177i q^{39} -47.9800i q^{41} -26.1962i q^{42} -81.8429 q^{43} +(5.01924 - 16.1321i) q^{44} -74.4918i q^{46} -30.1962i q^{47} -34.2679i q^{48} -7.67949 q^{49} +14.1171i q^{51} +11.8095 q^{52} +26.0526i q^{53} -12.2258i q^{54} +37.2679 q^{56} +52.6857 q^{57} +16.2102i q^{58} -82.7461 q^{59} -75.4148i q^{61} +120.412 q^{62} +19.2843 q^{63} +24.1769 q^{64} +(42.8038 + 13.3177i) q^{66} +34.0000i q^{67} +12.5184 q^{68} +54.8372 q^{69} -72.7321 q^{71} +17.3930 q^{72} +54.8696 q^{73} +45.7961i q^{74} -46.7191i q^{76} +(-21.0067 + 67.5167i) q^{77} +31.3346i q^{78} +24.3279i q^{79} +9.00000 q^{81} -112.890i q^{82} +0.923034 q^{83} -17.1004i q^{84} -192.564 q^{86} -11.9332 q^{87} +(-18.9465 + 60.8949i) q^{88} -44.8231 q^{89} -49.4256 q^{91} -48.6269i q^{92} +88.6410i q^{93} -71.0470i q^{94} -40.4599i q^{96} +21.2539i q^{97} -18.0687 q^{98} +(-9.80385 + 31.5101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 40 q^{4} - 24 q^{9} + 40 q^{11} - 24 q^{14} + 8 q^{16} + 408 q^{26} + 160 q^{31} - 96 q^{34} - 120 q^{36} + 248 q^{44} - 200 q^{49} + 312 q^{56} - 80 q^{59} - 56 q^{64} + 384 q^{66} + 120 q^{69} - 568 q^{71}+ \cdots - 120 q^{99}+O(q^{100}) $ 8 * q + 40 * q^4 - 24 * q^9 + 40 * q^11 - 24 * q^14 + 8 * q^16 + 408 * q^26 + 160 * q^31 - 96 * q^34 - 120 * q^36 + 248 * q^44 - 200 * q^49 + 312 * q^56 - 80 * q^59 - 56 * q^64 + 384 * q^66 + 120 * q^69 - 568 * q^71 + 72 * q^81 - 432 * q^86 - 608 * q^89 + 48 * q^91 - 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	2.35285			1.17642			0.588212	−	0.808707i	$-0.299832\pi$
$2$	2.35285			1.17642			0.588212	+	0.808707i	$0.299832\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	1.53590			0.383975
$5$		0			0
$5$		0			0
$6$			4.07525i			0.679209i
$7$	−6.42810			−0.918300			−0.459150	−	0.888359i	$-0.651846\pi$
$7$	−6.42810			−0.918300			−0.459150	+	0.888359i	$0.651846\pi$
$8$	−5.79766			−0.724707
$9$	−3.00000			−0.333333
$10$		0			0
$11$	3.26795	−	10.5034i	0.297086	−	0.954851i
$11$	3.26795	−	10.5034i	0.297086	−	0.954851i
$12$			2.66025i			0.221688i
$13$	7.68899			0.591461			0.295730	−	0.955271i	$-0.404437\pi$
$13$	7.68899			0.591461			0.295730	+	0.955271i	$0.404437\pi$
$14$	−15.1244			−1.08031
$15$		0			0
$16$	−19.7846			−1.23654
$17$	8.15051			0.479442			0.239721	−	0.970842i	$-0.422944\pi$
$17$	8.15051			0.479442			0.239721	+	0.970842i	$0.422944\pi$
$18$	−7.05855			−0.392141
$19$		−	30.4181i		−	1.60095i	−0.599364	−	0.800477i	$-0.704580\pi$
$19$		−	30.4181i		−	1.60095i	0.599364	−	0.800477i	$-0.295420\pi$
$20$		0			0
$21$		−	11.1338i		−	0.530181i
$22$	7.68899	−	24.7128i	0.349500	−	1.12331i
$23$		−	31.6603i		−	1.37653i	−0.725458	−	0.688266i	$-0.758372\pi$
$23$		−	31.6603i		−	1.37653i	0.725458	−	0.688266i	$-0.241628\pi$
$24$		−	10.0418i		−	0.418410i
$25$		0			0
$26$	18.0910			0.695809
$27$		−	5.19615i		−	0.192450i
$28$	−9.87291			−0.352604
$29$			6.88962i			0.237573i	0.992920	+	0.118787i	$0.0379004\pi$
$29$			6.88962i			0.237573i	−0.992920	+	0.118787i	$0.962100\pi$
$30$		0			0
$31$	51.1769			1.65087			0.825434	−	0.564498i	$-0.190930\pi$
$31$	51.1769			1.65087			0.825434	+	0.564498i	$0.190930\pi$
$32$	−23.3596			−0.729986
$33$	18.1923	+	5.66025i	0.551283	+	0.171523i
$34$	19.1769			0.564027
$35$		0			0
$36$	−4.60770			−0.127992
$37$			19.4641i			0.526057i	0.964788	+	0.263028i	$0.0847213\pi$
$37$			19.4641i			0.526057i	−0.964788	+	0.263028i	$0.915279\pi$
$38$		−	71.5692i		−	1.88340i
$39$			13.3177i			0.341480i
$40$		0			0
$41$		−	47.9800i		−	1.17024i	−0.810945	−	0.585122i	$-0.801047\pi$
$41$		−	47.9800i		−	1.17024i	0.810945	−	0.585122i	$-0.198953\pi$
$42$		−	26.1962i		−	0.623718i
$43$	−81.8429			−1.90332			−0.951662	−	0.307147i	$-0.900626\pi$
$43$	−81.8429			−1.90332			−0.951662	+	0.307147i	$0.900626\pi$
$44$	5.01924	−	16.1321i	0.114074	−	0.366638i
$45$		0			0
$46$		−	74.4918i		−	1.61939i
$47$		−	30.1962i		−	0.642471i	−0.946999	−	0.321236i	$-0.895902\pi$
$47$		−	30.1962i		−	0.642471i	0.946999	−	0.321236i	$-0.104098\pi$
$48$		−	34.2679i		−	0.713916i
$49$	−7.67949			−0.156724
$50$		0			0
$51$			14.1171i			0.276806i
$52$	11.8095			0.227106
$53$			26.0526i			0.491558i	0.969326	+	0.245779i	$0.0790437\pi$
$53$			26.0526i			0.491558i	−0.969326	+	0.245779i	$0.920956\pi$
$54$		−	12.2258i		−	0.226403i
$55$		0			0
$56$	37.2679			0.665499
$57$	52.6857			0.924311
$58$			16.2102i			0.279487i
$59$	−82.7461			−1.40248			−0.701238	−	0.712927i	$-0.747369\pi$
$59$	−82.7461			−1.40248			−0.701238	+	0.712927i	$0.747369\pi$
$60$		0			0
$61$		−	75.4148i		−	1.23631i	−0.786057	−	0.618154i	$-0.787881\pi$
$61$		−	75.4148i		−	1.23631i	0.786057	−	0.618154i	$-0.212119\pi$
$62$	120.412			1.94212
$63$	19.2843			0.306100
$64$	24.1769			0.377764
$65$		0			0
$66$	42.8038	+	13.3177i	0.648543	+	0.201784i
$67$			34.0000i			0.507463i	0.967275	+	0.253731i	$0.0816579\pi$
$67$			34.0000i			0.507463i	−0.967275	+	0.253731i	$0.918342\pi$
$68$	12.5184			0.184093
$69$	54.8372			0.794742
$70$		0			0
$71$	−72.7321			−1.02440			−0.512198	−	0.858868i	$-0.671168\pi$
$71$	−72.7321			−1.02440			−0.512198	+	0.858868i	$0.671168\pi$
$72$	17.3930			0.241569
$73$	54.8696			0.751639			0.375819	−	0.926693i	$-0.377361\pi$
$73$	54.8696			0.751639			0.375819	+	0.926693i	$0.377361\pi$
$74$			45.7961i			0.618866i
$75$		0			0
$76$		−	46.7191i		−	0.614725i
$77$	−21.0067	+	67.5167i	−0.272814	+	0.876840i
$78$			31.3346i			0.401726i
$79$			24.3279i			0.307948i	0.988075	+	0.153974i	$0.0492071\pi$
$79$			24.3279i			0.307948i	−0.988075	+	0.153974i	$0.950793\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	112.890i		−	1.37670i
$83$	0.923034			0.0111209			0.00556045	−	0.999985i	$-0.498230\pi$
$83$	0.923034			0.0111209			0.00556045	+	0.999985i	$0.498230\pi$
$84$		−	17.1004i		−	0.203576i
$85$		0			0
$86$	−192.564			−2.23912
$87$	−11.9332			−0.137163
$88$	−18.9465	+	60.8949i	−0.215301	+	0.691987i
$89$	−44.8231			−0.503630			−0.251815	−	0.967775i	$-0.581027\pi$
$89$	−44.8231			−0.503630			−0.251815	+	0.967775i	$0.581027\pi$
$90$		0			0
$91$	−49.4256			−0.543139
$92$		−	48.6269i		−	0.528554i
$93$			88.6410i			0.953129i
$94$		−	71.0470i		−	0.755819i
$95$		0			0
$96$		−	40.4599i		−	0.421458i
$97$			21.2539i			0.219112i	0.993981	+	0.109556i	$0.0349429\pi$
$97$			21.2539i			0.219112i	−0.993981	+	0.109556i	$0.965057\pi$
$98$	−18.0687			−0.184374
$99$	−9.80385	+	31.5101i	−0.0990288	+	0.318284i
$100$		0			0
$101$			52.3479i			0.518296i	0.965838	+	0.259148i	$0.0834417\pi$
$101$			52.3479i			0.518296i	−0.965838	+	0.259148i	$0.916558\pi$
$102$			33.2154i			0.325641i
$103$		−	4.74613i		−	0.0460790i	−0.999735	−	0.0230395i	$-0.992666\pi$
$103$		−	4.74613i		−	0.0460790i	0.999735	−	0.0230395i	$-0.00733434\pi$
$104$	−44.5781			−0.428636
$105$		0			0
$106$			61.2977i			0.578281i
$107$	147.723			1.38059			0.690293	−	0.723530i	$-0.257482\pi$
$107$	147.723			1.38059			0.690293	+	0.723530i	$0.257482\pi$
$108$		−	7.98076i		−	0.0738959i
$109$			3.56847i			0.0327383i	0.999866	+	0.0163691i	$0.00521069\pi$
$109$			3.56847i			0.0327383i	−0.999866	+	0.0163691i	$0.994789\pi$
$110$		0			0
$111$	−33.7128			−0.303719
$112$	127.178			1.13551
$113$		−	62.3154i		−	0.551463i	−0.961235	−	0.275732i	$-0.911080\pi$
$113$		−	62.3154i		−	0.551463i	0.961235	−	0.275732i	$-0.0889201\pi$
$114$	123.962			1.08738
$115$		0			0
$116$			10.5818i			0.0912220i
$117$	−23.0670			−0.197154
$118$	−194.689			−1.64991
$119$	−52.3923			−0.440271
$120$		0			0
$121$	−99.6410	−	68.6489i	−0.823479	−	0.567346i
$122$		−	177.440i		−	1.45442i
$123$	83.1038			0.675641
$124$	78.6025			0.633891
$125$		0			0
$126$	45.3731			0.360104
$127$	28.0200			0.220630			0.110315	−	0.993897i	$-0.464814\pi$
$127$	28.0200			0.220630			0.110315	+	0.993897i	$0.464814\pi$
$128$	150.323			1.17440
$129$		−	141.756i		−	1.09888i
$130$		0			0
$131$		−	113.184i		−	0.864001i	−0.901873	−	0.432000i	$-0.857808\pi$
$131$		−	113.184i		−	0.864001i	0.901873	−	0.432000i	$-0.142192\pi$
$132$	27.9416	+	8.69358i	0.211679	+	0.0658604i
$133$			195.531i			1.47016i
$134$			79.9969i			0.596992i
$135$		0			0
$136$	−47.2539			−0.347455
$137$			70.7846i			0.516676i	0.966055	+	0.258338i	$0.0831748\pi$
$137$			70.7846i			0.516676i	−0.966055	+	0.258338i	$0.916825\pi$
$138$	129.024			0.934953
$139$		−	130.499i		−	0.938839i	−0.882975	−	0.469420i	$-0.844463\pi$
$139$		−	130.499i		−	0.938839i	0.882975	−	0.469420i	$-0.155537\pi$
$140$		0			0
$141$	52.3013			0.370931
$142$	−171.128			−1.20512
$143$	25.1272	−	80.7602i	0.175715	−	0.564757i
$144$	59.3538			0.412179
$145$		0			0
$146$	129.100			0.884246
$147$		−	13.3013i		−	0.0904848i
$148$			29.8949i			0.201992i
$149$		−	125.793i		−	0.844248i	−0.906538	−	0.422124i	$-0.861285\pi$
$149$		−	125.793i		−	0.844248i	0.906538	−	0.422124i	$-0.138715\pi$
$150$		0			0
$151$		−	275.238i		−	1.82277i	−0.411556	−	0.911384i	$-0.635015\pi$
$151$		−	275.238i		−	1.82277i	0.411556	−	0.911384i	$-0.364985\pi$
$152$			176.354i			1.16022i
$153$	−24.4515			−0.159814
$154$	−49.4256	+	158.857i	−0.320946	+	1.03154i
$155$		0			0
$156$			20.4547i			0.131120i
$157$			273.138i			1.73974i	0.493285	+	0.869868i	$0.335796\pi$
$157$			273.138i			1.73974i	−0.493285	+	0.869868i	$0.664204\pi$
$158$			57.2398i			0.362277i
$159$	−45.1244			−0.283801
$160$		0			0
$161$			203.515i			1.26407i
$162$	21.1756			0.130714
$163$			62.0666i			0.380777i	0.981709	+	0.190388i	$0.0609748\pi$
$163$			62.0666i			0.380777i	−0.981709	+	0.190388i	$0.939025\pi$
$164$		−	73.6924i		−	0.449344i
$165$		0			0
$166$	2.17176			0.0130829
$167$	−47.9800			−0.287305			−0.143653	−	0.989628i	$-0.545885\pi$
$167$	−47.9800			−0.287305			−0.143653	+	0.989628i	$0.545885\pi$
$168$			64.5500i			0.384226i
$169$	−109.879			−0.650174
$170$		0			0
$171$			91.2543i			0.533651i
$172$	−125.702			−0.730828
$173$	−143.017			−0.826688			−0.413344	−	0.910575i	$-0.635639\pi$
$173$	−143.017			−0.826688			−0.413344	+	0.910575i	$0.635639\pi$
$174$	−28.0770			−0.161362
$175$		0			0
$176$	−64.6551	+	207.805i	−0.367359	+	1.18071i
$177$		−	143.321i		−	0.809720i
$178$	−105.462			−0.592483
$179$	−36.6025			−0.204483			−0.102242	−	0.994760i	$-0.532602\pi$
$179$	−36.6025			−0.204483			−0.102242	+	0.994760i	$0.532602\pi$
$180$		0			0
$181$	−84.1718			−0.465037			−0.232519	−	0.972592i	$-0.574697\pi$
$181$	−84.1718			−0.465037			−0.232519	+	0.972592i	$0.574697\pi$
$182$	−116.291			−0.638962
$183$	130.622			0.713783
$184$			183.555i			0.997583i
$185$		0			0
$186$			208.559i			1.12128i
$187$	26.6354	−	85.6077i	0.142436	−	0.457795i
$188$		−	46.3782i		−	0.246693i
$189$			33.4014i			0.176727i
$190$		0			0
$191$	44.2346			0.231595			0.115797	−	0.993273i	$-0.463058\pi$
$191$	44.2346			0.231595			0.115797	+	0.993273i	$0.463058\pi$
$192$			41.8756i			0.218102i
$193$	136.127			0.705323			0.352662	−	0.935751i	$-0.385277\pi$
$193$	136.127			0.705323			0.352662	+	0.935751i	$0.385277\pi$
$194$			50.0071i			0.257769i
$195$		0			0
$196$	−11.7949			−0.0601782
$197$	5.96659			0.0302872			0.0151436	−	0.999885i	$-0.495179\pi$
$197$	5.96659			0.0302872			0.0151436	+	0.999885i	$0.495179\pi$
$198$	−23.0670	+	74.1384i	−0.116500	+	0.374437i
$199$	234.056			1.17616			0.588081	−	0.808802i	$-0.299884\pi$
$199$	234.056			1.17616			0.588081	+	0.808802i	$0.299884\pi$
$200$		0			0
$201$	−58.8897			−0.292984
$202$			123.167i			0.609736i
$203$		−	44.2872i		−	0.218163i
$204$			21.6824i			0.106286i
$205$		0			0
$206$		−	11.1669i		−	0.0542084i
$207$			94.9808i			0.458844i
$208$	−152.124			−0.731364
$209$	−319.492	−	99.4048i	−1.52867	−	0.475621i
$210$		0			0
$211$			167.469i			0.793690i	0.917886	+	0.396845i	$0.129895\pi$
$211$			167.469i			0.793690i	−0.917886	+	0.396845i	$0.870105\pi$
$212$			40.0141i			0.188746i
$213$		−	125.976i		−	0.591435i
$214$	347.569			1.62416
$215$		0			0
$216$			30.1255i			0.139470i
$217$	−328.970			−1.51599
$218$			8.39608i			0.0385141i
$219$			95.0370i			0.433959i
$220$		0			0
$221$	62.6692			0.283571
$222$	−79.3212			−0.357303
$223$			82.2872i			0.369001i	0.982832	+	0.184500i	$0.0590667\pi$
$223$			82.2872i			0.369001i	−0.982832	+	0.184500i	$0.940933\pi$
$224$	150.158			0.670347
$225$		0			0
$226$		−	146.619i		−	0.648755i
$227$	40.9999			0.180616			0.0903081	−	0.995914i	$-0.471215\pi$
$227$	40.9999			0.180616			0.0903081	+	0.995914i	$0.471215\pi$
$228$	80.9199			0.354912
$229$	−160.718			−0.701825			−0.350913	−	0.936408i	$-0.614129\pi$
$229$	−160.718			−0.701825			−0.350913	+	0.936408i	$0.614129\pi$
$230$		0			0
$231$	−116.942	−	36.3847i	−0.506244	−	0.157510i
$232$		−	39.9437i		−	0.172171i
$233$	407.954			1.75087			0.875437	−	0.483332i	$-0.160573\pi$
$233$	407.954			1.75087			0.875437	+	0.483332i	$0.160573\pi$
$234$	−54.2731			−0.231936
$235$		0			0
$236$	−127.090			−0.538515
$237$	−42.1371			−0.177794
$238$	−123.271			−0.517946
$239$			202.254i			0.846253i	0.906071	+	0.423127i	$0.139067\pi$
$239$			202.254i			0.846253i	−0.906071	+	0.423127i	$0.860933\pi$
$240$		0			0
$241$		−	26.8828i		−	0.111547i	−0.998443	−	0.0557734i	$-0.982238\pi$
$241$		−	26.8828i		−	0.111547i	0.998443	−	0.0557734i	$-0.0177624\pi$
$242$	−234.440	−	161.520i	−0.968761	−	0.667440i
$243$			15.5885i			0.0641500i
$244$		−	115.830i		−	0.474711i
$245$		0			0
$246$	195.531			0.794840
$247$		−	233.885i		−	0.946901i
$248$	−296.706			−1.19640
$249$			1.59874i			0.00642065i
$250$		0			0
$251$	398.277			1.58676			0.793380	−	0.608726i	$-0.208319\pi$
$251$	398.277			1.58676			0.793380	+	0.608726i	$0.208319\pi$
$252$	29.6187			0.117535
$253$	−332.539	−	103.464i	−1.31438	−	0.408949i
$254$	65.9268			0.259554
$255$		0			0
$256$	256.979			1.00383
$257$			337.818i			1.31447i	0.753687	+	0.657233i	$0.228273\pi$
$257$			337.818i			1.31447i	−0.753687	+	0.657233i	$0.771727\pi$
$258$		−	333.531i		−	1.29275i
$259$		−	125.117i		−	0.483078i
$260$		0			0
$261$		−	20.6689i		−	0.0791910i
$262$		−	266.305i		−	1.01643i
$263$	134.529			0.511516			0.255758	−	0.966741i	$-0.417675\pi$
$263$	134.529			0.511516			0.255758	+	0.966741i	$0.417675\pi$
$264$	−105.473	−	32.8162i	−0.399519	−	0.124304i
$265$		0			0
$266$			460.054i			1.72953i
$267$		−	77.6359i		−	0.290771i
$268$			52.2205i			0.194853i
$269$	341.870			1.27089			0.635447	−	0.772144i	$-0.280816\pi$
$269$	341.870			1.27089			0.635447	+	0.772144i	$0.280816\pi$
$270$		0			0
$271$			213.298i			0.787077i	0.919308	+	0.393538i	$0.128749\pi$
$271$			213.298i			0.787077i	−0.919308	+	0.393538i	$0.871251\pi$
$272$	−161.255			−0.592848
$273$		−	85.6077i		−	0.313581i
$274$			166.545i			0.607830i
$275$		0			0
$276$	84.2243			0.305161
$277$	−84.5789			−0.305339			−0.152669	−	0.988277i	$-0.548787\pi$
$277$	−84.5789			−0.305339			−0.152669	+	0.988277i	$0.548787\pi$
$278$		−	307.044i		−	1.10447i
$279$	−153.531			−0.550289
$280$		0			0
$281$			351.148i			1.24964i	0.780771	+	0.624818i	$0.214827\pi$
$281$			351.148i			1.24964i	−0.780771	+	0.624818i	$0.785173\pi$
$282$	123.057			0.436372
$283$	−285.943			−1.01040			−0.505201	−	0.863002i	$-0.668581\pi$
$283$	−285.943			−1.01040			−0.505201	+	0.863002i	$0.668581\pi$
$284$	−111.709			−0.393342
$285$		0			0
$286$	59.1206	−	190.017i	0.206715	−	0.664394i
$287$			308.420i			1.07464i
$288$	70.0787			0.243329
$289$	−222.569			−0.770136
$290$		0			0
$291$	−36.8128			−0.126504
$292$	84.2742			0.288610
$293$	393.927			1.34446			0.672231	−	0.740342i	$-0.265336\pi$
$293$	393.927			1.34446			0.672231	+	0.740342i	$0.265336\pi$
$294$		−	31.2959i		−	0.106449i
$295$		0			0
$296$		−	112.846i		−	0.381237i
$297$	−54.5770	−	16.9808i	−0.183761	−	0.0571743i
$298$		−	295.972i		−	0.993194i
$299$		−	243.435i		−	0.814165i
$300$		0			0
$301$	526.095			1.74782
$302$		−	647.594i		−	2.14435i
$303$	−90.6691			−0.299238
$304$			601.810i			1.97964i
$305$		0			0
$306$	−57.5307			−0.188009
$307$	−58.2239			−0.189654			−0.0948272	−	0.995494i	$-0.530230\pi$
$307$	−58.2239			−0.189654			−0.0948272	+	0.995494i	$0.530230\pi$
$308$	−32.2642	+	103.699i	−0.104754	+	0.336684i
$309$	8.22055			0.0266037
$310$		0			0
$311$	207.611			0.667561			0.333780	−	0.942651i	$-0.391676\pi$
$311$	207.611			0.667561			0.333780	+	0.942651i	$0.391676\pi$
$312$		−	77.2116i		−	0.247473i
$313$		−	376.697i		−	1.20351i	−0.798682	−	0.601753i	$-0.794469\pi$
$313$		−	376.697i		−	1.20351i	0.798682	−	0.601753i	$-0.205531\pi$
$314$			642.654i			2.04667i
$315$		0			0
$316$			37.3651i			0.118244i
$317$		−	246.809i		−	0.778577i	−0.921116	−	0.389289i	$-0.872721\pi$
$317$		−	246.809i		−	0.778577i	0.921116	−	0.389289i	$-0.127279\pi$
$318$	−106.171			−0.333870
$319$	72.3641	+	22.5149i	0.226847	+	0.0705797i
$320$		0			0
$321$			255.863i			0.797082i
$322$			478.841i			1.48708i
$323$		−	247.923i		−	0.767564i
$324$	13.8231			0.0426638
$325$		0			0
$326$			146.033i			0.447955i
$327$	−6.18078			−0.0189015
$328$			278.172i			0.848085i
$329$			194.104i			0.589982i
$330$		0			0
$331$	146.431			0.442389			0.221195	−	0.975230i	$-0.429004\pi$
$331$	146.431			0.442389			0.221195	+	0.975230i	$0.429004\pi$
$332$	1.41769			0.00427014
$333$		−	58.3923i		−	0.175352i
$334$	−112.890			−0.337993
$335$		0			0
$336$			220.278i			0.655589i
$337$	−354.007			−1.05047			−0.525233	−	0.850958i	$-0.676022\pi$
$337$	−354.007			−1.05047			−0.525233	+	0.850958i	$0.676022\pi$
$338$	−258.530			−0.764881
$339$	107.933			0.318387
$340$		0			0
$341$	167.244	−	537.529i	0.490450	−	1.57633i
$342$			214.708i			0.627800i
$343$	364.342			1.06222
$344$	474.497			1.37935
$345$		0			0
$346$	−336.497			−0.972536
$347$	529.807			1.52682			0.763411	−	0.645913i	$-0.223523\pi$
$347$	529.807			1.52682			0.763411	+	0.645913i	$0.223523\pi$
$348$	−18.3281			−0.0526671
$349$		−	342.873i		−	0.982445i	−0.871034	−	0.491223i	$-0.836550\pi$
$349$		−	342.873i		−	0.982445i	0.871034	−	0.491223i	$-0.163450\pi$
$350$		0			0
$351$		−	39.9532i		−	0.113827i
$352$	−76.3379	+	245.354i	−0.216869	+	0.697028i
$353$			191.990i			0.543880i	0.962314	+	0.271940i	$0.0876653\pi$
$353$			191.990i			0.543880i	−0.962314	+	0.271940i	$0.912335\pi$
$354$		−	337.212i		−	0.952575i
$355$		0			0
$356$	−68.8437			−0.193381
$357$		−	90.7461i		−	0.254191i
$358$	−86.1203			−0.240559
$359$		−	601.654i		−	1.67592i	−0.545735	−	0.837958i	$-0.683750\pi$
$359$		−	601.654i		−	1.67592i	0.545735	−	0.837958i	$-0.316250\pi$
$360$		0			0
$361$	−564.261			−1.56305
$362$	−198.043			−0.547081
$363$	118.903	−	172.583i	0.327557	−	0.475436i
$364$	−75.9127			−0.208551
$365$		0			0
$366$	307.335			0.839712
$367$			139.415i			0.379878i	0.981796	+	0.189939i	$0.0608291\pi$
$367$			139.415i			0.379878i	−0.981796	+	0.189939i	$0.939171\pi$
$368$			626.386i			1.70214i
$369$			143.940i			0.390081i
$370$		0			0
$371$		−	167.469i		−	0.451398i
$372$			136.144i			0.365977i
$373$	−303.629			−0.814019			−0.407009	−	0.913424i	$-0.633428\pi$
$373$	−303.629			−0.814019			−0.407009	+	0.913424i	$0.633428\pi$
$374$	62.6692	−	201.422i	0.167565	−	0.538561i
$375$		0			0
$376$			175.067i			0.465604i
$377$			52.9742i			0.140515i
$378$			78.5885i			0.207906i
$379$	−690.046			−1.82070			−0.910351	−	0.413837i	$-0.864188\pi$
$379$	−690.046			−1.82070			−0.910351	+	0.413837i	$0.864188\pi$
$380$		0			0
$381$			48.5321i			0.127381i
$382$	104.077			0.272454
$383$		−	53.2576i		−	0.139054i	−0.997580	−	0.0695269i	$-0.977851\pi$
$383$		−	53.2576i		−	0.139054i	0.997580	−	0.0695269i	$-0.0221490\pi$
$384$			260.367i			0.678039i
$385$		0			0
$386$	320.287			0.829760
$387$	245.529			0.634441
$388$			32.6438i			0.0841334i
$389$	587.027			1.50907			0.754533	−	0.656262i	$-0.227863\pi$
$389$	587.027			1.50907			0.754533	+	0.656262i	$0.227863\pi$
$390$		0			0
$391$		−	258.047i		−	0.659967i
$392$	44.5231			0.113579
$393$	196.041			0.498831
$394$	14.0385			0.0356306
$395$		0			0
$396$	−15.0577	+	48.3963i	−0.0380245	+	0.122213i
$397$		−	485.797i		−	1.22367i	−0.790985	−	0.611835i	$-0.790431\pi$
$397$		−	485.797i		−	1.22367i	0.790985	−	0.611835i	$-0.209569\pi$
$398$	550.699			1.38367
$399$	−338.669			−0.848795
$400$		0			0
$401$	−166.469			−0.415135			−0.207568	−	0.978221i	$-0.566555\pi$
$401$	−166.469			−0.415135			−0.207568	+	0.978221i	$0.566555\pi$
$402$	−138.559			−0.344673
$403$	393.499			0.976424
$404$			80.4010i			0.199012i
$405$		0			0
$406$		−	104.201i		−	0.256653i
$407$	204.438	+	63.6077i	0.502306	+	0.156284i
$408$		−	81.8461i		−	0.200603i
$409$			270.161i			0.660541i	0.943886	+	0.330271i	$0.107140\pi$
$409$			270.161i			0.660541i	−0.943886	+	0.330271i	$0.892860\pi$
$410$		0			0
$411$	−122.603			−0.298303
$412$		−	7.28958i		−	0.0176932i
$413$	531.901			1.28790
$414$			223.475i			0.539796i
$415$		0			0
$416$	−179.611			−0.431758
$417$	226.030			0.542039
$418$	−751.717	−	233.885i	−1.79837	−	0.559532i
$419$	356.631			0.851147			0.425574	−	0.904924i	$-0.360072\pi$
$419$	356.631			0.851147			0.425574	+	0.904924i	$0.360072\pi$
$420$		0			0
$421$	−462.238			−1.09795			−0.548977	−	0.835838i	$-0.684982\pi$
$421$	−462.238			−1.09795			−0.548977	+	0.835838i	$0.684982\pi$
$422$			394.028i			0.933716i
$423$			90.5885i			0.214157i
$424$		−	151.044i		−	0.356236i
$425$		0			0
$426$		−	296.402i		−	0.695778i
$427$			484.774i			1.13530i
$428$	226.887			0.530110
$429$	139.881	+	43.5216i	0.326062	+	0.101449i
$430$		0			0
$431$			199.552i			0.462997i	0.972835	+	0.231498i	$0.0743628\pi$
$431$			199.552i			0.462997i	−0.972835	+	0.231498i	$0.925637\pi$
$432$			102.804i			0.237972i
$433$		−	45.3693i		−	0.104779i	−0.998627	−	0.0523895i	$-0.983316\pi$
$433$		−	45.3693i		−	0.104779i	0.998627	−	0.0523895i	$-0.0166837\pi$
$434$	−774.018			−1.78345
$435$		0			0
$436$			5.48081i			0.0125707i
$437$	−963.045			−2.20376
$438$			223.608i			0.510520i
$439$		−	484.630i		−	1.10394i	−0.833864	−	0.551970i	$-0.813876\pi$
$439$		−	484.630i		−	1.10394i	0.833864	−	0.551970i	$-0.186124\pi$
$440$		0			0
$441$	23.0385			0.0522414
$442$	147.451			0.333600
$443$			375.538i			0.847716i	0.905729	+	0.423858i	$0.139324\pi$
$443$			375.538i			0.847716i	−0.905729	+	0.423858i	$0.860676\pi$
$444$	−51.7795			−0.116620
$445$		0			0
$446$			193.609i			0.434102i
$447$	217.880			0.487427
$448$	−155.412			−0.346901
$449$	385.636			0.858877			0.429439	−	0.903096i	$-0.358711\pi$
$449$	385.636			0.858877			0.429439	+	0.903096i	$0.358711\pi$
$450$		0			0
$451$	−503.951	−	156.796i	−1.11741	−	0.347664i
$452$		−	95.7101i		−	0.211748i
$453$	476.726			1.05238
$454$	96.4665			0.212481
$455$		0			0
$456$	−305.454			−0.669855
$457$	−378.368			−0.827939			−0.413970	−	0.910291i	$-0.635858\pi$
$457$	−378.368			−0.827939			−0.413970	+	0.910291i	$0.635858\pi$
$458$	−378.145			−0.825644
$459$		−	42.3513i		−	0.0922686i
$460$		0			0
$461$			224.522i			0.487033i	0.969897	+	0.243516i	$0.0783010\pi$
$461$			224.522i			0.487033i	−0.969897	+	0.243516i	$0.921699\pi$
$462$	−275.148	−	85.6077i	−0.595557	−	0.185298i
$463$		−	52.3820i		−	0.113136i	−0.998399	−	0.0565680i	$-0.981984\pi$
$463$		−	52.3820i		−	0.113136i	0.998399	−	0.0565680i	$-0.0180158\pi$
$464$		−	136.308i		−	0.293768i
$465$		0			0
$466$	959.854			2.05977
$467$		−	513.387i		−	1.09933i	−0.835385	−	0.549665i	$-0.814755\pi$
$467$		−	513.387i		−	1.09933i	0.835385	−	0.549665i	$-0.185245\pi$
$468$	−35.4285			−0.0757020
$469$		−	218.556i		−	0.466003i
$470$		0			0
$471$	−473.090			−1.00444
$472$	479.734			1.01639
$473$	−267.459	+	859.626i	−0.565451	+	1.81739i
$474$	−99.1422			−0.209161
$475$		0			0
$476$	−80.4693			−0.169053
$477$		−	78.1577i		−	0.163853i
$478$			475.874i			0.995553i
$479$			238.730i			0.498392i	0.968453	+	0.249196i	$0.0801663\pi$
$479$			238.730i			0.498392i	−0.968453	+	0.249196i	$0.919834\pi$
$480$		0			0
$481$			149.659i			0.311142i
$482$		−	63.2511i		−	0.131226i
$483$	−352.499			−0.729812
$484$	−153.038	−	105.438i	−0.316195	−	0.217846i
$485$		0			0
$486$			36.6773i			0.0754677i
$487$		−	593.251i		−	1.21817i	−0.793103	−	0.609087i	$-0.791536\pi$
$487$		−	593.251i		−	1.21817i	0.793103	−	0.609087i	$-0.208464\pi$
$488$			437.229i			0.895962i
$489$	−107.503			−0.219842
$490$		0			0
$491$		−	858.935i		−	1.74936i	−0.484703	−	0.874679i	$-0.661072\pi$
$491$		−	858.935i		−	1.74936i	0.484703	−	0.874679i	$-0.338928\pi$
$492$	127.639			0.259429
$493$			56.1539i			0.113902i
$494$		−	550.295i		−	1.11396i
$495$		0			0
$496$	−1012.52			−2.04136
$497$	467.529			0.940702
$498$			3.76160i			0.00755341i
$499$	803.692			1.61061			0.805303	−	0.592864i	$-0.202003\pi$
$499$	803.692			1.61061			0.805303	+	0.592864i	$0.202003\pi$
$500$		0			0
$501$		−	83.1038i		−	0.165876i
$502$	937.085			1.86670
$503$	−752.302			−1.49563			−0.747815	−	0.663907i	$-0.768897\pi$
$503$	−752.302			−1.49563			−0.747815	+	0.663907i	$0.768897\pi$
$504$	−111.804			−0.221833
$505$		0			0
$506$	−782.414	−	243.435i	−1.54627	−	0.481098i
$507$		−	190.317i		−	0.375378i
$508$	43.0359			0.0847163
$509$	249.268			0.489721			0.244860	−	0.969558i	$-0.421258\pi$
$509$	249.268			0.489721			0.244860	+	0.969558i	$0.421258\pi$
$510$		0			0
$511$	−352.708			−0.690230
$512$	3.34215			0.00652764
$513$	−158.057			−0.308104
$514$			794.835i			1.54637i
$515$		0			0
$516$		−	217.723i		−	0.421944i
$517$	−317.161	−	98.6795i	−0.613464	−	0.190869i
$518$		−	294.382i		−	0.568305i
$519$		−	247.713i		−	0.477288i
$520$		0			0
$521$	475.864			0.913367			0.456683	−	0.889629i	$-0.349037\pi$
$521$	475.864			0.913367			0.456683	+	0.889629i	$0.349037\pi$
$522$		−	48.6307i		−	0.0931623i
$523$	362.833			0.693754			0.346877	−	0.937911i	$-0.387242\pi$
$523$	362.833			0.693754			0.346877	+	0.937911i	$0.387242\pi$
$524$		−	173.839i		−	0.331754i
$525$		0			0
$526$	316.526			0.601760
$527$	417.118			0.791495
$528$	−359.929	−	111.986i	−0.681683	−	0.212095i
$529$	−473.372			−0.894843
$530$		0			0
$531$	248.238			0.467492
$532$			300.315i			0.564503i
$533$		−	368.918i		−	0.692154i
$534$		−	182.665i		−	0.342070i
$535$		0			0
$536$		−	197.120i		−	0.367762i
$537$		−	63.3975i		−	0.118059i
$538$	804.370			1.49511
$539$	−25.0962	+	80.6604i	−0.0465606	+	0.149648i
$540$		0			0
$541$			830.667i			1.53543i	0.640792	+	0.767715i	$0.278606\pi$
$541$			830.667i			1.53543i	−0.640792	+	0.767715i	$0.721394\pi$
$542$			501.857i			0.925936i
$543$		−	145.790i		−	0.268489i
$544$	−190.392			−0.349986
$545$		0			0
$546$		−	201.422i		−	0.368905i
$547$	−456.091			−0.833804			−0.416902	−	0.908952i	$-0.636884\pi$
$547$	−456.091			−0.833804			−0.416902	+	0.908952i	$0.636884\pi$
$548$			108.718i			0.198390i
$549$			226.244i			0.412103i
$550$		0			0
$551$	209.569			0.380343
$552$	−317.927			−0.575955
$553$		−	156.382i		−	0.282788i
$554$	−199.001			−0.359208
$555$		0			0
$556$		−	200.433i		−	0.360490i
$557$	338.810			0.608277			0.304138	−	0.952628i	$-0.401631\pi$
$557$	338.810			0.608277			0.304138	+	0.952628i	$0.401631\pi$
$558$	−361.235			−0.647374
$559$	−629.290			−1.12574
$560$		0			0
$561$	148.277	+	46.1339i	0.264308	+	0.0822352i
$562$			826.197i			1.47010i
$563$	447.041			0.794034			0.397017	−	0.917811i	$-0.370045\pi$
$563$	447.041			0.794034			0.397017	+	0.917811i	$0.370045\pi$
$564$	80.3294			0.142428
$565$		0			0
$566$	−672.782			−1.18866
$567$	−57.8529			−0.102033
$568$	421.676			0.742387
$569$		−	522.893i		−	0.918969i	−0.888186	−	0.459485i	$-0.848034\pi$
$569$		−	522.893i		−	0.918969i	0.888186	−	0.459485i	$-0.151966\pi$
$570$		0			0
$571$		−	904.574i		−	1.58419i	−0.610396	−	0.792096i	$-0.708990\pi$
$571$		−	904.574i		−	1.58419i	0.610396	−	0.792096i	$-0.291010\pi$
$572$	38.5929	−	124.039i	0.0674701	−	0.216852i
$573$			76.6166i			0.133711i
$574$			725.667i			1.26423i
$575$		0			0
$576$	−72.5307			−0.125921
$577$		−	237.674i		−	0.411914i	−0.978561	−	0.205957i	$-0.933969\pi$
$577$		−	237.674i		−	0.411914i	0.978561	−	0.205957i	$-0.0660307\pi$
$578$	−523.672			−0.906007
$579$			235.780i			0.407219i
$580$		0			0
$581$	−5.93336			−0.0102123
$582$	−86.6149			−0.148823
$583$	273.639	+	85.1384i	0.469364	+	0.146035i
$584$	−318.115			−0.544718
$585$		0			0
$586$	926.851			1.58166
$587$			578.515i			0.985546i	0.870158	+	0.492773i	$0.164017\pi$
$587$			578.515i			0.985546i	−0.870158	+	0.492773i	$0.835983\pi$
$588$		−	20.4294i		−	0.0347439i
$589$		−	1556.71i		−	2.64296i
$590$		0			0
$591$			10.3344i			0.0174863i
$592$		−	385.090i		−	0.650489i
$593$	−333.857			−0.562997			−0.281499	−	0.959562i	$-0.590831\pi$
$593$	−333.857			−0.562997			−0.281499	+	0.959562i	$0.590831\pi$
$594$	−128.412	−	39.9532i	−0.216181	−	0.0672612i
$595$		0			0
$596$		−	193.205i		−	0.324170i
$597$			405.397i			0.679058i
$598$		−	572.767i		−	0.957804i
$599$	846.483			1.41316			0.706580	−	0.707633i	$-0.250237\pi$
$599$	846.483			1.41316			0.706580	+	0.707633i	$0.250237\pi$
$600$		0			0
$601$			455.011i			0.757089i	0.925583	+	0.378545i	$0.123575\pi$
$601$			455.011i			0.757089i	−0.925583	+	0.378545i	$0.876425\pi$
$602$	1237.82			2.05618
$603$		−	102.000i		−	0.169154i
$604$		−	422.738i		−	0.699897i
$605$		0			0
$606$	−213.331			−0.352031
$607$	726.557			1.19696			0.598482	−	0.801137i	$-0.295771\pi$
$607$	726.557			1.19696			0.598482	+	0.801137i	$0.295771\pi$
$608$			710.554i			1.16867i
$609$	76.7077			0.125957
$610$		0			0
$611$		−	232.178i		−	0.379997i
$612$	−37.5551			−0.0613645
$613$	−574.532			−0.937247			−0.468624	−	0.883398i	$-0.655250\pi$
$613$	−574.532			−0.937247			−0.468624	+	0.883398i	$0.655250\pi$
$614$	−136.992			−0.223114
$615$		0			0
$616$	121.790	−	391.439i	0.197711	−	0.635452i
$617$			278.946i			0.452101i	0.974116	+	0.226050i	$0.0725814\pi$
$617$			278.946i			0.452101i	−0.974116	+	0.226050i	$0.927419\pi$
$618$	19.3417			0.0312973
$619$	593.061			0.958096			0.479048	−	0.877789i	$-0.340982\pi$
$619$	593.061			0.958096			0.479048	+	0.877789i	$0.340982\pi$
$620$		0			0
$621$	−164.512			−0.264914
$622$	488.478			0.785335
$623$	288.127			0.462484
$624$		−	263.486i		−	0.422253i
$625$		0			0
$626$		−	886.312i		−	1.41583i
$627$	172.174	−	553.377i	0.274600	−	0.882579i
$628$			419.513i			0.668014i
$629$			158.642i			0.252214i
$630$		0			0
$631$	−361.664			−0.573160			−0.286580	−	0.958056i	$-0.592518\pi$
$631$	−361.664			−0.573160			−0.286580	+	0.958056i	$0.592518\pi$
$632$		−	141.045i		−	0.223172i
$633$	−290.064			−0.458237
$634$		−	580.704i		−	0.915937i
$635$		0			0
$636$	−69.3064			−0.108972
$637$	−59.0475			−0.0926963
$638$	170.262	+	52.9742i	0.266868	+	0.0830317i
$639$	218.196			0.341465
$640$		0			0
$641$	784.382			1.22368			0.611842	−	0.790980i	$-0.290429\pi$
$641$	784.382			1.22368			0.611842	+	0.790980i	$0.290429\pi$
$642$			602.008i			0.937706i
$643$			362.764i			0.564174i	0.959389	+	0.282087i	$0.0910267\pi$
$643$			362.764i			0.564174i	−0.959389	+	0.282087i	$0.908973\pi$
$644$			312.579i			0.485371i
$645$		0			0
$646$		−	583.325i		−	0.902981i
$647$		−	921.727i		−	1.42462i	−0.701867	−	0.712308i	$-0.747650\pi$
$647$		−	921.727i		−	1.42462i	0.701867	−	0.712308i	$-0.252350\pi$
$648$	−52.1789			−0.0805230
$649$	−270.410	+	869.112i	−0.416657	+	1.33916i
$650$		0			0
$651$		−	569.794i		−	0.875259i
$652$			95.3281i			0.146209i
$653$			26.8653i			0.0411414i	0.999788	+	0.0205707i	$0.00654832\pi$
$653$			26.8653i			0.0411414i	−0.999788	+	0.0205707i	$0.993452\pi$
$654$	−14.5424			−0.0222361
$655$		0			0
$656$			949.266i			1.44705i
$657$	−164.609			−0.250546
$658$			456.697i			0.694069i
$659$			320.820i			0.486828i	0.969922	+	0.243414i	$0.0782674\pi$
$659$			320.820i			0.486828i	−0.969922	+	0.243414i	$0.921733\pi$
$660$		0			0
$661$	331.969			0.502222			0.251111	−	0.967958i	$-0.419204\pi$
$661$	331.969			0.502222			0.251111	+	0.967958i	$0.419204\pi$
$662$	344.530			0.520437
$663$			108.546i			0.163720i
$664$	−5.35144			−0.00805939
$665$		0			0
$666$		−	137.388i		−	0.206289i
$667$	218.127			0.327027
$668$	−73.6924			−0.110318
$669$	−142.526			−0.213043
$670$		0			0
$671$	−792.109	−	246.452i	−1.18049	−	0.367290i
$672$			260.081i			0.387025i
$673$	−797.019			−1.18428			−0.592139	−	0.805836i	$-0.701716\pi$
$673$	−797.019			−1.18428			−0.592139	+	0.805836i	$0.701716\pi$
$674$	−832.925			−1.23579
$675$		0			0
$676$	−168.764			−0.249650
$677$	−534.175			−0.789033			−0.394516	−	0.918889i	$-0.629088\pi$
$677$	−534.175			−0.789033			−0.394516	+	0.918889i	$0.629088\pi$
$678$	253.951			0.374559
$679$		−	136.622i		−	0.201211i
$680$		0			0
$681$			71.0139i			0.104279i
$682$	393.499	−	1264.73i	0.576978	−	1.85444i
$683$		−	843.097i		−	1.23440i	−0.786805	−	0.617201i	$-0.788266\pi$
$683$		−	843.097i		−	1.23440i	0.786805	−	0.617201i	$-0.211734\pi$
$684$			140.157i			0.204908i
$685$		0			0
$686$	857.241			1.24962
$687$		−	278.372i		−	0.405199i
$688$	1619.23			2.35353
$689$			200.318i			0.290737i
$690$		0			0
$691$	−193.615			−0.280196			−0.140098	−	0.990138i	$-0.544742\pi$
$691$	−193.615			−0.280196			−0.140098	+	0.990138i	$0.544742\pi$
$692$	−219.660			−0.317427
$693$	63.0201	−	202.550i	0.0909382	−	0.292280i
$694$	1246.56			1.79619
$695$		0			0
$696$	69.1845			0.0994030
$697$		−	391.061i		−	0.561064i
$698$		−	806.729i		−	1.15577i
$699$			706.597i			1.01087i
$700$		0			0
$701$		−	448.863i		−	0.640318i	−0.947364	−	0.320159i	$-0.896264\pi$
$701$		−	448.863i		−	0.640318i	0.947364	−	0.320159i	$-0.103736\pi$
$702$		−	94.0038i		−	0.133909i
$703$	592.061			0.842192
$704$	79.0089	−	253.939i	0.112229	−	0.360708i
$705$		0			0
$706$			451.723i			0.639834i
$707$		−	336.497i		−	0.475951i
$708$		−	220.126i		−	0.310912i
$709$	311.031			0.438689			0.219345	−	0.975647i	$-0.429608\pi$
$709$	311.031			0.438689			0.219345	+	0.975647i	$0.429608\pi$
$710$		0			0
$711$		−	72.9836i		−	0.102649i
$712$	259.869			0.364985
$713$		−	1620.27i		−	2.27247i
$714$		−	213.512i		−	0.299036i
$715$		0			0
$716$	−56.2178			−0.0785165
$717$	−350.315			−0.488584
$718$		−	1415.60i		−	1.97159i
$719$	−486.014			−0.675958			−0.337979	−	0.941154i	$-0.609743\pi$
$719$	−486.014			−0.675958			−0.337979	+	0.941154i	$0.609743\pi$
$720$		0			0
$721$			30.5086i			0.0423143i
$722$	−1327.62			−1.83881
$723$	46.5623			0.0644016
$724$	−129.279			−0.178563
$725$		0			0
$726$	279.762	−	406.062i	0.385347	−	0.559315i
$727$		−	38.8616i		−	0.0534547i	−0.999643	−	0.0267273i	$-0.991491\pi$
$727$		−	38.8616i		−	0.0534547i	0.999643	−	0.0267273i	$-0.00850859\pi$
$728$	286.553			0.393617
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−667.061			−0.912533
$732$	200.623			0.274075
$733$	−175.562			−0.239511			−0.119756	−	0.992803i	$-0.538211\pi$
$733$	−175.562			−0.239511			−0.119756	+	0.992803i	$0.538211\pi$
$734$			328.023i			0.446898i
$735$		0			0
$736$			739.570i			1.00485i
$737$	357.114	+	111.110i	0.484551	+	0.150760i
$738$			338.669i			0.458901i
$739$			494.527i			0.669184i	0.942363	+	0.334592i	$0.108598\pi$
$739$			494.527i			0.669184i	−0.942363	+	0.334592i	$0.891402\pi$
$740$		0			0
$741$	405.100			0.546694
$742$		−	394.028i		−	0.531035i
$743$	−1150.84			−1.54892			−0.774458	−	0.632625i	$-0.781977\pi$
$743$	−1150.84			−1.54892			−0.774458	+	0.632625i	$0.781977\pi$
$744$		−	513.910i		−	0.690740i
$745$		0			0
$746$	−714.393			−0.957632
$747$	−2.76910			−0.00370696
$748$	40.9093	−	131.485i	0.0546916	−	0.175782i
$749$	−949.577			−1.26779
$750$		0			0
$751$	1343.73			1.78926			0.894628	−	0.446813i	$-0.147441\pi$
$751$	1343.73			1.78926			0.894628	+	0.446813i	$0.147441\pi$
$752$			597.419i			0.794440i
$753$			689.836i			0.916117i
$754$			124.640i			0.165306i
$755$		0			0
$756$			51.3012i			0.0678587i
$757$		−	1034.58i		−	1.36669i	−0.730097	−	0.683343i	$-0.760525\pi$
$757$		−	1034.58i		−	1.36669i	0.730097	−	0.683343i	$-0.239475\pi$
$758$	−1623.57			−2.14192
$759$	179.205	−	575.974i	0.236107	−	0.758859i
$760$		0			0
$761$		−	798.527i		−	1.04931i	−0.851314	−	0.524656i	$-0.824194\pi$
$761$		−	798.527i		−	1.04931i	0.851314	−	0.524656i	$-0.175806\pi$
$762$			114.189i			0.149854i
$763$		−	22.9385i		−	0.0300636i
$764$	67.9399			0.0889266
$765$		0			0
$766$		−	125.307i		−	0.163586i
$767$	−636.234			−0.829510
$768$			445.101i			0.579559i
$769$			261.311i			0.339806i	0.985461	+	0.169903i	$0.0543455\pi$
$769$			261.311i			0.339806i	−0.985461	+	0.169903i	$0.945655\pi$
$770$		0			0
$771$	−585.118			−0.758908
$772$	209.078			0.270826
$773$		−	327.734i		−	0.423977i	−0.977272	−	0.211989i	$-0.932006\pi$
$773$		−	327.734i		−	0.423977i	0.977272	−	0.211989i	$-0.0679940\pi$
$774$	577.692			0.746372
$775$		0			0
$776$		−	123.223i		−	0.158792i
$777$	216.709			0.278905
$778$	1381.19			1.77530
$779$	−1459.46			−1.87351
$780$		0			0
$781$	−237.685	+	763.931i	−0.304334	+	0.978144i
$782$		−	607.146i		−	0.776402i
$783$	35.7995			0.0457210
$784$	151.936			0.193796
$785$		0			0
$786$	461.254			0.586837
$787$	−289.388			−0.367711			−0.183855	−	0.982953i	$-0.558858\pi$
$787$	−289.388			−0.367711			−0.183855	+	0.982953i	$0.558858\pi$
$788$	9.16407			0.0116295
$789$			233.010i			0.295324i
$790$		0			0
$791$			400.570i			0.506409i
$792$	56.8394	−	182.685i	0.0717669	−	0.230662i
$793$		−	579.864i		−	0.731228i
$794$		−	1143.01i		−	1.43956i
$795$		0			0
$796$	359.487			0.451617
$797$		−	113.681i		−	0.142636i	−0.997454	−	0.0713180i	$-0.977279\pi$
$797$		−	113.681i		−	0.142636i	0.997454	−	0.0713180i	$-0.0227205\pi$
$798$	−796.837			−0.998543
$799$		−	246.114i		−	0.308028i
$800$		0			0
$801$	134.469			0.167877
$802$	−391.677			−0.488375
$803$	179.311	−	576.315i	0.223302	−	0.717703i
$804$	−90.4486			−0.112498
$805$		0			0
$806$	925.843			1.14869
$807$			592.137i			0.733751i
$808$		−	303.495i		−	0.375613i
$809$			854.163i			1.05583i	0.849299	+	0.527913i	$0.177025\pi$
$809$			854.163i			1.05583i	−0.849299	+	0.527913i	$0.822975\pi$
$810$		0			0
$811$			486.533i			0.599917i	0.953952	+	0.299959i	$0.0969729\pi$
$811$			486.533i			0.599917i	−0.953952	+	0.299959i	$0.903027\pi$
$812$		−	68.0206i		−	0.0837692i
$813$	−369.443			−0.454419
$814$	481.013	+	149.659i	0.590925	+	0.183857i
$815$		0			0
$816$		−	279.301i		−	0.342281i
$817$			2489.51i			3.04713i
$818$			635.649i			0.777077i
$819$	148.277			0.181046
$820$		0			0
$821$			527.104i			0.642027i	0.947075	+	0.321014i	$0.104024\pi$
$821$			527.104i			0.642027i	−0.947075	+	0.321014i	$0.895976\pi$
$822$	−288.465			−0.350931
$823$		−	314.805i		−	0.382509i	−0.981540	−	0.191255i	$-0.938744\pi$
$823$		−	314.805i		−	0.382509i	0.981540	−	0.191255i	$-0.0612556\pi$
$824$			27.5165i			0.0333938i
$825$		0			0
$826$	1251.48			1.51511
$827$	−111.652			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$827$	−111.652			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$828$			145.881i			0.176185i
$829$	695.395			0.838836			0.419418	−	0.907793i	$-0.362234\pi$
$829$	695.395			0.838836			0.419418	+	0.907793i	$0.362234\pi$
$830$		0			0
$831$		−	146.495i		−	0.176288i
$832$	185.896			0.223433
$833$	−62.5918			−0.0751402
$834$	531.815			0.637668
$835$		0			0
$836$	−490.708	−	152.676i	−0.586971	−	0.182626i
$837$		−	265.923i		−	0.317710i
$838$	839.098			1.00131
$839$	383.968			0.457650			0.228825	−	0.973468i	$-0.426512\pi$
$839$	383.968			0.457650			0.228825	+	0.973468i	$0.426512\pi$
$840$		0			0
$841$	793.533			0.943559
$842$	−1087.58			−1.29166
$843$	−608.205			−0.721477
$844$			257.215i			0.304757i
$845$		0			0
$846$			213.141i			0.251940i
$847$	640.503	+	441.282i	0.756202	+	0.520994i
$848$		−	515.440i		−	0.607830i
$849$		−	495.269i		−	0.583355i
$850$		0			0
$851$	616.238			0.724134
$852$		−	193.486i		−	0.227096i
$853$	570.527			0.668847			0.334424	−	0.942423i	$-0.391458\pi$
$853$	570.527			0.668847			0.334424	+	0.942423i	$0.391458\pi$
$854$			1140.60i			1.33560i
$855$		0			0
$856$	−856.446			−1.00052
$857$	−315.553			−0.368207			−0.184103	−	0.982907i	$-0.558938\pi$
$857$	−315.553			−0.368207			−0.184103	+	0.982907i	$0.558938\pi$
$858$	329.118	+	102.400i	0.383588	+	0.119347i
$859$	107.923			0.125638			0.0628190	−	0.998025i	$-0.479991\pi$
$859$	107.923			0.125638			0.0628190	+	0.998025i	$0.479991\pi$
$860$		0			0
$861$	−534.200			−0.620441
$862$			469.515i			0.544681i
$863$			1431.55i			1.65881i	0.558651	+	0.829403i	$0.311319\pi$
$863$			1431.55i			1.65881i	−0.558651	+	0.829403i	$0.688681\pi$
$864$			121.380i			0.140486i
$865$		0			0
$866$		−	106.747i		−	0.123265i
$867$		−	385.501i		−	0.444638i
$868$	−505.265			−0.582103
$869$	255.524	+	79.5022i	0.294044	+	0.0914870i
$870$		0			0
$871$			261.426i			0.300144i
$872$		−	20.6888i		−	0.0237257i
$873$		−	63.7616i		−	0.0730373i
$874$	−2265.90			−2.59256
$875$		0			0
$876$			145.967i			0.166629i
$877$	567.758			0.647386			0.323693	−	0.946162i	$-0.395075\pi$
$877$	567.758			0.647386			0.323693	+	0.946162i	$0.395075\pi$
$878$		−	1140.26i		−	1.29870i
$879$			682.302i			0.776225i
$880$		0			0
$881$	488.641			0.554644			0.277322	−	0.960777i	$-0.410553\pi$
$881$	488.641			0.554644			0.277322	+	0.960777i	$0.410553\pi$
$882$	54.2061			0.0614581
$883$			840.144i			0.951465i	0.879590	+	0.475732i	$0.157817\pi$
$883$			840.144i			0.951465i	−0.879590	+	0.475732i	$0.842183\pi$
$884$	96.2535			0.108884
$885$		0			0
$886$			883.585i			0.997274i
$887$	981.439			1.10647			0.553235	−	0.833025i	$-0.313393\pi$
$887$	981.439			1.10647			0.553235	+	0.833025i	$0.313393\pi$
$888$	195.455			0.220107
$889$	−180.115			−0.202605
$890$		0			0
$891$	29.4115	−	94.5302i	0.0330096	−	0.106095i
$892$			126.385i			0.141687i
$893$	−918.510			−1.02857
$894$	512.638			0.573421
$895$		0			0
$896$	−966.291			−1.07845
$897$	421.642			0.470059
$898$	907.343			1.01040
$899$			352.589i			0.392202i
$900$		0			0
$901$			212.342i			0.235673i
$902$	−1185.72	−	368.918i	−1.31455	−	0.409000i
$903$			911.223i			1.00911i
$904$			361.283i			0.399650i
$905$		0			0
$906$	1121.67			1.23804
$907$		−	438.610i		−	0.483583i	−0.970328	−	0.241792i	$-0.922265\pi$
$907$		−	438.610i		−	0.483583i	0.970328	−	0.241792i	$-0.0777351\pi$
$908$	62.9716			0.0693520
$909$		−	157.044i		−	0.172765i
$910$		0			0
$911$	−170.042			−0.186654			−0.0933272	−	0.995635i	$-0.529750\pi$
$911$	−170.042			−0.186654			−0.0933272	+	0.995635i	$0.529750\pi$
$912$	−1042.37			−1.14295
$913$	3.01643	−	9.69496i	0.00330386	−	0.0106188i
$914$	−890.243			−0.974008
$915$		0			0
$916$	−246.846			−0.269483
$917$			727.559i			0.793412i
$918$		−	99.6462i		−	0.108547i
$919$		−	1089.73i		−	1.18578i	−0.805285	−	0.592888i	$-0.797988\pi$
$919$		−	1089.73i		−	1.18578i	0.805285	−	0.592888i	$-0.202012\pi$
$920$		0			0
$921$		−	100.847i		−	0.109497i
$922$			528.267i			0.572957i
$923$	−559.236			−0.605890
$924$	−179.611	−	55.8832i	−0.194385	−	0.0604796i
$925$		0			0
$926$		−	123.247i		−	0.133096i
$927$			14.2384i			0.0153597i
$928$		−	160.939i		−	0.173425i
$929$	−769.446			−0.828252			−0.414126	−	0.910220i	$-0.635913\pi$
$929$	−769.446			−0.828252			−0.414126	+	0.910220i	$0.635913\pi$
$930$		0			0
$931$			233.596i			0.250908i
$932$	626.576			0.672291
$933$			359.594i			0.385417i
$934$		−	1207.92i		−	1.29328i
$935$		0			0
$936$	133.734			0.142879
$937$	−1606.78			−1.71481			−0.857406	−	0.514641i	$-0.827925\pi$
$937$	−1606.78			−1.71481			−0.857406	+	0.514641i	$0.827925\pi$
$938$		−	514.228i		−	0.548218i
$939$	652.459			0.694844
$940$		0			0
$941$			1279.34i			1.35955i	0.733419	+	0.679777i	$0.237923\pi$
$941$			1279.34i			1.35955i	−0.733419	+	0.679777i	$0.762077\pi$
$942$	−1113.11			−1.18164
$943$	−1519.06			−1.61088
$944$	1637.10			1.73422
$945$		0			0
$946$	−629.290	+	2022.57i	−0.665211	+	2.13802i
$947$			985.800i			1.04097i	0.853870	+	0.520486i	$0.174249\pi$
$947$			985.800i			1.04097i	−0.853870	+	0.520486i	$0.825751\pi$
$948$	−64.7183			−0.0682682
$949$	421.892			0.444565
$950$		0			0
$951$	427.486			0.449512
$952$	303.753			0.319068
$953$	761.038			0.798571			0.399285	−	0.916827i	$-0.369258\pi$
$953$	761.038			0.798571			0.399285	+	0.916827i	$0.369258\pi$
$954$		−	183.893i		−	0.192760i
$955$		0			0
$956$			310.642i			0.324940i
$957$	−38.9970	+	125.338i	−0.0407492	+	0.130970i
$958$			561.695i			0.586320i
$959$		−	455.011i		−	0.474464i
$960$		0			0
$961$	1658.08			1.72537
$962$			352.126i			0.366035i
$963$	−443.168			−0.460195
$964$		−	41.2892i		−	0.0428311i
$965$		0			0
$966$	−829.377			−0.858568
$967$	−702.938			−0.726926			−0.363463	−	0.931609i	$-0.618406\pi$
$967$	−702.938			−0.726926			−0.363463	+	0.931609i	$0.618406\pi$
$968$	577.685	+	398.003i	0.596782	+	0.411160i
$969$	429.415			0.443153
$970$		0			0
$971$	−1289.42			−1.32793			−0.663963	−	0.747766i	$-0.731127\pi$
$971$	−1289.42			−1.32793			−0.663963	+	0.747766i	$0.731127\pi$
$972$			23.9423i			0.0246320i
$973$			838.859i			0.862136i
$974$		−	1395.83i		−	1.43309i
$975$		0			0
$976$			1492.05i			1.52874i
$977$			690.526i			0.706782i	0.935476	+	0.353391i	$0.114971\pi$
$977$			690.526i			0.706782i	−0.935476	+	0.353391i	$0.885029\pi$
$978$	−252.937			−0.258627
$979$	−146.480	+	470.793i	−0.149622	+	0.480892i
$980$		0			0
$981$		−	10.7054i		−	0.0109128i
$982$		−	2020.94i		−	2.05799i
$983$			1080.40i			1.09908i	0.835467	+	0.549540i	$0.185197\pi$
$983$			1080.40i			1.09908i	−0.835467	+	0.549540i	$0.814803\pi$
$984$	−481.808			−0.489642
$985$		0			0
$986$			132.122i			0.133998i
$987$	−336.198			−0.340626
$988$		−	359.223i		−	0.363586i
$989$			2591.17i			2.61999i
$990$		0			0
$991$	−686.561			−0.692796			−0.346398	−	0.938088i	$-0.612595\pi$
$991$	−686.561			−0.692796			−0.346398	+	0.938088i	$0.612595\pi$
$992$	−1195.47			−1.20511
$993$			253.626i			0.255413i
$994$	1100.03			1.10667
$995$		0			0
$996$			2.45551i			0.00246537i
$997$	−1413.50			−1.41775			−0.708876	−	0.705333i	$-0.750797\pi$
$997$	−1413.50			−1.41775			−0.708876	+	0.705333i	$0.750797\pi$
$998$	1890.97			1.89476
$999$	101.138			0.101240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.3.h.a.274.6		8
5.2	odd	4		33.3.c.a.10.3	yes	4
5.3	odd	4		825.3.b.a.76.2		4
5.4	even	2	inner	825.3.h.a.274.3		8
11.10	odd	2	inner	825.3.h.a.274.4		8
15.2	even	4		99.3.c.b.10.2		4
20.7	even	4		528.3.j.c.241.2		4
40.27	even	4		2112.3.j.d.769.4		4
40.37	odd	4		2112.3.j.a.769.1		4
55.2	even	20		363.3.g.e.40.2		16
55.7	even	20		363.3.g.e.94.3		16
55.17	even	20		363.3.g.e.118.3		16
55.27	odd	20		363.3.g.e.118.2		16
55.32	even	4		33.3.c.a.10.2	✓	4
55.37	odd	20		363.3.g.e.94.2		16
55.42	odd	20		363.3.g.e.40.3		16
55.43	even	4		825.3.b.a.76.3		4
55.47	odd	20		363.3.g.e.112.3		16
55.52	even	20		363.3.g.e.112.2		16
55.54	odd	2	inner	825.3.h.a.274.5		8
60.47	odd	4		1584.3.j.f.1297.4		4
165.32	odd	4		99.3.c.b.10.3		4
220.87	odd	4		528.3.j.c.241.1		4
440.197	even	4		2112.3.j.a.769.2		4
440.307	odd	4		2112.3.j.d.769.3		4
660.527	even	4		1584.3.j.f.1297.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.c.a.10.2	✓	4	55.32	even	4
33.3.c.a.10.3	yes	4	5.2	odd	4
99.3.c.b.10.2		4	15.2	even	4
99.3.c.b.10.3		4	165.32	odd	4
363.3.g.e.40.2		16	55.2	even	20
363.3.g.e.40.3		16	55.42	odd	20
363.3.g.e.94.2		16	55.37	odd	20
363.3.g.e.94.3		16	55.7	even	20
363.3.g.e.112.2		16	55.52	even	20
363.3.g.e.112.3		16	55.47	odd	20
363.3.g.e.118.2		16	55.27	odd	20
363.3.g.e.118.3		16	55.17	even	20
528.3.j.c.241.1		4	220.87	odd	4
528.3.j.c.241.2		4	20.7	even	4
825.3.b.a.76.2		4	5.3	odd	4
825.3.b.a.76.3		4	55.43	even	4
825.3.h.a.274.3		8	5.4	even	2	inner
825.3.h.a.274.4		8	11.10	odd	2	inner
825.3.h.a.274.5		8	55.54	odd	2	inner
825.3.h.a.274.6		8	1.1	even	1	trivial
1584.3.j.f.1297.3		4	660.527	even	4
1584.3.j.f.1297.4		4	60.47	odd	4
2112.3.j.a.769.1		4	40.37	odd	4
2112.3.j.a.769.2		4	440.197	even	4
2112.3.j.d.769.3		4	440.307	odd	4
2112.3.j.d.769.4		4	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	825.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.35285 q^{2} +1.73205i q^{3} +1.53590 q^{4} +4.07525i q^{6} -6.42810 q^{7} -5.79766 q^{8} -3.00000 q^{9} +(3.26795 - 10.5034i) q^{11} +2.66025i q^{12} +7.68899 q^{13} -15.1244 q^{14} -19.7846 q^{16} +8.15051 q^{17} -7.05855 q^{18} -30.4181i q^{19} -11.1338i q^{21} +(7.68899 - 24.7128i) q^{22} -31.6603i q^{23} -10.0418i q^{24} +18.0910 q^{26} -5.19615i q^{27} -9.87291 q^{28} +6.88962i q^{29} +51.1769 q^{31} -23.3596 q^{32} +(18.1923 + 5.66025i) q^{33} +19.1769 q^{34} -4.60770 q^{36} +19.4641i q^{37} -71.5692i q^{38} +13.3177i q^{39} -47.9800i q^{41} -26.1962i q^{42} -81.8429 q^{43} +(5.01924 - 16.1321i) q^{44} -74.4918i q^{46} -30.1962i q^{47} -34.2679i q^{48} -7.67949 q^{49} +14.1171i q^{51} +11.8095 q^{52} +26.0526i q^{53} -12.2258i q^{54} +37.2679 q^{56} +52.6857 q^{57} +16.2102i q^{58} -82.7461 q^{59} -75.4148i q^{61} +120.412 q^{62} +19.2843 q^{63} +24.1769 q^{64} +(42.8038 + 13.3177i) q^{66} +34.0000i q^{67} +12.5184 q^{68} +54.8372 q^{69} -72.7321 q^{71} +17.3930 q^{72} +54.8696 q^{73} +45.7961i q^{74} -46.7191i q^{76} +(-21.0067 + 67.5167i) q^{77} +31.3346i q^{78} +24.3279i q^{79} +9.00000 q^{81} -112.890i q^{82} +0.923034 q^{83} -17.1004i q^{84} -192.564 q^{86} -11.9332 q^{87} +(-18.9465 + 60.8949i) q^{88} -44.8231 q^{89} -49.4256 q^{91} -48.6269i q^{92} +88.6410i q^{93} -71.0470i q^{94} -40.4599i q^{96} +21.2539i q^{97} -18.0687 q^{98} +(-9.80385 + 31.5101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 40 q^{4} - 24 q^{9} + 40 q^{11} - 24 q^{14} + 8 q^{16} + 408 q^{26} + 160 q^{31} - 96 q^{34} - 120 q^{36} + 248 q^{44} - 200 q^{49} + 312 q^{56} - 80 q^{59} - 56 q^{64} + 384 q^{66} + 120 q^{69} - 568 q^{71}+ \cdots - 120 q^{99}+O(q^{100}) \) 8 * q + 40 * q^4 - 24 * q^9 + 40 * q^11 - 24 * q^14 + 8 * q^16 + 408 * q^26 + 160 * q^31 - 96 * q^34 - 120 * q^36 + 248 * q^44 - 200 * q^49 + 312 * q^56 - 80 * q^59 - 56 * q^64 + 384 * q^66 + 120 * q^69 - 568 * q^71 + 72 * q^81 - 432 * q^86 - 608 * q^89 + 48 * q^91 - 120 * q^99

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