LMFDB - Embedded newform 825.3.h.b.274.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [825,3,Mod(274,825)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [32,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$22.4796218097$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.8
Character	$\chi$	$=$	825.274
Dual form			825.3.h.b.274.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.33103 q^{2} -1.73205i q^{3} +1.43371 q^{4} +4.03747i q^{6} -6.32430 q^{7} +5.98210 q^{8} -3.00000 q^{9} +(-10.3943 + 3.59991i) q^{11} -2.48326i q^{12} +17.3965 q^{13} +14.7421 q^{14} -19.6793 q^{16} +12.2603 q^{17} +6.99310 q^{18} +10.6069i q^{19} +10.9540i q^{21} +(24.2294 - 8.39151i) q^{22} -9.16729i q^{23} -10.3613i q^{24} -40.5519 q^{26} +5.19615i q^{27} -9.06722 q^{28} +0.592304i q^{29} +17.1631 q^{31} +21.9447 q^{32} +(6.23523 + 18.0034i) q^{33} -28.5791 q^{34} -4.30114 q^{36} -55.3012i q^{37} -24.7249i q^{38} -30.1317i q^{39} -13.5046i q^{41} -25.5341i q^{42} +36.0017 q^{43} +(-14.9024 + 5.16124i) q^{44} +21.3693i q^{46} +19.2531i q^{47} +34.0856i q^{48} -9.00325 q^{49} -21.2354i q^{51} +24.9416 q^{52} +70.4442i q^{53} -12.1124i q^{54} -37.8326 q^{56} +18.3716 q^{57} -1.38068i q^{58} -14.9479 q^{59} +36.1401i q^{61} -40.0077 q^{62} +18.9729 q^{63} +27.5634 q^{64} +(-14.5345 - 41.9665i) q^{66} -127.842i q^{67} +17.5777 q^{68} -15.8782 q^{69} -27.8440 q^{71} -17.9463 q^{72} +61.3643 q^{73} +128.909i q^{74} +15.2072i q^{76} +(65.7364 - 22.7669i) q^{77} +70.2379i q^{78} -141.550i q^{79} +9.00000 q^{81} +31.4798i q^{82} -137.804 q^{83} +15.7049i q^{84} -83.9212 q^{86} +1.02590 q^{87} +(-62.1795 + 21.5350i) q^{88} -160.353 q^{89} -110.021 q^{91} -13.1433i q^{92} -29.7273i q^{93} -44.8797i q^{94} -38.0094i q^{96} +57.7240i q^{97} +20.9869 q^{98} +(31.1828 - 10.7997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 96 q^{9} - 56 q^{11} - 32 q^{16} - 176 q^{26} - 192 q^{31} + 400 q^{34} - 48 q^{36} - 600 q^{44} + 992 q^{49} - 64 q^{56} + 272 q^{59} - 912 q^{64} - 360 q^{66} - 336 q^{69} + 432 q^{71}+ \cdots + 168 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 96 * q^9 - 56 * q^11 - 32 * q^16 - 176 * q^26 - 192 * q^31 + 400 * q^34 - 48 * q^36 - 600 * q^44 + 992 * q^49 - 64 * q^56 + 272 * q^59 - 912 * q^64 - 360 * q^66 - 336 * q^69 + 432 * q^71 + 288 * q^81 + 384 * q^86 + 672 * q^89 + 512 * q^91 + 168 * 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 $

$2$	−2.33103			−1.16552			−0.582758	−	0.812646i	$-0.698026\pi$
$2$	−2.33103			−1.16552			−0.582758	+	0.812646i	$0.698026\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.43371			0.358428
$5$		0			0
$5$		0			0
$6$			4.03747i			0.672911i
$7$	−6.32430			−0.903471			−0.451736	−	0.892152i	$-0.649195\pi$
$7$	−6.32430			−0.903471			−0.451736	+	0.892152i	$0.649195\pi$
$8$	5.98210			0.747763
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−10.3943	+	3.59991i	−0.944933	+	0.327265i
$11$	−10.3943	+	3.59991i	−0.944933	+	0.327265i
$12$		−	2.48326i		−	0.206938i
$13$	17.3965			1.33820			0.669098	−	0.743175i	$-0.266681\pi$
$13$	17.3965			1.33820			0.669098	+	0.743175i	$0.266681\pi$
$14$	14.7421			1.05301
$15$		0			0
$16$	−19.6793			−1.22996
$17$	12.2603			0.721192			0.360596	−	0.932722i	$-0.382573\pi$
$17$	12.2603			0.721192			0.360596	+	0.932722i	$0.382573\pi$
$18$	6.99310			0.388505
$19$			10.6069i			0.558256i	0.960254	+	0.279128i	$0.0900454\pi$
$19$			10.6069i			0.558256i	−0.960254	+	0.279128i	$0.909955\pi$
$20$		0			0
$21$			10.9540i			0.521619i
$22$	24.2294	−	8.39151i	1.10133	−	0.381432i
$23$		−	9.16729i		−	0.398578i	−0.979941	−	0.199289i	$-0.936137\pi$
$23$		−	9.16729i		−	0.398578i	0.979941	−	0.199289i	$-0.0638632\pi$
$24$		−	10.3613i		−	0.431721i
$25$		0			0
$26$	−40.5519			−1.55969
$27$			5.19615i			0.192450i
$28$	−9.06722			−0.323829
$29$			0.592304i			0.0204243i	0.999948	+	0.0102121i	$0.00325068\pi$
$29$			0.592304i			0.0204243i	−0.999948	+	0.0102121i	$0.996749\pi$
$30$		0			0
$31$	17.1631			0.553648			0.276824	−	0.960921i	$-0.410718\pi$
$31$	17.1631			0.553648			0.276824	+	0.960921i	$0.410718\pi$
$32$	21.9447			0.685773
$33$	6.23523	+	18.0034i	0.188946	+	0.545557i
$34$	−28.5791			−0.840561
$35$		0			0
$36$	−4.30114			−0.119476
$37$		−	55.3012i		−	1.49463i	−0.664472	−	0.747314i	$-0.731343\pi$
$37$		−	55.3012i		−	1.49463i	0.664472	−	0.747314i	$-0.268657\pi$
$38$		−	24.7249i		−	0.650656i
$39$		−	30.1317i		−	0.772607i
$40$		0			0
$41$		−	13.5046i		−	0.329382i	−0.986345	−	0.164691i	$-0.947337\pi$
$41$		−	13.5046i		−	0.329382i	0.986345	−	0.164691i	$-0.0526626\pi$
$42$		−	25.5341i		−	0.607956i
$43$	36.0017			0.837249			0.418625	−	0.908159i	$-0.362512\pi$
$43$	36.0017			0.837249			0.418625	+	0.908159i	$0.362512\pi$
$44$	−14.9024	+	5.16124i	−0.338690	+	0.117301i
$45$		0			0
$46$			21.3693i			0.464549i
$47$			19.2531i			0.409641i	0.978800	+	0.204821i	$0.0656611\pi$
$47$			19.2531i			0.409641i	−0.978800	+	0.204821i	$0.934339\pi$
$48$			34.0856i			0.710116i
$49$	−9.00325			−0.183740
$50$		0			0
$51$		−	21.2354i		−	0.416380i
$52$	24.9416			0.479646
$53$			70.4442i			1.32914i	0.747228	+	0.664568i	$0.231384\pi$
$53$			70.4442i			1.32914i	−0.747228	+	0.664568i	$0.768616\pi$
$54$		−	12.1124i		−	0.224304i
$55$		0			0
$56$	−37.8326			−0.675582
$57$	18.3716			0.322309
$58$		−	1.38068i		−	0.0238048i
$59$	−14.9479			−0.253354			−0.126677	−	0.991944i	$-0.540431\pi$
$59$	−14.9479			−0.253354			−0.126677	+	0.991944i	$0.540431\pi$
$60$		0			0
$61$			36.1401i			0.592461i	0.955116	+	0.296231i	$0.0957297\pi$
$61$			36.1401i			0.592461i	−0.955116	+	0.296231i	$0.904270\pi$
$62$	−40.0077			−0.645285
$63$	18.9729			0.301157
$64$	27.5634			0.430678
$65$		0			0
$66$	−14.5345	−	41.9665i	−0.220220	−	0.635856i
$67$		−	127.842i		−	1.90809i	−0.299660	−	0.954046i	$-0.596873\pi$
$67$		−	127.842i		−	1.90809i	0.299660	−	0.954046i	$-0.403127\pi$
$68$	17.5777			0.258495
$69$	−15.8782			−0.230119
$70$		0			0
$71$	−27.8440			−0.392169			−0.196084	−	0.980587i	$-0.562823\pi$
$71$	−27.8440			−0.392169			−0.196084	+	0.980587i	$0.562823\pi$
$72$	−17.9463			−0.249254
$73$	61.3643			0.840607			0.420304	−	0.907383i	$-0.361924\pi$
$73$	61.3643			0.840607			0.420304	+	0.907383i	$0.361924\pi$
$74$			128.909i			1.74201i
$75$		0			0
$76$			15.2072i			0.200095i
$77$	65.7364	−	22.7669i	0.853719	−	0.295674i
$78$			70.2379i			0.900486i
$79$		−	141.550i		−	1.79177i	−0.444289	−	0.895884i	$-0.646544\pi$
$79$		−	141.550i		−	1.79177i	0.444289	−	0.895884i	$-0.353456\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			31.4798i			0.383900i
$83$	−137.804			−1.66028			−0.830142	−	0.557552i	$-0.811741\pi$
$83$	−137.804			−1.66028			−0.830142	+	0.557552i	$0.811741\pi$
$84$			15.7049i			0.186963i
$85$		0			0
$86$	−83.9212			−0.975828
$87$	1.02590			0.0117920
$88$	−62.1795	+	21.5350i	−0.706585	+	0.244716i
$89$	−160.353			−1.80172			−0.900858	−	0.434113i	$-0.857062\pi$
$89$	−160.353			−1.80172			−0.900858	+	0.434113i	$0.857062\pi$
$90$		0			0
$91$	−110.021			−1.20902
$92$		−	13.1433i		−	0.142861i
$93$		−	29.7273i		−	0.319649i
$94$		−	44.8797i		−	0.477443i
$95$		0			0
$96$		−	38.0094i		−	0.395931i
$97$			57.7240i			0.595092i	0.954707	+	0.297546i	$0.0961682\pi$
$97$			57.7240i			0.595092i	−0.954707	+	0.297546i	$0.903832\pi$
$98$	20.9869			0.214152
$99$	31.1828	−	10.7997i	0.314978	−	0.109088i
$100$		0			0
$101$			147.055i			1.45599i	0.685585	+	0.727993i	$0.259547\pi$
$101$			147.055i			1.45599i	−0.685585	+	0.727993i	$0.740453\pi$
$102$			49.5004i			0.485298i
$103$		−	98.7792i		−	0.959022i	−0.877536	−	0.479511i	$-0.840814\pi$
$103$		−	98.7792i		−	0.959022i	0.877536	−	0.479511i	$-0.159186\pi$
$104$	104.068			1.00065
$105$		0			0
$106$		−	164.208i		−	1.54913i
$107$	−107.953			−1.00891			−0.504453	−	0.863439i	$-0.668306\pi$
$107$	−107.953			−1.00891			−0.504453	+	0.863439i	$0.668306\pi$
$108$			7.44978i			0.0689795i
$109$		−	33.0995i		−	0.303666i	−0.988406	−	0.151833i	$-0.951482\pi$
$109$		−	33.0995i		−	0.303666i	0.988406	−	0.151833i	$-0.0485175\pi$
$110$		0			0
$111$	−95.7845			−0.862923
$112$	124.458			1.11123
$113$		−	163.297i		−	1.44510i	−0.691316	−	0.722552i	$-0.742969\pi$
$113$		−	163.297i		−	1.44510i	0.691316	−	0.722552i	$-0.257031\pi$
$114$	−42.8249			−0.375657
$115$		0			0
$116$			0.849193i			0.00732063i
$117$	−52.1896			−0.446065
$118$	34.8441			0.295289
$119$	−77.5376			−0.651576
$120$		0			0
$121$	95.0813	−	74.8369i	0.785795	−	0.618486i
$122$		−	84.2438i		−	0.690523i
$123$	−23.3907			−0.190169
$124$	24.6069			0.198443
$125$		0			0
$126$	−44.2264			−0.351003
$127$	−204.213			−1.60798			−0.803988	−	0.594645i	$-0.797293\pi$
$127$	−204.213			−1.60798			−0.803988	+	0.594645i	$0.797293\pi$
$128$	−152.030			−1.18774
$129$		−	62.3568i		−	0.483386i
$130$		0			0
$131$		−	243.373i		−	1.85781i	−0.370316	−	0.928906i	$-0.620751\pi$
$131$		−	243.373i		−	1.85781i	0.370316	−	0.928906i	$-0.379249\pi$
$132$	8.93953	+	25.8117i	0.0677237	+	0.195543i
$133$		−	67.0810i		−	0.504368i
$134$			298.004i			2.22391i
$135$		0			0
$136$	73.3421			0.539280
$137$		−	68.3154i		−	0.498652i	−0.968420	−	0.249326i	$-0.919791\pi$
$137$		−	68.3154i		−	0.498652i	0.968420	−	0.249326i	$-0.0802091\pi$
$138$	37.0126			0.268208
$139$			21.5172i			0.154800i	0.997000	+	0.0774001i	$0.0246619\pi$
$139$			21.5172i			0.154800i	−0.997000	+	0.0774001i	$0.975338\pi$
$140$		0			0
$141$	33.3474			0.236506
$142$	64.9052			0.457079
$143$	−180.824	+	62.6260i	−1.26450	+	0.437944i
$144$	59.0380			0.409986
$145$		0			0
$146$	−143.042			−0.979742
$147$			15.5941i			0.106082i
$148$		−	79.2860i		−	0.535716i
$149$		−	45.9449i		−	0.308355i	−0.988043	−	0.154178i	$-0.950727\pi$
$149$		−	45.9449i		−	0.308355i	0.988043	−	0.154178i	$-0.0492728\pi$
$150$		0			0
$151$		−	123.582i		−	0.818425i	−0.912439	−	0.409212i	$-0.865803\pi$
$151$		−	123.582i		−	0.818425i	0.912439	−	0.409212i	$-0.134197\pi$
$152$			63.4513i			0.417443i
$153$	−36.7808			−0.240397
$154$	−153.234	+	53.0704i	−0.995024	+	0.344613i
$155$		0			0
$156$		−	43.2001i		−	0.276924i
$157$		−	65.4047i		−	0.416590i	−0.978066	−	0.208295i	$-0.933209\pi$
$157$		−	65.4047i		−	0.416590i	0.978066	−	0.208295i	$-0.0667914\pi$
$158$			329.957i			2.08833i
$159$	122.013			0.767377
$160$		0			0
$161$			57.9767i			0.360104i
$162$	−20.9793			−0.129502
$163$		−	318.348i		−	1.95305i	−0.215395	−	0.976527i	$-0.569104\pi$
$163$		−	318.348i		−	1.95305i	0.215395	−	0.976527i	$-0.430896\pi$
$164$		−	19.3618i		−	0.118060i
$165$		0			0
$166$	321.225			1.93509
$167$	−17.2478			−0.103280			−0.0516400	−	0.998666i	$-0.516445\pi$
$167$	−17.2478			−0.103280			−0.0516400	+	0.998666i	$0.516445\pi$
$168$			65.5280i			0.390047i
$169$	133.639			0.790766
$170$		0			0
$171$		−	31.8206i		−	0.186085i
$172$	51.6161			0.300094
$173$	−322.103			−1.86187			−0.930933	−	0.365190i	$-0.881004\pi$
$173$	−322.103			−1.86187			−0.930933	+	0.365190i	$0.881004\pi$
$174$	−2.39141			−0.0137437
$175$		0			0
$176$	204.552	−	70.8438i	1.16223	−	0.402522i
$177$			25.8905i			0.146274i
$178$	373.788			2.09993
$179$	−45.5484			−0.254460			−0.127230	−	0.991873i	$-0.540609\pi$
$179$	−45.5484			−0.254460			−0.127230	+	0.991873i	$0.540609\pi$
$180$		0			0
$181$	134.271			0.741830			0.370915	−	0.928667i	$-0.379044\pi$
$181$	134.271			0.741830			0.370915	+	0.928667i	$0.379044\pi$
$182$	256.462			1.40913
$183$	62.5965			0.342058
$184$		−	54.8397i		−	0.298042i
$185$		0			0
$186$			69.2954i			0.372556i
$187$	−127.436	+	44.1359i	−0.681478	+	0.236021i
$188$			27.6034i			0.146827i
$189$		−	32.8620i		−	0.173873i
$190$		0			0
$191$	−68.0366			−0.356212			−0.178106	−	0.984011i	$-0.556997\pi$
$191$	−68.0366			−0.356212			−0.178106	+	0.984011i	$0.556997\pi$
$192$		−	47.7412i		−	0.248652i
$193$	127.465			0.660443			0.330221	−	0.943904i	$-0.392877\pi$
$193$	127.465			0.660443			0.330221	+	0.943904i	$0.392877\pi$
$194$		−	134.556i		−	0.693590i
$195$		0			0
$196$	−12.9081			−0.0658575
$197$	−148.516			−0.753888			−0.376944	−	0.926236i	$-0.623025\pi$
$197$	−148.516			−0.753888			−0.376944	+	0.926236i	$0.623025\pi$
$198$	−72.6881	+	25.1745i	−0.367111	+	0.127144i
$199$	−63.0543			−0.316856			−0.158428	−	0.987371i	$-0.550643\pi$
$199$	−63.0543			−0.316856			−0.158428	+	0.987371i	$0.550643\pi$
$200$		0			0
$201$	−221.429			−1.10164
$202$		−	342.789i		−	1.69697i
$203$		−	3.74591i		−	0.0184527i
$204$		−	30.4454i		−	0.149242i
$205$		0			0
$206$			230.258i			1.11776i
$207$			27.5019i			0.132859i
$208$	−342.352			−1.64592
$209$	−38.1838	−	110.250i	−0.182698	−	0.527514i
$210$		0			0
$211$			228.972i			1.08517i	0.840000	+	0.542587i	$0.182555\pi$
$211$			228.972i			1.08517i	−0.840000	+	0.542587i	$0.817445\pi$
$212$			100.997i			0.476400i
$213$			48.2272i			0.226419i
$214$	251.642			1.17590
$215$		0			0
$216$			31.0839i			0.143907i
$217$	−108.544			−0.500205
$218$			77.1561i			0.353927i
$219$		−	106.286i		−	0.485325i
$220$		0			0
$221$	213.286			0.965096
$222$	223.277			1.00575
$223$		−	101.764i		−	0.456339i	−0.973621	−	0.228169i	$-0.926726\pi$
$223$		−	101.764i		−	0.456339i	0.973621	−	0.228169i	$-0.0732740\pi$
$224$	−138.785			−0.619576
$225$		0			0
$226$			380.650i			1.68429i
$227$	351.517			1.54853			0.774266	−	0.632861i	$-0.218119\pi$
$227$	351.517			1.54853			0.774266	+	0.632861i	$0.218119\pi$
$228$	26.3396			0.115525
$229$	−141.322			−0.617125			−0.308563	−	0.951204i	$-0.599848\pi$
$229$	−141.322			−0.617125			−0.308563	+	0.951204i	$0.599848\pi$
$230$		0			0
$231$	−39.4335	−	113.859i	−0.170708	−	0.492895i
$232$			3.54322i			0.0152725i
$233$	370.243			1.58903			0.794514	−	0.607246i	$-0.207726\pi$
$233$	370.243			1.58903			0.794514	+	0.607246i	$0.207726\pi$
$234$	121.656			0.519896
$235$		0			0
$236$	−21.4310			−0.0908093
$237$	−245.171			−1.03448
$238$	180.743			0.759423
$239$			68.3043i			0.285792i	0.989738	+	0.142896i	$0.0456414\pi$
$239$			68.3043i			0.285792i	−0.989738	+	0.142896i	$0.954359\pi$
$240$		0			0
$241$			200.283i			0.831052i	0.909581	+	0.415526i	$0.136402\pi$
$241$			200.283i			0.831052i	−0.909581	+	0.415526i	$0.863598\pi$
$242$	−221.637	+	174.447i	−0.915857	+	0.720856i
$243$		−	15.5885i		−	0.0641500i
$244$			51.8145i			0.212355i
$245$		0			0
$246$	54.5246			0.221645
$247$			184.523i			0.747055i
$248$	102.671			0.413997
$249$			238.683i			0.958565i
$250$		0			0
$251$	213.104			0.849019			0.424510	−	0.905423i	$-0.360447\pi$
$251$	213.104			0.849019			0.424510	+	0.905423i	$0.360447\pi$
$252$	27.2017			0.107943
$253$	33.0015	+	95.2872i	0.130441	+	0.376629i
$254$	476.027			1.87412
$255$		0			0
$256$	244.133			0.953646
$257$			30.3594i			0.118130i	0.998254	+	0.0590650i	$0.0188119\pi$
$257$			30.3594i			0.118130i	−0.998254	+	0.0590650i	$0.981188\pi$
$258$			145.356i			0.563394i
$259$			349.741i			1.35035i
$260$		0			0
$261$		−	1.77691i		−	0.00680809i
$262$			567.311i			2.16531i
$263$	359.742			1.36784			0.683920	−	0.729557i	$-0.260274\pi$
$263$	359.742			1.36784			0.683920	+	0.729557i	$0.260274\pi$
$264$	37.2998	+	107.698i	0.141287	+	0.407947i
$265$		0			0
$266$			156.368i			0.587849i
$267$			277.739i			1.04022i
$268$		−	183.289i		−	0.683914i
$269$	320.990			1.19327			0.596637	−	0.802512i	$-0.296503\pi$
$269$	320.990			1.19327			0.596637	+	0.802512i	$0.296503\pi$
$270$		0			0
$271$			419.497i			1.54796i	0.633211	+	0.773979i	$0.281736\pi$
$271$			419.497i			1.54796i	−0.633211	+	0.773979i	$0.718264\pi$
$272$	−241.274			−0.887036
$273$			190.562i			0.698028i
$274$			159.245i			0.581187i
$275$		0			0
$276$	−22.7648			−0.0824811
$277$	86.8213			0.313434			0.156717	−	0.987644i	$-0.449909\pi$
$277$	86.8213			0.313434			0.156717	+	0.987644i	$0.449909\pi$
$278$		−	50.1574i		−	0.180422i
$279$	−51.4892			−0.184549
$280$		0			0
$281$		−	300.755i		−	1.07030i	−0.844756	−	0.535152i	$-0.820255\pi$
$281$		−	300.755i		−	1.07030i	0.844756	−	0.535152i	$-0.179745\pi$
$282$	−77.7339			−0.275652
$283$	−319.781			−1.12997			−0.564984	−	0.825102i	$-0.691118\pi$
$283$	−319.781			−1.12997			−0.564984	+	0.825102i	$0.691118\pi$
$284$	−39.9202			−0.140564
$285$		0			0
$286$	421.507	−	145.983i	1.47380	−	0.510431i
$287$			85.4074i			0.297587i
$288$	−65.8342			−0.228591
$289$	−138.686			−0.479882
$290$		0			0
$291$	99.9808			0.343577
$292$	87.9788			0.301297
$293$	421.749			1.43942			0.719709	−	0.694276i	$-0.244275\pi$
$293$	421.749			1.43942			0.719709	+	0.694276i	$0.244275\pi$
$294$		−	36.3503i		−	0.123641i
$295$		0			0
$296$		−	330.817i		−	1.11763i
$297$	−18.7057	−	54.0102i	−0.0629821	−	0.181852i
$298$			107.099i			0.359393i
$299$		−	159.479i		−	0.533375i
$300$		0			0
$301$	−227.686			−0.756431
$302$			288.074i			0.953887i
$303$	254.706			0.840614
$304$		−	208.736i		−	0.686631i
$305$		0			0
$306$	85.7372			0.280187
$307$	65.1772			0.212303			0.106152	−	0.994350i	$-0.466147\pi$
$307$	65.1772			0.212303			0.106152	+	0.994350i	$0.466147\pi$
$308$	94.2470	−	32.6412i	0.305997	−	0.105978i
$309$	−171.091			−0.553691
$310$		0			0
$311$	−296.311			−0.952768			−0.476384	−	0.879237i	$-0.658053\pi$
$311$	−296.311			−0.952768			−0.476384	+	0.879237i	$0.658053\pi$
$312$		−	180.251i		−	0.577727i
$313$		−	430.760i		−	1.37623i	−0.725601	−	0.688115i	$-0.758438\pi$
$313$		−	430.760i		−	1.37623i	0.725601	−	0.688115i	$-0.241562\pi$
$314$			152.460i			0.485543i
$315$		0			0
$316$		−	202.941i		−	0.642219i
$317$			248.606i			0.784246i	0.919913	+	0.392123i	$0.128259\pi$
$317$			248.606i			0.784246i	−0.919913	+	0.392123i	$0.871741\pi$
$318$	−284.416			−0.894391
$319$	−2.13224	−	6.15656i	−0.00668414	−	0.0192996i
$320$		0			0
$321$			186.980i			0.582492i
$322$		−	135.146i		−	0.419707i
$323$			130.043i			0.402610i
$324$	12.9034			0.0398253
$325$		0			0
$326$			742.079i			2.27632i
$327$	−57.3301			−0.175321
$328$		−	80.7862i		−	0.246299i
$329$		−	121.763i		−	0.370099i
$330$		0			0
$331$	−379.595			−1.14681			−0.573406	−	0.819271i	$-0.694378\pi$
$331$	−379.595			−1.14681			−0.573406	+	0.819271i	$0.694378\pi$
$332$	−197.571			−0.595092
$333$			165.904i			0.498209i
$334$	40.2051			0.120375
$335$		0			0
$336$		−	215.567i		−	0.641570i
$337$	528.010			1.56680			0.783398	−	0.621521i	$-0.213485\pi$
$337$	528.010			1.56680			0.783398	+	0.621521i	$0.213485\pi$
$338$	−311.518			−0.921651
$339$	−282.838			−0.834332
$340$		0			0
$341$	−178.398	+	61.7856i	−0.523160	+	0.181189i
$342$			74.1748i			0.216885i
$343$	366.830			1.06947
$344$	215.366			0.626064
$345$		0			0
$346$	750.832			2.17004
$347$	−35.7638			−0.103066			−0.0515328	−	0.998671i	$-0.516411\pi$
$347$	−35.7638			−0.103066			−0.0515328	+	0.998671i	$0.516411\pi$
$348$	1.47084			0.00422657
$349$		−	453.183i		−	1.29852i	−0.760568	−	0.649259i	$-0.775079\pi$
$349$		−	453.183i		−	1.29852i	0.760568	−	0.649259i	$-0.224921\pi$
$350$		0			0
$351$			90.3951i			0.257536i
$352$	−228.099	+	78.9991i	−0.648009	+	0.224429i
$353$		−	76.8798i		−	0.217790i	−0.994053	−	0.108895i	$-0.965269\pi$
$353$		−	76.8798i		−	0.217790i	0.994053	−	0.108895i	$-0.0347312\pi$
$354$		−	60.3517i		−	0.170485i
$355$		0			0
$356$	−229.900			−0.645786
$357$			134.299i			0.376188i
$358$	106.175			0.296577
$359$		−	406.327i		−	1.13183i	−0.824463	−	0.565915i	$-0.808523\pi$
$359$		−	406.327i		−	1.13183i	0.824463	−	0.565915i	$-0.191477\pi$
$360$		0			0
$361$	248.494			0.688350
$362$	−312.991			−0.864615
$363$	−129.621	−	164.686i	−0.357083	−	0.453679i
$364$	−157.738			−0.433347
$365$		0			0
$366$	−145.915			−0.398674
$367$			287.030i			0.782098i	0.920370	+	0.391049i	$0.127888\pi$
$367$			287.030i			0.782098i	−0.920370	+	0.391049i	$0.872112\pi$
$368$			180.406i			0.490234i
$369$			40.5139i			0.109794i
$370$		0			0
$371$		−	445.510i		−	1.20084i
$372$		−	42.6204i		−	0.114571i
$373$	−359.705			−0.964356			−0.482178	−	0.876073i	$-0.660154\pi$
$373$	−359.705			−0.964356			−0.482178	+	0.876073i	$0.660154\pi$
$374$	297.058	−	102.882i	0.794274	−	0.275086i
$375$		0			0
$376$			115.174i			0.306314i
$377$			10.3040i			0.0273316i
$378$			76.6024i			0.202652i
$379$	−94.3980			−0.249071			−0.124536	−	0.992215i	$-0.539744\pi$
$379$	−94.3980			−0.249071			−0.124536	+	0.992215i	$0.539744\pi$
$380$		0			0
$381$			353.707i			0.928366i
$382$	158.595			0.415171
$383$		−	92.3643i		−	0.241160i	−0.992704	−	0.120580i	$-0.961525\pi$
$383$		−	92.3643i		−	0.241160i	0.992704	−	0.120580i	$-0.0384754\pi$
$384$			263.324i			0.685739i
$385$		0			0
$386$	−297.126			−0.769757
$387$	−108.005			−0.279083
$388$			82.7595i			0.213298i
$389$	−126.237			−0.324517			−0.162259	−	0.986748i	$-0.551878\pi$
$389$	−126.237			−0.324517			−0.162259	+	0.986748i	$0.551878\pi$
$390$		0			0
$391$		−	112.393i		−	0.287451i
$392$	−53.8583			−0.137394
$393$	−421.535			−1.07261
$394$	346.195			0.878668
$395$		0			0
$396$	44.7071	−	15.4837i	0.112897	−	0.0391003i
$397$		−	732.111i		−	1.84411i	−0.387060	−	0.922054i	$-0.626509\pi$
$397$		−	732.111i		−	1.84411i	0.387060	−	0.922054i	$-0.373491\pi$
$398$	146.982			0.369300
$399$	−116.188			−0.291197
$400$		0			0
$401$	288.306			0.718966			0.359483	−	0.933152i	$-0.382953\pi$
$401$	288.306			0.718966			0.359483	+	0.933152i	$0.382953\pi$
$402$	516.158			1.28398
$403$	298.578			0.740889
$404$			210.834i			0.521866i
$405$		0			0
$406$			8.73183i			0.0215070i
$407$	199.080	+	574.815i	0.489139	+	1.41232i
$408$		−	127.032i		−	0.311354i
$409$		−	536.385i		−	1.31146i	−0.754997	−	0.655728i	$-0.772362\pi$
$409$		−	536.385i		−	1.31146i	0.754997	−	0.655728i	$-0.227638\pi$
$410$		0			0
$411$	−118.326			−0.287897
$412$		−	141.621i		−	0.343740i
$413$	94.5350			0.228898
$414$		−	64.1078i		−	0.154850i
$415$		0			0
$416$	381.762			0.917697
$417$	37.2689			0.0893739
$418$	89.0076	+	256.997i	0.212937	+	0.614826i
$419$	−772.235			−1.84304			−0.921521	−	0.388328i	$-0.873053\pi$
$419$	−772.235			−1.84304			−0.921521	+	0.388328i	$0.873053\pi$
$420$		0			0
$421$	530.329			1.25969			0.629844	−	0.776721i	$-0.283119\pi$
$421$	530.329			1.25969			0.629844	+	0.776721i	$0.283119\pi$
$422$		−	533.740i		−	1.26479i
$423$		−	57.7594i		−	0.136547i
$424$			421.405i			0.993879i
$425$		0			0
$426$		−	112.419i		−	0.263895i
$427$		−	228.561i		−	0.535272i
$428$	−154.773			−0.361620
$429$	108.471	+	313.197i	0.252847	+	0.730062i
$430$		0			0
$431$		−	98.0885i		−	0.227584i	−0.993505	−	0.113792i	$-0.963700\pi$
$431$		−	98.0885i		−	0.227584i	0.993505	−	0.113792i	$-0.0362997\pi$
$432$		−	102.257i		−	0.236705i
$433$		−	467.819i		−	1.08041i	−0.841533	−	0.540206i	$-0.818346\pi$
$433$		−	467.819i		−	1.08041i	0.841533	−	0.540206i	$-0.181654\pi$
$434$	253.021			0.582997
$435$		0			0
$436$		−	47.4552i		−	0.108842i
$437$	97.2362			0.222509
$438$			247.756i			0.565654i
$439$			732.331i			1.66818i	0.551628	+	0.834090i	$0.314007\pi$
$439$			732.331i			1.66818i	−0.551628	+	0.834090i	$0.685993\pi$
$440$		0			0
$441$	27.0097			0.0612466
$442$	−497.177			−1.12483
$443$			522.885i			1.18033i	0.807284	+	0.590164i	$0.200937\pi$
$443$			522.885i			1.18033i	−0.807284	+	0.590164i	$0.799063\pi$
$444$	−137.327			−0.309296
$445$		0			0
$446$			237.214i			0.531870i
$447$	−79.5790			−0.178029
$448$	−174.319			−0.389105
$449$	−119.788			−0.266788			−0.133394	−	0.991063i	$-0.542588\pi$
$449$	−119.788			−0.266788			−0.133394	+	0.991063i	$0.542588\pi$
$450$		0			0
$451$	48.6156	+	140.371i	0.107795	+	0.311243i
$452$		−	234.121i		−	0.517966i
$453$	−214.051			−0.472518
$454$	−819.397			−1.80484
$455$		0			0
$456$	109.901			0.241011
$457$	4.81549			0.0105372			0.00526859	−	0.999986i	$-0.498323\pi$
$457$	4.81549			0.0105372			0.00526859	+	0.999986i	$0.498323\pi$
$458$	329.425			0.719269
$459$			63.7062i			0.138793i
$460$		0			0
$461$		−	570.680i		−	1.23792i	−0.785424	−	0.618958i	$-0.787555\pi$
$461$		−	570.680i		−	1.23792i	0.785424	−	0.618958i	$-0.212445\pi$
$462$	91.9207	+	265.409i	0.198963	+	0.574477i
$463$			131.935i			0.284956i	0.989798	+	0.142478i	$0.0455071\pi$
$463$			131.935i			0.284956i	−0.989798	+	0.142478i	$0.954493\pi$
$464$		−	11.6561i		−	0.0251210i
$465$		0			0
$466$	−863.050			−1.85204
$467$			89.8728i			0.192447i	0.995360	+	0.0962235i	$0.0306764\pi$
$467$			89.8728i			0.192447i	−0.995360	+	0.0962235i	$0.969324\pi$
$468$	−74.8249			−0.159882
$469$			808.512i			1.72391i
$470$		0			0
$471$	−113.284			−0.240518
$472$	−89.4199			−0.189449
$473$	−374.211	+	129.603i	−0.791144	+	0.274002i
$474$	571.502			1.20570
$475$		0			0
$476$	−111.167			−0.233543
$477$		−	211.333i		−	0.443045i
$478$		−	159.219i		−	0.333095i
$479$		−	717.047i		−	1.49697i	−0.663153	−	0.748484i	$-0.730782\pi$
$479$		−	717.047i		−	1.49697i	0.663153	−	0.748484i	$-0.269218\pi$
$480$		0			0
$481$		−	962.049i		−	2.00010i
$482$		−	466.867i		−	0.968604i
$483$	100.419			0.207906
$484$	136.319	−	107.294i	0.281651	−	0.221683i
$485$		0			0
$486$			36.3372i			0.0747679i
$487$		−	916.798i		−	1.88254i	−0.337653	−	0.941271i	$-0.609633\pi$
$487$		−	916.798i		−	1.88254i	0.337653	−	0.941271i	$-0.390367\pi$
$488$			216.194i			0.443020i
$489$	−551.395			−1.12760
$490$		0			0
$491$		−	302.142i		−	0.615361i	−0.951490	−	0.307680i	$-0.900447\pi$
$491$		−	302.142i		−	0.615361i	0.951490	−	0.307680i	$-0.0995527\pi$
$492$	−33.5356			−0.0681617
$493$			7.26180i			0.0147298i
$494$		−	430.128i		−	0.870705i
$495$		0			0
$496$	−337.758			−0.680963
$497$	176.094			0.354313
$498$		−	556.377i		−	1.11722i
$499$	102.798			0.206008			0.103004	−	0.994681i	$-0.467154\pi$
$499$	102.798			0.206008			0.103004	+	0.994681i	$0.467154\pi$
$500$		0			0
$501$			29.8740i			0.0596287i
$502$	−496.752			−0.989545
$503$	−567.728			−1.12868			−0.564342	−	0.825541i	$-0.690870\pi$
$503$	−567.728			−1.12868			−0.564342	+	0.825541i	$0.690870\pi$
$504$	113.498			0.225194
$505$		0			0
$506$	−76.9275	−	222.118i	−0.152031	−	0.438968i
$507$		−	231.470i		−	0.456549i
$508$	−292.783			−0.576344
$509$	423.197			0.831428			0.415714	−	0.909495i	$-0.363532\pi$
$509$	423.197			0.831428			0.415714	+	0.909495i	$0.363532\pi$
$510$		0			0
$511$	−388.086			−0.759465
$512$	39.0375			0.0762451
$513$	−55.1149			−0.107436
$514$		−	70.7687i		−	0.137682i
$515$		0			0
$516$		−	89.4017i		−	0.173259i
$517$	−69.3096	−	200.122i	−0.134061	−	0.387083i
$518$		−	815.258i		−	1.57386i
$519$			557.898i			1.07495i
$520$		0			0
$521$	−658.340			−1.26361			−0.631805	−	0.775128i	$-0.717685\pi$
$521$	−658.340			−1.26361			−0.631805	+	0.775128i	$0.717685\pi$
$522$			4.14204i			0.00793494i
$523$	−568.723			−1.08743			−0.543713	−	0.839272i	$-0.682982\pi$
$523$	−568.723			−1.08743			−0.543713	+	0.839272i	$0.682982\pi$
$524$		−	348.927i		−	0.665892i
$525$		0			0
$526$	−838.570			−1.59424
$527$	210.424			0.399286
$528$	−122.705	−	354.294i	−0.232396	−	0.671012i
$529$	444.961			0.841136
$530$		0			0
$531$	44.8437			0.0844515
$532$		−	96.1748i		−	0.180780i
$533$		−	234.934i		−	0.440777i
$534$		−	647.419i		−	1.21240i
$535$		0			0
$536$		−	764.765i		−	1.42680i
$537$			78.8921i			0.146913i
$538$	−748.239			−1.39078
$539$	93.5821	−	32.4109i	0.173622	−	0.0601316i
$540$		0			0
$541$			451.918i			0.835339i	0.908599	+	0.417669i	$0.137153\pi$
$541$			451.918i			0.835339i	−0.908599	+	0.417669i	$0.862847\pi$
$542$		−	977.860i		−	1.80417i
$543$		−	232.565i		−	0.428296i
$544$	269.048			0.494574
$545$		0			0
$546$		−	444.206i		−	0.813563i
$547$	149.931			0.274097			0.137048	−	0.990564i	$-0.456238\pi$
$547$	149.931			0.274097			0.137048	+	0.990564i	$0.456238\pi$
$548$		−	97.9446i		−	0.178731i
$549$		−	108.420i		−	0.197487i
$550$		0			0
$551$	−6.28248			−0.0114020
$552$	−94.9851			−0.172074
$553$			895.202i			1.61881i
$554$	−202.383			−0.365313
$555$		0			0
$556$			30.8495i			0.0554847i
$557$	−14.5869			−0.0261883			−0.0130941	−	0.999914i	$-0.504168\pi$
$557$	−14.5869			−0.0261883			−0.0130941	+	0.999914i	$0.504168\pi$
$558$	120.023			0.215095
$559$	626.305			1.12040
$560$		0			0
$561$	76.4456	+	220.726i	0.136267	+	0.393451i
$562$			701.070i			1.24746i
$563$	123.461			0.219291			0.109645	−	0.993971i	$-0.465028\pi$
$563$	123.461			0.219291			0.109645	+	0.993971i	$0.465028\pi$
$564$	47.8106			0.0847705
$565$		0			0
$566$	745.420			1.31700
$567$	−56.9187			−0.100386
$568$	−166.565			−0.293249
$569$			849.647i			1.49323i	0.665257	+	0.746614i	$0.268322\pi$
$569$			849.647i			1.49323i	−0.665257	+	0.746614i	$0.731678\pi$
$570$		0			0
$571$		−	607.460i		−	1.06385i	−0.846791	−	0.531926i	$-0.821468\pi$
$571$		−	607.460i		−	1.06385i	0.846791	−	0.531926i	$-0.178532\pi$
$572$	−259.250	+	89.7876i	−0.453234	+	0.156971i
$573$			117.843i			0.205659i
$574$		−	199.087i		−	0.346842i
$575$		0			0
$576$	−82.6902			−0.143559
$577$			345.393i			0.598602i	0.954159	+	0.299301i	$0.0967535\pi$
$577$			345.393i			0.598602i	−0.954159	+	0.299301i	$0.903246\pi$
$578$	323.281			0.559310
$579$		−	220.777i		−	0.381307i
$580$		0			0
$581$	871.511			1.50002
$582$	−233.059			−0.400444
$583$	−253.593	−	732.216i	−0.434980	−	1.25594i
$584$	367.088			0.628575
$585$		0			0
$586$	−983.111			−1.67766
$587$		−	800.135i		−	1.36309i	−0.731775	−	0.681546i	$-0.761308\pi$
$587$		−	800.135i		−	1.36309i	0.731775	−	0.681546i	$-0.238692\pi$
$588$			22.3574i			0.0380228i
$589$			182.046i			0.309077i
$590$		0			0
$591$			257.237i			0.435257i
$592$			1088.29i			1.83833i
$593$	−157.850			−0.266189			−0.133094	−	0.991103i	$-0.542491\pi$
$593$	−157.850			−0.266189			−0.133094	+	0.991103i	$0.542491\pi$
$594$	43.6036	+	125.899i	0.0734067	+	0.211952i
$595$		0			0
$596$		−	65.8718i		−	0.110523i
$597$			109.213i			0.182937i
$598$			371.751i			0.621657i
$599$	−623.613			−1.04109			−0.520545	−	0.853834i	$-0.674271\pi$
$599$	−623.613			−1.04109			−0.520545	+	0.853834i	$0.674271\pi$
$600$		0			0
$601$			140.001i			0.232947i	0.993194	+	0.116474i	$0.0371591\pi$
$601$			140.001i			0.232947i	−0.993194	+	0.116474i	$0.962841\pi$
$602$	530.743			0.881632
$603$			383.527i			0.636031i
$604$		−	177.181i		−	0.293346i
$605$		0			0
$606$	−593.728			−0.979749
$607$	758.571			1.24971			0.624853	−	0.780743i	$-0.285159\pi$
$607$	758.571			1.24971			0.624853	+	0.780743i	$0.285159\pi$
$608$			232.765i			0.382837i
$609$	−6.48810			−0.0106537
$610$		0			0
$611$			334.938i			0.548180i
$612$	−52.7331			−0.0861651
$613$	487.490			0.795253			0.397627	−	0.917547i	$-0.369834\pi$
$613$	487.490			0.795253			0.397627	+	0.917547i	$0.369834\pi$
$614$	−151.930			−0.247443
$615$		0			0
$616$	393.242	−	136.194i	0.638380	−	0.221094i
$617$			773.785i			1.25411i	0.778975	+	0.627054i	$0.215740\pi$
$617$			773.785i			1.25411i	−0.778975	+	0.627054i	$0.784260\pi$
$618$	398.818			0.645336
$619$	−1182.12			−1.90972			−0.954859	−	0.297059i	$-0.903994\pi$
$619$	−1182.12			−1.90972			−0.954859	+	0.297059i	$0.903994\pi$
$620$		0			0
$621$	47.6347			0.0767064
$622$	690.710			1.11047
$623$	1014.12			1.62780
$624$			592.971i			0.950274i
$625$		0			0
$626$			1004.12i			1.60402i
$627$	−190.959	+	66.1363i	−0.304561	+	0.105480i
$628$		−	93.7714i		−	0.149318i
$629$		−	678.007i		−	1.07791i
$630$		0			0
$631$	−1089.91			−1.72727			−0.863634	−	0.504120i	$-0.831817\pi$
$631$	−1089.91			−1.72727			−0.863634	+	0.504120i	$0.831817\pi$
$632$		−	846.764i		−	1.33982i
$633$	396.590			0.626525
$634$		−	579.509i		−	0.914051i
$635$		0			0
$636$	174.931			0.275049
$637$	−156.625			−0.245880
$638$	4.97032	+	14.3511i	0.00779048	+	0.0224939i
$639$	83.5319			0.130723
$640$		0			0
$641$	−661.586			−1.03212			−0.516058	−	0.856554i	$-0.672601\pi$
$641$	−661.586			−1.03212			−0.516058	+	0.856554i	$0.672601\pi$
$642$		−	435.856i		−	0.678904i
$643$			700.467i			1.08937i	0.838639	+	0.544687i	$0.183352\pi$
$643$			700.467i			1.08937i	−0.838639	+	0.544687i	$0.816648\pi$
$644$			83.1219i			0.129071i
$645$		0			0
$646$		−	303.134i		−	0.469248i
$647$		−	128.968i		−	0.199332i	−0.995021	−	0.0996658i	$-0.968223\pi$
$647$		−	128.968i		−	0.199332i	0.995021	−	0.0996658i	$-0.0317774\pi$
$648$	53.8389			0.0830847
$649$	155.372	−	53.8112i	0.239403	−	0.0829140i
$650$		0			0
$651$			188.005i			0.288793i
$652$		−	456.419i		−	0.700029i
$653$		−	828.659i		−	1.26900i	−0.772921	−	0.634502i	$-0.781205\pi$
$653$		−	828.659i		−	1.26900i	0.772921	−	0.634502i	$-0.218795\pi$
$654$	133.638			0.204340
$655$		0			0
$656$			265.762i			0.405125i
$657$	−184.093			−0.280202
$658$			283.832i			0.431356i
$659$			216.327i			0.328265i	0.986438	+	0.164133i	$0.0524825\pi$
$659$			216.327i			0.328265i	−0.986438	+	0.164133i	$0.947517\pi$
$660$		0			0
$661$	114.149			0.172691			0.0863457	−	0.996265i	$-0.472481\pi$
$661$	114.149			0.172691			0.0863457	+	0.996265i	$0.472481\pi$
$662$	884.848			1.33663
$663$		−	369.422i		−	0.557198i
$664$	−824.355			−1.24150
$665$		0			0
$666$		−	386.727i		−	0.580671i
$667$	5.42982			0.00814066
$668$	−24.7283			−0.0370184
$669$	−176.260			−0.263467
$670$		0			0
$671$	−130.101	−	375.650i	−0.193892	−	0.559836i
$672$			240.383i			0.357712i
$673$	1173.35			1.74346			0.871729	−	0.489989i	$-0.162999\pi$
$673$	1173.35			1.74346			0.871729	+	0.489989i	$0.162999\pi$
$674$	−1230.81			−1.82613
$675$		0			0
$676$	191.600			0.283433
$677$	−145.079			−0.214297			−0.107148	−	0.994243i	$-0.534172\pi$
$677$	−145.079			−0.214297			−0.107148	+	0.994243i	$0.534172\pi$
$678$	659.305			0.972427
$679$		−	365.064i		−	0.537649i
$680$		0			0
$681$		−	608.845i		−	0.894045i
$682$	415.850	−	144.024i	0.609751	−	0.211179i
$683$			542.580i			0.794407i	0.917731	+	0.397204i	$0.130019\pi$
$683$			542.580i			0.794407i	−0.917731	+	0.397204i	$0.869981\pi$
$684$		−	45.6216i		−	0.0666982i
$685$		0			0
$686$	−855.092			−1.24649
$687$			244.776i			0.356297i
$688$	−708.489			−1.02978
$689$			1225.49i			1.77864i
$690$		0			0
$691$	−190.564			−0.275780			−0.137890	−	0.990448i	$-0.544032\pi$
$691$	−190.564			−0.275780			−0.137890	+	0.990448i	$0.544032\pi$
$692$	−461.803			−0.667345
$693$	−197.209	+	68.3008i	−0.284573	+	0.0985581i
$694$	83.3665			0.120125
$695$		0			0
$696$	6.13704			0.00881758
$697$		−	165.571i		−	0.237547i
$698$			1056.38i			1.51344i
$699$		−	641.281i		−	0.917426i
$700$		0			0
$701$			149.736i			0.213603i	0.994280	+	0.106801i	$0.0340609\pi$
$701$			149.736i			0.213603i	−0.994280	+	0.106801i	$0.965939\pi$
$702$		−	210.714i		−	0.300162i
$703$	586.572			0.834385
$704$	−286.501	+	99.2259i	−0.406962	+	0.140946i
$705$		0			0
$706$			179.209i			0.253838i
$707$		−	930.017i		−	1.31544i
$708$			37.1196i			0.0524288i
$709$	225.902			0.318621			0.159310	−	0.987229i	$-0.449073\pi$
$709$	225.902			0.318621			0.159310	+	0.987229i	$0.449073\pi$
$710$		0			0
$711$			424.649i			0.597256i
$712$	−959.247			−1.34726
$713$		−	157.339i		−	0.220672i
$714$		−	313.055i		−	0.438453i
$715$		0			0
$716$	−65.3032			−0.0912056
$717$	118.306			0.165002
$718$			947.162i			1.31917i
$719$	−508.963			−0.707877			−0.353938	−	0.935269i	$-0.615158\pi$
$719$	−508.963			−0.707877			−0.353938	+	0.935269i	$0.615158\pi$
$720$		0			0
$721$			624.709i			0.866448i
$722$	−579.249			−0.802283
$723$	346.901			0.479808
$724$	192.506			0.265893
$725$		0			0
$726$	302.151	+	383.887i	0.416186	+	0.528770i
$727$			155.888i			0.214426i	0.994236	+	0.107213i	$0.0341927\pi$
$727$			155.888i			0.214426i	−0.994236	+	0.107213i	$0.965807\pi$
$728$	−658.156			−0.904061
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	441.391			0.603818
$732$	89.7454			0.122603
$733$	−393.332			−0.536605			−0.268303	−	0.963335i	$-0.586463\pi$
$733$	−393.332			−0.536605			−0.268303	+	0.963335i	$0.586463\pi$
$734$		−	669.076i		−	0.911548i
$735$		0			0
$736$		−	201.174i		−	0.273334i
$737$	460.221	+	1328.82i	0.624451	+	1.80302i
$738$		−	94.4393i		−	0.127967i
$739$		−	224.197i		−	0.303379i	−0.988428	−	0.151689i	$-0.951529\pi$
$739$		−	224.197i		−	0.303379i	0.988428	−	0.151689i	$-0.0484713\pi$
$740$		0			0
$741$	319.603			0.431313
$742$			1038.50i			1.39959i
$743$	115.127			0.154948			0.0774741	−	0.996994i	$-0.475314\pi$
$743$	115.127			0.154948			0.0774741	+	0.996994i	$0.475314\pi$
$744$		−	177.832i		−	0.239021i
$745$		0			0
$746$	838.484			1.12397
$747$	413.411			0.553428
$748$	−182.707	+	63.2781i	−0.244261	+	0.0845964i
$749$	682.727			0.911518
$750$		0			0
$751$	−494.453			−0.658392			−0.329196	−	0.944262i	$-0.606778\pi$
$751$	−494.453			−0.658392			−0.329196	+	0.944262i	$0.606778\pi$
$752$		−	378.888i		−	0.503841i
$753$		−	369.107i		−	0.490181i
$754$		−	24.0190i		−	0.0318555i
$755$		0			0
$756$		−	47.1147i		−	0.0623210i
$757$		−	531.890i		−	0.702629i	−0.936258	−	0.351314i	$-0.885735\pi$
$757$		−	531.890i		−	0.702629i	0.936258	−	0.351314i	$-0.114265\pi$
$758$	220.045			0.290297
$759$	165.042	−	57.1602i	0.217447	−	0.0753099i
$760$		0			0
$761$			1343.41i			1.76532i	0.470013	+	0.882660i	$0.344249\pi$
$761$			1343.41i			1.76532i	−0.470013	+	0.882660i	$0.655751\pi$
$762$		−	824.503i		−	1.08203i
$763$			209.331i			0.274353i
$764$	−97.5448			−0.127676
$765$		0			0
$766$			215.304i			0.281076i
$767$	−260.042			−0.339038
$768$		−	422.851i		−	0.550588i
$769$			735.802i			0.956830i	0.878134	+	0.478415i	$0.158788\pi$
$769$			735.802i			0.956830i	−0.878134	+	0.478415i	$0.841212\pi$
$770$		0			0
$771$	52.5840			0.0682023
$772$	182.749			0.236721
$773$		−	1135.40i		−	1.46882i	−0.678706	−	0.734410i	$-0.737459\pi$
$773$		−	1135.40i		−	1.46882i	0.678706	−	0.734410i	$-0.262541\pi$
$774$	251.764			0.325276
$775$		0			0
$776$			345.311i			0.444988i
$777$	605.770			0.779626
$778$	294.263			0.378230
$779$	143.242			0.183879
$780$		0			0
$781$	289.417	−	100.236i	0.370573	−	0.128343i
$782$			261.993i			0.335029i
$783$	−3.07770			−0.00393065
$784$	177.178			0.225992
$785$		0			0
$786$	982.612			1.25014
$787$	115.155			0.146321			0.0731605	−	0.997320i	$-0.476691\pi$
$787$	115.155			0.146321			0.0731605	+	0.997320i	$0.476691\pi$
$788$	−212.929			−0.270214
$789$		−	623.091i		−	0.789723i
$790$		0			0
$791$			1032.74i			1.30561i
$792$	186.539	−	64.6051i	0.235528	−	0.0815721i
$793$			628.713i			0.792828i
$794$			1706.57i			2.14934i
$795$		0			0
$796$	−90.4017			−0.113570
$797$			1486.27i			1.86483i	0.361387	+	0.932416i	$0.382303\pi$
$797$			1486.27i			1.86483i	−0.361387	+	0.932416i	$0.617697\pi$
$798$	270.837			0.339395
$799$			236.049i			0.295430i
$800$		0			0
$801$	481.058			0.600572
$802$	−672.049			−0.837967
$803$	−637.837	+	220.906i	−0.794317	+	0.275101i
$804$	−317.466			−0.394858
$805$		0			0
$806$	−695.995			−0.863518
$807$		−	555.972i		−	0.688937i
$808$			879.695i			1.08873i
$809$		−	546.514i		−	0.675543i	−0.941228	−	0.337771i	$-0.890327\pi$
$809$		−	546.514i		−	0.675543i	0.941228	−	0.337771i	$-0.109673\pi$
$810$		0			0
$811$			1066.45i			1.31499i	0.753460	+	0.657494i	$0.228383\pi$
$811$			1066.45i			1.31499i	−0.753460	+	0.657494i	$0.771617\pi$
$812$		−	5.37055i		−	0.00661398i
$813$	726.589			0.893714
$814$	−464.061	−	1339.91i	−0.570099	−	1.64608i
$815$		0			0
$816$			417.898i			0.512130i
$817$			381.865i			0.467399i
$818$			1250.33i			1.52852i
$819$	330.063			0.403007
$820$		0			0
$821$		−	1206.66i		−	1.46974i	−0.678207	−	0.734871i	$-0.737243\pi$
$821$		−	1206.66i		−	1.46974i	0.678207	−	0.734871i	$-0.262757\pi$
$822$	275.821			0.335549
$823$			312.518i			0.379730i	0.981810	+	0.189865i	$0.0608050\pi$
$823$			312.518i			0.379730i	−0.981810	+	0.189865i	$0.939195\pi$
$824$		−	590.907i		−	0.717120i
$825$		0			0
$826$	−220.364			−0.266785
$827$	1166.37			1.41036			0.705180	−	0.709029i	$-0.250866\pi$
$827$	1166.37			1.41036			0.705180	+	0.709029i	$0.250866\pi$
$828$			39.4298i			0.0476205i
$829$	205.935			0.248413			0.124207	−	0.992256i	$-0.460361\pi$
$829$	205.935			0.248413			0.124207	+	0.992256i	$0.460361\pi$
$830$		0			0
$831$		−	150.379i		−	0.180961i
$832$	479.508			0.576332
$833$	−110.382			−0.132512
$834$	−86.8751			−0.104167
$835$		0			0
$836$	−54.7445	−	158.067i	−0.0654839	−	0.189076i
$837$			89.1820i			0.106550i
$838$	1800.10			2.14810
$839$	619.889			0.738843			0.369422	−	0.929262i	$-0.379556\pi$
$839$	619.889			0.738843			0.369422	+	0.929262i	$0.379556\pi$
$840$		0			0
$841$	840.649			0.999583
$842$	−1236.21			−1.46819
$843$	−520.923			−0.617940
$844$			328.279i			0.388956i
$845$		0			0
$846$			134.639i			0.159148i
$847$	−601.322	+	473.291i	−0.709944	+	0.558785i
$848$		−	1386.29i		−	1.63478i
$849$			553.877i			0.652387i
$850$		0			0
$851$	−506.962			−0.595725
$852$			69.1439i			0.0811548i
$853$	−1067.19			−1.25110			−0.625549	−	0.780185i	$-0.715125\pi$
$853$	−1067.19			−1.25110			−0.625549	+	0.780185i	$0.715125\pi$
$854$			532.783i			0.623868i
$855$		0			0
$856$	−645.786			−0.754422
$857$	135.288			0.157862			0.0789310	−	0.996880i	$-0.474849\pi$
$857$	135.288			0.157862			0.0789310	+	0.996880i	$0.474849\pi$
$858$	−252.850	−	730.071i	−0.294697	−	0.850899i
$859$	88.1149			0.102578			0.0512892	−	0.998684i	$-0.483667\pi$
$859$	88.1149			0.102578			0.0512892	+	0.998684i	$0.483667\pi$
$860$		0			0
$861$	147.930			0.171812
$862$			228.648i			0.265252i
$863$		−	1506.50i		−	1.74566i	−0.488024	−	0.872830i	$-0.662282\pi$
$863$		−	1506.50i		−	1.74566i	0.488024	−	0.872830i	$-0.337718\pi$
$864$			114.028i			0.131977i
$865$		0			0
$866$			1090.50i			1.25924i
$867$			240.211i			0.277060i
$868$	−155.621			−0.179287
$869$	509.566	+	1471.30i	0.586382	+	1.69310i
$870$		0			0
$871$		−	2224.01i		−	2.55340i
$872$		−	198.005i		−	0.227070i
$873$		−	173.172i		−	0.198364i
$874$	−226.661			−0.259337
$875$		0			0
$876$		−	152.384i		−	0.173954i
$877$	−874.405			−0.997041			−0.498521	−	0.866878i	$-0.666123\pi$
$877$	−874.405			−0.997041			−0.498521	+	0.866878i	$0.666123\pi$
$878$		−	1707.09i		−	1.94429i
$879$		−	730.491i		−	0.831048i
$880$		0			0
$881$	628.003			0.712830			0.356415	−	0.934328i	$-0.383999\pi$
$881$	628.003			0.712830			0.356415	+	0.934328i	$0.383999\pi$
$882$	−62.9606			−0.0713839
$883$			1234.85i			1.39848i	0.714889	+	0.699238i	$0.246477\pi$
$883$			1234.85i			1.39848i	−0.714889	+	0.699238i	$0.753523\pi$
$884$	305.791			0.345917
$885$		0			0
$886$		−	1218.86i		−	1.37569i
$887$	−282.840			−0.318872			−0.159436	−	0.987208i	$-0.550968\pi$
$887$	−282.840			−0.318872			−0.159436	+	0.987208i	$0.550968\pi$
$888$	−572.992			−0.645262
$889$	1291.50			1.45276
$890$		0			0
$891$	−93.5483	+	32.3992i	−0.104993	+	0.0363628i
$892$		−	145.900i		−	0.163565i
$893$	−204.215			−0.228685
$894$	185.501			0.207496
$895$		0			0
$896$	961.484			1.07308
$897$	−276.226			−0.307944
$898$	279.229			0.310946
$899$			10.1658i			0.0113078i
$900$		0			0
$901$			863.665i			0.958563i
$902$	−113.324	−	327.209i	−0.125637	−	0.362759i
$903$			394.363i			0.436725i
$904$		−	976.858i		−	1.08060i
$905$		0			0
$906$	498.959			0.550727
$907$		−	604.942i		−	0.666970i	−0.942755	−	0.333485i	$-0.891775\pi$
$907$		−	604.942i		−	0.666970i	0.942755	−	0.333485i	$-0.108225\pi$
$908$	503.974			0.555037
$909$		−	441.164i		−	0.485329i
$910$		0			0
$911$	339.992			0.373208			0.186604	−	0.982435i	$-0.440252\pi$
$911$	339.992			0.373208			0.186604	+	0.982435i	$0.440252\pi$
$912$	−361.541			−0.396427
$913$	1432.37	−	496.081i	1.56886	−	0.543352i
$914$	−11.2251			−0.0122813
$915$		0			0
$916$	−202.615			−0.221195
$917$			1539.17i			1.67848i
$918$		−	148.501i		−	0.161766i
$919$			885.348i			0.963382i	0.876341	+	0.481691i	$0.159977\pi$
$919$			885.348i			0.963382i	−0.876341	+	0.481691i	$0.840023\pi$
$920$		0			0
$921$		−	112.890i		−	0.122573i
$922$			1330.27i			1.44281i
$923$	−484.389			−0.524798
$924$	−56.5362	−	163.241i	−0.0611864	−	0.176667i
$925$		0			0
$926$		−	307.544i		−	0.332121i
$927$			296.338i			0.319674i
$928$			12.9979i			0.0140064i
$929$	821.063			0.883814			0.441907	−	0.897061i	$-0.354302\pi$
$929$	821.063			0.883814			0.441907	+	0.897061i	$0.354302\pi$
$930$		0			0
$931$		−	95.4962i		−	0.102574i
$932$	530.822			0.569552
$933$			513.225i			0.550081i
$934$		−	209.496i		−	0.224300i
$935$		0			0
$936$	−312.203			−0.333551
$937$	−1507.89			−1.60927			−0.804636	−	0.593768i	$-0.797639\pi$
$937$	−1507.89			−1.60927			−0.804636	+	0.593768i	$0.797639\pi$
$938$		−	1884.67i		−	2.00924i
$939$	−746.099			−0.794567
$940$		0			0
$941$			138.310i			0.146982i	0.997296	+	0.0734909i	$0.0234140\pi$
$941$			138.310i			0.146982i	−0.997296	+	0.0734909i	$0.976586\pi$
$942$	264.069			0.280328
$943$	−123.801			−0.131284
$944$	294.165			0.311615
$945$		0			0
$946$	872.298	−	302.109i	0.922091	−	0.319354i
$947$		−	1559.87i		−	1.64717i	−0.567192	−	0.823586i	$-0.691970\pi$
$947$		−	1559.87i		−	1.64717i	0.567192	−	0.823586i	$-0.308030\pi$
$948$	−351.505			−0.370786
$949$	1067.53			1.12490
$950$		0			0
$951$	430.598			0.452785
$952$	−463.838			−0.487224
$953$	−1073.64			−1.12659			−0.563296	−	0.826255i	$-0.690467\pi$
$953$	−1073.64			−1.12659			−0.563296	+	0.826255i	$0.690467\pi$
$954$			492.623i			0.516377i
$955$		0			0
$956$			97.9286i			0.102436i
$957$	−10.6635	+	3.69315i	−0.0111426	+	0.00385909i
$958$			1671.46i			1.74474i
$959$			432.047i			0.450518i
$960$		0			0
$961$	−666.429			−0.693474
$962$			2242.57i			2.33115i
$963$	323.859			0.336302
$964$			287.149i			0.297872i
$965$		0			0
$966$	−234.079			−0.242318
$967$	1403.40			1.45130			0.725648	−	0.688066i	$-0.241540\pi$
$967$	1403.40			1.45130			0.725648	+	0.688066i	$0.241540\pi$
$968$	568.786	−	447.682i	0.587588	−	0.462481i
$969$	225.241			0.232447
$970$		0			0
$971$	724.260			0.745891			0.372945	−	0.927853i	$-0.378348\pi$
$971$	724.260			0.745891			0.372945	+	0.927853i	$0.378348\pi$
$972$		−	22.3494i		−	0.0229932i
$973$		−	136.081i		−	0.139858i
$974$			2137.09i			2.19413i
$975$		0			0
$976$		−	711.213i		−	0.728702i
$977$		−	943.252i		−	0.965458i	−0.875770	−	0.482729i	$-0.839646\pi$
$977$		−	943.252i		−	0.965458i	0.875770	−	0.482729i	$-0.160354\pi$
$978$	1285.32			1.31423
$979$	1666.75	−	577.256i	1.70250	−	0.589639i
$980$		0			0
$981$			99.2986i			0.101222i
$982$			704.303i			0.717213i
$983$			1101.28i			1.12033i	0.828383	+	0.560163i	$0.189261\pi$
$983$			1101.28i			1.12033i	−0.828383	+	0.560163i	$0.810739\pi$
$984$	−139.926			−0.142201
$985$		0			0
$986$		−	16.9275i		−	0.0171678i
$987$	−210.899			−0.213677
$988$			264.552i			0.267766i
$989$		−	330.038i		−	0.333709i
$990$		0			0
$991$	−639.463			−0.645271			−0.322635	−	0.946523i	$-0.604569\pi$
$991$	−639.463			−0.645271			−0.322635	+	0.946523i	$0.604569\pi$
$992$	376.639			0.379676
$993$			657.478i			0.662112i
$994$	−410.480			−0.412958
$995$		0			0
$996$			342.202i			0.343577i
$997$	351.666			0.352724			0.176362	−	0.984325i	$-0.443567\pi$
$997$	351.666			0.352724			0.176362	+	0.984325i	$0.443567\pi$
$998$	−239.626			−0.240106
$999$	287.353			0.287641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.3.h.b.274.8		32
5.2	odd	4		165.3.b.a.76.4	✓	16
5.3	odd	4		825.3.b.d.76.13		16
5.4	even	2	inner	825.3.h.b.274.26		32
11.10	odd	2	inner	825.3.h.b.274.25		32
15.2	even	4		495.3.b.c.406.13		16
20.7	even	4		2640.3.c.c.241.15		16
55.32	even	4		165.3.b.a.76.13	yes	16
55.43	even	4		825.3.b.d.76.4		16
55.54	odd	2	inner	825.3.h.b.274.7		32
165.32	odd	4		495.3.b.c.406.4		16
220.87	odd	4		2640.3.c.c.241.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.3.b.a.76.4	✓	16	5.2	odd	4
165.3.b.a.76.13	yes	16	55.32	even	4
495.3.b.c.406.4		16	165.32	odd	4
495.3.b.c.406.13		16	15.2	even	4
825.3.b.d.76.4		16	55.43	even	4
825.3.b.d.76.13		16	5.3	odd	4
825.3.h.b.274.7		32	55.54	odd	2	inner
825.3.h.b.274.8		32	1.1	even	1	trivial
825.3.h.b.274.25		32	11.10	odd	2	inner
825.3.h.b.274.26		32	5.4	even	2	inner
2640.3.c.c.241.14		16	220.87	odd	4
2640.3.c.c.241.15		16	20.7	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.33103 q^{2} -1.73205i q^{3} +1.43371 q^{4} +4.03747i q^{6} -6.32430 q^{7} +5.98210 q^{8} -3.00000 q^{9} +(-10.3943 + 3.59991i) q^{11} -2.48326i q^{12} +17.3965 q^{13} +14.7421 q^{14} -19.6793 q^{16} +12.2603 q^{17} +6.99310 q^{18} +10.6069i q^{19} +10.9540i q^{21} +(24.2294 - 8.39151i) q^{22} -9.16729i q^{23} -10.3613i q^{24} -40.5519 q^{26} +5.19615i q^{27} -9.06722 q^{28} +0.592304i q^{29} +17.1631 q^{31} +21.9447 q^{32} +(6.23523 + 18.0034i) q^{33} -28.5791 q^{34} -4.30114 q^{36} -55.3012i q^{37} -24.7249i q^{38} -30.1317i q^{39} -13.5046i q^{41} -25.5341i q^{42} +36.0017 q^{43} +(-14.9024 + 5.16124i) q^{44} +21.3693i q^{46} +19.2531i q^{47} +34.0856i q^{48} -9.00325 q^{49} -21.2354i q^{51} +24.9416 q^{52} +70.4442i q^{53} -12.1124i q^{54} -37.8326 q^{56} +18.3716 q^{57} -1.38068i q^{58} -14.9479 q^{59} +36.1401i q^{61} -40.0077 q^{62} +18.9729 q^{63} +27.5634 q^{64} +(-14.5345 - 41.9665i) q^{66} -127.842i q^{67} +17.5777 q^{68} -15.8782 q^{69} -27.8440 q^{71} -17.9463 q^{72} +61.3643 q^{73} +128.909i q^{74} +15.2072i q^{76} +(65.7364 - 22.7669i) q^{77} +70.2379i q^{78} -141.550i q^{79} +9.00000 q^{81} +31.4798i q^{82} -137.804 q^{83} +15.7049i q^{84} -83.9212 q^{86} +1.02590 q^{87} +(-62.1795 + 21.5350i) q^{88} -160.353 q^{89} -110.021 q^{91} -13.1433i q^{92} -29.7273i q^{93} -44.8797i q^{94} -38.0094i q^{96} +57.7240i q^{97} +20.9869 q^{98} +(31.1828 - 10.7997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 96 q^{9} - 56 q^{11} - 32 q^{16} - 176 q^{26} - 192 q^{31} + 400 q^{34} - 48 q^{36} - 600 q^{44} + 992 q^{49} - 64 q^{56} + 272 q^{59} - 912 q^{64} - 360 q^{66} - 336 q^{69} + 432 q^{71}+ \cdots + 168 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 96 * q^9 - 56 * q^11 - 32 * q^16 - 176 * q^26 - 192 * q^31 + 400 * q^34 - 48 * q^36 - 600 * q^44 + 992 * q^49 - 64 * q^56 + 272 * q^59 - 912 * q^64 - 360 * q^66 - 336 * q^69 + 432 * q^71 + 288 * q^81 + 384 * q^86 + 672 * q^89 + 512 * q^91 + 168 * q^99

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