LMFDB - Embedded newform 275.3.c.h.76.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(76,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.76"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,4,-10] 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:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 21x^{6} + 130x^{4} + 215x^{2} + 25 $ x^8 + 21x^6 + 130x^4 + 215*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.1
Root			$-3.27682i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.h.76.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.27682i q^{2} -1.25169 q^{3} -6.73752 q^{4} +4.10155i q^{6} -3.94258i q^{7} +8.97034i q^{8} -7.43328 q^{9} +(-6.83371 + 8.61977i) q^{11} +8.43328 q^{12} +6.61973i q^{13} -12.9191 q^{14} +2.44407 q^{16} +1.49050i q^{17} +24.3575i q^{18} +18.5757i q^{19} +4.93488i q^{21} +(28.2454 + 22.3928i) q^{22} +18.1115 q^{23} -11.2281i q^{24} +21.6916 q^{26} +20.5693 q^{27} +26.5632i q^{28} -24.3055i q^{29} -16.8211 q^{31} +27.8726i q^{32} +(8.55368 - 10.7893i) q^{33} +4.88410 q^{34} +50.0818 q^{36} -65.2003 q^{37} +60.8692 q^{38} -8.28584i q^{39} +67.5290i q^{41} +16.1707 q^{42} -65.6159i q^{43} +(46.0422 - 58.0759i) q^{44} -59.3480i q^{46} -81.4098 q^{47} -3.05921 q^{48} +33.4561 q^{49} -1.86564i q^{51} -44.6005i q^{52} +16.2112 q^{53} -67.4019i q^{54} +35.3663 q^{56} -23.2510i q^{57} -79.6445 q^{58} -75.7037 q^{59} +4.85215i q^{61} +55.1197i q^{62} +29.3063i q^{63} +101.110 q^{64} +(-35.3544 - 28.0288i) q^{66} -12.1006 q^{67} -10.0423i q^{68} -22.6699 q^{69} -79.6844 q^{71} -66.6790i q^{72} -42.6954i q^{73} +213.649i q^{74} -125.154i q^{76} +(33.9841 + 26.9424i) q^{77} -27.1512 q^{78} +77.6420i q^{79} +41.1531 q^{81} +221.280 q^{82} +37.1521i q^{83} -33.2489i q^{84} -215.011 q^{86} +30.4229i q^{87} +(-77.3223 - 61.3007i) q^{88} -102.707 q^{89} +26.0988 q^{91} -122.026 q^{92} +21.0548 q^{93} +266.765i q^{94} -34.8878i q^{96} -11.4069 q^{97} -109.629i q^{98} +(50.7968 - 64.0731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 10 q^{4} + 32 q^{9} - q^{11} - 24 q^{12} + 18 q^{14} - 14 q^{16} - 35 q^{22} + 4 q^{23} + 68 q^{26} + 142 q^{27} - 42 q^{31} - 31 q^{33} - 142 q^{34} - 84 q^{36} - 104 q^{37} + 190 q^{38}+ \cdots + 368 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 10 * q^4 + 32 * q^9 - q^11 - 24 * q^12 + 18 * q^14 - 14 * q^16 - 35 * q^22 + 4 * q^23 + 68 * q^26 + 142 * q^27 - 42 * q^31 - 31 * q^33 - 142 * q^34 - 84 * q^36 - 104 * q^37 + 190 * q^38 + 50 * q^42 + 69 * q^44 - 64 * q^47 - 86 * q^48 - 50 * q^49 - 286 * q^53 + 166 * q^56 - 130 * q^58 - 160 * q^59 + 288 * q^64 - 315 * q^66 + 46 * q^67 - 16 * q^69 + 246 * q^71 + 80 * q^77 + 620 * q^78 + 304 * q^81 + 280 * q^82 - 282 * q^86 - 365 * q^88 - 18 * q^89 - 142 * q^91 + 26 * q^92 + 818 * q^93 - 264 * q^97 + 368 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		−	3.27682i		−	1.63841i	−0.573503	−	0.819204i	$-0.694416\pi$
$2$		−	3.27682i		−	1.63841i	0.573503	−	0.819204i	$-0.305584\pi$
$3$	−1.25169			−0.417230			−0.208615	−	0.977998i	$-0.566895\pi$
$3$	−1.25169			−0.417230			−0.208615	+	0.977998i	$0.566895\pi$
$4$	−6.73752			−1.68438
$5$		0			0
$5$		0			0
$6$			4.10155i			0.683592i
$7$		−	3.94258i		−	0.563226i	−0.959528	−	0.281613i	$-0.909131\pi$
$7$		−	3.94258i		−	0.563226i	0.959528	−	0.281613i	$-0.0908694\pi$
$8$			8.97034i			1.12129i
$9$	−7.43328			−0.825919
$10$		0			0
$11$	−6.83371	+	8.61977i	−0.621246	+	0.783616i
$11$	−6.83371	+	8.61977i	−0.621246	+	0.783616i
$12$	8.43328			0.702773
$13$			6.61973i			0.509210i	0.967045	+	0.254605i	$0.0819454\pi$
$13$			6.61973i			0.509210i	−0.967045	+	0.254605i	$0.918055\pi$
$14$	−12.9191			−0.922793
$15$		0			0
$16$	2.44407			0.152754
$17$			1.49050i			0.0876766i	0.999039	+	0.0438383i	$0.0139586\pi$
$17$			1.49050i			0.0876766i	−0.999039	+	0.0438383i	$0.986041\pi$
$18$			24.3575i			1.35319i
$19$			18.5757i			0.977669i	0.872377	+	0.488835i	$0.162578\pi$
$19$			18.5757i			0.977669i	−0.872377	+	0.488835i	$0.837422\pi$
$20$		0			0
$21$			4.93488i			0.234994i
$22$	28.2454	+	22.3928i	1.28388	+	1.01785i
$23$	18.1115			0.787456			0.393728	−	0.919227i	$-0.371185\pi$
$23$	18.1115			0.787456			0.393728	+	0.919227i	$0.371185\pi$
$24$		−	11.2281i		−	0.467836i
$25$		0			0
$26$	21.6916			0.834293
$27$	20.5693			0.761828
$28$			26.5632i			0.948686i
$29$		−	24.3055i		−	0.838119i	−0.907959	−	0.419060i	$-0.862360\pi$
$29$		−	24.3055i		−	0.838119i	0.907959	−	0.419060i	$-0.137640\pi$
$30$		0			0
$31$	−16.8211			−0.542617			−0.271309	−	0.962492i	$-0.587456\pi$
$31$	−16.8211			−0.542617			−0.271309	+	0.962492i	$0.587456\pi$
$32$			27.8726i			0.871018i
$33$	8.55368	−	10.7893i	0.259202	−	0.326948i
$34$	4.88410			0.143650
$35$		0			0
$36$	50.0818			1.39116
$37$	−65.2003			−1.76217			−0.881086	−	0.472957i	$-0.843187\pi$
$37$	−65.2003			−1.76217			−0.881086	+	0.472957i	$0.843187\pi$
$38$	60.8692			1.60182
$39$		−	8.28584i		−	0.212457i
$40$		0			0
$41$			67.5290i			1.64705i	0.567282	+	0.823524i	$0.307995\pi$
$41$			67.5290i			1.64705i	−0.567282	+	0.823524i	$0.692005\pi$
$42$	16.1707			0.385017
$43$		−	65.6159i		−	1.52595i	−0.646427	−	0.762976i	$-0.723737\pi$
$43$		−	65.6159i		−	1.52595i	0.646427	−	0.762976i	$-0.276263\pi$
$44$	46.0422	−	58.0759i	1.04641	−	1.31991i
$45$		0			0
$46$		−	59.3480i		−	1.29017i
$47$	−81.4098			−1.73212			−0.866062	−	0.499937i	$-0.833356\pi$
$47$	−81.4098			−1.73212			−0.866062	+	0.499937i	$0.833356\pi$
$48$	−3.05921			−0.0637336
$49$	33.4561			0.682777
$50$		0			0
$51$		−	1.86564i		−	0.0365813i
$52$		−	44.6005i		−	0.857703i
$53$	16.2112			0.305872			0.152936	−	0.988236i	$-0.451127\pi$
$53$	16.2112			0.305872			0.152936	+	0.988236i	$0.451127\pi$
$54$		−	67.4019i		−	1.24818i
$55$		0			0
$56$	35.3663			0.631540
$57$		−	23.2510i		−	0.407912i
$58$	−79.6445			−1.37318
$59$	−75.7037			−1.28311			−0.641557	−	0.767075i	$-0.721711\pi$
$59$	−75.7037			−1.28311			−0.641557	+	0.767075i	$0.721711\pi$
$60$		0			0
$61$			4.85215i			0.0795434i	0.999209	+	0.0397717i	$0.0126631\pi$
$61$			4.85215i			0.0795434i	−0.999209	+	0.0397717i	$0.987337\pi$
$62$			55.1197i			0.889028i
$63$			29.3063i			0.465179i
$64$	101.110			1.57984
$65$		0			0
$66$	−35.3544	−	28.0288i	−0.535673	−	0.424679i
$67$	−12.1006			−0.180606			−0.0903029	−	0.995914i	$-0.528784\pi$
$67$	−12.1006			−0.180606			−0.0903029	+	0.995914i	$0.528784\pi$
$68$		−	10.0423i		−	0.147681i
$69$	−22.6699			−0.328550
$70$		0			0
$71$	−79.6844			−1.12232			−0.561158	−	0.827709i	$-0.689644\pi$
$71$	−79.6844			−1.12232			−0.561158	+	0.827709i	$0.689644\pi$
$72$		−	66.6790i		−	0.926097i
$73$		−	42.6954i		−	0.584869i	−0.956286	−	0.292434i	$-0.905535\pi$
$73$		−	42.6954i		−	0.584869i	0.956286	−	0.292434i	$-0.0944653\pi$
$74$			213.649i			2.88715i
$75$		0			0
$76$		−	125.154i		−	1.64677i
$77$	33.9841	+	26.9424i	0.441352	+	0.349902i
$78$	−27.1512			−0.348092
$79$			77.6420i			0.982810i	0.870931	+	0.491405i	$0.163516\pi$
$79$			77.6420i			0.982810i	−0.870931	+	0.491405i	$0.836484\pi$
$80$		0			0
$81$	41.1531			0.508062
$82$	221.280			2.69854
$83$			37.1521i			0.447616i	0.974633	+	0.223808i	$0.0718488\pi$
$83$			37.1521i			0.447616i	−0.974633	+	0.223808i	$0.928151\pi$
$84$		−	33.2489i		−	0.395820i
$85$		0			0
$86$	−215.011			−2.50013
$87$			30.4229i			0.349688i
$88$	−77.3223	−	61.3007i	−0.878662	−	0.696598i
$89$	−102.707			−1.15401			−0.577006	−	0.816740i	$-0.695779\pi$
$89$	−102.707			−1.15401			−0.577006	+	0.816740i	$0.695779\pi$
$90$		0			0
$91$	26.0988			0.286800
$92$	−122.026			−1.32637
$93$	21.0548			0.226396
$94$			266.765i			2.83792i
$95$		0			0
$96$		−	34.8878i		−	0.363415i
$97$	−11.4069			−0.117597			−0.0587985	−	0.998270i	$-0.518727\pi$
$97$	−11.4069			−0.117597			−0.0587985	+	0.998270i	$0.518727\pi$
$98$		−	109.629i		−	1.11867i
$99$	50.7968	−	64.0731i	0.513099	−	0.647203i
$100$		0			0
$101$			156.659i			1.55108i	0.631301	+	0.775538i	$0.282521\pi$
$101$			156.659i			1.55108i	−0.631301	+	0.775538i	$0.717479\pi$
$102$	−6.11337			−0.0599350
$103$	−105.744			−1.02664			−0.513322	−	0.858196i	$-0.671585\pi$
$103$	−105.744			−1.02664			−0.513322	+	0.858196i	$0.671585\pi$
$104$	−59.3812			−0.570973
$105$		0			0
$106$		−	53.1212i		−	0.501143i
$107$		−	192.014i		−	1.79453i	−0.441497	−	0.897263i	$-0.645552\pi$
$107$		−	192.014i		−	1.79453i	0.441497	−	0.897263i	$-0.354448\pi$
$108$	−138.586			−1.28321
$109$		−	162.478i		−	1.49062i	−0.666716	−	0.745312i	$-0.732301\pi$
$109$		−	162.478i		−	1.49062i	0.666716	−	0.745312i	$-0.267699\pi$
$110$		0			0
$111$	81.6105			0.735230
$112$		−	9.63594i		−	0.0860351i
$113$	−75.5761			−0.668815			−0.334408	−	0.942429i	$-0.608536\pi$
$113$	−75.5761			−0.668815			−0.334408	+	0.942429i	$0.608536\pi$
$114$	−76.1893			−0.668327
$115$		0			0
$116$			163.758i			1.41171i
$117$		−	49.2063i		−	0.420566i
$118$			248.067i			2.10226i
$119$	5.87642			0.0493817
$120$		0			0
$121$	−27.6009	−	117.810i	−0.228107	−	0.973636i
$122$	15.8996			0.130325
$123$		−	84.5252i		−	0.687197i
$124$	113.333			0.913973
$125$		0			0
$126$	96.0312			0.762153
$127$		−	125.050i		−	0.984647i	−0.870412	−	0.492323i	$-0.836148\pi$
$127$		−	125.050i		−	0.984647i	0.870412	−	0.492323i	$-0.163852\pi$
$128$		−	219.827i		−	1.71740i
$129$			82.1307i			0.636672i
$130$		0			0
$131$		−	10.1412i		−	0.0774136i	−0.999251	−	0.0387068i	$-0.987676\pi$
$131$		−	10.1412i		−	0.0774136i	0.999251	−	0.0387068i	$-0.0123238\pi$
$132$	−57.6305	+	72.6929i	−0.436595	+	0.550704i
$133$	73.2362			0.550648
$134$			39.6514i			0.295906i
$135$		0			0
$136$	−13.3703			−0.0983111
$137$	−70.4327			−0.514107			−0.257054	−	0.966397i	$-0.582752\pi$
$137$	−70.4327			−0.514107			−0.257054	+	0.966397i	$0.582752\pi$
$138$			74.2852i			0.538299i
$139$		−	203.327i		−	1.46279i	−0.681957	−	0.731393i	$-0.738871\pi$
$139$		−	203.327i		−	1.46279i	0.681957	−	0.731393i	$-0.261129\pi$
$140$		0			0
$141$	101.900			0.722693
$142$			261.111i			1.83881i
$143$	−57.0605	−	45.2373i	−0.399025	−	0.316345i
$144$	−18.1674			−0.126163
$145$		0			0
$146$	−139.905			−0.958253
$147$	−41.8766			−0.284875
$148$	439.288			2.96816
$149$			98.2512i			0.659404i	0.944085	+	0.329702i	$0.106948\pi$
$149$			98.2512i			0.659404i	−0.944085	+	0.329702i	$0.893052\pi$
$150$		0			0
$151$			2.04381i			0.0135351i	0.999977	+	0.00676757i	$0.00215420\pi$
$151$			2.04381i			0.0135351i	−0.999977	+	0.00676757i	$0.997846\pi$
$152$	−166.630			−1.09625
$153$		−	11.0793i		−	0.0724138i
$154$	88.2854	−	111.360i	0.573282	−	0.723115i
$155$		0			0
$156$			55.8260i			0.357859i
$157$	160.316			1.02112			0.510561	−	0.859841i	$-0.329438\pi$
$157$	160.316			1.02112			0.510561	+	0.859841i	$0.329438\pi$
$158$	254.418			1.61024
$159$	−20.2914			−0.127619
$160$		0			0
$161$		−	71.4060i		−	0.443515i
$162$		−	134.851i		−	0.832413i
$163$	−59.3198			−0.363925			−0.181962	−	0.983305i	$-0.558245\pi$
$163$	−59.3198			−0.363925			−0.181962	+	0.983305i	$0.558245\pi$
$164$		−	454.977i		−	2.77425i
$165$		0			0
$166$	121.741			0.733377
$167$			149.432i			0.894800i	0.894334	+	0.447400i	$0.147650\pi$
$167$			149.432i			0.894800i	−0.894334	+	0.447400i	$0.852350\pi$
$168$	−44.2676			−0.263497
$169$	125.179			0.740705
$170$		0			0
$171$		−	138.078i		−	0.807476i
$172$			442.089i			2.57028i
$173$			71.7530i			0.414757i	0.978261	+	0.207379i	$0.0664932\pi$
$173$			71.7530i			0.414757i	−0.978261	+	0.207379i	$0.933507\pi$
$174$	99.6901			0.572932
$175$		0			0
$176$	−16.7021	+	21.0673i	−0.0948980	+	0.119701i
$177$	94.7575			0.535353
$178$			336.552i			1.89074i
$179$	143.137			0.799647			0.399824	−	0.916592i	$-0.369071\pi$
$179$	143.137			0.799647			0.399824	+	0.916592i	$0.369071\pi$
$180$		0			0
$181$	305.844			1.68974			0.844872	−	0.534968i	$-0.179676\pi$
$181$	305.844			1.68974			0.844872	+	0.534968i	$0.179676\pi$
$182$		−	85.5210i		−	0.469895i
$183$		−	6.07338i		−	0.0331879i
$184$			162.466i			0.882968i
$185$		0			0
$186$		−	68.9928i		−	0.370929i
$187$	−12.8478	−	10.1857i	−0.0687047	−	0.0544687i
$188$	548.500			2.91755
$189$		−	81.0963i		−	0.429081i
$190$		0			0
$191$	−1.64065			−0.00858982			−0.00429491	−	0.999991i	$-0.501367\pi$
$191$	−1.64065			−0.00858982			−0.00429491	+	0.999991i	$0.501367\pi$
$192$	−126.558			−0.659155
$193$			287.478i			1.48952i	0.667330	+	0.744762i	$0.267437\pi$
$193$			287.478i			1.48952i	−0.667330	+	0.744762i	$0.732563\pi$
$194$			37.3784i			0.192672i
$195$		0			0
$196$	−225.411			−1.15006
$197$			109.774i			0.557227i	0.960403	+	0.278614i	$0.0898749\pi$
$197$			109.774i			0.557227i	−0.960403	+	0.278614i	$0.910125\pi$
$198$	−209.956	−	166.452i	−1.06038	−	0.840666i
$199$	38.8559			0.195256			0.0976279	−	0.995223i	$-0.468874\pi$
$199$	38.8559			0.195256			0.0976279	+	0.995223i	$0.468874\pi$
$200$		0			0
$201$	15.1462			0.0753541
$202$	513.341			2.54129
$203$	−95.8262			−0.472050
$204$			12.5698i			0.0616167i
$205$		0			0
$206$			346.504i			1.68206i
$207$	−134.628			−0.650375
$208$			16.1791i			0.0777840i
$209$	−160.118	−	126.941i	−0.766117	−	0.607373i
$210$		0			0
$211$		−	89.4659i		−	0.424009i	−0.977269	−	0.212005i	$-0.932001\pi$
$211$		−	89.4659i		−	0.424009i	0.977269	−	0.212005i	$-0.0679992\pi$
$212$	−109.223			−0.515205
$213$	99.7400			0.468263
$214$	−629.195			−2.94016
$215$		0			0
$216$			184.514i			0.854231i
$217$			66.3186i			0.305616i
$218$	−532.410			−2.44225
$219$			53.4414i			0.244025i
$220$		0			0
$221$	−9.86672			−0.0446458
$222$		−	267.423i		−	1.20461i
$223$	189.941			0.851752			0.425876	−	0.904782i	$-0.359966\pi$
$223$	189.941			0.851752			0.425876	+	0.904782i	$0.359966\pi$
$224$	109.890			0.490580
$225$		0			0
$226$			247.649i			1.09579i
$227$		−	344.741i		−	1.51868i	−0.650691	−	0.759342i	$-0.725521\pi$
$227$		−	344.741i		−	1.51868i	0.650691	−	0.759342i	$-0.274479\pi$
$228$			156.654i			0.687079i
$229$	−114.108			−0.498288			−0.249144	−	0.968466i	$-0.580149\pi$
$229$	−114.108			−0.498288			−0.249144	+	0.968466i	$0.580149\pi$
$230$		0			0
$231$	−42.5376	−	33.7235i	−0.184145	−	0.145989i
$232$	218.028			0.939777
$233$			16.9887i			0.0729129i	0.999335	+	0.0364565i	$0.0116070\pi$
$233$			16.9887i			0.0729129i	−0.999335	+	0.0364565i	$0.988393\pi$
$234$	−161.240			−0.689059
$235$		0			0
$236$	510.055			2.16125
$237$		−	97.1836i		−	0.410057i
$238$		−	19.2559i		−	0.0809074i
$239$			212.744i			0.890144i	0.895495	+	0.445072i	$0.146822\pi$
$239$			212.744i			0.890144i	−0.895495	+	0.445072i	$0.853178\pi$
$240$		0			0
$241$			362.416i			1.50380i	0.659277	+	0.751900i	$0.270862\pi$
$241$			362.416i			1.50380i	−0.659277	+	0.751900i	$0.729138\pi$
$242$	−386.042	+	90.4430i	−1.59521	+	0.373731i
$243$	−236.635			−0.973806
$244$		−	32.6914i		−	0.133981i
$245$		0			0
$246$	−276.974			−1.12591
$247$	−122.966			−0.497839
$248$		−	150.891i		−	0.608432i
$249$		−	46.5029i		−	0.186759i
$250$		0			0
$251$	50.5799			0.201514			0.100757	−	0.994911i	$-0.467874\pi$
$251$	50.5799			0.201514			0.100757	+	0.994911i	$0.467874\pi$
$252$		−	197.452i		−	0.783538i
$253$	−123.769	+	156.117i	−0.489204	+	0.617063i
$254$	−409.766			−1.61325
$255$		0			0
$256$	−315.894			−1.23396
$257$	429.305			1.67045			0.835224	−	0.549910i	$-0.185338\pi$
$257$	429.305			1.67045			0.835224	+	0.549910i	$0.185338\pi$
$258$	269.127			1.04313
$259$			257.058i			0.992500i
$260$		0			0
$261$			180.669i			0.692219i
$262$	−33.2308			−0.126835
$263$		−	157.886i		−	0.600329i	−0.953888	−	0.300164i	$-0.902958\pi$
$263$		−	157.886i		−	0.600329i	0.953888	−	0.300164i	$-0.0970415\pi$
$264$	96.7834	+	76.7294i	0.366604	+	0.290641i
$265$		0			0
$266$		−	239.982i		−	0.902186i
$267$	128.557			0.481488
$268$	81.5280			0.304209
$269$	−213.381			−0.793237			−0.396618	−	0.917984i	$-0.629816\pi$
$269$	−213.381			−0.793237			−0.396618	+	0.917984i	$0.629816\pi$
$270$		0			0
$271$		−	466.412i		−	1.72108i	−0.509384	−	0.860540i	$-0.670127\pi$
$271$		−	466.412i		−	1.72108i	0.509384	−	0.860540i	$-0.329873\pi$
$272$			3.64289i			0.0133930i
$273$	−32.6676			−0.119661
$274$			230.795i			0.842317i
$275$		0			0
$276$	152.739			0.553403
$277$			66.3436i			0.239508i	0.992804	+	0.119754i	$0.0382105\pi$
$277$			66.3436i			0.239508i	−0.992804	+	0.119754i	$0.961789\pi$
$278$	−666.265			−2.39664
$279$	125.036			0.448158
$280$		0			0
$281$		−	240.196i		−	0.854791i	−0.904065	−	0.427396i	$-0.859431\pi$
$281$		−	240.196i		−	0.854791i	0.904065	−	0.427396i	$-0.140569\pi$
$282$		−	333.907i		−	1.18407i
$283$		−	270.527i		−	0.955924i	−0.878380	−	0.477962i	$-0.841376\pi$
$283$		−	270.527i		−	0.955924i	0.878380	−	0.477962i	$-0.158624\pi$
$284$	536.875			1.89040
$285$		0			0
$286$	−148.234	+	186.977i	−0.518301	+	0.653765i
$287$	266.238			0.927659
$288$		−	207.185i		−	0.719391i
$289$	286.778			0.992313
$290$		0			0
$291$	14.2779			0.0490650
$292$			287.661i			0.985141i
$293$			543.407i			1.85463i	0.374282	+	0.927315i	$0.377889\pi$
$293$			543.407i			1.85463i	−0.374282	+	0.927315i	$0.622111\pi$
$294$			137.222i			0.466741i
$295$		0			0
$296$		−	584.869i		−	1.97591i
$297$	−140.565	+	177.303i	−0.473282	+	0.596980i
$298$	321.951			1.08037
$299$			119.893i			0.400980i
$300$		0			0
$301$	−258.696			−0.859455
$302$	6.69718			0.0221761
$303$		−	196.088i		−	0.647154i
$304$			45.4003i			0.149343i
$305$		0			0
$306$	−36.3049			−0.118643
$307$			314.156i			1.02331i	0.859191	+	0.511654i	$0.170967\pi$
$307$			314.156i			1.02331i	−0.859191	+	0.511654i	$0.829033\pi$
$308$	−228.969	−	181.525i	−0.743405	−	0.589367i
$309$	132.359			0.428346
$310$		0			0
$311$	−374.834			−1.20525			−0.602627	−	0.798023i	$-0.705879\pi$
$311$	−374.834			−1.20525			−0.602627	+	0.798023i	$0.705879\pi$
$312$	74.3268			0.238227
$313$	206.435			0.659538			0.329769	−	0.944062i	$-0.393029\pi$
$313$	206.435			0.659538			0.329769	+	0.944062i	$0.393029\pi$
$314$		−	525.327i		−	1.67301i
$315$		0			0
$316$		−	523.114i		−	1.65542i
$317$	−273.867			−0.863935			−0.431968	−	0.901889i	$-0.642181\pi$
$317$	−273.867			−0.863935			−0.431968	+	0.901889i	$0.642181\pi$
$318$			66.4912i			0.209092i
$319$	209.508	+	166.096i	0.656763	+	0.520678i
$320$		0			0
$321$			240.342i			0.748729i
$322$	−233.984			−0.726659
$323$	−27.6871			−0.0857187
$324$	−277.269			−0.855770
$325$		0			0
$326$			194.380i			0.596257i
$327$			203.372i			0.621932i
$328$	−605.758			−1.84682
$329$			320.965i			0.975576i
$330$		0			0
$331$	−441.950			−1.33520			−0.667598	−	0.744522i	$-0.732677\pi$
$331$	−441.950			−1.33520			−0.667598	+	0.744522i	$0.732677\pi$
$332$		−	250.313i		−	0.753955i
$333$	484.652			1.45541
$334$	489.660			1.46605
$335$		0			0
$336$			12.0612i			0.0358964i
$337$			130.963i			0.388613i	0.980941	+	0.194307i	$0.0622457\pi$
$337$			130.963i			0.388613i	−0.980941	+	0.194307i	$0.937754\pi$
$338$		−	410.189i		−	1.21358i
$339$	94.5978			0.279049
$340$		0			0
$341$	114.951	−	144.994i	0.337099	−	0.425203i
$342$	−452.457			−1.32297
$343$		−	325.090i		−	0.947783i
$344$	588.597			1.71104
$345$		0			0
$346$	235.121			0.679541
$347$			188.943i			0.544503i	0.962226	+	0.272251i	$0.0877683\pi$
$347$			188.943i			0.544503i	−0.962226	+	0.272251i	$0.912232\pi$
$348$		−	204.975i		−	0.589008i
$349$		−	500.080i		−	1.43289i	−0.697642	−	0.716446i	$-0.745767\pi$
$349$		−	500.080i		−	1.43289i	0.697642	−	0.716446i	$-0.254233\pi$
$350$		0			0
$351$			136.163i			0.387930i
$352$	−240.255	−	190.473i	−0.682544	−	0.541117i
$353$	414.398			1.17393			0.586966	−	0.809611i	$-0.300322\pi$
$353$	414.398			1.17393			0.586966	+	0.809611i	$0.300322\pi$
$354$		−	310.503i		−	0.877127i
$355$		0			0
$356$	691.991			1.94379
$357$	−7.35545			−0.0206035
$358$		−	469.033i		−	1.31015i
$359$			212.272i			0.591288i	0.955298	+	0.295644i	$0.0955342\pi$
$359$			212.272i			0.591288i	−0.955298	+	0.295644i	$0.904466\pi$
$360$		0			0
$361$	15.9429			0.0441633
$362$		−	1002.19i		−	2.76849i
$363$	34.5477	+	147.461i	0.0951728	+	0.406230i
$364$	−175.841			−0.483080
$365$		0			0
$366$	−19.9013			−0.0543753
$367$	−460.146			−1.25380			−0.626902	−	0.779098i	$-0.715677\pi$
$367$	−460.146			−1.25380			−0.626902	+	0.779098i	$0.715677\pi$
$368$	44.2657			0.120287
$369$		−	501.961i		−	1.36033i
$370$		0			0
$371$		−	63.9141i		−	0.172275i
$372$	−141.857			−0.381337
$373$		−	483.099i		−	1.29517i	−0.761992	−	0.647586i	$-0.775779\pi$
$373$		−	483.099i		−	1.29517i	0.761992	−	0.647586i	$-0.224221\pi$
$374$	−33.3765	+	42.0998i	−0.0892420	+	0.112566i
$375$		0			0
$376$		−	730.273i		−	1.94222i
$377$	160.896			0.426779
$378$	−265.738			−0.703009
$379$	262.073			0.691486			0.345743	−	0.938329i	$-0.387627\pi$
$379$	262.073			0.691486			0.345743	+	0.938329i	$0.387627\pi$
$380$		0			0
$381$			156.524i			0.410824i
$382$			5.37612i			0.0140736i
$383$	−326.405			−0.852233			−0.426116	−	0.904668i	$-0.640119\pi$
$383$	−326.405			−0.852233			−0.426116	+	0.904668i	$0.640119\pi$
$384$			275.155i			0.716550i
$385$		0			0
$386$	942.013			2.44045
$387$			487.741i			1.26031i
$388$	76.8543			0.198078
$389$	−647.719			−1.66509			−0.832544	−	0.553960i	$-0.813116\pi$
$389$	−647.719			−1.66509			−0.832544	+	0.553960i	$0.813116\pi$
$390$		0			0
$391$			26.9952i			0.0690414i
$392$			300.112i			0.765592i
$393$			12.6936i			0.0322992i
$394$	359.708			0.912965
$395$		0			0
$396$	−342.244	+	431.694i	−0.864254	+	1.09014i
$397$	−122.651			−0.308946			−0.154473	−	0.987997i	$-0.549368\pi$
$397$	−122.651			−0.308946			−0.154473	+	0.987997i	$0.549368\pi$
$398$		−	127.324i		−	0.319909i
$399$	−91.6690			−0.229747
$400$		0			0
$401$	−243.279			−0.606680			−0.303340	−	0.952882i	$-0.598102\pi$
$401$	−243.279			−0.606680			−0.303340	+	0.952882i	$0.598102\pi$
$402$		−	49.6312i		−	0.123461i
$403$		−	111.351i		−	0.276306i
$404$		−	1055.49i		−	2.61260i
$405$		0			0
$406$			314.005i			0.773411i
$407$	445.560	−	562.012i	1.09474	−	1.38086i
$408$	16.7355			0.0410183
$409$			424.434i			1.03774i	0.854854	+	0.518868i	$0.173647\pi$
$409$			424.434i			1.03774i	−0.854854	+	0.518868i	$0.826353\pi$
$410$		0			0
$411$	88.1598			0.214501
$412$	712.454			1.72926
$413$			298.468i			0.722683i
$414$			441.150i			1.06558i
$415$		0			0
$416$	−184.509			−0.443531
$417$			254.502i			0.610317i
$418$	−415.962	+	524.678i	−0.995125	+	1.25521i
$419$	−68.6588			−0.163864			−0.0819318	−	0.996638i	$-0.526109\pi$
$419$	−68.6588			−0.163864			−0.0819318	+	0.996638i	$0.526109\pi$
$420$		0			0
$421$	−78.1961			−0.185739			−0.0928694	−	0.995678i	$-0.529604\pi$
$421$	−78.1961			−0.185739			−0.0928694	+	0.995678i	$0.529604\pi$
$422$	−293.163			−0.694700
$423$	605.141			1.43059
$424$			145.420i			0.342972i
$425$		0			0
$426$		−	326.830i		−	0.767206i
$427$	19.1300			0.0448009
$428$			1293.70i			3.02266i
$429$	71.4220	+	56.6230i	0.166485	+	0.131988i
$430$		0			0
$431$			592.143i			1.37388i	0.726714	+	0.686940i	$0.241047\pi$
$431$			592.143i			1.37388i	−0.726714	+	0.686940i	$0.758953\pi$
$432$	50.2729			0.116372
$433$	92.7053			0.214100			0.107050	−	0.994254i	$-0.465860\pi$
$433$	92.7053			0.214100			0.107050	+	0.994254i	$0.465860\pi$
$434$	217.314			0.500723
$435$		0			0
$436$			1094.70i			2.51078i
$437$			336.434i			0.769871i
$438$	175.118			0.399812
$439$			745.450i			1.69806i	0.528342	+	0.849031i	$0.322814\pi$
$439$			745.450i			1.69806i	−0.528342	+	0.849031i	$0.677186\pi$
$440$		0			0
$441$	−248.688			−0.563919
$442$			32.3314i			0.0731480i
$443$	−583.895			−1.31805			−0.659023	−	0.752123i	$-0.729030\pi$
$443$	−583.895			−1.31805			−0.659023	+	0.752123i	$0.729030\pi$
$444$	−549.852			−1.23841
$445$		0			0
$446$		−	622.401i		−	1.39552i
$447$		−	122.980i		−	0.275123i
$448$		−	398.633i		−	0.889805i
$449$	−344.083			−0.766332			−0.383166	−	0.923679i	$-0.625166\pi$
$449$	−344.083			−0.766332			−0.383166	+	0.923679i	$0.625166\pi$
$450$		0			0
$451$	−582.084	−	461.473i	−1.29065	−	1.02322i
$452$	509.195			1.12654
$453$		−	2.55821i		−	0.00564726i
$454$	−1129.65			−2.48822
$455$		0			0
$456$	208.569			0.457389
$457$			409.596i			0.896272i	0.893965	+	0.448136i	$0.147912\pi$
$457$			409.596i			0.896272i	−0.893965	+	0.448136i	$0.852088\pi$
$458$			373.910i			0.816398i
$459$			30.6587i			0.0667945i
$460$		0			0
$461$			599.882i			1.30126i	0.759394	+	0.650632i	$0.225496\pi$
$461$			599.882i			1.30126i	−0.759394	+	0.650632i	$0.774504\pi$
$462$	−110.506	+	139.388i	−0.239190	+	0.301705i
$463$	−497.936			−1.07546			−0.537728	−	0.843119i	$-0.680717\pi$
$463$	−497.936			−1.07546			−0.537728	+	0.843119i	$0.680717\pi$
$464$		−	59.4042i		−	0.128026i
$465$		0			0
$466$	55.6689			0.119461
$467$	440.806			0.943909			0.471955	−	0.881623i	$-0.343549\pi$
$467$	440.806			0.943909			0.471955	+	0.881623i	$0.343549\pi$
$468$			331.528i			0.708393i
$469$			47.7076i			0.101722i
$470$		0			0
$471$	−200.666			−0.426043
$472$		−	679.088i		−	1.43875i
$473$	565.594	+	448.400i	1.19576	+	0.947992i
$474$	−318.453			−0.671841
$475$		0			0
$476$	−39.5925			−0.0831775
$477$	−120.503			−0.252626
$478$	697.124			1.45842
$479$		−	521.375i		−	1.08847i	−0.838934	−	0.544233i	$-0.816821\pi$
$479$		−	521.375i		−	1.08847i	0.838934	−	0.544233i	$-0.183179\pi$
$480$		0			0
$481$		−	431.609i		−	0.897315i
$482$	1187.57			2.46384
$483$			89.3780i			0.185048i
$484$	185.961	+	793.747i	0.384218	+	1.63997i
$485$		0			0
$486$			775.409i			1.59549i
$487$	−158.630			−0.325728			−0.162864	−	0.986648i	$-0.552073\pi$
$487$	−158.630			−0.325728			−0.162864	+	0.986648i	$0.552073\pi$
$488$	−43.5254			−0.0891914
$489$	74.2499			0.151840
$490$		0			0
$491$		−	558.903i		−	1.13829i	−0.822236	−	0.569147i	$-0.807273\pi$
$491$		−	558.903i		−	1.13829i	0.822236	−	0.569147i	$-0.192727\pi$
$492$			569.490i			1.15750i
$493$	36.2273			0.0734834
$494$			402.937i			0.815663i
$495$		0			0
$496$	−41.1120			−0.0828871
$497$			314.162i			0.632117i
$498$	−152.381			−0.305987
$499$	−297.691			−0.596575			−0.298288	−	0.954476i	$-0.596415\pi$
$499$	−297.691			−0.596575			−0.298288	+	0.954476i	$0.596415\pi$
$500$		0			0
$501$		−	187.042i		−	0.373337i
$502$		−	165.741i		−	0.330161i
$503$			169.632i			0.337241i	0.985681	+	0.168620i	$0.0539312\pi$
$503$			169.632i			0.337241i	−0.985681	+	0.168620i	$0.946069\pi$
$504$	−262.887			−0.521602
$505$		0			0
$506$	511.566	+	405.567i	1.01100	+	0.801515i
$507$	−156.685			−0.309044
$508$			842.527i			1.65852i
$509$	473.225			0.929715			0.464858	−	0.885385i	$-0.346106\pi$
$509$	473.225			0.929715			0.464858	+	0.885385i	$0.346106\pi$
$510$		0			0
$511$	−168.330			−0.329413
$512$			155.819i			0.304334i
$513$			382.090i			0.744815i
$514$		−	1406.75i		−	2.73687i
$515$		0			0
$516$		−	553.357i		−	1.07240i
$517$	556.331	−	701.734i	1.07607	−	1.35732i
$518$	842.330			1.62612
$519$		−	89.8124i		−	0.173049i
$520$		0			0
$521$	974.599			1.87063			0.935316	−	0.353813i	$-0.115115\pi$
$521$	974.599			1.87063			0.935316	+	0.353813i	$0.115115\pi$
$522$	592.020			1.13414
$523$		−	628.934i		−	1.20255i	−0.799042	−	0.601275i	$-0.794660\pi$
$523$		−	628.934i		−	1.20255i	0.799042	−	0.601275i	$-0.205340\pi$
$524$			68.3264i			0.130394i
$525$		0			0
$526$	−517.365			−0.983583
$527$		−	25.0719i		−	0.0475748i
$528$	20.9058	−	26.3697i	0.0395943	−	0.0499427i
$529$	−200.974			−0.379913
$530$		0			0
$531$	562.727			1.05975
$532$	−493.430			−0.927500
$533$	−447.023			−0.838693
$534$		−	421.259i		−	0.788874i
$535$		0			0
$536$		−	108.546i		−	0.202512i
$537$	−179.163			−0.333637
$538$			699.209i			1.29964i
$539$	−228.629	+	288.384i	−0.424173	+	0.535035i
$540$		0			0
$541$			5.72311i			0.0105788i	0.999986	+	0.00528938i	$0.00168367\pi$
$541$			5.72311i			0.0105788i	−0.999986	+	0.00528938i	$0.998316\pi$
$542$	−1528.35			−2.81983
$543$	−382.821			−0.705011
$544$	−41.5441			−0.0763679
$545$		0			0
$546$			107.046i			0.196054i
$547$			167.284i			0.305820i	0.988240	+	0.152910i	$0.0488645\pi$
$547$			167.284i			0.305820i	−0.988240	+	0.152910i	$0.951136\pi$
$548$	474.541			0.865952
$549$		−	36.0674i		−	0.0656965i
$550$		0			0
$551$	451.491			0.819403
$552$		−	203.357i		−	0.368400i
$553$	306.110			0.553544
$554$	217.396			0.392411
$555$		0			0
$556$			1369.92i			2.46389i
$557$		−	458.071i		−	0.822390i	−0.911548	−	0.411195i	$-0.865112\pi$
$557$		−	458.071i		−	0.822390i	0.911548	−	0.411195i	$-0.134888\pi$
$558$		−	409.720i		−	0.734265i
$559$	434.360			0.777030
$560$		0			0
$561$	16.0814	+	12.7493i	0.0286656	+	0.0227260i
$562$	−787.079			−1.40050
$563$		−	570.622i		−	1.01354i	−0.862082	−	0.506769i	$-0.830840\pi$
$563$		−	570.622i		−	1.01354i	0.862082	−	0.506769i	$-0.169160\pi$
$564$	−686.551			−1.21729
$565$		0			0
$566$	−886.465			−1.56619
$567$		−	162.249i		−	0.286154i
$568$		−	714.796i		−	1.25844i
$569$		−	399.293i		−	0.701745i	−0.936423	−	0.350873i	$-0.885885\pi$
$569$		−	399.293i		−	0.701745i	0.936423	−	0.350873i	$-0.114115\pi$
$570$		0			0
$571$			1048.75i			1.83668i	0.395790	+	0.918341i	$0.370471\pi$
$571$			1048.75i			1.83668i	−0.395790	+	0.918341i	$0.629529\pi$
$572$	384.446	+	304.787i	0.672109	+	0.532844i
$573$	2.05359			0.00358393
$574$		−	872.414i		−	1.51988i
$575$		0			0
$576$	−751.575			−1.30482
$577$	−65.8975			−0.114207			−0.0571036	−	0.998368i	$-0.518187\pi$
$577$	−65.8975			−0.114207			−0.0571036	+	0.998368i	$0.518187\pi$
$578$		−	939.720i		−	1.62581i
$579$		−	359.833i		−	0.621474i
$580$		0			0
$581$	146.475			0.252109
$582$		−	46.7861i		−	0.0803884i
$583$	−110.783	+	139.737i	−0.190022	+	0.239686i
$584$	382.992			0.655809
$585$		0			0
$586$	1780.64			3.03864
$587$	−971.299			−1.65468			−0.827342	−	0.561699i	$-0.810148\pi$
$587$	−971.299			−1.65468			−0.827342	+	0.561699i	$0.810148\pi$
$588$	282.144			0.479837
$589$		−	312.464i		−	0.530500i
$590$		0			0
$591$		−	137.403i		−	0.232492i
$592$	−159.354			−0.269179
$593$			381.457i			0.643266i	0.946864	+	0.321633i	$0.104232\pi$
$593$			381.457i			0.643266i	−0.946864	+	0.321633i	$0.895768\pi$
$594$	580.989	+	460.605i	0.978096	+	0.775430i
$595$		0			0
$596$		−	661.969i		−	1.11069i
$597$	−48.6355			−0.0814665
$598$	392.868			0.656969
$599$	372.420			0.621737			0.310869	−	0.950453i	$-0.399380\pi$
$599$	372.420			0.621737			0.310869	+	0.950453i	$0.399380\pi$
$600$		0			0
$601$		−	941.497i		−	1.56655i	−0.621674	−	0.783276i	$-0.713547\pi$
$601$		−	941.497i		−	1.56655i	0.621674	−	0.783276i	$-0.286453\pi$
$602$			847.699i			1.40814i
$603$	89.9471			0.149166
$604$		−	13.7702i		−	0.0227983i
$605$		0			0
$606$	−642.543			−1.06030
$607$		−	803.140i		−	1.32313i	−0.749888	−	0.661565i	$-0.769893\pi$
$607$		−	803.140i		−	1.32313i	0.749888	−	0.661565i	$-0.230107\pi$
$608$	−517.753			−0.851568
$609$	119.945			0.196953
$610$		0			0
$611$		−	538.911i		−	0.882014i
$612$			74.6471i			0.121972i
$613$		−	438.888i		−	0.715968i	−0.933728	−	0.357984i	$-0.883464\pi$
$613$		−	438.888i		−	0.715968i	0.933728	−	0.357984i	$-0.116536\pi$
$614$	1029.43			1.67660
$615$		0			0
$616$	−241.683	+	304.849i	−0.392342	+	0.494885i
$617$	1053.80			1.70795			0.853973	−	0.520317i	$-0.174186\pi$
$617$	1053.80			1.70795			0.853973	+	0.520317i	$0.174186\pi$
$618$		−	433.716i		−	0.701805i
$619$	113.476			0.183322			0.0916608	−	0.995790i	$-0.470782\pi$
$619$	113.476			0.183322			0.0916608	+	0.995790i	$0.470782\pi$
$620$		0			0
$621$	372.541			0.599906
$622$			1228.26i			1.97470i
$623$			404.931i			0.649969i
$624$		−	20.2512i		−	0.0324538i
$625$		0			0
$626$		−	676.451i		−	1.08059i
$627$	200.418	+	158.891i	0.319647	+	0.253414i
$628$	−1080.13			−1.71996
$629$		−	97.1812i		−	0.154501i
$630$		0			0
$631$	405.042			0.641905			0.320952	−	0.947095i	$-0.395997\pi$
$631$	405.042			0.641905			0.320952	+	0.947095i	$0.395997\pi$
$632$	−696.475			−1.10202
$633$			111.984i			0.176909i
$634$			897.413i			1.41548i
$635$		0			0
$636$	136.714			0.214959
$637$			221.470i			0.347677i
$638$	544.267	−	686.517i	0.853083	−	1.07605i
$639$	592.316			0.926942
$640$		0			0
$641$	−836.111			−1.30439			−0.652193	−	0.758053i	$-0.726151\pi$
$641$	−836.111			−1.30439			−0.652193	+	0.758053i	$0.726151\pi$
$642$	787.557			1.22672
$643$	−466.764			−0.725917			−0.362958	−	0.931805i	$-0.618233\pi$
$643$	−466.764			−0.725917			−0.362958	+	0.931805i	$0.618233\pi$
$644$			481.099i			0.747048i
$645$		0			0
$646$			90.7256i			0.140442i
$647$	−400.219			−0.618577			−0.309289	−	0.950968i	$-0.600091\pi$
$647$	−400.219			−0.618577			−0.309289	+	0.950968i	$0.600091\pi$
$648$			369.157i			0.569686i
$649$	517.337	−	652.549i	0.797130	−	1.00547i
$650$		0			0
$651$		−	83.0103i		−	0.127512i
$652$	399.668			0.612988
$653$	105.848			0.162096			0.0810478	−	0.996710i	$-0.474173\pi$
$653$	105.848			0.162096			0.0810478	+	0.996710i	$0.474173\pi$
$654$	666.412			1.01898
$655$		0			0
$656$			165.045i			0.251594i
$657$			317.367i			0.483055i
$658$	1051.74			1.59839
$659$			491.956i			0.746519i	0.927727	+	0.373260i	$0.121760\pi$
$659$			491.956i			0.746519i	−0.927727	+	0.373260i	$0.878240\pi$
$660$		0			0
$661$	407.084			0.615861			0.307931	−	0.951409i	$-0.400364\pi$
$661$	407.084			0.615861			0.307931	+	0.951409i	$0.400364\pi$
$662$			1448.19i			2.18759i
$663$	12.3501			0.0186275
$664$	−333.267			−0.501908
$665$		0			0
$666$		−	1588.12i		−	2.38456i
$667$		−	440.208i		−	0.659982i
$668$		−	1006.80i		−	1.50718i
$669$	−237.747			−0.355376
$670$		0			0
$671$	−41.8244	−	33.1582i	−0.0623315	−	0.0494160i
$672$	−137.548			−0.204684
$673$			908.695i			1.35022i	0.737719	+	0.675108i	$0.235903\pi$
$673$			908.695i			1.35022i	−0.737719	+	0.675108i	$0.764097\pi$
$674$	429.140			0.636707
$675$		0			0
$676$	−843.397			−1.24763
$677$		−	1064.55i		−	1.57245i	−0.617941	−	0.786224i	$-0.712033\pi$
$677$		−	1064.55i		−	1.57245i	0.617941	−	0.786224i	$-0.287967\pi$
$678$		−	309.979i		−	0.457197i
$679$			44.9727i			0.0662337i
$680$		0			0
$681$			431.509i			0.633640i
$682$	−475.119	−	376.672i	−0.696656	−	0.552305i
$683$	332.676			0.487081			0.243540	−	0.969891i	$-0.421691\pi$
$683$	332.676			0.487081			0.243540	+	0.969891i	$0.421691\pi$
$684$			930.305i			1.36010i
$685$		0			0
$686$	−1065.26			−1.55285
$687$	142.828			0.207900
$688$		−	160.370i		−	0.233096i
$689$			107.314i			0.155753i
$690$		0			0
$691$	880.234			1.27385			0.636927	−	0.770924i	$-0.280205\pi$
$691$	880.234			1.27385			0.636927	+	0.770924i	$0.280205\pi$
$692$		−	483.437i		−	0.698608i
$693$	−252.613	−	200.271i	−0.364521	−	0.288991i
$694$	619.130			0.892118
$695$		0			0
$696$	−272.903			−0.392103
$697$	−100.652			−0.144408
$698$	−1638.67			−2.34766
$699$		−	21.2646i		−	0.0304214i
$700$		0			0
$701$			743.435i			1.06054i	0.847830	+	0.530268i	$0.177909\pi$
$701$			743.435i			1.06054i	−0.847830	+	0.530268i	$0.822091\pi$
$702$	446.183			0.635588
$703$		−	1211.14i		−	1.72282i
$704$	−690.953	+	871.542i	−0.981468	+	1.23799i
$705$		0			0
$706$		−	1357.91i		−	1.92338i
$707$	617.639			0.873605
$708$	−638.430			−0.901738
$709$	−459.136			−0.647583			−0.323791	−	0.946128i	$-0.604958\pi$
$709$	−459.136			−0.647583			−0.323791	+	0.946128i	$0.604958\pi$
$710$		0			0
$711$		−	577.134i		−	0.811722i
$712$		−	921.317i		−	1.29399i
$713$	−304.656			−0.427287
$714$			24.1025i			0.0337569i
$715$		0			0
$716$	−964.387			−1.34691
$717$		−	266.290i		−	0.371394i
$718$	695.578			0.968771
$719$	−571.747			−0.795197			−0.397599	−	0.917559i	$-0.630156\pi$
$719$	−571.747			−0.795197			−0.397599	+	0.917559i	$0.630156\pi$
$720$		0			0
$721$			416.905i			0.578232i
$722$		−	52.2421i		−	0.0723574i
$723$		−	453.632i		−	0.627430i
$724$	−2060.63			−2.84617
$725$		0			0
$726$	483.204	−	113.207i	0.665570	−	0.155932i
$727$	−188.665			−0.259511			−0.129756	−	0.991546i	$-0.541419\pi$
$727$	−188.665			−0.259511			−0.129756	+	0.991546i	$0.541419\pi$
$728$			234.115i			0.321587i
$729$	−74.1842			−0.101762
$730$		0			0
$731$	97.8007			0.133790
$732$			40.9195i			0.0559010i
$733$			542.416i			0.739994i	0.929033	+	0.369997i	$0.120641\pi$
$733$			542.416i			0.739994i	−0.929033	+	0.369997i	$0.879359\pi$
$734$			1507.81i			2.05424i
$735$		0			0
$736$			504.814i			0.685888i
$737$	82.6919	−	104.304i	0.112201	−	0.141526i
$738$	−1644.83			−2.22877
$739$		−	637.670i		−	0.862882i	−0.902141	−	0.431441i	$-0.858005\pi$
$739$		−	637.670i		−	0.862882i	0.902141	−	0.431441i	$-0.141995\pi$
$740$		0			0
$741$	153.915			0.207713
$742$	−209.435			−0.282257
$743$			728.223i			0.980112i	0.871691	+	0.490056i	$0.163024\pi$
$743$			728.223i			0.980112i	−0.871691	+	0.490056i	$0.836976\pi$
$744$			188.869i			0.253856i
$745$		0			0
$746$	−1583.03			−2.12202
$747$		−	276.162i		−	0.369695i
$748$	86.5622	+	68.6260i	0.115725	+	0.0917460i
$749$	−757.031			−1.01072
$750$		0			0
$751$	33.5510			0.0446750			0.0223375	−	0.999750i	$-0.492889\pi$
$751$	33.5510			0.0446750			0.0223375	+	0.999750i	$0.492889\pi$
$752$	−198.971			−0.264589
$753$	−63.3103			−0.0840774
$754$		−	527.225i		−	0.699237i
$755$		0			0
$756$			546.388i			0.722735i
$757$	−1223.98			−1.61688			−0.808438	−	0.588581i	$-0.799687\pi$
$757$	−1223.98			−1.61688			−0.808438	+	0.588581i	$0.799687\pi$
$758$		−	858.765i		−	1.13294i
$759$	154.920	−	195.410i	0.204110	−	0.257457i
$760$		0			0
$761$			711.474i			0.934920i	0.884014	+	0.467460i	$0.154831\pi$
$761$			711.474i			0.934920i	−0.884014	+	0.467460i	$0.845169\pi$
$762$	512.900			0.673097
$763$	−640.582			−0.839557
$764$	11.0539			0.0144685
$765$		0			0
$766$			1069.57i			1.39630i
$767$		−	501.138i		−	0.653374i
$768$	395.401			0.514846
$769$			418.803i			0.544607i	0.962211	+	0.272304i	$0.0877855\pi$
$769$			418.803i			0.544607i	−0.962211	+	0.272304i	$0.912214\pi$
$770$		0			0
$771$	−537.356			−0.696960
$772$		−	1936.89i		−	2.50892i
$773$	−708.180			−0.916145			−0.458073	−	0.888915i	$-0.651460\pi$
$773$	−708.180			−0.916145			−0.458073	+	0.888915i	$0.651460\pi$
$774$	1598.24			2.06491
$775$		0			0
$776$		−	102.324i		−	0.131861i
$777$		−	321.756i		−	0.414100i
$778$			2122.46i			2.72809i
$779$	−1254.40			−1.61027
$780$		0			0
$781$	544.540	−	686.861i	0.697234	−	0.879464i
$782$	88.4583			0.113118
$783$		−	499.947i		−	0.638503i
$784$	81.7689			0.104297
$785$		0			0
$786$	41.5946			0.0529193
$787$		−	629.493i		−	0.799864i	−0.916545	−	0.399932i	$-0.869034\pi$
$787$		−	629.493i		−	0.799864i	0.916545	−	0.399932i	$-0.130966\pi$
$788$		−	739.603i		−	0.938582i
$789$			197.625i			0.250475i
$790$		0			0
$791$			297.965i			0.376694i
$792$	574.758	+	455.665i	0.725704	+	0.575334i
$793$	−32.1199			−0.0405043
$794$			401.906i			0.506179i
$795$		0			0
$796$	−261.792			−0.328885
$797$	−1278.65			−1.60433			−0.802165	−	0.597103i	$-0.796318\pi$
$797$	−1278.65			−1.60433			−0.802165	+	0.597103i	$0.796318\pi$
$798$			300.382i			0.376419i
$799$		−	121.341i		−	0.151867i
$800$		0			0
$801$	763.450			0.953121
$802$			797.179i			0.993989i
$803$	368.025	+	291.768i	0.458312	+	0.363347i
$804$	−102.048			−0.126925
$805$		0			0
$806$	−364.878			−0.452702
$807$	267.086			0.330962
$808$	−1405.28			−1.73921
$809$			516.115i			0.637966i	0.947760	+	0.318983i	$0.103341\pi$
$809$			516.115i			0.637966i	−0.947760	+	0.318983i	$0.896659\pi$
$810$		0			0
$811$		−	307.425i		−	0.379069i	−0.981874	−	0.189534i	$-0.939302\pi$
$811$		−	307.425i		−	0.379069i	0.981874	−	0.189534i	$-0.0606978\pi$
$812$	645.631			0.795112
$813$			583.803i			0.718085i
$814$	−1841.61	−	1460.02i	−2.26242	−	1.79363i
$815$		0			0
$816$		−	4.55976i		−	0.00558795i
$817$	1218.86			1.49188
$818$	1390.79			1.70024
$819$	−194.000			−0.236874
$820$		0			0
$821$			181.868i			0.221520i	0.993847	+	0.110760i	$0.0353285\pi$
$821$			181.868i			0.221520i	−0.993847	+	0.110760i	$0.964672\pi$
$822$		−	288.883i		−	0.351440i
$823$	−719.382			−0.874097			−0.437049	−	0.899438i	$-0.643976\pi$
$823$	−719.382			−0.874097			−0.437049	+	0.899438i	$0.643976\pi$
$824$		−	948.562i		−	1.15117i
$825$		0			0
$826$	978.024			1.18405
$827$			555.837i			0.672113i	0.941842	+	0.336056i	$0.109093\pi$
$827$			555.837i			0.672113i	−0.941842	+	0.336056i	$0.890907\pi$
$828$	907.056			1.09548
$829$	448.221			0.540677			0.270338	−	0.962765i	$-0.412864\pi$
$829$	448.221			0.540677			0.270338	+	0.962765i	$0.412864\pi$
$830$		0			0
$831$		−	83.0416i		−	0.0999297i
$832$			669.318i			0.804469i
$833$			49.8663i			0.0598635i
$834$	833.957			0.999948
$835$		0			0
$836$	1078.80	+	855.267i	1.29043	+	1.02305i
$837$	−346.000			−0.413381
$838$			224.982i			0.268475i
$839$	682.509			0.813479			0.406740	−	0.913544i	$-0.366666\pi$
$839$	682.509			0.813479			0.406740	+	0.913544i	$0.366666\pi$
$840$		0			0
$841$	250.245			0.297556
$842$			256.234i			0.304316i
$843$			300.651i			0.356644i
$844$			602.778i			0.714192i
$845$		0			0
$846$		−	1982.94i		−	2.34390i
$847$	−464.475	+	108.819i	−0.548377	+	0.128475i
$848$	39.6214			0.0467233
$849$			338.615i			0.398840i
$850$		0			0
$851$	−1180.87			−1.38763
$852$	−672.000			−0.788733
$853$		−	1370.47i		−	1.60665i	−0.595544	−	0.803323i	$-0.703063\pi$
$853$		−	1370.47i		−	1.60665i	0.595544	−	0.803323i	$-0.296937\pi$
$854$		−	62.6854i		−	0.0734021i
$855$		0			0
$856$	1722.43			2.01219
$857$			1074.81i			1.25416i	0.778956	+	0.627078i	$0.215749\pi$
$857$			1074.81i			1.25416i	−0.778956	+	0.627078i	$0.784251\pi$
$858$	185.543	−	234.037i	0.216251	−	0.272770i
$859$	969.712			1.12888			0.564442	−	0.825472i	$-0.309091\pi$
$859$	969.712			1.12888			0.564442	+	0.825472i	$0.309091\pi$
$860$		0			0
$861$	−333.247			−0.387047
$862$	1940.34			2.25098
$863$	129.003			0.149482			0.0747408	−	0.997203i	$-0.476187\pi$
$863$	129.003			0.149482			0.0747408	+	0.997203i	$0.476187\pi$
$864$			573.321i			0.663566i
$865$		0			0
$866$		−	303.778i		−	0.350783i
$867$	−358.957			−0.414022
$868$		−	446.823i		−	0.514773i
$869$	−669.256	−	530.583i	−0.770145	−	0.610567i
$870$		0			0
$871$		−	80.1026i		−	0.0919663i
$872$	1457.48			1.67142
$873$	84.7907			0.0971257
$874$	1102.43			1.26136
$875$		0			0
$876$		−	360.062i		−	0.411030i
$877$		−	490.300i		−	0.559065i	−0.960136	−	0.279532i	$-0.909821\pi$
$877$		−	490.300i		−	0.559065i	0.960136	−	0.279532i	$-0.0901794\pi$
$878$	2442.70			2.78212
$879$		−	680.176i		−	0.773807i
$880$		0			0
$881$	−772.952			−0.877358			−0.438679	−	0.898644i	$-0.644553\pi$
$881$	−772.952			−0.877358			−0.438679	+	0.898644i	$0.644553\pi$
$882$			814.905i			0.923929i
$883$	1723.84			1.95225			0.976124	−	0.217212i	$-0.0696963\pi$
$883$	1723.84			1.95225			0.976124	+	0.217212i	$0.0696963\pi$
$884$	66.4772			0.0752004
$885$		0			0
$886$			1913.31i			2.15950i
$887$			1064.55i			1.20017i	0.799936	+	0.600085i	$0.204867\pi$
$887$			1064.55i			1.20017i	−0.799936	+	0.600085i	$0.795133\pi$
$888$			732.074i			0.824408i
$889$	−493.020			−0.554578
$890$		0			0
$891$	−281.228	+	354.730i	−0.315632	+	0.398126i
$892$	−1279.73			−1.43467
$893$		−	1512.24i		−	1.69344i
$894$	−402.982			−0.450763
$895$		0			0
$896$	−866.686			−0.967283
$897$		−	150.069i		−	0.167301i
$898$			1127.50i			1.25556i
$899$			408.845i			0.454778i
$900$		0			0
$901$			24.1629i			0.0268178i
$902$	−1512.16	+	1907.38i	−1.67645	+	2.11461i
$903$	323.807			0.358590
$904$		−	677.943i		−	0.749937i
$905$		0			0
$906$	−8.38278			−0.00925252
$907$	−1115.09			−1.22943			−0.614713	−	0.788751i	$-0.710728\pi$
$907$	−1115.09			−1.22943			−0.614713	+	0.788751i	$0.710728\pi$
$908$			2322.70i			2.55804i
$909$		−	1164.49i		−	1.28106i
$910$		0			0
$911$	834.815			0.916372			0.458186	−	0.888856i	$-0.348499\pi$
$911$	834.815			0.916372			0.458186	+	0.888856i	$0.348499\pi$
$912$		−	56.8271i		−	0.0623104i
$913$	−320.243	−	253.887i	−0.350759	−	0.278080i
$914$	1342.17			1.46846
$915$		0			0
$916$	768.804			0.839305
$917$	−39.9824			−0.0436013
$918$	100.463			0.109437
$919$			284.457i			0.309529i	0.987951	+	0.154765i	$0.0494619\pi$
$919$			284.457i			0.309529i	−0.987951	+	0.154765i	$0.950538\pi$
$920$		0			0
$921$		−	393.225i		−	0.426955i
$922$	1965.70			2.13200
$923$		−	527.489i		−	0.571494i
$924$	286.598	+	227.213i	0.310170	+	0.245901i
$925$		0			0
$926$			1631.64i			1.76203i
$927$	786.026			0.847925
$928$	677.456			0.730017
$929$	337.429			0.363218			0.181609	−	0.983371i	$-0.441870\pi$
$929$	337.429			0.363218			0.181609	+	0.983371i	$0.441870\pi$
$930$		0			0
$931$			621.470i			0.667530i
$932$		−	114.462i		−	0.122813i
$933$	469.176			0.502868
$934$		−	1444.44i		−	1.54651i
$935$		0			0
$936$	441.397			0.471578
$937$			736.226i			0.785726i	0.919597	+	0.392863i	$0.128515\pi$
$937$			736.226i			0.785726i	−0.919597	+	0.392863i	$0.871485\pi$
$938$	156.329			0.166662
$939$	−258.393			−0.275179
$940$		0			0
$941$			433.395i			0.460569i	0.973123	+	0.230284i	$0.0739656\pi$
$941$			433.395i			0.460569i	−0.973123	+	0.230284i	$0.926034\pi$
$942$			657.545i			0.698031i
$943$			1223.05i			1.29698i
$944$	−185.025			−0.196001
$945$		0			0
$946$	1469.32	−	1853.35i	1.55320	−	1.95914i
$947$	439.058			0.463631			0.231815	−	0.972760i	$-0.425534\pi$
$947$	439.058			0.463631			0.231815	+	0.972760i	$0.425534\pi$
$948$			654.776i			0.690692i
$949$	282.632			0.297821
$950$		0			0
$951$	342.797			0.360459
$952$			52.7135i			0.0553713i
$953$		−	1108.12i		−	1.16277i	−0.813630	−	0.581383i	$-0.802512\pi$
$953$		−	1108.12i		−	1.16277i	0.813630	−	0.581383i	$-0.197488\pi$
$954$			394.865i			0.413904i
$955$		0			0
$956$		−	1433.37i		−	1.49934i
$957$	−262.238	−	207.901i	−0.274021	−	0.217242i
$958$	−1708.45			−1.78335
$959$			277.686i			0.289558i
$960$		0			0
$961$	−678.050			−0.705567
$962$	−1414.30			−1.47017
$963$			1427.29i			1.48213i
$964$		−	2441.78i		−	2.53297i
$965$		0			0
$966$	292.875			0.303184
$967$			108.838i			0.112553i	0.998415	+	0.0562763i	$0.0179228\pi$
$967$			108.838i			0.112553i	−0.998415	+	0.0562763i	$0.982077\pi$
$968$	1056.80	−	247.589i	1.09173	−	0.255774i
$969$	34.6557			0.0357644
$970$		0			0
$971$	−312.516			−0.321850			−0.160925	−	0.986967i	$-0.551448\pi$
$971$	−312.516			−0.321850			−0.160925	+	0.986967i	$0.551448\pi$
$972$	1594.33			1.64026
$973$	−801.633			−0.823878
$974$			519.800i			0.533676i
$975$		0			0
$976$			11.8590i			0.0121506i
$977$	−594.696			−0.608696			−0.304348	−	0.952561i	$-0.598439\pi$
$977$	−594.696			−0.608696			−0.304348	+	0.952561i	$0.598439\pi$
$978$		−	243.303i		−	0.248776i
$979$	701.870	−	885.312i	0.716926	−	0.904302i
$980$		0			0
$981$			1207.74i			1.23113i
$982$	−1831.42			−1.86499
$983$	554.324			0.563910			0.281955	−	0.959428i	$-0.409017\pi$
$983$	554.324			0.563910			0.281955	+	0.959428i	$0.409017\pi$
$984$	758.220			0.770549
$985$		0			0
$986$		−	118.710i		−	0.120396i
$987$		−	401.748i		−	0.407039i
$988$	828.487			0.838549
$989$		−	1188.40i		−	1.20162i
$990$		0			0
$991$	−148.655			−0.150005			−0.0750023	−	0.997183i	$-0.523896\pi$
$991$	−148.655			−0.150005			−0.0750023	+	0.997183i	$0.523896\pi$
$992$		−	468.848i		−	0.472629i
$993$	553.183			0.557083
$994$	1029.45			1.03566
$995$		0			0
$996$			313.314i			0.314572i
$997$		−	1023.25i		−	1.02633i	−0.858291	−	0.513164i	$-0.828473\pi$
$997$		−	1023.25i		−	1.02633i	0.858291	−	0.513164i	$-0.171527\pi$
$998$			975.479i			0.977433i
$999$	−1341.13			−1.34247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.c.h.76.1	yes	8
5.2	odd	4		275.3.d.b.274.16		16
5.3	odd	4		275.3.d.b.274.1		16
5.4	even	2		275.3.c.g.76.8	yes	8
11.10	odd	2	inner	275.3.c.h.76.8	yes	8
55.32	even	4		275.3.d.b.274.2		16
55.43	even	4		275.3.d.b.274.15		16
55.54	odd	2		275.3.c.g.76.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.c.g.76.1	✓	8	55.54	odd	2
275.3.c.g.76.8	yes	8	5.4	even	2
275.3.c.h.76.1	yes	8	1.1	even	1	trivial
275.3.c.h.76.8	yes	8	11.10	odd	2	inner
275.3.d.b.274.1		16	5.3	odd	4
275.3.d.b.274.2		16	55.32	even	4
275.3.d.b.274.15		16	55.43	even	4
275.3.d.b.274.16		16	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.27682i q^{2} -1.25169 q^{3} -6.73752 q^{4} +4.10155i q^{6} -3.94258i q^{7} +8.97034i q^{8} -7.43328 q^{9} +(-6.83371 + 8.61977i) q^{11} +8.43328 q^{12} +6.61973i q^{13} -12.9191 q^{14} +2.44407 q^{16} +1.49050i q^{17} +24.3575i q^{18} +18.5757i q^{19} +4.93488i q^{21} +(28.2454 + 22.3928i) q^{22} +18.1115 q^{23} -11.2281i q^{24} +21.6916 q^{26} +20.5693 q^{27} +26.5632i q^{28} -24.3055i q^{29} -16.8211 q^{31} +27.8726i q^{32} +(8.55368 - 10.7893i) q^{33} +4.88410 q^{34} +50.0818 q^{36} -65.2003 q^{37} +60.8692 q^{38} -8.28584i q^{39} +67.5290i q^{41} +16.1707 q^{42} -65.6159i q^{43} +(46.0422 - 58.0759i) q^{44} -59.3480i q^{46} -81.4098 q^{47} -3.05921 q^{48} +33.4561 q^{49} -1.86564i q^{51} -44.6005i q^{52} +16.2112 q^{53} -67.4019i q^{54} +35.3663 q^{56} -23.2510i q^{57} -79.6445 q^{58} -75.7037 q^{59} +4.85215i q^{61} +55.1197i q^{62} +29.3063i q^{63} +101.110 q^{64} +(-35.3544 - 28.0288i) q^{66} -12.1006 q^{67} -10.0423i q^{68} -22.6699 q^{69} -79.6844 q^{71} -66.6790i q^{72} -42.6954i q^{73} +213.649i q^{74} -125.154i q^{76} +(33.9841 + 26.9424i) q^{77} -27.1512 q^{78} +77.6420i q^{79} +41.1531 q^{81} +221.280 q^{82} +37.1521i q^{83} -33.2489i q^{84} -215.011 q^{86} +30.4229i q^{87} +(-77.3223 - 61.3007i) q^{88} -102.707 q^{89} +26.0988 q^{91} -122.026 q^{92} +21.0548 q^{93} +266.765i q^{94} -34.8878i q^{96} -11.4069 q^{97} -109.629i q^{98} +(50.7968 - 64.0731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 10 q^{4} + 32 q^{9} - q^{11} - 24 q^{12} + 18 q^{14} - 14 q^{16} - 35 q^{22} + 4 q^{23} + 68 q^{26} + 142 q^{27} - 42 q^{31} - 31 q^{33} - 142 q^{34} - 84 q^{36} - 104 q^{37} + 190 q^{38}+ \cdots + 368 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 10 * q^4 + 32 * q^9 - q^11 - 24 * q^12 + 18 * q^14 - 14 * q^16 - 35 * q^22 + 4 * q^23 + 68 * q^26 + 142 * q^27 - 42 * q^31 - 31 * q^33 - 142 * q^34 - 84 * q^36 - 104 * q^37 + 190 * q^38 + 50 * q^42 + 69 * q^44 - 64 * q^47 - 86 * q^48 - 50 * q^49 - 286 * q^53 + 166 * q^56 - 130 * q^58 - 160 * q^59 + 288 * q^64 - 315 * q^66 + 46 * q^67 - 16 * q^69 + 246 * q^71 + 80 * q^77 + 620 * q^78 + 304 * q^81 + 280 * q^82 - 282 * q^86 - 365 * q^88 - 18 * q^89 - 142 * q^91 + 26 * q^92 + 818 * q^93 - 264 * q^97 + 368 * q^99

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