LMFDB - Embedded newform 48.5.e.c.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(17,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("48.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - x^{2} + 2x + 27 $ x^4 - 2x^3 - x^2 + 2x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			17.2
Root			$-1.30278 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	48.17
Dual form			48.5.e.c.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.21110 + 6.51323i) q^{3} -16.4520i q^{5} -49.2666 q^{7} +(-3.84441 - 80.9087i) q^{9} +O(q^{10})$	\(q+(-6.21110 + 6.51323i) q^{3} -16.4520i q^{5} -49.2666 q^{7} +(-3.84441 - 80.9087i) q^{9} -207.748i q^{11} -235.066 q^{13} +(107.156 + 102.185i) q^{15} +337.337i q^{17} -162.733 q^{19} +(306.000 - 320.885i) q^{21} +185.073i q^{23} +354.332 q^{25} +(550.855 + 477.493i) q^{27} -361.991i q^{29} -474.067 q^{31} +(1353.11 + 1290.34i) q^{33} +810.533i q^{35} -1913.47 q^{37} +(1460.02 - 1531.04i) q^{39} +460.560i q^{41} -60.8663 q^{43} +(-1331.11 + 63.2482i) q^{45} -238.530i q^{47} +26.1994 q^{49} +(-2197.15 - 2095.23i) q^{51} -5282.04i q^{53} -3417.86 q^{55} +(1010.75 - 1059.92i) q^{57} -306.745i q^{59} +242.269 q^{61} +(189.401 + 3986.10i) q^{63} +3867.31i q^{65} +3994.33 q^{67} +(-1205.42 - 1149.51i) q^{69} -908.770i q^{71} +3454.80 q^{73} +(-2200.79 + 2307.85i) q^{75} +10235.0i q^{77} +6280.06 q^{79} +(-6531.44 + 622.093i) q^{81} -5132.51i q^{83} +5549.86 q^{85} +(2357.73 + 2248.36i) q^{87} -4665.49i q^{89} +11580.9 q^{91} +(2944.48 - 3087.71i) q^{93} +2677.29i q^{95} +3787.34 q^{97} +(-16808.6 + 798.668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 24 q^{7} + 100 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 24 * q^7 + 100 * q^9	$ 4 q + 4 q^{3} - 24 q^{7} + 100 q^{9} - 248 q^{13} + 544 q^{15} - 824 q^{19} + 1224 q^{21} - 2044 q^{25} + 1540 q^{27} - 3800 q^{31} + 2528 q^{33} - 2808 q^{37} + 4744 q^{39} + 968 q^{43} + 2752 q^{45} - 1972 q^{49} - 3712 q^{51} - 4672 q^{55} - 2072 q^{57} + 8584 q^{61} + 4392 q^{63} + 15112 q^{67} - 7360 q^{69} + 5512 q^{73} - 27004 q^{75} + 1064 q^{79} - 14588 q^{81} + 2816 q^{85} + 7008 q^{87} + 31440 q^{91} - 17528 q^{93} + 32456 q^{97} - 36544 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 24 * q^7 + 100 * q^9 - 248 * q^13 + 544 * q^15 - 824 * q^19 + 1224 * q^21 - 2044 * q^25 + 1540 * q^27 - 3800 * q^31 + 2528 * q^33 - 2808 * q^37 + 4744 * q^39 + 968 * q^43 + 2752 * q^45 - 1972 * q^49 - 3712 * q^51 - 4672 * q^55 - 2072 * q^57 + 8584 * q^61 + 4392 * q^63 + 15112 * q^67 - 7360 * q^69 + 5512 * q^73 - 27004 * q^75 + 1064 * q^79 - 14588 * q^81 + 2816 * q^85 + 7008 * q^87 + 31440 * q^91 - 17528 * q^93 + 32456 * q^97 - 36544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−6.21110	+	6.51323i	−0.690123	+	0.723693i
$3$	−6.21110	+	6.51323i	−0.690123	+	0.723693i
$4$		0			0
$5$		−	16.4520i		−	0.658079i	−0.944316	−	0.329040i	$-0.893275\pi$
$5$		−	16.4520i		−	0.658079i	0.944316	−	0.329040i	$-0.106725\pi$
$6$		0			0
$7$	−49.2666			−1.00544			−0.502721	−	0.864449i	$-0.667668\pi$
$7$	−49.2666			−1.00544			−0.502721	+	0.864449i	$0.667668\pi$
$8$		0			0
$9$	−3.84441	−	80.9087i	−0.0474619	−	0.998873i
$10$		0			0
$11$		−	207.748i		−	1.71692i	−0.512877	−	0.858462i	$-0.671420\pi$
$11$		−	207.748i		−	1.71692i	0.512877	−	0.858462i	$-0.328580\pi$
$12$		0			0
$13$	−235.066			−1.39093			−0.695463	−	0.718562i	$-0.744801\pi$
$13$	−235.066			−1.39093			−0.695463	+	0.718562i	$0.744801\pi$
$14$		0			0
$15$	107.156	+	102.185i	0.476247	+	0.454155i
$16$		0			0
$17$			337.337i			1.16726i	0.812021	+	0.583628i	$0.198367\pi$
$17$			337.337i			1.16726i	−0.812021	+	0.583628i	$0.801633\pi$
$18$		0			0
$19$	−162.733			−0.450785			−0.225392	−	0.974268i	$-0.572366\pi$
$19$	−162.733			−0.450785			−0.225392	+	0.974268i	$0.572366\pi$
$20$		0			0
$21$	306.000	−	320.885i	0.693878	−	0.727630i
$22$		0			0
$23$			185.073i			0.349854i	0.984581	+	0.174927i	$0.0559690\pi$
$23$			185.073i			0.349854i	−0.984581	+	0.174927i	$0.944031\pi$
$24$		0			0
$25$	354.332			0.566932
$26$		0			0
$27$	550.855	+	477.493i	0.755631	+	0.654997i
$28$		0			0
$29$		−	361.991i		−	0.430429i	−0.976567	−	0.215215i	$-0.930955\pi$
$29$		−	361.991i		−	0.430429i	0.976567	−	0.215215i	$-0.0690451\pi$
$30$		0			0
$31$	−474.067			−0.493306			−0.246653	−	0.969104i	$-0.579331\pi$
$31$	−474.067			−0.493306			−0.246653	+	0.969104i	$0.579331\pi$
$32$		0			0
$33$	1353.11	+	1290.34i	1.24253	+	1.18489i
$34$		0			0
$35$			810.533i			0.661660i
$36$		0			0
$37$	−1913.47			−1.39771			−0.698855	−	0.715263i	$-0.746307\pi$
$37$	−1913.47			−1.39771			−0.698855	+	0.715263i	$0.746307\pi$
$38$		0			0
$39$	1460.02	−	1531.04i	0.959909	−	1.00660i
$40$		0			0
$41$			460.560i			0.273980i	0.990572	+	0.136990i	$0.0437428\pi$
$41$			460.560i			0.273980i	−0.990572	+	0.136990i	$0.956257\pi$
$42$		0			0
$43$	−60.8663			−0.0329185			−0.0164593	−	0.999865i	$-0.505239\pi$
$43$	−60.8663			−0.0329185			−0.0164593	+	0.999865i	$0.505239\pi$
$44$		0			0
$45$	−1331.11	+	63.2482i	−0.657338	+	0.0312337i
$46$		0			0
$47$		−	238.530i		−	0.107981i	−0.998541	−	0.0539905i	$-0.982806\pi$
$47$		−	238.530i		−	0.107981i	0.998541	−	0.0539905i	$-0.0171941\pi$
$48$		0			0
$49$	26.1994			0.0109119
$50$		0			0
$51$	−2197.15	−	2095.23i	−0.844734	−	0.805550i
$52$		0			0
$53$		−	5282.04i		−	1.88040i	−0.340626	−	0.940199i	$-0.610639\pi$
$53$		−	5282.04i		−	1.88040i	0.340626	−	0.940199i	$-0.389361\pi$
$54$		0			0
$55$	−3417.86			−1.12987
$56$		0			0
$57$	1010.75	−	1059.92i	0.311097	−	0.326230i
$58$		0			0
$59$		−	306.745i		−	0.0881198i	−0.999029	−	0.0440599i	$-0.985971\pi$
$59$		−	306.745i		−	0.0881198i	0.999029	−	0.0440599i	$-0.0140292\pi$
$60$		0			0
$61$	242.269			0.0651086			0.0325543	−	0.999470i	$-0.489636\pi$
$61$	242.269			0.0651086			0.0325543	+	0.999470i	$0.489636\pi$
$62$		0			0
$63$	189.401	+	3986.10i	0.0477201	+	1.00431i
$64$		0			0
$65$			3867.31i			0.915339i
$66$		0			0
$67$	3994.33			0.889805			0.444902	−	0.895579i	$-0.353238\pi$
$67$	3994.33			0.889805			0.444902	+	0.895579i	$0.353238\pi$
$68$		0			0
$69$	−1205.42	−	1149.51i	−0.253187	−	0.241442i
$70$		0			0
$71$		−	908.770i		−	0.180276i	−0.995929	−	0.0901379i	$-0.971269\pi$
$71$		−	908.770i		−	0.180276i	0.995929	−	0.0901379i	$-0.0287308\pi$
$72$		0			0
$73$	3454.80			0.648301			0.324151	−	0.946005i	$-0.394922\pi$
$73$	3454.80			0.648301			0.324151	+	0.946005i	$0.394922\pi$
$74$		0			0
$75$	−2200.79	+	2307.85i	−0.391252	+	0.410284i
$76$		0			0
$77$			10235.0i			1.72627i
$78$		0			0
$79$	6280.06			1.00626			0.503129	−	0.864211i	$-0.332182\pi$
$79$	6280.06			1.00626			0.503129	+	0.864211i	$0.332182\pi$
$80$		0			0
$81$	−6531.44	+	622.093i	−0.995495	+	0.0948167i
$82$		0			0
$83$		−	5132.51i		−	0.745030i	−0.928026	−	0.372515i	$-0.878495\pi$
$83$		−	5132.51i		−	0.745030i	0.928026	−	0.372515i	$-0.121505\pi$
$84$		0			0
$85$	5549.86			0.768147
$86$		0			0
$87$	2357.73	+	2248.36i	0.311499	+	0.297049i
$88$		0			0
$89$		−	4665.49i		−	0.589003i	−0.955651	−	0.294501i	$-0.904846\pi$
$89$		−	4665.49i		−	0.589003i	0.955651	−	0.294501i	$-0.0951536\pi$
$90$		0			0
$91$	11580.9			1.39849
$92$		0			0
$93$	2944.48	−	3087.71i	0.340442	−	0.357002i
$94$		0			0
$95$			2677.29i			0.296652i
$96$		0			0
$97$	3787.34			0.402523			0.201261	−	0.979538i	$-0.435496\pi$
$97$	3787.34			0.402523			0.201261	+	0.979538i	$0.435496\pi$
$98$		0			0
$99$	−16808.6	+	798.668i	−1.71499	+	0.0814884i
$100$		0			0
$101$			4739.45i			0.464607i	0.972643	+	0.232303i	$0.0746262\pi$
$101$			4739.45i			0.464607i	−0.972643	+	0.232303i	$0.925374\pi$
$102$		0			0
$103$	−18695.1			−1.76219			−0.881097	−	0.472935i	$-0.843194\pi$
$103$	−18695.1			−1.76219			−0.881097	+	0.472935i	$0.843194\pi$
$104$		0			0
$105$	−5279.19	−	5034.31i	−0.478838	−	0.456626i
$106$		0			0
$107$			17491.0i			1.52774i	0.645373	+	0.763868i	$0.276702\pi$
$107$			17491.0i			1.52774i	−0.645373	+	0.763868i	$0.723298\pi$
$108$		0			0
$109$	4168.66			0.350868			0.175434	−	0.984491i	$-0.443867\pi$
$109$	4168.66			0.350868			0.175434	+	0.984491i	$0.443867\pi$
$110$		0			0
$111$	11884.7	−	12462.8i	0.964591	−	1.01151i
$112$		0			0
$113$		−	20057.9i		−	1.57083i	−0.618973	−	0.785413i	$-0.712451\pi$
$113$		−	20057.9i		−	1.57083i	0.618973	−	0.785413i	$-0.287549\pi$
$114$		0			0
$115$	3044.82			0.230232
$116$		0			0
$117$	903.692	+	19018.9i	0.0660159	+	1.38936i
$118$		0			0
$119$		−	16619.4i		−	1.17361i
$120$		0			0
$121$	−28518.2			−1.94783
$122$		0			0
$123$	−2999.74	−	2860.59i	−0.198277	−	0.189080i
$124$		0			0
$125$		−	16112.0i		−	1.03117i
$126$		0			0
$127$	−6671.95			−0.413662			−0.206831	−	0.978377i	$-0.566315\pi$
$127$	−6671.95			−0.413662			−0.206831	+	0.978377i	$0.566315\pi$
$128$		0			0
$129$	378.047	−	396.436i	0.0227178	−	0.0238229i
$130$		0			0
$131$		−	22490.2i		−	1.31054i	−0.755395	−	0.655270i	$-0.772555\pi$
$131$		−	22490.2i		−	1.31054i	0.755395	−	0.655270i	$-0.227445\pi$
$132$		0			0
$133$	8017.32			0.453238
$134$		0			0
$135$	7855.70	−	9062.66i	0.431040	−	0.497265i
$136$		0			0
$137$			14003.4i			0.746094i	0.927812	+	0.373047i	$0.121687\pi$
$137$			14003.4i			0.746094i	−0.927812	+	0.373047i	$0.878313\pi$
$138$		0			0
$139$	13193.2			0.682845			0.341422	−	0.939910i	$-0.389091\pi$
$139$	13193.2			0.682845			0.341422	+	0.939910i	$0.389091\pi$
$140$		0			0
$141$	1553.60	+	1481.53i	0.0781450	+	0.0745201i
$142$		0			0
$143$			48834.6i			2.38811i
$144$		0			0
$145$	−5955.47			−0.283257
$146$		0			0
$147$	−162.727	+	170.643i	−0.00753052	+	0.00789683i
$148$		0			0
$149$			24207.1i			1.09036i	0.838318	+	0.545181i	$0.183539\pi$
$149$			24207.1i			1.09036i	−0.838318	+	0.545181i	$0.816461\pi$
$150$		0			0
$151$	−15169.3			−0.665289			−0.332644	−	0.943052i	$-0.607941\pi$
$151$	−15169.3			−0.665289			−0.332644	+	0.943052i	$0.607941\pi$
$152$		0			0
$153$	27293.5	−	1296.86i	1.16594	−	0.0554001i
$154$		0			0
$155$			7799.35i			0.324635i
$156$		0			0
$157$	2828.38			0.114746			0.0573731	−	0.998353i	$-0.481728\pi$
$157$	2828.38			0.114746			0.0573731	+	0.998353i	$0.481728\pi$
$158$		0			0
$159$	34403.1	+	32807.3i	1.36083	+	1.29770i
$160$		0			0
$161$		−	9117.92i		−	0.351758i
$162$		0			0
$163$	−22386.2			−0.842568			−0.421284	−	0.906929i	$-0.638420\pi$
$163$	−22386.2			−0.842568			−0.421284	+	0.906929i	$0.638420\pi$
$164$		0			0
$165$	21228.7	−	22261.3i	0.779750	−	0.817680i
$166$		0			0
$167$		−	25757.1i		−	0.923556i	−0.886995	−	0.461778i	$-0.847212\pi$
$167$		−	25757.1i		−	0.923556i	0.886995	−	0.461778i	$-0.152788\pi$
$168$		0			0
$169$	26695.2			0.934675
$170$		0			0
$171$	625.614	+	13166.5i	0.0213951	+	0.450277i
$172$		0			0
$173$			15288.8i			0.510837i	0.966831	+	0.255418i	$0.0822132\pi$
$173$			15288.8i			0.510837i	−0.966831	+	0.255418i	$0.917787\pi$
$174$		0			0
$175$	−17456.8			−0.570016
$176$		0			0
$177$	1997.90	+	1905.22i	0.0637716	+	0.0608135i
$178$		0			0
$179$		−	12725.1i		−	0.397151i	−0.980086	−	0.198576i	$-0.936368\pi$
$179$		−	12725.1i		−	0.397151i	0.980086	−	0.198576i	$-0.0636316\pi$
$180$		0			0
$181$	−60252.1			−1.83914			−0.919570	−	0.392926i	$-0.871463\pi$
$181$	−60252.1			−1.83914			−0.919570	+	0.392926i	$0.871463\pi$
$182$		0			0
$183$	−1504.76	+	1577.95i	−0.0449329	+	0.0471186i
$184$		0			0
$185$			31480.3i			0.919804i
$186$		0			0
$187$	70081.0			2.00409
$188$		0			0
$189$	−27138.8	−	23524.5i	−0.759743	−	0.658561i
$190$		0			0
$191$		−	50432.7i		−	1.38244i	−0.722646	−	0.691219i	$-0.757074\pi$
$191$		−	50432.7i		−	1.38244i	0.722646	−	0.691219i	$-0.242926\pi$
$192$		0			0
$193$	−709.481			−0.0190470			−0.00952349	−	0.999955i	$-0.503031\pi$
$193$	−709.481			−0.0190470			−0.00952349	+	0.999955i	$0.503031\pi$
$194$		0			0
$195$	−25188.7	−	24020.3i	−0.662424	−	0.631696i
$196$		0			0
$197$		−	45450.0i		−	1.17112i	−0.810629	−	0.585560i	$-0.800875\pi$
$197$		−	45450.0i		−	1.17112i	0.810629	−	0.585560i	$-0.199125\pi$
$198$		0			0
$199$	−28496.2			−0.719582			−0.359791	−	0.933033i	$-0.617152\pi$
$199$	−28496.2			−0.719582			−0.359791	+	0.933033i	$0.617152\pi$
$200$		0			0
$201$	−24809.2	+	26016.0i	−0.614074	+	0.643945i
$202$		0			0
$203$			17834.1i			0.432771i
$204$		0			0
$205$	7577.13			0.180301
$206$		0			0
$207$	14974.0	−	711.496i	0.349460	−	0.0166047i
$208$		0			0
$209$			33807.5i			0.773964i
$210$		0			0
$211$	−62416.8			−1.40196			−0.700981	−	0.713180i	$-0.747254\pi$
$211$	−62416.8			−1.40196			−0.700981	+	0.713180i	$0.747254\pi$
$212$		0			0
$213$	5919.03	+	5644.46i	0.130464	+	0.124412i
$214$		0			0
$215$			1001.37i			0.0216630i
$216$		0			0
$217$	23355.7			0.495990
$218$		0			0
$219$	−21458.1	+	22501.9i	−0.447407	+	0.469171i
$220$		0			0
$221$		−	79296.6i		−	1.62357i
$222$		0			0
$223$	54436.9			1.09467			0.547335	−	0.836914i	$-0.315642\pi$
$223$	54436.9			1.09467			0.547335	+	0.836914i	$0.315642\pi$
$224$		0			0
$225$	−1362.20	−	28668.6i	−0.0269076	−	0.566293i
$226$		0			0
$227$			36719.3i			0.712595i	0.934373	+	0.356297i	$0.115961\pi$
$227$			36719.3i			0.712595i	−0.934373	+	0.356297i	$0.884039\pi$
$228$		0			0
$229$	−22178.5			−0.422924			−0.211462	−	0.977386i	$-0.567822\pi$
$229$	−22178.5			−0.422924			−0.211462	+	0.977386i	$0.567822\pi$
$230$		0			0
$231$	−66663.2	−	63570.8i	−1.24929	−	1.19134i
$232$		0			0
$233$		−	37216.4i		−	0.685523i	−0.939422	−	0.342761i	$-0.888638\pi$
$233$		−	37216.4i		−	0.685523i	0.939422	−	0.342761i	$-0.111362\pi$
$234$		0			0
$235$	−3924.29			−0.0710600
$236$		0			0
$237$	−39006.1	+	40903.5i	−0.694442	+	0.728222i
$238$		0			0
$239$			65971.5i			1.15494i	0.816411	+	0.577471i	$0.195960\pi$
$239$			65971.5i			1.15494i	−0.816411	+	0.577471i	$0.804040\pi$
$240$		0			0
$241$	106526.			1.83409			0.917044	−	0.398785i	$-0.130568\pi$
$241$	106526.			1.83409			0.917044	+	0.398785i	$0.130568\pi$
$242$		0			0
$243$	36515.6	−	46404.7i	0.618395	−	0.785867i
$244$		0			0
$245$		−	431.032i		−	0.00718087i
$246$		0			0
$247$	38253.2			0.627008
$248$		0			0
$249$	33429.3	+	31878.6i	0.539173	+	0.514162i
$250$		0			0
$251$			5877.37i			0.0932901i	0.998912	+	0.0466450i	$0.0148530\pi$
$251$			5877.37i			0.0932901i	−0.998912	+	0.0466450i	$0.985147\pi$
$252$		0			0
$253$	38448.5			0.600673
$254$		0			0
$255$	−34470.8	+	36147.5i	−0.530115	+	0.555902i
$256$		0			0
$257$			69055.8i			1.04552i	0.852479	+	0.522762i	$0.175098\pi$
$257$			69055.8i			1.04552i	−0.852479	+	0.522762i	$0.824902\pi$
$258$		0			0
$259$	94270.0			1.40532
$260$		0			0
$261$	−29288.2	+	1391.64i	−0.429944	+	0.0204290i
$262$		0			0
$263$			27993.3i			0.404708i	0.979312	+	0.202354i	$0.0648592\pi$
$263$			27993.3i			0.404708i	−0.979312	+	0.202354i	$0.935141\pi$
$264$		0			0
$265$	−86900.0			−1.23745
$266$		0			0
$267$	30387.4	+	28977.8i	0.426257	+	0.406484i
$268$		0			0
$269$			122384.i			1.69130i	0.533740	+	0.845649i	$0.320786\pi$
$269$			122384.i			1.69130i	−0.533740	+	0.845649i	$0.679214\pi$
$270$		0			0
$271$	65752.0			0.895304			0.447652	−	0.894208i	$-0.352260\pi$
$271$	65752.0			0.895304			0.447652	+	0.894208i	$0.352260\pi$
$272$		0			0
$273$	−71930.3	+	75429.3i	−0.965132	+	1.01208i
$274$		0			0
$275$		−	73611.8i		−	0.973379i
$276$		0			0
$277$	96874.7			1.26256			0.631278	−	0.775556i	$-0.282531\pi$
$277$	96874.7			1.26256			0.631278	+	0.775556i	$0.282531\pi$
$278$		0			0
$279$	1822.51	+	38356.2i	0.0234132	+	0.492750i
$280$		0			0
$281$		−	119632.i		−	1.51507i	−0.652794	−	0.757535i	$-0.726403\pi$
$281$		−	119632.i		−	1.51507i	0.652794	−	0.757535i	$-0.273597\pi$
$282$		0			0
$283$	−71310.8			−0.890394			−0.445197	−	0.895433i	$-0.646866\pi$
$283$	−71310.8			−0.890394			−0.445197	+	0.895433i	$0.646866\pi$
$284$		0			0
$285$	−17437.8	−	16628.9i	−0.214685	−	0.204726i
$286$		0			0
$287$		−	22690.3i		−	0.275471i
$288$		0			0
$289$	−30275.2			−0.362486
$290$		0			0
$291$	−23523.5	+	24667.8i	−0.277790	+	0.291303i
$292$		0			0
$293$			11379.0i			0.132547i	0.997801	+	0.0662735i	$0.0211110\pi$
$293$			11379.0i			0.132547i	−0.997801	+	0.0662735i	$0.978889\pi$
$294$		0			0
$295$	−5046.56			−0.0579898
$296$		0			0
$297$	99198.1	−	114439.i	1.12458	−	1.29736i
$298$		0			0
$299$		−	43504.4i		−	0.486621i
$300$		0			0
$301$	2998.68			0.0330976
$302$		0			0
$303$	−30869.2	−	29437.2i	−0.336233	−	0.320636i
$304$		0			0
$305$		−	3985.80i		−	0.0428466i
$306$		0			0
$307$	−124865.			−1.32484			−0.662420	−	0.749133i	$-0.730471\pi$
$307$	−124865.			−1.32484			−0.662420	+	0.749133i	$0.730471\pi$
$308$		0			0
$309$	116117.	−	121766.i	1.21613	−	1.27529i
$310$		0			0
$311$			11726.9i			0.121244i	0.998161	+	0.0606221i	$0.0193084\pi$
$311$			11726.9i			0.121244i	−0.998161	+	0.0606221i	$0.980692\pi$
$312$		0			0
$313$	−98872.3			−1.00922			−0.504610	−	0.863347i	$-0.668364\pi$
$313$	−98872.3			−1.00922			−0.504610	+	0.863347i	$0.668364\pi$
$314$		0			0
$315$	65579.2	−	3116.02i	0.660914	−	0.0314036i
$316$		0			0
$317$			115.069i			0.00114509i	1.00000		0.000572544i	$0.000182246\pi$
$317$			115.069i			0.00114509i	−1.00000		0.000572544i	$0.999818\pi$
$318$		0			0
$319$	−75202.9			−0.739015
$320$		0			0
$321$	−113923.	−	108639.i	−1.10561	−	1.05432i
$322$		0			0
$323$		−	54896.0i		−	0.526181i
$324$		0			0
$325$	−83291.6			−0.788560
$326$		0			0
$327$	−25892.0	+	27151.5i	−0.242142	+	0.253920i
$328$		0			0
$329$			11751.6i			0.108569i
$330$		0			0
$331$	−90895.1			−0.829630			−0.414815	−	0.909906i	$-0.636154\pi$
$331$	−90895.1			−0.829630			−0.414815	+	0.909906i	$0.636154\pi$
$332$		0			0
$333$	7356.15	+	154816.i	0.0663379	+	1.39614i
$334$		0			0
$335$		−	65714.7i		−	0.585562i
$336$		0			0
$337$	−24399.3			−0.214841			−0.107421	−	0.994214i	$-0.534259\pi$
$337$	−24399.3			−0.214841			−0.107421	+	0.994214i	$0.534259\pi$
$338$		0			0
$339$	130642.	+	124581.i	1.13679	+	1.08406i
$340$		0			0
$341$			98486.5i			0.846969i
$342$		0			0
$343$	116998.			0.994470
$344$		0			0
$345$	−18911.7	+	19831.6i	−0.158888	+	0.166617i
$346$		0			0
$347$			98110.8i			0.814813i	0.913247	+	0.407407i	$0.133567\pi$
$347$			98110.8i			0.814813i	−0.913247	+	0.407407i	$0.866433\pi$
$348$		0			0
$349$	90018.8			0.739064			0.369532	−	0.929218i	$-0.379518\pi$
$349$	90018.8			0.739064			0.369532	+	0.929218i	$0.379518\pi$
$350$		0			0
$351$	−129488.	−	112243.i	−1.05103	−	0.911052i
$352$		0			0
$353$		−	74360.2i		−	0.596748i	−0.954449	−	0.298374i	$-0.903556\pi$
$353$		−	74360.2i		−	0.596748i	0.954449	−	0.298374i	$-0.0964443\pi$
$354$		0			0
$355$	−14951.1			−0.118636
$356$		0			0
$357$	108246.	+	103225.i	0.849331	+	0.809933i
$358$		0			0
$359$		−	191976.i		−	1.48956i	−0.667311	−	0.744779i	$-0.732555\pi$
$359$		−	191976.i		−	1.48956i	0.667311	−	0.744779i	$-0.267445\pi$
$360$		0			0
$361$	−103839.			−0.796793
$362$		0			0
$363$	177129.	−	185746.i	1.34424	−	1.40963i
$364$		0			0
$365$		−	56838.3i		−	0.426634i
$366$		0			0
$367$	142798.			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$367$	142798.			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$368$		0			0
$369$	37263.4	−	1770.58i	0.273671	−	0.0130036i
$370$		0			0
$371$			260228.i			1.89063i
$372$		0			0
$373$	−209063.			−1.50265			−0.751327	−	0.659930i	$-0.770586\pi$
$373$	−209063.			−1.50265			−0.751327	+	0.659930i	$0.770586\pi$
$374$		0			0
$375$	104941.	+	100073.i	0.746247	+	0.711630i
$376$		0			0
$377$			85092.0i			0.598695i
$378$		0			0
$379$	−181338.			−1.26244			−0.631220	−	0.775604i	$-0.717446\pi$
$379$	−181338.			−1.26244			−0.631220	+	0.775604i	$0.717446\pi$
$380$		0			0
$381$	41440.1	−	43455.9i	0.285477	−	0.299364i
$382$		0			0
$383$			118645.i			0.808818i	0.914578	+	0.404409i	$0.132523\pi$
$383$			118645.i			0.808818i	−0.914578	+	0.404409i	$0.867477\pi$
$384$		0			0
$385$	168387.			1.13602
$386$		0			0
$387$	233.995	+	4924.61i	0.00156237	+	0.0328814i
$388$		0			0
$389$		−	34079.8i		−	0.225215i	−0.993640	−	0.112607i	$-0.964080\pi$
$389$		−	34079.8i		−	0.225215i	0.993640	−	0.112607i	$-0.0359203\pi$
$390$		0			0
$391$	−62431.9			−0.408369
$392$		0			0
$393$	146484.	+	139689.i	0.948427	+	0.904433i
$394$		0			0
$395$		−	103319.i		−	0.662198i
$396$		0			0
$397$	197691.			1.25431			0.627155	−	0.778894i	$-0.284219\pi$
$397$	197691.			1.25431			0.627155	+	0.778894i	$0.284219\pi$
$398$		0			0
$399$	−49796.4	+	52218.7i	−0.312790	+	0.328005i
$400$		0			0
$401$		−	226361.i		−	1.40771i	−0.710346	−	0.703853i	$-0.751461\pi$
$401$		−	226361.i		−	1.40771i	0.710346	−	0.703853i	$-0.248539\pi$
$402$		0			0
$403$	111437.			0.686152
$404$		0			0
$405$	10234.7	+	107455.i	0.0623969	+	0.655114i
$406$		0			0
$407$			397518.i			2.39976i
$408$		0			0
$409$	55162.3			0.329759			0.164879	−	0.986314i	$-0.447277\pi$
$409$	55162.3			0.329759			0.164879	+	0.986314i	$0.447277\pi$
$410$		0			0
$411$	−91207.7	−	86976.8i	−0.539943	−	0.514896i
$412$		0			0
$413$			15112.3i			0.0885993i
$414$		0			0
$415$	−84440.0			−0.490289
$416$		0			0
$417$	−81944.6	+	85930.7i	−0.471247	+	0.494170i
$418$		0			0
$419$		−	14609.5i		−	0.0832161i	−0.999134	−	0.0416080i	$-0.986752\pi$
$419$		−	14609.5i		−	0.0832161i	0.999134	−	0.0416080i	$-0.0132481\pi$
$420$		0			0
$421$	3913.32			0.0220791			0.0110396	−	0.999939i	$-0.496486\pi$
$421$	3913.32			0.0220791			0.0110396	+	0.999939i	$0.496486\pi$
$422$		0			0
$423$	−19299.2	+	917.007i	−0.107859	+	0.00512498i
$424$		0			0
$425$			119529.i			0.661754i
$426$		0			0
$427$	−11935.8			−0.0654628
$428$		0			0
$429$	−318071.	−	303316.i	−1.72826	−	1.64809i
$430$		0			0
$431$		−	146069.i		−	0.786329i	−0.919468	−	0.393164i	$-0.871380\pi$
$431$		−	146069.i		−	0.786329i	0.919468	−	0.393164i	$-0.128620\pi$
$432$		0			0
$433$	−79929.9			−0.426318			−0.213159	−	0.977018i	$-0.568375\pi$
$433$	−79929.9			−0.426318			−0.213159	+	0.977018i	$0.568375\pi$
$434$		0			0
$435$	36990.0	−	38789.4i	0.195482	−	0.204991i
$436$		0			0
$437$		−	30117.5i		−	0.157709i
$438$		0			0
$439$	267142.			1.38616			0.693079	−	0.720861i	$-0.256253\pi$
$439$	267142.			1.38616			0.693079	+	0.720861i	$0.256253\pi$
$440$		0			0
$441$	−100.721	−	2119.76i	−0.000517897	−	0.0108996i
$442$		0			0
$443$		−	278272.i		−	1.41795i	−0.705231	−	0.708977i	$-0.749157\pi$
$443$		−	278272.i		−	1.41795i	0.705231	−	0.708977i	$-0.250843\pi$
$444$		0			0
$445$	−76756.6			−0.387611
$446$		0			0
$447$	−157667.	−	150353.i	−0.789087	−	0.752484i
$448$		0			0
$449$			291498.i			1.44591i	0.690893	+	0.722957i	$0.257217\pi$
$449$			291498.i			1.44591i	−0.690893	+	0.722957i	$0.742783\pi$
$450$		0			0
$451$	95680.4			0.470403
$452$		0			0
$453$	94217.8	−	98800.9i	0.459131	−	0.481465i
$454$		0			0
$455$		−	190529.i		−	0.920320i
$456$		0			0
$457$	−69539.2			−0.332964			−0.166482	−	0.986044i	$-0.553241\pi$
$457$	−69539.2			−0.332964			−0.166482	+	0.986044i	$0.553241\pi$
$458$		0			0
$459$	−161076.	+	185824.i	−0.764549	+	0.882015i
$460$		0			0
$461$		−	247261.i		−	1.16347i	−0.813379	−	0.581733i	$-0.802375\pi$
$461$		−	247261.i		−	1.16347i	0.813379	−	0.581733i	$-0.197625\pi$
$462$		0			0
$463$	−156558.			−0.730319			−0.365159	−	0.930945i	$-0.618985\pi$
$463$	−156558.			−0.730319			−0.365159	+	0.930945i	$0.618985\pi$
$464$		0			0
$465$	−50799.0	−	48442.5i	−0.234936	−	0.224038i
$466$		0			0
$467$		−	56133.2i		−	0.257387i	−0.991684	−	0.128693i	$-0.958922\pi$
$467$		−	56133.2i		−	0.257387i	0.991684	−	0.128693i	$-0.0410783\pi$
$468$		0			0
$469$	−196787.			−0.894646
$470$		0			0
$471$	−17567.3	+	18421.9i	−0.0791889	+	0.0830409i
$472$		0			0
$473$			12644.8i			0.0565186i
$474$		0			0
$475$	−57661.7			−0.255564
$476$		0			0
$477$	−427363.	+	20306.3i	−1.87828	+	0.0892472i
$478$		0			0
$479$		−	312034.i		−	1.35997i	−0.733224	−	0.679987i	$-0.761985\pi$
$479$		−	312034.i		−	1.35997i	0.733224	−	0.679987i	$-0.238015\pi$
$480$		0			0
$481$	449791.			1.94411
$482$		0			0
$483$	59387.1	+	56632.3i	0.254565	+	0.242756i
$484$		0			0
$485$		−	62309.2i		−	0.264892i
$486$		0			0
$487$	110399.			0.465488			0.232744	−	0.972538i	$-0.425230\pi$
$487$	110399.			0.465488			0.232744	+	0.972538i	$0.425230\pi$
$488$		0			0
$489$	139043.	−	145806.i	0.581475	−	0.609760i
$490$		0			0
$491$			12915.9i			0.0535750i	0.999641	+	0.0267875i	$0.00852775\pi$
$491$			12915.9i			0.0535750i	−0.999641	+	0.0267875i	$0.991472\pi$
$492$		0			0
$493$	122113.			0.502421
$494$		0			0
$495$	13139.7	+	276535.i	0.0536258	+	1.12860i
$496$		0			0
$497$			44772.0i			0.181257i
$498$		0			0
$499$	164847.			0.662034			0.331017	−	0.943625i	$-0.392608\pi$
$499$	164847.			0.662034			0.331017	+	0.943625i	$0.392608\pi$
$500$		0			0
$501$	167762.	+	159980.i	0.668371	+	0.637367i
$502$		0			0
$503$			447186.i			1.76747i	0.467987	+	0.883735i	$0.344979\pi$
$503$			447186.i			1.76747i	−0.467987	+	0.883735i	$0.655021\pi$
$504$		0			0
$505$	77973.4			0.305748
$506$		0			0
$507$	−165807.	+	173872.i	−0.645040	+	0.676417i
$508$		0			0
$509$			176786.i			0.682359i	0.939998	+	0.341179i	$0.110826\pi$
$509$			176786.i			0.682359i	−0.939998	+	0.341179i	$0.889174\pi$
$510$		0			0
$511$	−170206.			−0.651829
$512$		0			0
$513$	−89642.6	−	77704.0i	−0.340627	−	0.295263i
$514$		0			0
$515$			307572.i			1.15966i
$516$		0			0
$517$	−49554.1			−0.185395
$518$		0			0
$519$	−99579.7	−	94960.5i	−0.369689	−	0.352540i
$520$		0			0
$521$			272654.i			1.00447i	0.864731	+	0.502235i	$0.167489\pi$
$521$			272654.i			1.00447i	−0.864731	+	0.502235i	$0.832511\pi$
$522$		0			0
$523$	−79710.0			−0.291413			−0.145707	−	0.989328i	$-0.546546\pi$
$523$	−79710.0			−0.291413			−0.145707	+	0.989328i	$0.546546\pi$
$524$		0			0
$525$	108426.	−	113700.i	0.393381	−	0.412517i
$526$		0			0
$527$		−	159920.i		−	0.575814i
$528$		0			0
$529$	245589.			0.877602
$530$		0			0
$531$	−24818.3	+	1179.25i	−0.0880205	+	0.00418233i
$532$		0			0
$533$		−	108262.i		−	0.381086i
$534$		0			0
$535$	287762.			1.00537
$536$		0			0
$537$	82881.7	+	79037.1i	0.287415	+	0.274083i
$538$		0			0
$539$		−	5442.87i		−	0.0187348i
$540$		0			0
$541$	209745.			0.716634			0.358317	−	0.933600i	$-0.383351\pi$
$541$	209745.			0.716634			0.358317	+	0.933600i	$0.383351\pi$
$542$		0			0
$543$	374232.	−	392436.i	1.26923	−	1.33097i
$544$		0			0
$545$		−	68582.7i		−	0.230899i
$546$		0			0
$547$	298226.			0.996714			0.498357	−	0.866972i	$-0.333937\pi$
$547$	298226.			0.996714			0.498357	+	0.866972i	$0.333937\pi$
$548$		0			0
$549$	−931.381	−	19601.7i	−0.00309017	−	0.0650352i
$550$		0			0
$551$			58908.0i			0.194031i
$552$		0			0
$553$	−309397.			−1.01173
$554$		0			0
$555$	−205038.	−	195527.i	−0.665655	−	0.634777i
$556$		0			0
$557$		−	90217.1i		−	0.290789i	−0.989374	−	0.145395i	$-0.953555\pi$
$557$		−	90217.1i		−	0.290789i	0.989374	−	0.145395i	$-0.0464452\pi$
$558$		0			0
$559$	14307.6			0.0457872
$560$		0			0
$561$	−435280.	+	456454.i	−1.38307	+	1.45035i
$562$		0			0
$563$			168778.i			0.532475i	0.963907	+	0.266238i	$0.0857806\pi$
$563$			168778.i			0.532475i	−0.963907	+	0.266238i	$0.914219\pi$
$564$		0			0
$565$	−329992.			−1.03373
$566$		0			0
$567$	321782.	−	30648.4i	1.00091	−	0.0953326i
$568$		0			0
$569$		−	123485.i		−	0.381409i	−0.981648	−	0.190704i	$-0.938923\pi$
$569$		−	123485.i		−	0.381409i	0.981648	−	0.190704i	$-0.0610772\pi$
$570$		0			0
$571$	459979.			1.41080			0.705400	−	0.708809i	$-0.250767\pi$
$571$	459979.			1.41080			0.705400	+	0.708809i	$0.250767\pi$
$572$		0			0
$573$	328480.	+	313243.i	1.00046	+	0.954051i
$574$		0			0
$575$			65577.3i			0.198343i
$576$		0			0
$577$	−84602.8			−0.254117			−0.127058	−	0.991895i	$-0.540554\pi$
$577$	−84602.8			−0.254117			−0.127058	+	0.991895i	$0.540554\pi$
$578$		0			0
$579$	4406.66	−	4621.01i	0.0131447	−	0.0137842i
$580$		0			0
$581$			252862.i			0.749084i
$582$		0			0
$583$	−1.09733e6			−3.22850
$584$		0			0
$585$	312899.	−	14867.5i	0.914308	−	0.0434437i
$586$		0			0
$587$		−	335005.i		−	0.972243i	−0.873891	−	0.486122i	$-0.838411\pi$
$587$		−	335005.i		−	0.972243i	0.873891	−	0.486122i	$-0.161589\pi$
$588$		0			0
$589$	77146.6			0.222375
$590$		0			0
$591$	296027.	+	282295.i	0.847531	+	0.808217i
$592$		0			0
$593$		−	675910.i		−	1.92212i	−0.276346	−	0.961058i	$-0.589124\pi$
$593$		−	675910.i		−	1.92212i	0.276346	−	0.961058i	$-0.410876\pi$
$594$		0			0
$595$	−273423.			−0.772326
$596$		0			0
$597$	176993.	−	185602.i	0.496600	−	0.520756i
$598$		0			0
$599$			198616.i			0.553555i	0.960934	+	0.276778i	$0.0892666\pi$
$599$			198616.i			0.553555i	−0.960934	+	0.276778i	$0.910733\pi$
$600$		0			0
$601$	−590828.			−1.63573			−0.817865	−	0.575410i	$-0.804843\pi$
$601$	−590828.			−1.63573			−0.817865	+	0.575410i	$0.804843\pi$
$602$		0			0
$603$	−15355.9	−	323176.i	−0.0422318	−	0.888802i
$604$		0			0
$605$			469180.i			1.28183i
$606$		0			0
$607$	−520116.			−1.41164			−0.705818	−	0.708393i	$-0.749420\pi$
$607$	−520116.			−1.41164			−0.705818	+	0.708393i	$0.749420\pi$
$608$		0			0
$609$	−116158.	−	110769.i	−0.313193	−	0.298665i
$610$		0			0
$611$			56070.4i			0.150194i
$612$		0			0
$613$	93765.0			0.249528			0.124764	−	0.992186i	$-0.460183\pi$
$613$	93765.0			0.249528			0.124764	+	0.992186i	$0.460183\pi$
$614$		0			0
$615$	−47062.3	+	49351.6i	−0.124429	+	0.130482i
$616$		0			0
$617$		−	533090.i		−	1.40033i	−0.713982	−	0.700165i	$-0.753110\pi$
$617$		−	533090.i		−	1.40033i	0.713982	−	0.700165i	$-0.246890\pi$
$618$		0			0
$619$	−51579.0			−0.134614			−0.0673072	−	0.997732i	$-0.521441\pi$
$619$	−51579.0			−0.134614			−0.0673072	+	0.997732i	$0.521441\pi$
$620$		0			0
$621$	−88371.0	+	101948.i	−0.229153	+	0.264361i
$622$		0			0
$623$			229853.i			0.592208i
$624$		0			0
$625$	−43615.9			−0.111657
$626$		0			0
$627$	−220196.	−	209982.i	−0.560112	−	0.534130i
$628$		0			0
$629$		−	645482.i		−	1.63149i
$630$		0			0
$631$	746526.			1.87493			0.937467	−	0.348074i	$-0.113164\pi$
$631$	746526.			1.87493			0.937467	+	0.348074i	$0.113164\pi$
$632$		0			0
$633$	387677.	−	406535.i	0.967526	−	1.01459i
$634$		0			0
$635$			109767.i			0.272222i
$636$		0			0
$637$	−6158.60			−0.0151776
$638$		0			0
$639$	−73527.4	+	3493.68i	−0.180073	+	0.00855622i
$640$		0			0
$641$			340710.i			0.829218i	0.910000	+	0.414609i	$0.136082\pi$
$641$			340710.i			0.829218i	−0.910000	+	0.414609i	$0.863918\pi$
$642$		0			0
$643$	−390978.			−0.945649			−0.472825	−	0.881157i	$-0.656766\pi$
$643$	−390978.			−0.945649			−0.472825	+	0.881157i	$0.656766\pi$
$644$		0			0
$645$	−6522.17	−	6219.62i	−0.0156773	−	0.0149501i
$646$		0			0
$647$		−	765071.i		−	1.82765i	−0.406106	−	0.913826i	$-0.633114\pi$
$647$		−	765071.i		−	1.82765i	0.406106	−	0.913826i	$-0.366886\pi$
$648$		0			0
$649$	−63725.6			−0.151295
$650$		0			0
$651$	−145065.	+	152121.i	−0.342294	+	0.358945i
$652$		0			0
$653$			257007.i			0.602723i	0.953510	+	0.301362i	$0.0974411\pi$
$653$			257007.i			0.602723i	−0.953510	+	0.301362i	$0.902559\pi$
$654$		0			0
$655$	−370008.			−0.862439
$656$		0			0
$657$	−13281.7	−	279523.i	−0.0307696	−	0.647571i
$658$		0			0
$659$		−	630779.i		−	1.45247i	−0.687448	−	0.726234i	$-0.741269\pi$
$659$		−	630779.i		−	1.45247i	0.687448	−	0.726234i	$-0.258731\pi$
$660$		0			0
$661$	387314.			0.886462			0.443231	−	0.896408i	$-0.353832\pi$
$661$	387314.			0.886462			0.443231	+	0.896408i	$0.353832\pi$
$662$		0			0
$663$	516477.	+	492519.i	1.17496	+	1.12046i
$664$		0			0
$665$		−	131901.i		−	0.298266i
$666$		0			0
$667$	66994.8			0.150588
$668$		0			0
$669$	−338113.	+	354560.i	−0.755457	+	0.792205i
$670$		0			0
$671$		−	50330.9i		−	0.111786i
$672$		0			0
$673$	−616270.			−1.36063			−0.680316	−	0.732919i	$-0.738158\pi$
$673$	−616270.			−1.36063			−0.680316	+	0.732919i	$0.738158\pi$
$674$		0			0
$675$	195186.	+	169191.i	0.428391	+	0.371339i
$676$		0			0
$677$			622685.i			1.35860i	0.733861	+	0.679300i	$0.237716\pi$
$677$			622685.i			1.35860i	−0.733861	+	0.679300i	$0.762284\pi$
$678$		0			0
$679$	−186589.			−0.404713
$680$		0			0
$681$	−239161.	−	228067.i	−0.515700	−	0.491778i
$682$		0			0
$683$			864762.i			1.85377i	0.375350	+	0.926883i	$0.377522\pi$
$683$			864762.i			1.85377i	−0.375350	+	0.926883i	$0.622478\pi$
$684$		0			0
$685$	230384.			0.490989
$686$		0			0
$687$	137753.	−	144454.i	0.291869	−	0.306067i
$688$		0			0
$689$			1.24163e6i			2.61549i
$690$		0			0
$691$	839151.			1.75745			0.878727	−	0.477325i	$-0.158393\pi$
$691$	839151.			1.75745			0.878727	+	0.477325i	$0.158393\pi$
$692$		0			0
$693$	828103.	−	39347.7i	1.72432	−	0.0819318i
$694$		0			0
$695$		−	217055.i		−	0.449366i
$696$		0			0
$697$	−155364.			−0.319805
$698$		0			0
$699$	242399.	+	231155.i	0.496108	+	0.473095i
$700$		0			0
$701$			332133.i			0.675889i	0.941166	+	0.337945i	$0.109732\pi$
$701$			332133.i			0.675889i	−0.941166	+	0.337945i	$0.890268\pi$
$702$		0			0
$703$	311385.			0.630067
$704$		0			0
$705$	24374.2	−	25559.8i	0.0490401	−	0.0514256i
$706$		0			0
$707$		−	233497.i		−	0.467135i
$708$		0			0
$709$	−366668.			−0.729425			−0.364713	−	0.931120i	$-0.618833\pi$
$709$	−366668.			−0.729425			−0.364713	+	0.931120i	$0.618833\pi$
$710$		0			0
$711$	−24143.1	−	508112.i	−0.0477589	−	1.00512i
$712$		0			0
$713$		−	87737.0i		−	0.172585i
$714$		0			0
$715$	803425.			1.57157
$716$		0			0
$717$	−429688.	−	409756.i	−0.835823	−	0.797052i
$718$		0			0
$719$			775115.i			1.49937i	0.661795	+	0.749685i	$0.269795\pi$
$719$			775115.i			1.49937i	−0.661795	+	0.749685i	$0.730205\pi$
$720$		0			0
$721$	921045.			1.77178
$722$		0			0
$723$	−661642.	+	693827.i	−1.26575	+	1.32732i
$724$		0			0
$725$		−	128265.i		−	0.244024i
$726$		0			0
$727$	−808520.			−1.52976			−0.764878	−	0.644176i	$-0.777201\pi$
$727$	−808520.			−1.52976			−0.764878	+	0.644176i	$0.777201\pi$
$728$		0			0
$729$	75442.3	+	526059.i	0.141958	+	0.989873i
$730$		0			0
$731$		−	20532.5i		−	0.0384243i
$732$		0			0
$733$	718640.			1.33753			0.668765	−	0.743474i	$-0.266823\pi$
$733$	718640.			1.33753			0.668765	+	0.743474i	$0.266823\pi$
$734$		0			0
$735$	2807.41	+	2677.18i	0.00519674	+	0.00495568i
$736$		0			0
$737$		−	829814.i		−	1.52773i
$738$		0			0
$739$	−575601.			−1.05398			−0.526990	−	0.849871i	$-0.676680\pi$
$739$	−575601.			−1.05398			−0.526990	+	0.849871i	$0.676680\pi$
$740$		0			0
$741$	−237594.	+	249152.i	−0.432713	+	0.453761i
$742$		0			0
$743$		−	756944.i		−	1.37115i	−0.728000	−	0.685577i	$-0.759550\pi$
$743$		−	756944.i		−	1.37115i	0.728000	−	0.685577i	$-0.240450\pi$
$744$		0			0
$745$	398255.			0.717545
$746$		0			0
$747$	−415265.	+	19731.5i	−0.744191	+	0.0353605i
$748$		0			0
$749$		−	861724.i		−	1.53605i
$750$		0			0
$751$	908964.			1.61163			0.805817	−	0.592164i	$-0.201726\pi$
$751$	908964.			1.61163			0.805817	+	0.592164i	$0.201726\pi$
$752$		0			0
$753$	−38280.7	−	36504.9i	−0.0675133	−	0.0643816i
$754$		0			0
$755$			249564.i			0.437813i
$756$		0			0
$757$	−534049.			−0.931942			−0.465971	−	0.884800i	$-0.654295\pi$
$757$	−534049.			−0.931942			−0.465971	+	0.884800i	$0.654295\pi$
$758$		0			0
$759$	−238808.	+	250424.i	−0.414538	+	0.434703i
$760$		0			0
$761$			33632.8i			0.0580756i	0.999578	+	0.0290378i	$0.00924432\pi$
$761$			33632.8i			0.0580756i	−0.999578	+	0.0290378i	$0.990756\pi$
$762$		0			0
$763$	−205376.			−0.352777
$764$		0			0
$765$	−21335.9	−	449032.i	−0.0364577	−	0.767281i
$766$		0			0
$767$			72105.5i			0.122568i
$768$		0			0
$769$	479343.			0.810575			0.405288	−	0.914189i	$-0.367171\pi$
$769$	479343.			0.810575			0.405288	+	0.914189i	$0.367171\pi$
$770$		0			0
$771$	−449776.	−	428912.i	−0.756637	−	0.721539i
$772$		0			0
$773$			120395.i			0.201487i	0.994912	+	0.100744i	$0.0321222\pi$
$773$			120395.i			0.201487i	−0.994912	+	0.100744i	$0.967878\pi$
$774$		0			0
$775$	−167977.			−0.279671
$776$		0			0
$777$	−585520.	+	614002.i	−0.969840	+	1.01702i
$778$		0			0
$779$		−	74948.6i		−	0.123506i
$780$		0			0
$781$	−188795.			−0.309520
$782$		0			0
$783$	172848.	−	199405.i	0.281930	−	0.325246i
$784$		0			0
$785$		−	46532.4i		−	0.0755120i
$786$		0			0
$787$	445832.			0.719817			0.359908	−	0.932988i	$-0.382808\pi$
$787$	445832.			0.719817			0.359908	+	0.932988i	$0.382808\pi$
$788$		0			0
$789$	−182327.	−	173869.i	−0.292884	−	0.279298i
$790$		0			0
$791$			988183.i			1.57937i
$792$		0			0
$793$	−56949.3			−0.0905612
$794$		0			0
$795$	539745.	−	566000.i	0.853993	−	0.895534i
$796$		0			0
$797$		−	869571.i		−	1.36895i	−0.729035	−	0.684476i	$-0.760031\pi$
$797$		−	869571.i		−	1.36895i	0.729035	−	0.684476i	$-0.239969\pi$
$798$		0			0
$799$	80465.0			0.126041
$800$		0			0
$801$	−377479.	+	17936.1i	−0.588339	+	0.0279552i
$802$		0			0
$803$		−	717727.i		−	1.11308i
$804$		0			0
$805$	−150008.			−0.231485
$806$		0			0
$807$	−797116.	−	760140.i	−1.22398	−	1.16720i
$808$		0			0
$809$			246257.i			0.376263i	0.982144	+	0.188131i	$0.0602431\pi$
$809$			246257.i			0.376263i	−0.982144	+	0.188131i	$0.939757\pi$
$810$		0			0
$811$	−282694.			−0.429808			−0.214904	−	0.976635i	$-0.568944\pi$
$811$	−282694.			−0.429808			−0.214904	+	0.976635i	$0.568944\pi$
$812$		0			0
$813$	−408393.	+	428258.i	−0.617870	+	0.647925i
$814$		0			0
$815$			368297.i			0.554476i
$816$		0			0
$817$	9904.98			0.0148392
$818$		0			0
$819$	−44521.8	−	936998.i	−0.0663751	−	1.39692i
$820$		0			0
$821$			647700.i			0.960920i	0.877017	+	0.480460i	$0.159530\pi$
$821$			647700.i			0.960920i	−0.877017	+	0.480460i	$0.840470\pi$
$822$		0			0
$823$	47943.5			0.0707832			0.0353916	−	0.999374i	$-0.488732\pi$
$823$	47943.5			0.0707832			0.0353916	+	0.999374i	$0.488732\pi$
$824$		0			0
$825$	479451.	+	457210.i	0.704427	+	0.671751i
$826$		0			0
$827$			35695.1i			0.0521912i	0.999659	+	0.0260956i	$0.00830743\pi$
$827$			35695.1i			0.0521912i	−0.999659	+	0.0260956i	$0.991693\pi$
$828$		0			0
$829$	−1.01412e6			−1.47564			−0.737820	−	0.674998i	$-0.764144\pi$
$829$	−1.01412e6			−1.47564			−0.737820	+	0.674998i	$0.764144\pi$
$830$		0			0
$831$	−601699.	+	630968.i	−0.871319	+	0.913703i
$832$		0			0
$833$			8838.02i			0.0127369i
$834$		0			0
$835$	−423755.			−0.607773
$836$		0			0
$837$	−261142.	−	226364.i	−0.372758	−	0.323114i
$838$		0			0
$839$		−	128892.i		−	0.183105i	−0.995800	−	0.0915527i	$-0.970817\pi$
$839$		−	128892.i		−	0.183105i	0.995800	−	0.0915527i	$-0.0291830\pi$
$840$		0			0
$841$	576243.			0.814731
$842$		0			0
$843$	779188.	+	743044.i	1.09645	+	1.04558i
$844$		0			0
$845$		−	439190.i		−	0.615090i
$846$		0			0
$847$	1.40499e6			1.95843
$848$		0			0
$849$	442918.	−	464464.i	0.614481	−	0.644371i
$850$		0			0
$851$		−	354131.i		−	0.488995i
$852$		0			0
$853$	−784753.			−1.07854			−0.539268	−	0.842134i	$-0.681299\pi$
$853$	−784753.			−1.07854			−0.539268	+	0.842134i	$0.681299\pi$
$854$		0			0
$855$	216616.	−	10292.6i	0.296318	−	0.0140797i
$856$		0			0
$857$			697644.i			0.949888i	0.880016	+	0.474944i	$0.157532\pi$
$857$			697644.i			0.949888i	−0.880016	+	0.474944i	$0.842468\pi$
$858$		0			0
$859$	191027.			0.258886			0.129443	−	0.991587i	$-0.458681\pi$
$859$	191027.			0.258886			0.129443	+	0.991587i	$0.458681\pi$
$860$		0			0
$861$	147787.	+	140931.i	0.199356	+	0.190109i
$862$		0			0
$863$		−	826680.i		−	1.10998i	−0.831857	−	0.554991i	$-0.812722\pi$
$863$		−	826680.i		−	1.10998i	0.831857	−	0.554991i	$-0.187278\pi$
$864$		0			0
$865$	251532.			0.336171
$866$		0			0
$867$	188042.	−	197189.i	0.250160	−	0.262329i
$868$		0			0
$869$		−	1.30467e6i		−	1.72767i
$870$		0			0
$871$	−938934.			−1.23765
$872$		0			0
$873$	−14560.1	−	306429.i	−0.0191045	−	0.402069i
$874$		0			0
$875$			793782.i			1.03678i
$876$		0			0
$877$	1.03774e6			1.34923			0.674617	−	0.738168i	$-0.264309\pi$
$877$	1.03774e6			1.34923			0.674617	+	0.738168i	$0.264309\pi$
$878$		0			0
$879$	−74114.2	−	70676.3i	−0.0959232	−	0.0914736i
$880$		0			0
$881$			151594.i			0.195312i	0.995220	+	0.0976562i	$0.0311345\pi$
$881$			151594.i			0.195312i	−0.995220	+	0.0976562i	$0.968865\pi$
$882$		0			0
$883$	−863861.			−1.10796			−0.553978	−	0.832531i	$-0.686891\pi$
$883$	−863861.			−1.10796			−0.553978	+	0.832531i	$0.686891\pi$
$884$		0			0
$885$	31344.7	−	32869.4i	0.0400201	−	0.0419668i
$886$		0			0
$887$			308258.i			0.391803i	0.980624	+	0.195901i	$0.0627633\pi$
$887$			308258.i			0.391803i	−0.980624	+	0.195901i	$0.937237\pi$
$888$		0			0
$889$	328704.			0.415912
$890$		0			0
$891$	129238.	+	1.35689e6i	0.162793	+	1.70919i
$892$		0			0
$893$			38816.8i			0.0486762i
$894$		0			0
$895$	−209354.			−0.261357
$896$		0			0
$897$	283355.	+	270210.i	0.352164	+	0.335828i
$898$		0			0
$899$			171608.i			0.212333i
$900$		0			0
$901$	1.78183e6			2.19491
$902$		0			0
$903$	−18625.1	+	19531.1i	−0.0228414	+	0.0239525i
$904$		0			0
$905$			991266.i			1.21030i
$906$		0			0
$907$	61898.5			0.0752429			0.0376214	−	0.999292i	$-0.488022\pi$
$907$	61898.5			0.0752429			0.0376214	+	0.999292i	$0.488022\pi$
$908$		0			0
$909$	383463.	−	18220.4i	0.464083	−	0.0220511i
$910$		0			0
$911$			521217.i			0.628032i	0.949418	+	0.314016i	$0.101675\pi$
$911$			521217.i			0.628032i	−0.949418	+	0.314016i	$0.898325\pi$
$912$		0			0
$913$	−1.06627e6			−1.27916
$914$		0			0
$915$	25960.5	+	24756.2i	0.0310078	+	0.0295694i
$916$		0			0
$917$			1.10801e6i			1.31767i
$918$		0			0
$919$	1.29334e6			1.53138			0.765691	−	0.643209i	$-0.222397\pi$
$919$	1.29334e6			1.53138			0.765691	+	0.643209i	$0.222397\pi$
$920$		0			0
$921$	775548.	−	813274.i	0.914302	−	0.958777i
$922$		0			0
$923$			213621.i			0.250750i
$924$		0			0
$925$	−678003.			−0.792406
$926$		0			0
$927$	71871.7	+	1.51260e6i	0.0836370	+	1.76021i
$928$		0			0
$929$			11108.9i			0.0128718i	0.999979	+	0.00643589i	$0.00204862\pi$
$929$			11108.9i			0.0128718i	−0.999979	+	0.00643589i	$0.997951\pi$
$930$		0			0
$931$	−4263.51			−0.00491890
$932$		0			0
$933$	−76379.7	−	72836.7i	−0.0877435	−	0.0836733i
$934$		0			0
$935$		−	1.15297e6i		−	1.31885i
$936$		0			0
$937$	−585633.			−0.667032			−0.333516	−	0.942744i	$-0.608235\pi$
$937$	−585633.			−0.667032			−0.333516	+	0.942744i	$0.608235\pi$
$938$		0			0
$939$	614106.	−	643978.i	0.696486	−	0.730365i
$940$		0			0
$941$			1.06797e6i			1.20609i	0.797706	+	0.603047i	$0.206047\pi$
$941$			1.06797e6i			1.20609i	−0.797706	+	0.603047i	$0.793953\pi$
$942$		0			0
$943$	−85237.3			−0.0958531
$944$		0			0
$945$	−387024.	+	446487.i	−0.433385	+	0.499971i
$946$		0			0
$947$			573756.i			0.639775i	0.947456	+	0.319888i	$0.103645\pi$
$947$			573756.i			0.639775i	−0.947456	+	0.319888i	$0.896355\pi$
$948$		0			0
$949$	−812107.			−0.901739
$950$		0			0
$951$	−749.470	−	714.704i	−0.000828692	−	0.000790251i
$952$		0			0
$953$			173662.i			0.191213i	0.995419	+	0.0956067i	$0.0304791\pi$
$953$			173662.i			0.191213i	−0.995419	+	0.0956067i	$0.969521\pi$
$954$		0			0
$955$	−829718.			−0.909753
$956$		0			0
$957$	467093.	−	489814.i	0.510011	−	0.534820i
$958$		0			0
$959$		−	689902.i		−	0.750154i
$960$		0			0
$961$	−698781.			−0.756649
$962$		0			0
$963$	1.41518e6	−	67242.7i	1.52601	−	0.0725091i
$964$		0			0
$965$			11672.4i			0.0125344i
$966$		0			0
$967$	−598163.			−0.639686			−0.319843	−	0.947471i	$-0.603630\pi$
$967$	−598163.			−0.639686			−0.319843	+	0.947471i	$0.603630\pi$
$968$		0			0
$969$	357550.	+	340965.i	0.380794	+	0.363130i
$970$		0			0
$971$		−	1.40734e6i		−	1.49266i	−0.665574	−	0.746332i	$-0.731813\pi$
$971$		−	1.40734e6i		−	1.49266i	0.665574	−	0.746332i	$-0.268187\pi$
$972$		0			0
$973$	−649987.			−0.686560
$974$		0			0
$975$	517333.	−	542498.i	0.544203	−	0.570675i
$976$		0			0
$977$		−	1.10475e6i		−	1.15738i	−0.815547	−	0.578690i	$-0.803564\pi$
$977$		−	1.10475e6i		−	1.15738i	0.815547	−	0.578690i	$-0.196436\pi$
$978$		0			0
$979$	−969246.			−1.01127
$980$		0			0
$981$	−16026.0	−	337281.i	−0.0166528	−	0.350472i
$982$		0			0
$983$		−	1.47757e6i		−	1.52912i	−0.644554	−	0.764559i	$-0.722957\pi$
$983$		−	1.47757e6i		−	1.52912i	0.644554	−	0.764559i	$-0.277043\pi$
$984$		0			0
$985$	−747743.			−0.770690
$986$		0			0
$987$	−76540.7	−	72990.2i	−0.0785702	−	0.0749256i
$988$		0			0
$989$		−	11264.7i		−	0.0115167i
$990$		0			0
$991$	486590.			0.495468			0.247734	−	0.968828i	$-0.420314\pi$
$991$	486590.			0.495468			0.247734	+	0.968828i	$0.420314\pi$
$992$		0			0
$993$	564559.	−	592021.i	0.572546	−	0.600397i
$994$		0			0
$995$			468818.i			0.473542i
$996$		0			0
$997$	500820.			0.503839			0.251919	−	0.967748i	$-0.418938\pi$
$997$	500820.			0.503839			0.251919	+	0.967748i	$0.418938\pi$
$998$		0			0
$999$	−1.05404e6	−	913666.i	−1.05615	−	0.915496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.e.c.17.2		4
3.2	odd	2	inner	48.5.e.c.17.1		4
4.3	odd	2		24.5.e.a.17.3	✓	4
8.3	odd	2		192.5.e.f.65.2		4
8.5	even	2		192.5.e.e.65.3		4
12.11	even	2		24.5.e.a.17.4	yes	4
20.3	even	4		600.5.c.a.449.8		8
20.7	even	4		600.5.c.a.449.1		8
20.19	odd	2		600.5.l.a.401.2		4
24.5	odd	2		192.5.e.e.65.4		4
24.11	even	2		192.5.e.f.65.1		4
36.7	odd	6		648.5.m.e.377.3		8
36.11	even	6		648.5.m.e.377.2		8
36.23	even	6		648.5.m.e.593.3		8
36.31	odd	6		648.5.m.e.593.2		8
60.23	odd	4		600.5.c.a.449.2		8
60.47	odd	4		600.5.c.a.449.7		8
60.59	even	2		600.5.l.a.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.5.e.a.17.3	✓	4	4.3	odd	2
24.5.e.a.17.4	yes	4	12.11	even	2
48.5.e.c.17.1		4	3.2	odd	2	inner
48.5.e.c.17.2		4	1.1	even	1	trivial
192.5.e.e.65.3		4	8.5	even	2
192.5.e.e.65.4		4	24.5	odd	2
192.5.e.f.65.1		4	24.11	even	2
192.5.e.f.65.2		4	8.3	odd	2
600.5.c.a.449.1		8	20.7	even	4
600.5.c.a.449.2		8	60.23	odd	4
600.5.c.a.449.7		8	60.47	odd	4
600.5.c.a.449.8		8	20.3	even	4
600.5.l.a.401.1		4	60.59	even	2
600.5.l.a.401.2		4	20.19	odd	2
648.5.m.e.377.2		8	36.11	even	6
648.5.m.e.377.3		8	36.7	odd	6
648.5.m.e.593.2		8	36.31	odd	6
648.5.m.e.593.3		8	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.21110 + 6.51323i) q^{3} -16.4520i q^{5} -49.2666 q^{7} +(-3.84441 - 80.9087i) q^{9} +O(q^{10})\)	\(q+(-6.21110 + 6.51323i) q^{3} -16.4520i q^{5} -49.2666 q^{7} +(-3.84441 - 80.9087i) q^{9} -207.748i q^{11} -235.066 q^{13} +(107.156 + 102.185i) q^{15} +337.337i q^{17} -162.733 q^{19} +(306.000 - 320.885i) q^{21} +185.073i q^{23} +354.332 q^{25} +(550.855 + 477.493i) q^{27} -361.991i q^{29} -474.067 q^{31} +(1353.11 + 1290.34i) q^{33} +810.533i q^{35} -1913.47 q^{37} +(1460.02 - 1531.04i) q^{39} +460.560i q^{41} -60.8663 q^{43} +(-1331.11 + 63.2482i) q^{45} -238.530i q^{47} +26.1994 q^{49} +(-2197.15 - 2095.23i) q^{51} -5282.04i q^{53} -3417.86 q^{55} +(1010.75 - 1059.92i) q^{57} -306.745i q^{59} +242.269 q^{61} +(189.401 + 3986.10i) q^{63} +3867.31i q^{65} +3994.33 q^{67} +(-1205.42 - 1149.51i) q^{69} -908.770i q^{71} +3454.80 q^{73} +(-2200.79 + 2307.85i) q^{75} +10235.0i q^{77} +6280.06 q^{79} +(-6531.44 + 622.093i) q^{81} -5132.51i q^{83} +5549.86 q^{85} +(2357.73 + 2248.36i) q^{87} -4665.49i q^{89} +11580.9 q^{91} +(2944.48 - 3087.71i) q^{93} +2677.29i q^{95} +3787.34 q^{97} +(-16808.6 + 798.668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 24 q^{7} + 100 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 24 * q^7 + 100 * q^9	\( 4 q + 4 q^{3} - 24 q^{7} + 100 q^{9} - 248 q^{13} + 544 q^{15} - 824 q^{19} + 1224 q^{21} - 2044 q^{25} + 1540 q^{27} - 3800 q^{31} + 2528 q^{33} - 2808 q^{37} + 4744 q^{39} + 968 q^{43} + 2752 q^{45} - 1972 q^{49} - 3712 q^{51} - 4672 q^{55} - 2072 q^{57} + 8584 q^{61} + 4392 q^{63} + 15112 q^{67} - 7360 q^{69} + 5512 q^{73} - 27004 q^{75} + 1064 q^{79} - 14588 q^{81} + 2816 q^{85} + 7008 q^{87} + 31440 q^{91} - 17528 q^{93} + 32456 q^{97} - 36544 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 24 * q^7 + 100 * q^9 - 248 * q^13 + 544 * q^15 - 824 * q^19 + 1224 * q^21 - 2044 * q^25 + 1540 * q^27 - 3800 * q^31 + 2528 * q^33 - 2808 * q^37 + 4744 * q^39 + 968 * q^43 + 2752 * q^45 - 1972 * q^49 - 3712 * q^51 - 4672 * q^55 - 2072 * q^57 + 8584 * q^61 + 4392 * q^63 + 15112 * q^67 - 7360 * q^69 + 5512 * q^73 - 27004 * q^75 + 1064 * q^79 - 14588 * q^81 + 2816 * q^85 + 7008 * q^87 + 31440 * q^91 - 17528 * q^93 + 32456 * q^97 - 36544 * q^99

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