LMFDB - Embedded newform 354.6.c.a.353.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.11
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-11.6908 - 10.3115i) q^{3} +16.0000 q^{4} -106.082i q^{5} +(46.7630 + 41.2458i) q^{6} +71.9340 q^{7} -64.0000 q^{8} +(30.3476 + 241.098i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-11.6908 - 10.3115i) q^{3} +16.0000 q^{4} -106.082i q^{5} +(46.7630 + 41.2458i) q^{6} +71.9340 q^{7} -64.0000 q^{8} +(30.3476 + 241.098i) q^{9} +424.326i q^{10} +484.580 q^{11} +(-187.052 - 164.983i) q^{12} +699.407i q^{13} -287.736 q^{14} +(-1093.86 + 1240.17i) q^{15} +256.000 q^{16} -2022.64i q^{17} +(-121.390 - 964.390i) q^{18} +219.981 q^{19} -1697.30i q^{20} +(-840.963 - 741.744i) q^{21} -1938.32 q^{22} -2068.62 q^{23} +(748.208 + 659.933i) q^{24} -8128.29 q^{25} -2797.63i q^{26} +(2131.28 - 3131.54i) q^{27} +1150.94 q^{28} +259.882i q^{29} +(4375.42 - 4960.69i) q^{30} -3949.77i q^{31} -1024.00 q^{32} +(-5665.11 - 4996.73i) q^{33} +8090.56i q^{34} -7630.87i q^{35} +(485.562 + 3857.56i) q^{36} +12268.9i q^{37} -879.923 q^{38} +(7211.90 - 8176.59i) q^{39} +6789.22i q^{40} -6337.49i q^{41} +(3363.85 + 2966.98i) q^{42} -16976.7i q^{43} +7753.28 q^{44} +(25576.0 - 3219.32i) q^{45} +8274.46 q^{46} -7339.59 q^{47} +(-2992.83 - 2639.73i) q^{48} -11632.5 q^{49} +32513.2 q^{50} +(-20856.4 + 23646.2i) q^{51} +11190.5i q^{52} +28405.7i q^{53} +(-8525.12 + 12526.2i) q^{54} -51405.0i q^{55} -4603.77 q^{56} +(-2571.74 - 2268.32i) q^{57} -1039.53i q^{58} +(-26256.2 - 5053.23i) q^{59} +(-17501.7 + 19842.8i) q^{60} -52783.9i q^{61} +15799.1i q^{62} +(2183.02 + 17343.1i) q^{63} +4096.00 q^{64} +74194.1 q^{65} +(22660.4 + 19986.9i) q^{66} +20843.7i q^{67} -32362.3i q^{68} +(24183.7 + 21330.5i) q^{69} +30523.5i q^{70} -22716.8i q^{71} +(-1942.25 - 15430.2i) q^{72} -10171.5i q^{73} -49075.6i q^{74} +(95025.9 + 83814.5i) q^{75} +3519.69 q^{76} +34857.8 q^{77} +(-28847.6 + 32706.4i) q^{78} -88871.6 q^{79} -27156.9i q^{80} +(-57207.0 + 14633.5i) q^{81} +25350.0i q^{82} -83195.1 q^{83} +(-13455.4 - 11867.9i) q^{84} -214565. q^{85} +67906.7i q^{86} +(2679.76 - 3038.22i) q^{87} -31013.1 q^{88} +47066.8 q^{89} +(-102304. + 12877.3i) q^{90} +50311.1i q^{91} -33097.9 q^{92} +(-40727.9 + 46175.8i) q^{93} +29358.4 q^{94} -23335.9i q^{95} +(11971.3 + 10558.9i) q^{96} +147657. i q^{97} +46530.0 q^{98} +(14705.9 + 116831. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.00000			−0.707107
$2$	−4.00000			−0.707107
$3$	−11.6908	−	10.3115i	−0.749962	−	0.661480i
$3$	−11.6908	−	10.3115i	−0.749962	−	0.661480i
$4$	16.0000			0.500000
$5$		−	106.082i		−	1.89764i	−0.315811	−	0.948822i	$-0.602277\pi$
$5$		−	106.082i		−	1.89764i	0.315811	−	0.948822i	$-0.397723\pi$
$6$	46.7630	+	41.2458i	0.530304	+	0.467737i
$7$	71.9340			0.554867			0.277434	−	0.960745i	$-0.410516\pi$
$7$	71.9340			0.554867			0.277434	+	0.960745i	$0.410516\pi$
$8$	−64.0000			−0.353553
$9$	30.3476	+	241.098i	0.124887	+	0.992171i
$10$			424.326i			1.34184i
$11$	484.580			1.20749			0.603746	−	0.797177i	$-0.293674\pi$
$11$	484.580			1.20749			0.603746	+	0.797177i	$0.293674\pi$
$12$	−187.052	−	164.983i	−0.374981	−	0.330740i
$13$			699.407i			1.14781i	0.818921	+	0.573907i	$0.194573\pi$
$13$			699.407i			1.14781i	−0.818921	+	0.573907i	$0.805427\pi$
$14$	−287.736			−0.392350
$15$	−1093.86	+	1240.17i	−1.25525	+	1.42316i
$16$	256.000			0.250000
$17$		−	2022.64i		−	1.69745i	−0.528836	−	0.848724i	$-0.677371\pi$
$17$		−	2022.64i		−	1.69745i	0.528836	−	0.848724i	$-0.322629\pi$
$18$	−121.390	−	964.390i	−0.0883087	−	0.701571i
$19$	219.981			0.139798			0.0698990	−	0.997554i	$-0.477732\pi$
$19$	219.981			0.139798			0.0698990	+	0.997554i	$0.477732\pi$
$20$		−	1697.30i		−	0.948822i
$21$	−840.963	−	741.744i	−0.416129	−	0.367034i
$22$	−1938.32			−0.853825
$23$	−2068.62			−0.815381			−0.407690	−	0.913120i	$-0.633666\pi$
$23$	−2068.62			−0.815381			−0.407690	+	0.913120i	$0.633666\pi$
$24$	748.208	+	659.933i	0.265152	+	0.233869i
$25$	−8128.29			−2.60105
$26$		−	2797.63i		−	0.811627i
$27$	2131.28	−	3131.54i	0.562641	−	0.826701i
$28$	1150.94			0.277434
$29$			259.882i			0.0573827i	0.999588	+	0.0286914i	$0.00913399\pi$
$29$			259.882i			0.0573827i	−0.999588	+	0.0286914i	$0.990866\pi$
$30$	4375.42	−	4960.69i	0.887599	−	1.00633i
$31$		−	3949.77i		−	0.738190i	−0.929392	−	0.369095i	$-0.879668\pi$
$31$		−	3949.77i		−	0.738190i	0.929392	−	0.369095i	$-0.120332\pi$
$32$	−1024.00			−0.176777
$33$	−5665.11	−	4996.73i	−0.905573	−	0.798732i
$34$			8090.56i			1.20028i
$35$		−	7630.87i		−	1.05294i
$36$	485.562	+	3857.56i	0.0624437	+	0.496085i
$37$			12268.9i			1.47333i	0.676256	+	0.736667i	$0.263601\pi$
$37$			12268.9i			1.47333i	−0.676256	+	0.736667i	$0.736399\pi$
$38$	−879.923			−0.0988520
$39$	7211.90	−	8176.59i	0.759256	−	0.860817i
$40$			6789.22i			0.670919i
$41$		−	6337.49i		−	0.588787i	−0.955684	−	0.294393i	$-0.904882\pi$
$41$		−	6337.49i		−	0.588787i	0.955684	−	0.294393i	$-0.0951176\pi$
$42$	3363.85	+	2966.98i	0.294248	+	0.259532i
$43$		−	16976.7i		−	1.40017i	−0.714059	−	0.700086i	$-0.753145\pi$
$43$		−	16976.7i		−	1.40017i	0.714059	−	0.700086i	$-0.246855\pi$
$44$	7753.28			0.603746
$45$	25576.0	−	3219.32i	1.88279	−	0.236992i
$46$	8274.46			0.576561
$47$	−7339.59			−0.484649			−0.242324	−	0.970195i	$-0.577910\pi$
$47$	−7339.59			−0.484649			−0.242324	+	0.970195i	$0.577910\pi$
$48$	−2992.83	−	2639.73i	−0.187491	−	0.165370i
$49$	−11632.5			−0.692123
$50$	32513.2			1.83922
$51$	−20856.4	+	23646.2i	−1.12283	+	1.27302i
$52$			11190.5i			0.573907i
$53$			28405.7i			1.38904i	0.719472	+	0.694521i	$0.244384\pi$
$53$			28405.7i			1.38904i	−0.719472	+	0.694521i	$0.755616\pi$
$54$	−8525.12	+	12526.2i	−0.397847	+	0.584566i
$55$		−	51405.0i		−	2.29139i
$56$	−4603.77			−0.196175
$57$	−2571.74	−	2268.32i	−0.104843	−	0.0924736i
$58$		−	1039.53i		−	0.0405757i
$59$	−26256.2	−	5053.23i	−0.981979	−	0.188990i
$59$	−26256.2	−	5053.23i	−0.981979	−	0.188990i
$60$	−17501.7	+	19842.8i	−0.627627	+	0.711581i
$61$		−	52783.9i		−	1.81625i	−0.418695	−	0.908127i	$-0.637512\pi$
$61$		−	52783.9i		−	1.81625i	0.418695	−	0.908127i	$-0.362488\pi$
$62$			15799.1i			0.521979i
$63$	2183.02	+	17343.1i	0.0692959	+	0.550523i
$64$	4096.00			0.125000
$65$	74194.1			2.17814
$66$	22660.4	+	19986.9i	0.640337	+	0.564789i
$67$			20843.7i			0.567267i	0.958933	+	0.283633i	$0.0915398\pi$
$67$			20843.7i			0.567267i	−0.958933	+	0.283633i	$0.908460\pi$
$68$		−	32362.3i		−	0.848724i
$69$	24183.7	+	21330.5i	0.611505	+	0.539358i
$70$			30523.5i			0.744541i
$71$		−	22716.8i		−	0.534813i	−0.963584	−	0.267406i	$-0.913833\pi$
$71$		−	22716.8i		−	0.534813i	0.963584	−	0.267406i	$-0.0861666\pi$
$72$	−1942.25	−	15430.2i	−0.0441543	−	0.350785i
$73$		−	10171.5i		−	0.223398i	−0.993742	−	0.111699i	$-0.964371\pi$
$73$		−	10171.5i		−	0.223398i	0.993742	−	0.111699i	$-0.0356292\pi$
$74$		−	49075.6i		−	1.04180i
$75$	95025.9	+	83814.5i	1.95069	+	1.72055i
$76$	3519.69			0.0698990
$77$	34857.8			0.669997
$78$	−28847.6	+	32706.4i	−0.536875	+	0.608690i
$79$	−88871.6			−1.60212			−0.801060	−	0.598584i	$-0.795730\pi$
$79$	−88871.6			−1.60212			−0.801060	+	0.598584i	$0.795730\pi$
$80$		−	27156.9i		−	0.474411i
$81$	−57207.0	+	14633.5i	−0.968806	+	0.247819i
$82$			25350.0i			0.416335i
$83$	−83195.1			−1.32557			−0.662785	−	0.748810i	$-0.730625\pi$
$83$	−83195.1			−1.32557			−0.662785	+	0.748810i	$0.730625\pi$
$84$	−13455.4	−	11867.9i	−0.208065	−	0.183517i
$85$	−214565.			−3.22115
$86$			67906.7i			0.990071i
$87$	2679.76	−	3038.22i	0.0379575	−	0.0430349i
$88$	−31013.1			−0.426913
$89$	47066.8			0.629853			0.314927	−	0.949116i	$-0.398020\pi$
$89$	47066.8			0.629853			0.314927	+	0.949116i	$0.398020\pi$
$90$	−102304.	+	12877.3i	−1.33133	+	0.167578i
$91$			50311.1i			0.636884i
$92$	−33097.9			−0.407690
$93$	−40727.9	+	46175.8i	−0.488298	+	0.553614i
$94$	29358.4			0.342699
$95$		−	23335.9i		−	0.265287i
$96$	11971.3	+	10558.9i	0.132576	+	0.116934i
$97$			147657.i			1.59340i	0.604377	+	0.796699i	$0.293422\pi$
$97$			147657.i			1.59340i	−0.604377	+	0.796699i	$0.706578\pi$
$98$	46530.0			0.489405
$99$	14705.9	+	116831.i	0.150800	+	1.19804i
$100$	−130053.			−1.30053
$101$	−8045.18			−0.0784752			−0.0392376	−	0.999230i	$-0.512493\pi$
$101$	−8045.18			−0.0784752			−0.0392376	+	0.999230i	$0.512493\pi$
$102$	83425.5	−	94584.8i	0.793960	−	0.900163i
$103$			11808.3i			0.109672i	0.998495	+	0.0548360i	$0.0174636\pi$
$103$			11808.3i			0.109672i	−0.998495	+	0.0548360i	$0.982536\pi$
$104$		−	44762.0i		−	0.405813i
$105$	−78685.4	+	89210.6i	−0.696499	+	0.789666i
$106$		−	113623.i		−	0.982202i
$107$			140645.i			1.18759i	0.804618	+	0.593793i	$0.202370\pi$
$107$			140645.i			1.18759i	−0.804618	+	0.593793i	$0.797630\pi$
$108$	34100.5	−	50104.7i	0.281320	−	0.413351i
$109$		−	198260.i		−	1.59834i	−0.601105	−	0.799170i	$-0.705272\pi$
$109$		−	198260.i		−	1.59834i	0.601105	−	0.799170i	$-0.294728\pi$
$110$			205620.i			1.62026i
$111$	126510.	−	143433.i	0.974581	−	1.10494i
$112$	18415.1			0.138717
$113$	23565.2			0.173610			0.0868050	−	0.996225i	$-0.472334\pi$
$113$	23565.2			0.173610			0.0868050	+	0.996225i	$0.472334\pi$
$114$	10287.0	+	9073.29i	0.0741353	+	0.0653887i
$115$			219442.i			1.54730i
$116$			4158.11i			0.0286914i
$117$	−168625.	+	21225.3i	−1.13883	+	0.143347i
$118$	105025.	+	20212.9i	0.694364	+	0.133636i
$119$		−	145497.i		−	0.941858i
$120$	70006.7	−	79371.1i	0.443799	−	0.503164i
$121$	73767.0			0.458035
$122$			211135.i			1.28429i
$123$	−65348.8	+	74090.1i	−0.389471	+	0.441568i
$124$		−	63196.4i		−	0.369095i
$125$			530757.i			3.03823i
$126$	−8732.10	−	69372.4i	−0.0489996	−	0.389279i
$127$	122713.			0.675121			0.337561	−	0.941304i	$-0.390398\pi$
$127$	122713.			0.675121			0.337561	+	0.941304i	$0.390398\pi$
$128$	−16384.0			−0.0883883
$129$	−175054.	+	198470.i	−0.926186	+	1.05008i
$130$	−296776.			−1.54018
$131$	264589.			1.34708			0.673541	−	0.739150i	$-0.264772\pi$
$131$	264589.			1.34708			0.673541	+	0.739150i	$0.264772\pi$
$132$	−90641.8	−	79947.7i	−0.452787	−	0.399366i
$133$	15824.1			0.0775693
$134$		−	83374.7i		−	0.401118i
$135$	−332199.	−	226090.i	−1.56879	−	1.06769i
$136$			129449.i			0.600139i
$137$		−	223971.i		−	1.01951i	−0.860321	−	0.509753i	$-0.829737\pi$
$137$		−	223971.i		−	1.01951i	0.860321	−	0.509753i	$-0.170263\pi$
$138$	−96734.8	−	85321.8i	−0.432399	−	0.381384i
$139$	−199108.			−0.874082			−0.437041	−	0.899442i	$-0.643974\pi$
$139$	−199108.			−0.874082			−0.437041	+	0.899442i	$0.643974\pi$
$140$		−	122094.i		−	0.526470i
$141$	85805.4	+	75681.9i	0.363468	+	0.320586i
$142$			90867.3i			0.378170i
$143$			338919.i			1.38597i
$144$	7768.99	+	61721.0i	0.0312218	+	0.248043i
$145$	27568.7			0.108892
$146$			40686.1i			0.157966i
$147$	135993.	+	119948.i	0.519066	+	0.457826i
$148$			196302.i			0.736667i
$149$	−384853.			−1.42014			−0.710068	−	0.704134i	$-0.751336\pi$
$149$	−384853.			−1.42014			−0.710068	+	0.704134i	$0.751336\pi$
$150$	−380104.	−	335258.i	−1.37935	−	1.21661i
$151$			184660.i			0.659068i	0.944144	+	0.329534i	$0.106892\pi$
$151$			184660.i			0.659068i	−0.944144	+	0.329534i	$0.893108\pi$
$152$	−14078.8			−0.0494260
$153$	487654.	−	61382.3i	1.68416	−	0.211990i
$154$	−139431.			−0.473759
$155$	−418998.			−1.40082
$156$	115390.	−	130825.i	0.379628	−	0.430409i
$157$			131630.i			0.426193i	0.977031	+	0.213096i	$0.0683548\pi$
$157$			131630.i			0.426193i	−0.977031	+	0.213096i	$0.931645\pi$
$158$	355486.			1.13287
$159$	292904.	−	332084.i	0.918825	−	1.04173i
$160$			108627.i			0.335459i
$161$	−148804.			−0.452428
$162$	228828.	−	58533.9i	0.685050	−	0.175235i
$163$	−22216.3			−0.0654942			−0.0327471	−	0.999464i	$-0.510426\pi$
$163$	−22216.3			−0.0654942			−0.0327471	+	0.999464i	$0.510426\pi$
$164$		−	101400.i		−	0.294393i
$165$	−530061.	+	600964.i	−1.51571	+	1.71846i
$166$	332780.			0.937319
$167$			211041.i			0.585566i	0.956179	+	0.292783i	$0.0945814\pi$
$167$			211041.i			0.585566i	−0.956179	+	0.292783i	$0.905419\pi$
$168$	53821.6	+	47471.6i	0.147124	+	0.129766i
$169$	−117877.			−0.317476
$170$	858259.			2.27770
$171$	6675.89	+	53036.8i	0.0174590	+	0.138703i
$172$		−	271627.i		−	0.700086i
$173$	−353048.			−0.896848			−0.448424	−	0.893821i	$-0.648014\pi$
$173$	−353048.			−0.896848			−0.448424	+	0.893821i	$0.648014\pi$
$174$	−10719.0	+	12152.9i	−0.0268400	+	0.0304303i
$175$	−584700.			−1.44324
$176$	124053.			0.301873
$177$	254849.	+	329816.i	0.611434	+	0.791295i
$178$	−188267.			−0.445373
$179$	−316459.			−0.738218			−0.369109	−	0.929386i	$-0.620337\pi$
$179$	−316459.			−0.738218			−0.369109	+	0.929386i	$0.620337\pi$
$180$	409216.	−	51509.1i	0.941394	−	0.118496i
$181$	196246.			0.445250			0.222625	−	0.974904i	$-0.428537\pi$
$181$	196246.			0.445250			0.222625	+	0.974904i	$0.428537\pi$
$182$		−	201244.i		−	0.450345i
$183$	−544279.	+	617083.i	−1.20142	+	1.36212i
$184$	132391.			0.288281
$185$	1.30150e6			2.79586
$186$	162912.	−	184703.i	0.345279	−	0.391465i
$187$		−	980132.i		−	2.04965i
$188$	−117433.			−0.242324
$189$	153311.	−	225264.i	0.312191	−	0.458709i
$190$			93343.6i			0.187586i
$191$	174942.			0.346985			0.173492	−	0.984835i	$-0.444495\pi$
$191$	174942.			0.346985			0.173492	+	0.984835i	$0.444495\pi$
$192$	−47885.3	−	42235.7i	−0.0937453	−	0.0826851i
$193$	538716.			1.04104			0.520519	−	0.853850i	$-0.325738\pi$
$193$	538716.			1.04104			0.520519	+	0.853850i	$0.325738\pi$
$194$		−	590627.i		−	1.12670i
$195$	−867385.	−	765050.i	−1.63352	−	1.44080i
$196$	−186120.			−0.346061
$197$		−	777445.i		−	1.42726i	−0.700521	−	0.713632i	$-0.747049\pi$
$197$		−	777445.i		−	1.42726i	0.700521	−	0.713632i	$-0.252951\pi$
$198$	−58823.4	−	467324.i	−0.106632	−	0.847141i
$199$	−496079.			−0.888011			−0.444005	−	0.896024i	$-0.646443\pi$
$199$	−496079.			−0.888011			−0.444005	+	0.896024i	$0.646443\pi$
$200$	520211.			0.919611
$201$	214929.	−	243678.i	0.375236	−	0.425429i
$202$	32180.7			0.0554903
$203$			18694.3i			0.0318398i
$204$	−333702.	+	378339.i	−0.561414	+	0.636511i
$205$	−672291.			−1.11731
$206$		−	47233.4i		−	0.0775499i
$207$	−62777.6	−	498738.i	−0.101831	−	0.808997i
$208$			179048.i			0.286953i
$209$	106598.			0.168805
$210$	314741.	−	356842.i	0.492499	−	0.558378i
$211$			917402.i			1.41858i	0.704917	+	0.709290i	$0.250984\pi$
$211$			917402.i			1.41858i	−0.704917	+	0.709290i	$0.749016\pi$
$212$			454491.i			0.694521i
$213$	−234244.	+	265577.i	−0.353768	+	0.401089i
$214$		−	562580.i		−	0.839750i
$215$	−1.80091e6			−2.65703
$216$	−136402.	+	200419.i	−0.198924	+	0.292283i
$217$		−	284123.i		−	0.409597i
$218$			793041.i			1.13020i
$219$	−104883.	+	118913.i	−0.147773	+	0.167540i
$220$		−	822480.i		−	1.14569i
$221$	1.41465e6			1.94835
$222$	−506041.	+	573730.i	−0.689133	+	0.781314i
$223$	289761.			0.390191			0.195095	−	0.980784i	$-0.437498\pi$
$223$	289761.			0.390191			0.195095	+	0.980784i	$0.437498\pi$
$224$	−73660.4			−0.0980876
$225$	−246674.	−	1.95971e6i	−0.324839	−	2.58069i
$226$	−94260.7			−0.122761
$227$	1.01100e6			1.30222			0.651110	−	0.758983i	$-0.274304\pi$
$227$	1.01100e6			1.30222			0.651110	+	0.758983i	$0.274304\pi$
$228$	−41147.9	−	36293.2i	−0.0524216	−	0.0462368i
$229$			50972.1i			0.0642309i	0.999484	+	0.0321154i	$0.0102244\pi$
$229$			50972.1i			0.0642309i	−0.999484	+	0.0321154i	$0.989776\pi$
$230$		−	877768.i		−	1.09411i
$231$	−407514.	−	359435.i	−0.502473	−	0.443190i
$232$		−	16632.4i		−	0.0202878i
$233$	−111536.			−0.134594			−0.0672970	−	0.997733i	$-0.521438\pi$
$233$	−111536.			−0.134594			−0.0672970	+	0.997733i	$0.521438\pi$
$234$	674501.	−	84901.3i	0.805272	−	0.101362i
$235$			778595.i			0.919691i
$236$	−420100.	−	80851.7i	−0.490989	−	0.0944951i
$237$	1.03898e6	+	916396.i	1.20153	+	1.05977i
$238$			581986.i			0.665994i
$239$		−	557603.i		−	0.631437i	−0.948853	−	0.315719i	$-0.897754\pi$
$239$		−	557603.i		−	0.631437i	0.948853	−	0.315719i	$-0.102246\pi$
$240$	−280027.	+	317484.i	−0.313814	+	0.355790i
$241$	182708.			0.202635			0.101317	−	0.994854i	$-0.467694\pi$
$241$	182708.			0.202635			0.101317	+	0.994854i	$0.467694\pi$
$242$	−295068.			−0.323880
$243$	819686.	+	418812.i	0.890496	+	0.454991i
$244$		−	844542.i		−	0.908127i
$245$			1.23399e6i			1.31340i
$246$	261395.	−	296360.i	0.275397	−	0.312236i
$247$			153856.i			0.160462i
$248$			252785.i			0.260989i
$249$	972613.	+	857863.i	0.994127	+	0.876838i
$250$		−	2.12303e6i		−	2.14835i
$251$		−	610343.i		−	0.611490i	−0.952113	−	0.305745i	$-0.901094\pi$
$251$		−	610343.i		−	0.611490i	0.952113	−	0.305745i	$-0.0989055\pi$
$252$	34928.4	+	277490.i	0.0346479	+	0.275261i
$253$	−1.00241e6			−0.984565
$254$	−490852.			−0.477383
$255$	2.50843e6	+	2.21248e6i	2.41574	+	2.13073i
$256$	65536.0			0.0625000
$257$			576130.i			0.544112i	0.962281	+	0.272056i	$0.0877035\pi$
$257$			576130.i			0.544112i	−0.962281	+	0.272056i	$0.912296\pi$
$258$	700217.	−	793880.i	0.654912	−	0.742516i
$259$			882550.i			0.817504i
$260$	1.18711e6			1.08907
$261$	−62656.9	+	7886.80i	−0.0569335	+	0.00716637i
$262$	−1.05836e6			−0.952531
$263$			521428.i			0.464841i	0.972615	+	0.232421i	$0.0746646\pi$
$263$			521428.i			0.464841i	−0.972615	+	0.232421i	$0.925335\pi$
$264$	362567.	+	319791.i	0.320168	+	0.282394i
$265$	3.01332e6			2.63591
$266$	−63296.4			−0.0548497
$267$	−550246.	−	485327.i	−0.472366	−	0.416636i
$268$			333499.i			0.283633i
$269$	1.64027e6			1.38209			0.691043	−	0.722813i	$-0.257151\pi$
$269$	1.64027e6			1.38209			0.691043	+	0.722813i	$0.257151\pi$
$270$	1.32879e6	+	904358.i	1.10930	+	0.754972i
$271$	−234508.			−0.193970			−0.0969852	−	0.995286i	$-0.530920\pi$
$271$	−234508.			−0.193970			−0.0969852	+	0.995286i	$0.530920\pi$
$272$		−	517796.i		−	0.424362i
$273$	518781.	−	588175.i	0.421286	−	0.477639i
$274$			895883.i			0.720899i
$275$	−3.93881e6			−3.14075
$276$	386939.	+	341287.i	0.305752	+	0.269679i
$277$	492194.			0.385423			0.192711	−	0.981255i	$-0.438272\pi$
$277$	492194.			0.385423			0.192711	+	0.981255i	$0.438272\pi$
$278$	796433.			0.618069
$279$	952281.	−	119866.i	0.732410	−	0.0921905i
$280$			488375.i			0.372271i
$281$		−	368969.i		−	0.278756i	−0.990239	−	0.139378i	$-0.955490\pi$
$281$		−	368969.i		−	0.278756i	0.990239	−	0.139378i	$-0.0445103\pi$
$282$	−343222.	−	302728.i	−0.257011	−	0.226688i
$283$			995571.i			0.738935i	0.929244	+	0.369468i	$0.120460\pi$
$283$			995571.i			0.738935i	−0.929244	+	0.369468i	$0.879540\pi$
$284$		−	363469.i		−	0.267406i
$285$	−240627.	+	272814.i	−0.175482	+	0.198955i
$286$		−	1.35567e6i		−	0.980032i
$287$		−	455881.i		−	0.326698i
$288$	−31076.0	−	246884.i	−0.0220772	−	0.175393i
$289$	−2.67122e6			−1.88133
$290$	−110275.			−0.0769982
$291$	1.52256e6	−	1.72622e6i	1.05400	−	1.19499i
$292$		−	162744.i		−	0.111699i
$293$		−	2.77480e6i		−	1.88826i	−0.329567	−	0.944132i	$-0.606903\pi$
$293$		−	2.77480e6i		−	1.88826i	0.329567	−	0.944132i	$-0.393097\pi$
$294$	−543971.	−	479792.i	−0.367035	−	0.323732i
$295$	−536055.	+	2.78530e6i	−0.358636	+	1.86345i
$296$		−	785209.i		−	0.520902i
$297$	1.03278e6	−	1.51748e6i	0.679384	−	0.998235i
$298$	1.53941e6			1.00419
$299$		−	1.44680e6i		−	0.935905i
$300$	1.52041e6	+	1.34103e6i	0.975346	+	0.860273i
$301$		−	1.22120e6i		−	0.776909i
$302$		−	738640.i		−	0.466032i
$303$	94054.2	+	82957.5i	0.0588534	+	0.0519098i
$304$	56315.1			0.0349495
$305$	−5.59939e6			−3.44660
$306$	−1.95062e6	+	245529.i	−1.19088	+	0.149899i
$307$	2.41250e6			1.46091			0.730453	−	0.682963i	$-0.239309\pi$
$307$	2.41250e6			1.46091			0.730453	+	0.682963i	$0.239309\pi$
$308$	557724.			0.334999
$309$	121761.	−	138049.i	0.0725459	−	0.0822499i
$310$	1.67599e6			0.990530
$311$		−	2.30821e6i		−	1.35324i	−0.736334	−	0.676618i	$-0.763445\pi$
$311$		−	2.30821e6i		−	1.35324i	0.736334	−	0.676618i	$-0.236555\pi$
$312$	−461562.	+	523302.i	−0.268438	+	0.304345i
$313$			1.93566e6i			1.11678i	0.829577	+	0.558392i	$0.188581\pi$
$313$			1.93566e6i			1.11678i	−0.829577	+	0.558392i	$0.811419\pi$
$314$		−	526520.i		−	0.301364i
$315$	1.83978e6	−	231579.i	1.04470	−	0.131499i
$316$	−1.42195e6			−0.801060
$317$		−	337432.i		−	0.188599i	−0.995544	−	0.0942993i	$-0.969939\pi$
$317$		−	337432.i		−	0.188599i	0.995544	−	0.0942993i	$-0.0300611\pi$
$318$	−1.17162e6	+	1.32834e6i	−0.649707	+	0.736614i
$319$			125934.i			0.0692891i
$320$		−	434510.i		−	0.237206i
$321$	1.45026e6	−	1.64425e6i	0.785565	−	0.890645i
$322$	595215.			0.319915
$323$		−	444942.i		−	0.237300i
$324$	−915313.	+	234136.i	−0.484403	+	0.123910i
$325$		−	5.68498e6i		−	2.98552i
$326$	88865.2			0.0463114
$327$	−2.04435e6	+	2.31781e6i	−1.05727	+	1.19870i
$328$			405600.i			0.208168i
$329$	−527966.			−0.268916
$330$	2.12024e6	−	2.40385e6i	1.07177	−	1.21513i
$331$	−1.14768e6			−0.575771			−0.287885	−	0.957665i	$-0.592952\pi$
$331$	−1.14768e6			−0.575771			−0.287885	+	0.957665i	$0.592952\pi$
$332$	−1.33112e6			−0.662785
$333$	−2.95800e6	+	372332.i	−1.46180	+	0.184001i
$334$		−	844165.i		−	0.414058i
$335$	2.21113e6			1.07647
$336$	−215286.	−	189887.i	−0.104032	−	0.0917584i
$337$			1.60890e6i			0.771708i	0.922560	+	0.385854i	$0.126093\pi$
$337$			1.60890e6i			0.771708i	−0.922560	+	0.385854i	$0.873907\pi$
$338$	471506.			0.224489
$339$	−275495.	−	242991.i	−0.130201	−	0.114840i
$340$	−3.43304e6			−1.61058
$341$		−	1.91398e6i		−	0.891357i
$342$	−26703.6	−	212147.i	−0.0123454	−	0.0980781i
$343$	−2.04577e6			−0.938903
$344$			1.08651e6i			0.495035i
$345$	2.26277e6	−	2.56544e6i	1.02351	−	1.16042i
$346$	1.41219e6			0.634167
$347$	1.56591e6			0.698141			0.349070	−	0.937097i	$-0.386497\pi$
$347$	1.56591e6			0.698141			0.349070	+	0.937097i	$0.386497\pi$
$348$	42876.2	−	48611.5i	0.0189788	−	0.0215174i
$349$			1.83508e6i			0.806476i	0.915095	+	0.403238i	$0.132115\pi$
$349$			1.83508e6i			0.806476i	−0.915095	+	0.403238i	$0.867885\pi$
$350$	2.33880e6			1.02052
$351$	2.19022e6	+	1.49063e6i	0.948899	+	0.645807i
$352$	−496210.			−0.213456
$353$	−2.33436e6			−0.997082			−0.498541	−	0.866866i	$-0.666131\pi$
$353$	−2.33436e6			−0.997082			−0.498541	+	0.866866i	$0.666131\pi$
$354$	−1.01940e6	−	1.31926e6i	−0.432349	−	0.559530i
$355$	−2.40984e6			−1.01488
$356$	753068.			0.314927
$357$	−1.50028e6	+	1.70097e6i	−0.623021	+	0.706358i
$358$	1.26584e6			0.521999
$359$		−	386152.i		−	0.158133i	−0.996869	−	0.0790665i	$-0.974806\pi$
$359$		−	386152.i		−	0.158133i	0.996869	−	0.0790665i	$-0.0251939\pi$
$360$	−1.63686e6	+	206037.i	−0.665666	+	0.0837892i
$361$	−2.42771e6			−0.980457
$362$	−784983.			−0.314839
$363$	−862392.	−	760645.i	−0.343509	−	0.302981i
$364$			804977.i			0.318442i
$365$	−1.07901e6			−0.423929
$366$	2.17711e6	−	2.46833e6i	0.849530	−	0.963166i
$367$			3.53904e6i			1.37158i	0.727801	+	0.685789i	$0.240542\pi$
$367$			3.53904e6i			1.37158i	−0.727801	+	0.685789i	$0.759458\pi$
$368$	−529566.			−0.203845
$369$	1.52795e6	−	192328.i	0.584177	−	0.0735320i
$370$	−5.20601e6			−1.97697
$371$			2.04333e6i			0.770734i
$372$	−651647.	+	738813.i	−0.244149	+	0.276807i
$373$	−5.30650e6			−1.97486			−0.987430	−	0.158055i	$-0.949478\pi$
$373$	−5.30650e6			−1.97486			−0.987430	+	0.158055i	$0.949478\pi$
$374$			3.92053e6i			1.44932i
$375$	5.47288e6	−	6.20495e6i	2.00973	−	2.27856i
$376$	469734.			0.171349
$377$	−181763.			−0.0658646
$378$	−613246.	+	901057.i	−0.220752	+	0.324357i
$379$	3.12162e6			1.11630			0.558151	−	0.829739i	$-0.311511\pi$
$379$	3.12162e6			1.11630			0.558151	+	0.829739i	$0.311511\pi$
$380$		−	373374.i		−	0.132643i
$381$	−1.43461e6	−	1.26535e6i	−0.506315	−	0.446579i
$382$	−699767.			−0.245355
$383$		−	4.48293e6i		−	1.56158i	−0.624793	−	0.780791i	$-0.714817\pi$
$383$		−	4.48293e6i		−	1.56158i	0.624793	−	0.780791i	$-0.285183\pi$
$384$	191541.	+	168943.i	0.0662879	+	0.0584672i
$385$		−	3.69777e6i		−	1.27142i
$386$	−2.15487e6			−0.736126
$387$	4.09303e6	−	515201.i	1.38921	−	0.174864i
$388$			2.36251e6i			0.796699i
$389$			2.63036e6i			0.881336i	0.897670	+	0.440668i	$0.145258\pi$
$389$			2.63036e6i			0.881336i	−0.897670	+	0.440668i	$0.854742\pi$
$390$	3.46954e6	+	3.06020e6i	1.15508	+	1.01880i
$391$			4.18407e6i			1.38407i
$392$	744480.			0.244702
$393$	−3.09325e6	−	2.72830e6i	−1.01026	−	0.891069i
$394$			3.10978e6i			1.00923i
$395$			9.42763e6i			3.04026i
$396$	235294.	+	1.86930e6i	0.0754002	+	0.599019i
$397$		−	4.53806e6i		−	1.44509i	−0.691326	−	0.722543i	$-0.742973\pi$
$397$		−	4.53806e6i		−	1.44509i	0.691326	−	0.722543i	$-0.257027\pi$
$398$	1.98432e6			0.627918
$399$	−184996.	−	163169.i	−0.0581740	−	0.0513105i
$400$	−2.08084e6			−0.650263
$401$	4.06243e6			1.26161			0.630805	−	0.775941i	$-0.282725\pi$
$401$	4.06243e6			1.26161			0.630805	+	0.775941i	$0.282725\pi$
$402$	−859715.	+	974713.i	−0.265332	+	0.300823i
$403$	2.76250e6			0.847304
$404$	−128723.			−0.0392376
$405$	1.55234e6	+	6.06861e6i	0.470272	+	1.83845i
$406$		−	74777.3i		−	0.0225141i
$407$			5.94526e6i			1.77904i
$408$	1.33481e6	−	1.51336e6i	0.396980	−	0.450081i
$409$		−	3.96351e6i		−	1.17158i	−0.810463	−	0.585790i	$-0.800784\pi$
$409$		−	3.96351e6i		−	1.17158i	0.810463	−	0.585790i	$-0.199216\pi$
$410$	2.68916e6			0.790056
$411$	−2.30946e6	+	2.61839e6i	−0.674383	+	0.764591i
$412$			188934.i			0.0548360i
$413$	−1.88871e6	−	363499.i	−0.544868	−	0.104864i
$414$	251110.	+	1.99495e6i	0.0720052	+	0.572047i
$415$			8.82546e6i			2.51546i
$416$		−	716192.i		−	0.202907i
$417$	2.32773e6	+	2.05310e6i	0.655529	+	0.578188i
$418$	−426393.			−0.119363
$419$	−4.52322e6			−1.25867			−0.629336	−	0.777134i	$-0.716673\pi$
$419$	−4.52322e6			−1.25867			−0.629336	+	0.777134i	$0.716673\pi$
$420$	−1.25897e6	+	1.42737e6i	−0.348250	+	0.394833i
$421$		−	1.35162e6i		−	0.371663i	−0.982582	−	0.185831i	$-0.940502\pi$
$421$		−	1.35162e6i		−	0.371663i	0.982582	−	0.185831i	$-0.0594979\pi$
$422$		−	3.66961e6i		−	1.00309i
$423$	−222739.	−	1.76956e6i	−0.0605265	−	0.480855i
$424$		−	1.81796e6i		−	0.491101i
$425$			1.64406e7i			4.41515i
$426$	936974.	−	1.06231e6i	0.250152	−	0.283613i
$427$		−	3.79695e6i		−	1.00778i
$428$			2.25032e6i			0.593793i
$429$	3.49475e6	−	3.96221e6i	0.916795	−	1.03943i
$430$	7.20364e6			1.87880
$431$	−4.97962e6			−1.29123			−0.645614	−	0.763664i	$-0.723398\pi$
$431$	−4.97962e6			−1.29123			−0.645614	+	0.763664i	$0.723398\pi$
$432$	545608.	−	801674.i	0.140660	−	0.206675i
$433$	−265629.			−0.0680858			−0.0340429	−	0.999420i	$-0.510838\pi$
$433$	−265629.			−0.0680858			−0.0340429	+	0.999420i	$0.510838\pi$
$434$			1.13649e6i			0.289629i
$435$	−322299.	−	284273.i	−0.0816649	−	0.0720299i
$436$		−	3.17216e6i		−	0.799170i
$437$	−455056.			−0.113988
$438$	419533.	−	475651.i	0.104491	−	0.118469i
$439$	−7.17540e6			−1.77699			−0.888494	−	0.458888i	$-0.848248\pi$
$439$	−7.17540e6			−1.77699			−0.888494	+	0.458888i	$0.848248\pi$
$440$			3.28992e6i			0.810128i
$441$	−353019.	−	2.80457e6i	−0.0864373	−	0.686704i
$442$	−5.65859e6			−1.37769
$443$	−3.11261e6			−0.753557			−0.376778	−	0.926303i	$-0.622968\pi$
$443$	−3.11261e6			−0.753557			−0.376778	+	0.926303i	$0.622968\pi$
$444$	2.02416e6	−	2.29492e6i	0.487291	−	0.552472i
$445$		−	4.99291e6i		−	1.19524i
$446$	−1.15904e6			−0.275907
$447$	4.49923e6	+	3.96840e6i	1.06505	+	0.939392i
$448$	294642.			0.0693584
$449$		−	1.47393e6i		−	0.345033i	−0.985007	−	0.172516i	$-0.944810\pi$
$449$		−	1.47393e6i		−	0.345033i	0.985007	−	0.172516i	$-0.0551898\pi$
$450$	986697.	+	7.83884e6i	0.229696	+	1.82482i
$451$		−	3.07102e6i		−	0.710955i
$452$	377043.			0.0868050
$453$	1.90411e6	−	2.15881e6i	0.435961	−	0.494276i
$454$	−4.04398e6			−0.920809
$455$	5.33708e6			1.20858
$456$	164591.	+	145173.i	0.0370677	+	0.0326943i
$457$			754706.i			0.169039i	0.996422	+	0.0845196i	$0.0269355\pi$
$457$			754706.i			0.169039i	−0.996422	+	0.0845196i	$0.973064\pi$
$458$		−	203888.i		−	0.0454181i
$459$	−6.33398e6	−	4.31082e6i	−1.40328	−	0.955054i
$460$			3.51107e6i			0.773651i
$461$			4.87701e6i			1.06881i	0.845228	+	0.534406i	$0.179465\pi$
$461$			4.87701e6i			1.06881i	−0.845228	+	0.534406i	$0.820535\pi$
$462$	1.63006e6	+	1.43774e6i	0.355302	+	0.313383i
$463$			8.50543e6i			1.84393i	0.387277	+	0.921963i	$0.373416\pi$
$463$			8.50543e6i			1.84393i	−0.387277	+	0.921963i	$0.626584\pi$
$464$			66529.8i			0.0143457i
$465$	4.89840e6	+	4.32048e6i	1.05056	+	0.926616i
$466$	446145.			0.0951724
$467$	−6.16033e6			−1.30711			−0.653554	−	0.756880i	$-0.726723\pi$
$467$	−6.16033e6			−1.30711			−0.653554	+	0.756880i	$0.726723\pi$
$468$	−2.69800e6	+	339605.i	−0.569414	+	0.0716737i
$469$			1.49937e6i			0.314758i
$470$		−	3.11438e6i		−	0.650320i
$471$	1.35730e6	−	1.53886e6i	0.281918	−	0.319629i
$472$	1.68040e6	+	323407.i	0.347182	+	0.0668181i
$473$		−	8.22655e6i		−	1.69069i
$474$	−4.15591e6	−	3.66558e6i	−0.849610	−	0.749372i
$475$	−1.78807e6			−0.363622
$476$		−	2.32795e6i		−	0.470929i
$477$	−6.84854e6	+	862045.i	−1.37817	+	0.173474i
$478$			2.23041e6i			0.446493i
$479$			4.13113e6i			0.822678i	0.911483	+	0.411339i	$0.134939\pi$
$479$			4.13113e6i			0.822678i	−0.911483	+	0.411339i	$0.865061\pi$
$480$	1.12011e6	−	1.26994e6i	0.221900	−	0.251582i
$481$	−8.58094e6			−1.69111
$482$	−730831.			−0.143284
$483$	1.73963e6	+	1.53438e6i	0.339304	+	0.299272i
$484$	1.18027e6			0.229017
$485$	1.56637e7			3.02370
$486$	−3.27874e6	−	1.67525e6i	−0.629676	−	0.321727i
$487$	−4.84828e6			−0.926329			−0.463165	−	0.886272i	$-0.653286\pi$
$487$	−4.84828e6			−0.926329			−0.463165	+	0.886272i	$0.653286\pi$
$488$			3.37817e6i			0.642143i
$489$	259725.	+	229083.i	0.0491182	+	0.0433231i
$490$		−	4.93598e6i		−	0.928716i
$491$			779448.i			0.145909i	0.997335	+	0.0729547i	$0.0232429\pi$
$491$			779448.i			0.145909i	−0.997335	+	0.0729547i	$0.976757\pi$
$492$	−1.04558e6	+	1.18544e6i	−0.194735	+	0.220784i
$493$	525648.			0.0974042
$494$		−	615424.i		−	0.113464i
$495$	1.23936e7	−	1.56002e6i	2.27345	−	0.286165i
$496$		−	1.01114e6i		−	0.184547i
$497$		−	1.63411e6i		−	0.296750i
$498$	−3.89045e6	−	3.43145e6i	−0.702954	−	0.620018i
$499$	−7.18406e6			−1.29157			−0.645786	−	0.763519i	$-0.723470\pi$
$499$	−7.18406e6			−1.29157			−0.645786	+	0.763519i	$0.723470\pi$
$500$			8.49211e6i			1.51911i
$501$	2.17614e6	−	2.46723e6i	0.387341	−	0.439153i
$502$			2.44137e6i			0.432389i
$503$	8.37248e6			1.47548			0.737742	−	0.675083i	$-0.235892\pi$
$503$	8.37248e6			1.47548			0.737742	+	0.675083i	$0.235892\pi$
$504$	−139714.	−	1.10996e6i	−0.0244998	−	0.194639i
$505$			853445.i			0.148918i
$506$	4.00964e6			0.696192
$507$	1.37807e6	+	1.21548e6i	0.238095	+	0.210004i
$508$	1.96341e6			0.337561
$509$	−2.38248e6			−0.407600			−0.203800	−	0.979013i	$-0.565329\pi$
$509$	−2.38248e6			−0.407600			−0.203800	+	0.979013i	$0.565329\pi$
$510$	−1.00337e7	−	8.84991e6i	−1.70819	−	1.50665i
$511$		−	731678.i		−	0.123956i
$512$	−262144.			−0.0441942
$513$	468841.	−	688879.i	0.0786560	−	0.115571i
$514$		−	2.30452e6i		−	0.384745i
$515$	1.25265e6			0.208119
$516$	−2.80087e6	+	3.17552e6i	−0.463093	+	0.525038i
$517$	−3.55662e6			−0.585209
$518$		−	3.53020e6i		−	0.578063i
$519$	4.12740e6	+	3.64044e6i	0.672602	+	0.593247i
$520$	−4.74842e6			−0.770089
$521$		−	1.21971e7i		−	1.96862i	−0.176448	−	0.984310i	$-0.556461\pi$
$521$		−	1.21971e7i		−	1.96862i	0.176448	−	0.984310i	$-0.443539\pi$
$522$	250628.	−	31547.2i	0.0402580	−	0.00506739i
$523$	5.75601e6			0.920168			0.460084	−	0.887875i	$-0.347819\pi$
$523$	5.75601e6			0.920168			0.460084	+	0.887875i	$0.347819\pi$
$524$	4.23343e6			0.673541
$525$	6.83559e6	+	6.02911e6i	1.08237	+	0.954674i
$526$		−	2.08571e6i		−	0.328692i
$527$	−7.98897e6			−1.25304
$528$	−1.45027e6	−	1.27916e6i	−0.226393	−	0.199683i
$529$	−2.15717e6			−0.335155
$530$	−1.20533e7			−1.86387
$531$	421508.	−	6.48366e6i	0.0648738	−	0.997893i
$532$	253185.			0.0387846
$533$	4.43249e6			0.675817
$534$	2.20098e6	+	1.94131e6i	0.334013	+	0.294606i
$535$	1.49198e7			2.25362
$536$		−	1.33399e6i		−	0.200559i
$537$	3.69964e6	+	3.26315e6i	0.553636	+	0.488317i
$538$	−6.56109e6			−0.977283
$539$	−5.63688e6			−0.835732
$540$	−5.31518e6	−	3.61743e6i	−0.784393	−	0.533846i
$541$		−	1.01853e7i		−	1.49616i	−0.663606	−	0.748082i	$-0.730975\pi$
$541$		−	1.01853e7i		−	1.49616i	0.663606	−	0.748082i	$-0.269025\pi$
$542$	938034.			0.137158
$543$	−2.29426e6	−	2.02358e6i	−0.333921	−	0.294524i
$544$			2.07118e6i			0.300069i
$545$	−2.10317e7			−3.03308
$546$	−2.07512e6	+	2.35270e6i	−0.297894	+	0.337742i
$547$	−3.22777e6			−0.461247			−0.230624	−	0.973043i	$-0.574077\pi$
$547$	−3.22777e6			−0.461247			−0.230624	+	0.973043i	$0.574077\pi$
$548$		−	3.58353e6i		−	0.509753i
$549$	1.27261e7	−	1.60186e6i	1.80203	−	0.226827i
$550$	1.57552e7			2.22084
$551$			57169.0i			0.00802198i
$552$	−1.54776e6	−	1.36515e6i	−0.216200	−	0.190692i
$553$	−6.39289e6			−0.888964
$554$	−1.96878e6			−0.272535
$555$	−1.52156e7	−	1.34204e7i	−2.09679	−	1.84941i
$556$	−3.18573e6			−0.437041
$557$		−	1.35305e7i		−	1.84789i	−0.382531	−	0.923943i	$-0.624948\pi$
$557$		−	1.35305e7i		−	1.84789i	0.382531	−	0.923943i	$-0.375052\pi$
$558$	−3.80912e6	+	479465.i	−0.517892	+	0.0651885i
$559$	1.18736e7			1.60714
$560$		−	1.95350e6i		−	0.263235i
$561$	−1.01066e7	+	1.14585e7i	−1.35581	+	1.53716i
$562$			1.47588e6i			0.197110i
$563$	2.82186e6			0.375202			0.187601	−	0.982245i	$-0.439929\pi$
$563$	2.82186e6			0.375202			0.187601	+	0.982245i	$0.439929\pi$
$564$	1.37289e6	+	1.21091e6i	0.181734	+	0.160293i
$565$		−	2.49983e6i		−	0.329450i
$566$		−	3.98229e6i		−	0.522506i
$567$	−4.11513e6	+	1.05264e6i	−0.537559	+	0.137507i
$568$			1.45388e6i			0.189085i
$569$	1.33693e7			1.73112			0.865559	−	0.500807i	$-0.166963\pi$
$569$	1.33693e7			1.73112			0.865559	+	0.500807i	$0.166963\pi$
$570$	962508.	−	1.09126e6i	0.124084	−	0.140682i
$571$		−	5.51678e6i		−	0.708101i	−0.935226	−	0.354050i	$-0.884804\pi$
$571$		−	5.51678e6i		−	0.708101i	0.935226	−	0.354050i	$-0.115196\pi$
$572$			5.42270e6i			0.692987i
$573$	−2.04520e6	−	1.80391e6i	−0.260226	−	0.229524i
$574$			1.82352e6i			0.231011i
$575$	1.68143e7			2.12085
$576$	124304.	+	987536.i	0.0156109	+	0.124021i
$577$	8.32530e6			1.04102			0.520511	−	0.853855i	$-0.325741\pi$
$577$	8.32530e6			1.04102			0.520511	+	0.853855i	$0.325741\pi$
$578$	1.06849e7			1.33030
$579$	−6.29800e6	−	5.55495e6i	−0.780740	−	0.688627i
$580$	441099.			0.0544460
$581$	−5.98455e6			−0.735515
$582$	−6.09023e6	+	6.90488e6i	−0.745291	+	0.844984i
$583$			1.37648e7i			1.67726i
$584$			650977.i			0.0789830i
$585$	2.25161e6	+	1.78880e7i	0.272022	+	2.16109i
$586$			1.10992e7i			1.33520i
$587$	−1.46195e6			−0.175121			−0.0875606	−	0.996159i	$-0.527907\pi$
$587$	−1.46195e6			−0.175121			−0.0875606	+	0.996159i	$0.527907\pi$
$588$	2.17588e6	+	1.91917e6i	0.259533	+	0.228913i
$589$		−	868874.i		−	0.103197i
$590$	2.14422e6	−	1.11412e7i	0.253594	−	1.31766i
$591$	−8.01660e6	+	9.08893e6i	−0.944107	+	1.07039i
$592$			3.14084e6i			0.368333i
$593$			1.57145e6i			0.183511i	0.995782	+	0.0917557i	$0.0292479\pi$
$593$			1.57145e6i			0.183511i	−0.995782	+	0.0917557i	$0.970752\pi$
$594$	−4.13111e6	+	6.06993e6i	−0.480397	+	0.705859i
$595$	−1.54345e7			−1.78731
$596$	−6.15765e6			−0.710068
$597$	5.79954e6	+	5.11530e6i	0.665975	+	0.587402i
$598$			5.78721e6i			0.661785i
$599$		−	681088.i		−	0.0775598i	−0.999248	−	0.0387799i	$-0.987653\pi$
$599$		−	681088.i		−	0.0775598i	0.999248	−	0.0387799i	$-0.0123471\pi$
$600$	−6.08166e6	−	5.36413e6i	−0.689674	−	0.608305i
$601$		−	1.34863e7i		−	1.52303i	−0.648150	−	0.761513i	$-0.724457\pi$
$601$		−	1.34863e7i		−	1.52303i	0.648150	−	0.761513i	$-0.275543\pi$
$602$			4.88480e6i			0.549358i
$603$	−5.02536e6	+	632556.i	−0.562825	+	0.0708444i
$604$			2.95456e6i			0.329534i
$605$		−	7.82531e6i		−	0.869187i
$606$	−376217.	−	331830.i	−0.0416157	−	0.0367058i
$607$	−9.82266e6			−1.08208			−0.541038	−	0.840998i	$-0.681968\pi$
$607$	−9.82266e6			−1.08208			−0.541038	+	0.840998i	$0.681968\pi$
$608$	−225260.			−0.0247130
$609$	192766.	−	218551.i	0.0210614	−	0.0238786i
$610$	2.23976e7			2.43712
$611$		−	5.13336e6i		−	0.556287i
$612$	7.80246e6	−	982117.i	0.842079	−	0.105995i
$613$		−	9.85346e6i		−	1.05910i	−0.848278	−	0.529551i	$-0.822360\pi$
$613$		−	9.85346e6i		−	1.05910i	0.848278	−	0.529551i	$-0.177640\pi$
$614$	−9.65001e6			−1.03302
$615$	7.85959e6	+	6.93230e6i	0.837939	+	0.739077i
$616$	−2.23090e6			−0.236880
$617$			4.43671e6i			0.469189i	0.972093	+	0.234595i	$0.0753763\pi$
$617$			4.43671e6i			0.469189i	−0.972093	+	0.234595i	$0.924624\pi$
$618$	−487045.	+	552194.i	−0.0512977	+	0.0581595i
$619$	1.59261e7			1.67064			0.835319	−	0.549766i	$-0.185283\pi$
$619$	1.59261e7			1.67064			0.835319	+	0.549766i	$0.185283\pi$
$620$	−6.70397e6			−0.700411
$621$	−4.40880e6	+	6.47796e6i	−0.458766	+	0.674076i
$622$			9.23282e6i			0.956882i
$623$	3.38570e6			0.349485
$624$	1.84625e6	−	2.09321e6i	0.189814	−	0.215204i
$625$	3.09026e7			3.16442
$626$		−	7.74265e6i		−	0.789685i
$627$	−1.24621e6	−	1.09918e6i	−0.126597	−	0.111661i
$628$			2.10608e6i			0.213096i
$629$	2.48156e7			2.50091
$630$	−7.35913e6	+	926314.i	−0.738712	+	0.0929837i
$631$	1.67599e7			1.67571			0.837856	−	0.545892i	$-0.183809\pi$
$631$	1.67599e7			1.67571			0.837856	+	0.545892i	$0.183809\pi$
$632$	5.68778e6			0.566435
$633$	9.45975e6	−	1.07251e7i	0.938362	−	1.06388i
$634$			1.34973e6i			0.133359i
$635$		−	1.30176e7i		−	1.28114i
$636$	4.68647e6	−	5.31334e6i	0.459412	−	0.520865i
$637$		−	8.13585e6i		−	0.794428i
$638$		−	503734.i		−	0.0489948i
$639$	5.47697e6	−	689401.i	0.530626	−	0.0667913i
$640$			1.73804e6i			0.167730i
$641$			6.05003e6i			0.581584i	0.956786	+	0.290792i	$0.0939187\pi$
$641$			6.05003e6i			0.581584i	−0.956786	+	0.290792i	$0.906081\pi$
$642$	−5.80103e6	+	6.57699e6i	−0.555478	+	0.629781i
$643$	564457.			0.0538398			0.0269199	−	0.999638i	$-0.491430\pi$
$643$	564457.			0.0538398			0.0269199	+	0.999638i	$0.491430\pi$
$644$	−2.38086e6			−0.226214
$645$	2.10540e7	+	1.85700e7i	1.99267	+	1.75757i
$646$			1.77977e6i			0.167796i
$647$			1.01403e7i			0.952339i	0.879353	+	0.476170i	$0.157975\pi$
$647$			1.01403e7i			0.952339i	−0.879353	+	0.476170i	$0.842025\pi$
$648$	3.66125e6	−	936542.i	0.342525	−	0.0876173i
$649$	−1.27232e7	−	2.44870e6i	−1.18573	−	0.228204i
$650$			2.27399e7i			2.11108i
$651$	−2.92972e6	+	3.32161e6i	−0.270940	+	0.307182i
$652$	−355461.			−0.0327471
$653$			5.83590e6i			0.535580i	0.963477	+	0.267790i	$0.0862934\pi$
$653$			5.83590e6i			0.535580i	−0.963477	+	0.267790i	$0.913707\pi$
$654$	8.17741e6	−	9.27125e6i	0.747604	−	0.847606i
$655$		−	2.80680e7i		−	2.55628i
$656$		−	1.62240e6i		−	0.147197i
$657$	2.45233e6	−	308681.i	0.221649	−	0.0278995i
$658$	2.11186e6			0.190152
$659$	−1.93511e7			−1.73577			−0.867886	−	0.496763i	$-0.834522\pi$
$659$	−1.93511e7			−1.73577			−0.867886	+	0.496763i	$0.834522\pi$
$660$	−8.48097e6	+	9.61542e6i	−0.757854	+	0.859228i
$661$	−8.58971e6			−0.764671			−0.382336	−	0.924023i	$-0.624880\pi$
$661$	−8.58971e6			−0.764671			−0.382336	+	0.924023i	$0.624880\pi$
$662$	4.59071e6			0.407132
$663$	−1.65383e7	−	1.45871e7i	−1.46119	−	1.28880i
$664$	5.32448e6			0.468659
$665$		−	1.67864e6i		−	0.147199i
$666$	1.18320e7	−	1.48933e6i	1.03365	−	0.130108i
$667$		−	537596.i		−	0.0467887i
$668$			3.37666e6i			0.292783i
$669$	−3.38752e6	−	2.98786e6i	−0.292629	−	0.258104i
$670$	−8.84451e6			−0.761179
$671$		−	2.55780e7i		−	2.19311i
$672$	861146.	+	759546.i	0.0735620	+	0.0648830i
$673$			4.00554e6i			0.340897i	0.985367	+	0.170449i	$0.0545217\pi$
$673$			4.00554e6i			0.340897i	−0.985367	+	0.170449i	$0.945478\pi$
$674$		−	6.43558e6i		−	0.545680i
$675$	−1.73237e7	+	2.54541e7i	−1.46346	+	2.15029i
$676$	−1.88602e6			−0.158738
$677$		−	1.44074e7i		−	1.20813i	−0.796934	−	0.604066i	$-0.793546\pi$
$677$		−	1.44074e7i		−	1.20813i	0.796934	−	0.604066i	$-0.206454\pi$
$678$	1.10198e6	+	971965.i	0.0920660	+	0.0812038i
$679$			1.06215e7i			0.884124i
$680$	1.37322e7			1.13885
$681$	−1.18193e7	−	1.04248e7i	−0.976617	−	0.861393i
$682$			7.65593e6i			0.630285i
$683$	−2.23844e7			−1.83609			−0.918043	−	0.396481i	$-0.870231\pi$
$683$	−2.23844e7			−1.83609			−0.918043	+	0.396481i	$0.870231\pi$
$684$	106814.	+	848589.i	0.00872949	+	0.0693517i
$685$	−2.37591e7			−1.93466
$686$	8.18307e6			0.663905
$687$	525597.	−	595903.i	0.0424875	−	0.0481708i
$688$		−	4.34603e6i		−	0.350043i
$689$	−1.98671e7			−1.59436
$690$	−9.05107e6	+	1.02618e7i	−0.723731	+	0.820540i
$691$		−	5.03760e6i		−	0.401355i	−0.979657	−	0.200677i	$-0.935686\pi$
$691$		−	5.03760e6i		−	0.401355i	0.979657	−	0.200677i	$-0.0643143\pi$
$692$	−5.64877e6			−0.448424
$693$	1.05785e6	+	8.40412e6i	0.0836741	+	0.664752i
$694$	−6.26364e6			−0.493660
$695$			2.11217e7i			1.65870i
$696$	−171505.	+	194446.i	−0.0134200	+	0.0152151i
$697$	−1.28185e7			−0.999435
$698$		−	7.34032e6i		−	0.570265i
$699$	1.30394e6	+	1.15010e6i	0.100941	+	0.0890314i
$700$	−9.35520e6			−0.721619
$701$	−1.10898e7			−0.852372			−0.426186	−	0.904636i	$-0.640143\pi$
$701$	−1.10898e7			−0.852372			−0.426186	+	0.904636i	$0.640143\pi$
$702$	−8.76088e6	−	5.96253e6i	−0.670973	−	0.456654i
$703$			2.69892e6i			0.205969i
$704$	1.98484e6			0.150936
$705$	8.02845e6	−	9.10237e6i	0.608358	−	0.689734i
$706$	9.33744e6			0.705044
$707$	−578722.			−0.0435433
$708$	4.07758e6	+	5.27706e6i	0.305717	+	0.395648i
$709$	1.06040e7			0.792237			0.396119	−	0.918199i	$-0.370357\pi$
$709$	1.06040e7			0.792237			0.396119	+	0.918199i	$0.370357\pi$
$710$	9.63934e6			0.717631
$711$	−2.69704e6	−	2.14267e7i	−0.200085	−	1.58958i
$712$	−3.01227e6			−0.222687
$713$			8.17056e6i			0.601905i
$714$	6.00113e6	−	6.80386e6i	0.440542	−	0.499471i
$715$	3.59530e7			2.63009
$716$	−5.06334e6			−0.369109
$717$	−5.74970e6	+	6.51880e6i	−0.417683	+	0.473554i
$718$			1.54461e6i			0.111817i
$719$	2.88077e6			0.207820			0.103910	−	0.994587i	$-0.466865\pi$
$719$	2.88077e6			0.207820			0.103910	+	0.994587i	$0.466865\pi$
$720$	6.54746e6	−	824146.i	0.470697	−	0.0592479i
$721$			849421.i			0.0608534i
$722$	9.71083e6			0.693287
$723$	−2.13599e6	−	1.88398e6i	−0.151969	−	0.134039i
$724$	3.13993e6			0.222625
$725$		−	2.11240e6i		−	0.149255i
$726$	3.44957e6	+	3.04258e6i	0.242898	+	0.214240i
$727$	−6.43864e6			−0.451812			−0.225906	−	0.974149i	$-0.572534\pi$
$727$	−6.43864e6			−0.451812			−0.225906	+	0.974149i	$0.572534\pi$
$728$		−	3.21991e6i		−	0.225172i
$729$	−5.26419e6	−	1.33484e7i	−0.366871	−	0.930272i
$730$	4.31604e6			0.299763
$731$	−3.43377e7			−2.37672
$732$	−8.70846e6	+	9.87333e6i	−0.600708	+	0.681061i
$733$	2.69601e7			1.85337			0.926684	−	0.375841i	$-0.122646\pi$
$733$	2.69601e7			1.85337			0.926684	+	0.375841i	$0.122646\pi$
$734$		−	1.41562e7i		−	0.969851i
$735$	1.27243e7	−	1.44263e7i	0.868790	−	0.985002i
$736$	2.11826e6			0.144140
$737$			1.01004e7i			0.684969i
$738$	−6.11182e6	+	769311.i	−0.413075	+	0.0519950i
$739$		−	2.28582e7i		−	1.53968i	−0.638235	−	0.769842i	$-0.720335\pi$
$739$		−	2.28582e7i		−	1.53968i	0.638235	−	0.769842i	$-0.279665\pi$
$740$	2.08240e7			1.39793
$741$	1.58648e6	−	1.79869e6i	0.106142	−	0.120340i
$742$		−	8.17334e6i		−	0.544991i
$743$			1.61482e7i			1.07313i	0.843859	+	0.536564i	$0.180278\pi$
$743$			1.61482e7i			1.07313i	−0.843859	+	0.536564i	$0.819722\pi$
$744$	2.60659e6	−	2.95525e6i	0.172639	−	0.195732i
$745$			4.08258e7i			2.69491i
$746$	2.12260e7			1.39644
$747$	−2.52477e6	−	2.00581e7i	−0.165547	−	1.31519i
$748$		−	1.56821e7i		−	1.02483i
$749$			1.01172e7i			0.658953i
$750$	−2.18915e7	+	2.48198e7i	−1.42109	+	1.61118i
$751$		−	2.19454e6i		−	0.141986i	−0.997477	−	0.0709929i	$-0.977383\pi$
$751$		−	2.19454e6i		−	0.141986i	0.997477	−	0.0709929i	$-0.0226168\pi$
$752$	−1.87894e6			−0.121162
$753$	−6.29353e6	+	7.13537e6i	−0.404489	+	0.458595i
$754$	727052.			0.0465733
$755$	1.95890e7			1.25068
$756$	2.45298e6	−	3.60423e6i	0.156095	−	0.229355i
$757$	1.34310e7			0.851861			0.425931	−	0.904756i	$-0.359947\pi$
$757$	1.34310e7			0.851861			0.425931	+	0.904756i	$0.359947\pi$
$758$	−1.24865e7			−0.789345
$759$	1.17189e7	+	1.03363e7i	0.738387	+	0.651270i
$760$			1.49350e6i			0.0937930i
$761$			1.32516e6i			0.0829484i	0.999140	+	0.0414742i	$0.0132054\pi$
$761$			1.32516e6i			0.0829484i	−0.999140	+	0.0414742i	$0.986795\pi$
$762$	5.73844e6	+	5.06141e6i	0.358019	+	0.315779i
$763$		−	1.42616e7i		−	0.886867i
$764$	2.79907e6			0.173492
$765$	−6.51153e6	−	5.17311e7i	−0.402281	−	3.19593i
$766$			1.79317e7i			1.10420i
$767$	3.53426e6	−	1.83638e7i	0.216925	−	1.12713i
$768$	−766165.	−	675772.i	−0.0468727	−	0.0413425i
$769$		−	3.21053e6i		−	0.195777i	−0.995197	−	0.0978884i	$-0.968791\pi$
$769$		−	3.21053e6i		−	0.195777i	0.995197	−	0.0978884i	$-0.0312088\pi$
$770$			1.47911e7i			0.899027i
$771$	5.94074e6	−	6.73540e6i	0.359919	−	0.408063i
$772$	8.61946e6			0.520519
$773$	4.58260e6			0.275844			0.137922	−	0.990443i	$-0.455958\pi$
$773$	4.58260e6			0.275844			0.137922	+	0.990443i	$0.455958\pi$
$774$	−1.63721e7	+	2.06081e6i	−0.982319	+	0.123647i
$775$			3.21049e7i			1.92007i
$776$		−	9.45003e6i		−	0.563351i
$777$	9.10038e6	−	1.03177e7i	0.540763	−	0.613097i
$778$		−	1.05215e7i		−	0.623199i
$779$		−	1.39413e6i		−	0.0823111i
$780$	−1.38782e7	−	1.22408e7i	−0.816762	−	0.720399i
$781$		−	1.10081e7i		−	0.645782i
$782$		−	1.67363e7i		−	0.978683i
$783$	813831.	+	553881.i	0.0474384	+	0.0322859i
$784$	−2.97792e6			−0.173031
$785$	1.39635e7			0.808762
$786$	1.23730e7	+	1.09132e7i	0.714363	+	0.630081i
$787$	−4.33373e6			−0.249417			−0.124708	−	0.992193i	$-0.539799\pi$
$787$	−4.33373e6			−0.249417			−0.124708	+	0.992193i	$0.539799\pi$
$788$		−	1.24391e7i		−	0.713632i
$789$	5.37668e6	−	6.09588e6i	0.307483	−	0.348613i
$790$		−	3.77105e7i		−	2.14978i
$791$	1.69514e6			0.0963304
$792$	−941175.	−	7.47719e6i	−0.0533160	−	0.423570i
$793$	3.69174e7			2.08472
$794$			1.81522e7i			1.02183i
$795$	−3.52280e7	−	3.10717e7i	−1.97683	−	1.74360i
$796$	−7.93726e6			−0.444005
$797$	1.20218e7			0.670382			0.335191	−	0.942150i	$-0.391199\pi$
$797$	1.20218e7			0.670382			0.335191	+	0.942150i	$0.391199\pi$
$798$	739982.	+	652678.i	0.0411352	+	0.0362820i
$799$			1.48454e7i			0.822666i
$800$	8.32337e6			0.459806
$801$	1.42836e6	+	1.13477e7i	0.0786607	+	0.624922i
$802$	−1.62497e7			−0.892093
$803$		−	4.92892e6i		−	0.269751i
$804$	3.43886e6	−	3.89885e6i	0.187618	−	0.212714i
$805$			1.57853e7i			0.858547i
$806$	−1.10500e7			−0.599134
$807$	−1.91760e7	−	1.69136e7i	−1.03651	−	0.914223i
$808$	514891.			0.0277452
$809$	8.26764e6			0.444130			0.222065	−	0.975032i	$-0.428720\pi$
$809$	8.26764e6			0.444130			0.222065	+	0.975032i	$0.428720\pi$
$810$	−6.20936e6	−	2.42744e7i	−0.332533	−	1.29998i
$811$			2.97849e7i			1.59017i	0.606497	+	0.795085i	$0.292574\pi$
$811$			2.97849e7i			1.59017i	−0.606497	+	0.795085i	$0.707426\pi$
$812$			299109.i			0.0159199i
$813$	2.74158e6	+	2.41812e6i	0.145470	+	0.128308i
$814$		−	2.37810e7i		−	1.25797i
$815$			2.35674e6i			0.124285i
$816$	−5.33923e6	+	6.05343e6i	−0.280707	+	0.318256i
$817$		−	3.73454e6i		−	0.195741i
$818$			1.58540e7i			0.828432i
$819$	−1.21299e7	+	1.52682e6i	−0.631898	+	0.0795387i
$820$	−1.07567e7			−0.558654
$821$	2.31121e7			1.19669			0.598344	−	0.801239i	$-0.295826\pi$
$821$	2.31121e7			1.19669			0.598344	+	0.801239i	$0.295826\pi$
$822$	9.23786e6	−	1.04735e7i	0.476861	−	0.540648i
$823$			1.76799e7i			0.909874i	0.890524	+	0.454937i	$0.150338\pi$
$823$			1.76799e7i			0.909874i	−0.890524	+	0.454937i	$0.849662\pi$
$824$		−	755734.i		−	0.0387749i
$825$	4.60477e7	+	4.06149e7i	2.35544	+	2.07754i
$826$	7.55486e6	+	1.45400e6i	0.385280	+	0.0741503i
$827$		−	8.05558e6i		−	0.409574i	−0.978807	−	0.204787i	$-0.934350\pi$
$827$		−	8.05558e6i		−	0.409574i	0.978807	−	0.204787i	$-0.0656502\pi$
$828$	−1.00444e6	−	7.97981e6i	−0.0509153	−	0.404498i
$829$	9.35931e6			0.472996			0.236498	−	0.971632i	$-0.424000\pi$
$829$	9.35931e6			0.472996			0.236498	+	0.971632i	$0.424000\pi$
$830$		−	3.53018e7i		−	1.77870i
$831$	−5.75412e6	−	5.07524e6i	−0.289052	−	0.254950i
$832$			2.86477e6i			0.143477i
$833$			2.35284e7i			1.17484i
$834$	−9.31090e6	−	8.21239e6i	−0.463529	−	0.408841i
$835$	2.23876e7			1.11120
$836$	1.70557e6			0.0844024
$837$	−1.23689e7	−	8.41808e6i	−0.610262	−	0.415336i
$838$	1.80929e7			0.890015
$839$	−9.03048e6			−0.442900			−0.221450	−	0.975172i	$-0.571079\pi$
$839$	−9.03048e6			−0.442900			−0.221450	+	0.975172i	$0.571079\pi$
$840$	5.03586e6	−	5.70948e6i	0.246250	−	0.279189i
$841$	2.04436e7			0.996707
$842$			5.40648e6i			0.262805i
$843$	−3.80461e6	+	4.31353e6i	−0.184392	+	0.209056i
$844$			1.46784e7i			0.709290i
$845$			1.25045e7i			0.602456i
$846$	890956.	+	7.07823e6i	0.0427987	+	0.340016i
$847$	5.30635e6			0.254148
$848$			7.27186e6i			0.347261i
$849$	1.02658e7	−	1.16390e7i	0.488791	−	0.554174i
$850$		−	6.57625e7i		−	3.12198i
$851$		−	2.53796e7i		−	1.20133i
$852$	−3.74790e6	+	4.24923e6i	−0.176884	+	0.200545i
$853$	−2.45536e6			−0.115543			−0.0577714	−	0.998330i	$-0.518399\pi$
$853$	−2.45536e6			−0.115543			−0.0577714	+	0.998330i	$0.518399\pi$
$854$			1.51878e7i			0.712608i
$855$	5.62623e6	−	708189.i	0.263210	−	0.0331309i
$856$		−	9.00129e6i		−	0.419875i
$857$	1.50083e7			0.698041			0.349020	−	0.937115i	$-0.386514\pi$
$857$	1.50083e7			0.698041			0.349020	+	0.937115i	$0.386514\pi$
$858$	−1.39790e7	+	1.58489e7i	−0.648272	+	0.734987i
$859$		−	1.07671e7i		−	0.497870i	−0.968520	−	0.248935i	$-0.919919\pi$
$859$		−	1.07671e7i		−	0.497870i	0.968520	−	0.248935i	$-0.0800806\pi$
$860$	−2.88146e7			−1.32851
$861$	−4.70080e6	+	5.32960e6i	−0.216105	+	0.245011i
$862$	1.99185e7			0.913035
$863$	−1.00630e6			−0.0459939			−0.0229969	−	0.999736i	$-0.507321\pi$
$863$	−1.00630e6			−0.0459939			−0.0229969	+	0.999736i	$0.507321\pi$
$864$	−2.18243e6	+	3.20670e6i	−0.0994618	+	0.146142i
$865$			3.74519e7i			1.70190i
$866$	1.06252e6			0.0481439
$867$	3.12286e7	+	2.75442e7i	1.41093	+	1.24446i
$868$		−	4.54597e6i		−	0.204799i
$869$	−4.30654e7			−1.93455
$870$	1.28919e6	+	1.13709e6i	0.0577458	+	0.0509328i
$871$	−1.45782e7			−0.651116
$872$			1.26887e7i			0.565099i
$873$	−3.55997e7	+	4.48103e6i	−1.58092	+	0.198995i
$874$	1.82022e6			0.0806020
$875$			3.81794e7i			1.68581i
$876$	−1.67813e6	+	1.90260e6i	−0.0738866	+	0.0837699i
$877$	−3.76378e7			−1.65244			−0.826219	−	0.563349i	$-0.809512\pi$
$877$	−3.76378e7			−1.65244			−0.826219	+	0.563349i	$0.809512\pi$
$878$	2.87016e7			1.25652
$879$	−2.86122e7	+	3.24395e7i	−1.24905	+	1.41613i
$880$		−	1.31597e7i		−	0.572847i
$881$	2.32385e7			1.00872			0.504358	−	0.863495i	$-0.331729\pi$
$881$	2.32385e7			1.00872			0.504358	+	0.863495i	$0.331729\pi$
$882$	1.41208e6	+	1.12183e7i	0.0611204	+	0.485573i
$883$	−1.91840e7			−0.828013			−0.414007	−	0.910274i	$-0.635871\pi$
$883$	−1.91840e7			−0.828013			−0.414007	+	0.910274i	$0.635871\pi$
$884$	2.26344e7			0.974177
$885$	3.49874e7	−	2.70348e7i	1.50160	−	1.16028i
$886$	1.24505e7			0.532845
$887$	−2.45045e7			−1.04577			−0.522885	−	0.852403i	$-0.675144\pi$
$887$	−2.45045e7			−1.04577			−0.522885	+	0.852403i	$0.675144\pi$
$888$	−8.09665e6	+	9.17969e6i	−0.344566	+	0.390657i
$889$	8.82724e6			0.374602
$890$			1.99717e7i			0.845160i
$891$	−2.77214e7	+	7.09109e6i	−1.16983	+	0.299239i
$892$	4.63617e6			0.195095
$893$	−1.61457e6			−0.0677529
$894$	−1.79969e7	−	1.58736e7i	−0.753103	−	0.664250i
$895$			3.35704e7i			1.40088i
$896$	−1.17857e6			−0.0490438
$897$	−1.49187e7	+	1.69142e7i	−0.619083	+	0.701893i
$898$			5.89571e6i			0.243975i
$899$	1.02647e6			0.0423593
$900$	−3.94679e6	−	3.13554e7i	−0.162419	−	1.29034i
$901$	5.74545e7			2.35783
$902$			1.22841e7i			0.502721i
$903$	−1.25923e7	+	1.42767e7i	−0.513910	+	0.582653i
$904$	−1.50817e6			−0.0613804
$905$		−	2.08180e7i		−	0.844926i
$906$	−7.61645e6	+	8.63526e6i	−0.308271	+	0.349506i
$907$	−1.91677e7			−0.773665			−0.386832	−	0.922150i	$-0.626431\pi$
$907$	−1.91677e7			−0.773665			−0.386832	+	0.922150i	$0.626431\pi$
$908$	1.61759e7			0.651110
$909$	−244152.	−	1.93967e6i	−0.00980055	−	0.0778608i
$910$	−2.13483e7			−0.854594
$911$			2.32692e7i			0.928936i	0.885590	+	0.464468i	$0.153754\pi$
$911$			2.32692e7i			0.928936i	−0.885590	+	0.464468i	$0.846246\pi$
$912$	−658366.	−	580691.i	−0.0262108	−	0.0231184i
$913$	−4.03147e7			−1.60061
$914$		−	3.01882e6i		−	0.119529i
$915$	6.54611e7	+	5.77379e7i	2.58482	+	2.27986i
$916$			815554.i			0.0321154i
$917$	1.90330e7			0.747452
$918$	2.53359e7	+	1.72433e7i	0.992271	+	0.675325i
$919$		−	3.24562e7i		−	1.26768i	−0.773465	−	0.633839i	$-0.781478\pi$
$919$		−	3.24562e7i		−	1.26768i	0.773465	−	0.633839i	$-0.218522\pi$
$920$		−	1.40443e7i		−	0.547054i
$921$	−2.82040e7	−	2.48764e7i	−1.09562	−	0.966360i
$922$		−	1.95080e7i		−	0.755764i
$923$	1.58883e7			0.613865
$924$	−6.52022e6	−	5.75095e6i	−0.251236	−	0.221595i
$925$		−	9.97251e7i		−	3.83222i
$926$		−	3.40217e7i		−	1.30385i
$927$	−2.84696e6	+	358355.i	−0.108813	+	0.0136967i
$928$		−	266119.i		−	0.0101439i
$929$	2.32205e7			0.882739			0.441370	−	0.897325i	$-0.354493\pi$
$929$	2.32205e7			0.882739			0.441370	+	0.897325i	$0.354493\pi$
$930$	−1.95936e7	−	1.72819e7i	−0.742860	−	0.655216i
$931$	−2.55893e6			−0.0967573
$932$	−1.78458e6			−0.0672970
$933$	−2.38010e7	+	2.69847e7i	−0.895139	+	1.01488i
$934$	2.46413e7			0.924265
$935$	−1.03974e8			−3.88951
$936$	1.07920e7	−	1.35842e6i	0.402636	−	0.0506809i
$937$			1.55553e7i			0.578800i	0.957208	+	0.289400i	$0.0934558\pi$
$937$			1.55553e7i			0.578800i	−0.957208	+	0.289400i	$0.906544\pi$
$938$		−	5.99747e6i		−	0.222567i
$939$	1.99595e7	−	2.26294e7i	0.738730	−	0.837546i
$940$			1.24575e7i			0.459846i
$941$	−3.46360e7			−1.27513			−0.637563	−	0.770398i	$-0.720058\pi$
$941$	−3.46360e7			−1.27513			−0.637563	+	0.770398i	$0.720058\pi$
$942$	−5.42919e6	+	6.15542e6i	−0.199346	+	0.226012i
$943$			1.31098e7i			0.480085i
$944$	−6.72159e6	−	1.29363e6i	−0.245495	−	0.0472475i
$945$	−2.38964e7	−	1.62635e7i	−0.870467	−	0.592427i
$946$			3.29062e7i			1.19550i
$947$			3.74358e7i			1.35648i	0.734843	+	0.678238i	$0.237256\pi$
$947$			3.74358e7i			1.35648i	−0.734843	+	0.678238i	$0.762744\pi$
$948$	1.66236e7	+	1.46623e7i	0.600765	+	0.529886i
$949$	7.11403e6			0.256419
$950$	7.15227e6			0.257119
$951$	−3.47942e6	+	3.94484e6i	−0.124754	+	0.141442i
$952$			9.31178e6i			0.332997i
$953$		−	4.32417e7i		−	1.54231i	−0.636650	−	0.771153i	$-0.719680\pi$
$953$		−	4.32417e7i		−	1.54231i	0.636650	−	0.771153i	$-0.280320\pi$
$954$	2.73942e7	−	3.44818e6i	0.974512	−	0.122665i
$955$		−	1.85581e7i		−	0.658454i
$956$		−	8.92164e6i		−	0.315719i
$957$	1.29856e6	−	1.47226e6i	0.0458334	−	0.0519642i
$958$		−	1.65245e7i		−	0.581721i
$959$		−	1.61111e7i		−	0.565690i
$960$	−4.48043e6	+	5.07975e6i	−0.156907	+	0.177895i
$961$	1.30284e7			0.455076
$962$	3.43238e7			1.19580
$963$	−3.39092e7	+	4.26824e6i	−1.17829	+	0.148314i
$964$	2.92332e6			0.101317
$965$		−	5.71479e7i		−	1.97552i
$966$	−6.95852e6	−	6.13754e6i	−0.239924	−	0.211617i
$967$		−	3.93578e6i		−	0.135352i	−0.997707	−	0.0676760i	$-0.978442\pi$
$967$		−	3.93578e6i		−	0.135352i	0.997707	−	0.0676760i	$-0.0215584\pi$
$968$	−4.72109e6			−0.161940
$969$	−4.58800e6	+	5.20171e6i	−0.156969	+	0.177966i
$970$	−6.26546e7			−2.13808
$971$		−	4.32016e7i		−	1.47046i	−0.677820	−	0.735228i	$-0.737075\pi$
$971$		−	4.32016e7i		−	1.47046i	0.677820	−	0.735228i	$-0.262925\pi$
$972$	1.31150e7	+	6.70099e6i	0.445248	+	0.227496i
$973$	−1.43226e7			−0.484999
$974$	1.93931e7			0.655014
$975$	−5.86204e7	+	6.64617e7i	−1.97487	+	2.23903i
$976$		−	1.35127e7i		−	0.454063i
$977$	−2.03951e6			−0.0683582			−0.0341791	−	0.999416i	$-0.510882\pi$
$977$	−2.03951e6			−0.0683582			−0.0341791	+	0.999416i	$0.510882\pi$
$978$	−1.03890e6	−	916330.i	−0.0347318	−	0.0306341i
$979$	2.28076e7			0.760542
$980$			1.97439e7i			0.656701i
$981$	4.78001e7	−	6.01673e6i	1.58583	−	0.199612i
$982$		−	3.11779e6i		−	0.103174i
$983$	−4.94923e7			−1.63363			−0.816815	−	0.576900i	$-0.804262\pi$
$983$	−4.94923e7			−1.63363			−0.816815	+	0.576900i	$0.804262\pi$
$984$	4.18232e6	−	4.74177e6i	0.137699	−	0.156118i
$985$	−8.24726e7			−2.70844
$986$	−2.10259e6			−0.0688751
$987$	6.17232e6	+	5.44410e6i	0.201677	+	0.177882i
$988$			2.46170e6i			0.0802310i
$989$			3.51182e7i			1.14167i
$990$	−4.95745e7	+	6.24008e6i	−1.60757	+	0.202349i
$991$			5.04715e7i			1.63253i	0.577674	+	0.816267i	$0.303960\pi$
$991$			5.04715e7i			1.63253i	−0.577674	+	0.816267i	$0.696040\pi$
$992$			4.04457e6i			0.130495i
$993$	1.34172e7	+	1.18342e7i	0.431807	+	0.380861i
$994$			6.53645e6i			0.209834i
$995$			5.26248e7i			1.68513i
$996$	1.55618e7	+	1.37258e7i	0.497064	+	0.438419i
$997$	2.85394e7			0.909300			0.454650	−	0.890670i	$-0.349764\pi$
$997$	2.85394e7			0.909300			0.454650	+	0.890670i	$0.349764\pi$
$998$	2.87362e7			0.913279
$999$	3.84205e7	+	2.61485e7i	1.21801	+	0.828957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.11	✓	50
3.2	odd	2		354.6.c.b.353.12	yes	50
59.58	odd	2		354.6.c.b.353.11	yes	50
177.176	even	2	inner	354.6.c.a.353.12	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.11	✓	50	1.1	even	1	trivial
354.6.c.a.353.12	yes	50	177.176	even	2	inner
354.6.c.b.353.11	yes	50	59.58	odd	2
354.6.c.b.353.12	yes	50	3.2	odd	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-11.6908 - 10.3115i) q^{3} +16.0000 q^{4} -106.082i q^{5} +(46.7630 + 41.2458i) q^{6} +71.9340 q^{7} -64.0000 q^{8} +(30.3476 + 241.098i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-11.6908 - 10.3115i) q^{3} +16.0000 q^{4} -106.082i q^{5} +(46.7630 + 41.2458i) q^{6} +71.9340 q^{7} -64.0000 q^{8} +(30.3476 + 241.098i) q^{9} +424.326i q^{10} +484.580 q^{11} +(-187.052 - 164.983i) q^{12} +699.407i q^{13} -287.736 q^{14} +(-1093.86 + 1240.17i) q^{15} +256.000 q^{16} -2022.64i q^{17} +(-121.390 - 964.390i) q^{18} +219.981 q^{19} -1697.30i q^{20} +(-840.963 - 741.744i) q^{21} -1938.32 q^{22} -2068.62 q^{23} +(748.208 + 659.933i) q^{24} -8128.29 q^{25} -2797.63i q^{26} +(2131.28 - 3131.54i) q^{27} +1150.94 q^{28} +259.882i q^{29} +(4375.42 - 4960.69i) q^{30} -3949.77i q^{31} -1024.00 q^{32} +(-5665.11 - 4996.73i) q^{33} +8090.56i q^{34} -7630.87i q^{35} +(485.562 + 3857.56i) q^{36} +12268.9i q^{37} -879.923 q^{38} +(7211.90 - 8176.59i) q^{39} +6789.22i q^{40} -6337.49i q^{41} +(3363.85 + 2966.98i) q^{42} -16976.7i q^{43} +7753.28 q^{44} +(25576.0 - 3219.32i) q^{45} +8274.46 q^{46} -7339.59 q^{47} +(-2992.83 - 2639.73i) q^{48} -11632.5 q^{49} +32513.2 q^{50} +(-20856.4 + 23646.2i) q^{51} +11190.5i q^{52} +28405.7i q^{53} +(-8525.12 + 12526.2i) q^{54} -51405.0i q^{55} -4603.77 q^{56} +(-2571.74 - 2268.32i) q^{57} -1039.53i q^{58} +(-26256.2 - 5053.23i) q^{59} +(-17501.7 + 19842.8i) q^{60} -52783.9i q^{61} +15799.1i q^{62} +(2183.02 + 17343.1i) q^{63} +4096.00 q^{64} +74194.1 q^{65} +(22660.4 + 19986.9i) q^{66} +20843.7i q^{67} -32362.3i q^{68} +(24183.7 + 21330.5i) q^{69} +30523.5i q^{70} -22716.8i q^{71} +(-1942.25 - 15430.2i) q^{72} -10171.5i q^{73} -49075.6i q^{74} +(95025.9 + 83814.5i) q^{75} +3519.69 q^{76} +34857.8 q^{77} +(-28847.6 + 32706.4i) q^{78} -88871.6 q^{79} -27156.9i q^{80} +(-57207.0 + 14633.5i) q^{81} +25350.0i q^{82} -83195.1 q^{83} +(-13455.4 - 11867.9i) q^{84} -214565. q^{85} +67906.7i q^{86} +(2679.76 - 3038.22i) q^{87} -31013.1 q^{88} +47066.8 q^{89} +(-102304. + 12877.3i) q^{90} +50311.1i q^{91} -33097.9 q^{92} +(-40727.9 + 46175.8i) q^{93} +29358.4 q^{94} -23335.9i q^{95} +(11971.3 + 10558.9i) q^{96} +147657. i q^{97} +46530.0 q^{98} +(14705.9 + 116831. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) \) 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	\( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) \) 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

Introduction

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