LMFDB - Embedded newform 40.6.d.a.21.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(21,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("40.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.d (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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.16
Root			$0.236693 + 3.99299i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.6.d.a.21.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.22968 + 3.75630i) q^{2} +25.0521i q^{3} +(3.78045 + 31.7759i) q^{4} -25.0000i q^{5} +(-94.1031 + 105.962i) q^{6} +103.624 q^{7} +(-103.370 + 148.603i) q^{8} -384.607 q^{9} +(93.9075 - 105.742i) q^{10} -740.776i q^{11} +(-796.053 + 94.7080i) q^{12} +892.067i q^{13} +(438.297 + 389.243i) q^{14} +626.302 q^{15} +(-995.416 + 240.254i) q^{16} +1138.81 q^{17} +(-1626.77 - 1444.70i) q^{18} +1155.46i q^{19} +(794.398 - 94.5111i) q^{20} +2596.00i q^{21} +(2782.58 - 3133.25i) q^{22} +1602.57 q^{23} +(-3722.80 - 2589.63i) q^{24} -625.000 q^{25} +(-3350.87 + 3773.16i) q^{26} -3547.55i q^{27} +(391.745 + 3292.75i) q^{28} -2158.47i q^{29} +(2649.06 + 2352.58i) q^{30} +4955.24 q^{31} +(-5112.76 - 2722.88i) q^{32} +18558.0 q^{33} +(4816.81 + 4277.71i) q^{34} -2590.60i q^{35} +(-1453.99 - 12221.2i) q^{36} -4403.89i q^{37} +(-4340.24 + 4887.22i) q^{38} -22348.1 q^{39} +(3715.06 + 2584.24i) q^{40} +3780.62 q^{41} +(-9751.34 + 10980.3i) q^{42} -13068.3i q^{43} +(23538.8 - 2800.46i) q^{44} +9615.17i q^{45} +(6778.38 + 6019.75i) q^{46} -8000.58 q^{47} +(-6018.87 - 24937.3i) q^{48} -6069.06 q^{49} +(-2643.55 - 2347.69i) q^{50} +28529.6i q^{51} +(-28346.2 + 3372.41i) q^{52} +34313.6i q^{53} +(13325.6 - 15005.0i) q^{54} -18519.4 q^{55} +(-10711.6 + 15398.8i) q^{56} -28946.6 q^{57} +(8107.85 - 9129.64i) q^{58} -22065.0i q^{59} +(2367.70 + 19901.3i) q^{60} -2822.53i q^{61} +(20959.1 + 18613.4i) q^{62} -39854.5 q^{63} +(-11397.4 - 30722.0i) q^{64} +22301.7 q^{65} +(78494.4 + 69709.3i) q^{66} -54981.5i q^{67} +(4305.21 + 36186.7i) q^{68} +40147.8i q^{69} +(9731.07 - 10957.4i) q^{70} +42879.2 q^{71} +(39756.7 - 57153.5i) q^{72} -20893.2 q^{73} +(16542.3 - 18627.1i) q^{74} -15657.6i q^{75} +(-36715.7 + 4368.14i) q^{76} -76762.2i q^{77} +(-94525.5 - 83946.2i) q^{78} +30227.6 q^{79} +(6006.35 + 24885.4i) q^{80} -4586.03 q^{81} +(15990.8 + 14201.1i) q^{82} -93949.9i q^{83} +(-82490.2 + 9814.03i) q^{84} -28470.3i q^{85} +(49088.5 - 55274.9i) q^{86} +54074.1 q^{87} +(110081. + 76573.8i) q^{88} +1178.06 q^{89} +(-36117.5 + 40669.1i) q^{90} +92439.5i q^{91} +(6058.44 + 50923.2i) q^{92} +124139. i q^{93} +(-33839.9 - 30052.6i) q^{94} +28886.4 q^{95} +(68213.9 - 128085. i) q^{96} +74100.8 q^{97} +(-25670.2 - 22797.2i) q^{98} +284908. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24}+ \cdots + 216942 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	4.22968	+	3.75630i	0.747709	+	0.664026i
$2$	4.22968	+	3.75630i	0.747709	+	0.664026i
$3$			25.0521i			1.60709i	0.595243	+	0.803546i	$0.297056\pi$
$3$			25.0521i			1.60709i	−0.595243	+	0.803546i	$0.702944\pi$
$4$	3.78045	+	31.7759i	0.118139	+	0.992997i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	−94.1031	+	105.962i	−1.06715	+	1.20164i
$7$	103.624			0.799310			0.399655	−	0.916666i	$-0.369130\pi$
$7$	103.624			0.799310			0.399655	+	0.916666i	$0.369130\pi$
$8$	−103.370	+	148.603i	−0.571042	+	0.820921i
$9$	−384.607			−1.58274
$10$	93.9075	−	105.742i	0.296961	−	0.334386i
$11$		−	740.776i		−	1.84589i	−0.384935	−	0.922944i	$-0.625776\pi$
$11$		−	740.776i		−	1.84589i	0.384935	−	0.922944i	$-0.374224\pi$
$12$	−796.053	+	94.7080i	−1.59584	+	0.189860i
$13$			892.067i			1.46399i	0.681309	+	0.731996i	$0.261411\pi$
$13$			892.067i			1.46399i	−0.681309	+	0.731996i	$0.738589\pi$
$14$	438.297	+	389.243i	0.597652	+	0.530763i
$15$	626.302			0.718713
$16$	−995.416	+	240.254i	−0.972086	+	0.234623i
$17$	1138.81			0.955717			0.477859	−	0.878437i	$-0.341413\pi$
$17$	1138.81			0.955717			0.477859	+	0.878437i	$0.341413\pi$
$18$	−1626.77	−	1444.70i	−1.18343	−	1.05098i
$19$			1155.46i			0.734294i	0.930163	+	0.367147i	$0.119665\pi$
$19$			1155.46i			0.734294i	−0.930163	+	0.367147i	$0.880335\pi$
$20$	794.398	−	94.5111i	0.444082	−	0.0528333i
$21$			2596.00i			1.28457i
$22$	2782.58	−	3133.25i	1.22572	−	1.38019i
$23$	1602.57			0.631682			0.315841	−	0.948812i	$-0.397713\pi$
$23$	1602.57			0.631682			0.315841	+	0.948812i	$0.397713\pi$
$24$	−3722.80	−	2589.63i	−1.31929	−	0.917717i
$25$	−625.000			−0.200000
$26$	−3350.87	+	3773.16i	−0.972129	+	1.09464i
$27$		−	3547.55i		−	0.936524i
$28$	391.745	+	3292.75i	0.0944297	+	0.793713i
$29$		−	2158.47i		−	0.476596i	−0.971192	−	0.238298i	$-0.923410\pi$
$29$		−	2158.47i		−	0.476596i	0.971192	−	0.238298i	$-0.0765896\pi$
$30$	2649.06	+	2352.58i	0.537389	+	0.477244i
$31$	4955.24			0.926106			0.463053	−	0.886331i	$-0.346754\pi$
$31$	4955.24			0.926106			0.463053	+	0.886331i	$0.346754\pi$
$32$	−5112.76	−	2722.88i	−0.882634	−	0.470061i
$33$	18558.0			2.96651
$34$	4816.81	+	4277.71i	0.714599	+	0.634621i
$35$		−	2590.60i		−	0.357462i
$36$	−1453.99	−	12221.2i	−0.186984	−	1.57166i
$37$		−	4403.89i		−	0.528850i	−0.964406	−	0.264425i	$-0.914818\pi$
$37$		−	4403.89i		−	0.528850i	0.964406	−	0.264425i	$-0.0851821\pi$
$38$	−4340.24	+	4887.22i	−0.487590	+	0.549039i
$39$	−22348.1			−2.35277
$40$	3715.06	+	2584.24i	0.367127	+	0.255378i
$41$	3780.62			0.351240			0.175620	−	0.984458i	$-0.443807\pi$
$41$	3780.62			0.351240			0.175620	+	0.984458i	$0.443807\pi$
$42$	−9751.34	+	10980.3i	−0.852985	+	0.960482i
$43$		−	13068.3i		−	1.07783i	−0.842361	−	0.538913i	$-0.818835\pi$
$43$		−	13068.3i		−	1.07783i	0.842361	−	0.538913i	$-0.181165\pi$
$44$	23538.8	−	2800.46i	1.83296	−	0.218071i
$45$			9615.17i			0.707825i
$46$	6778.38	+	6019.75i	0.472315	+	0.419453i
$47$	−8000.58			−0.528296			−0.264148	−	0.964482i	$-0.585091\pi$
$47$	−8000.58			−0.528296			−0.264148	+	0.964482i	$0.585091\pi$
$48$	−6018.87	−	24937.3i	−0.377061	−	1.56223i
$49$	−6069.06			−0.361103
$50$	−2643.55	−	2347.69i	−0.149542	−	0.132805i
$51$			28529.6i			1.53593i
$52$	−28346.2	+	3372.41i	−1.45374	+	0.172955i
$53$			34313.6i			1.67794i	0.544175	+	0.838971i	$0.316843\pi$
$53$			34313.6i			1.67794i	−0.544175	+	0.838971i	$0.683157\pi$
$54$	13325.6	−	15005.0i	0.621876	−	0.700248i
$55$	−18519.4			−0.825506
$56$	−10711.6	+	15398.8i	−0.456440	+	0.656170i
$57$	−28946.6			−1.18008
$58$	8107.85	−	9129.64i	0.316472	−	0.356356i
$59$		−	22065.0i		−	0.825227i	−0.910906	−	0.412613i	$-0.864616\pi$
$59$		−	22065.0i		−	0.825227i	0.910906	−	0.412613i	$-0.135384\pi$
$60$	2367.70	+	19901.3i	0.0849080	+	0.713680i
$61$		−	2822.53i		−	0.0971212i	−0.998820	−	0.0485606i	$-0.984537\pi$
$61$		−	2822.53i		−	0.0971212i	0.998820	−	0.0485606i	$-0.0154634\pi$
$62$	20959.1	+	18613.4i	0.692458	+	0.614959i
$63$	−39854.5			−1.26510
$64$	−11397.4	−	30722.0i	−0.347821	−	0.937561i
$65$	22301.7			0.654717
$66$	78494.4	+	69709.3i	2.21809	+	1.96984i
$67$		−	54981.5i		−	1.49634i	−0.663509	−	0.748168i	$-0.730934\pi$
$67$		−	54981.5i		−	1.49634i	0.663509	−	0.748168i	$-0.269066\pi$
$68$	4305.21	+	36186.7i	0.112907	+	0.949024i
$69$			40147.8i			1.01517i
$70$	9731.07	−	10957.4i	0.237364	−	0.267278i
$71$	42879.2			1.00949			0.504744	−	0.863269i	$-0.331587\pi$
$71$	42879.2			1.00949			0.504744	+	0.863269i	$0.331587\pi$
$72$	39756.7	−	57153.5i	0.903814	−	1.29931i
$73$	−20893.2			−0.458879			−0.229440	−	0.973323i	$-0.573689\pi$
$73$	−20893.2			−0.458879			−0.229440	+	0.973323i	$0.573689\pi$
$74$	16542.3	−	18627.1i	0.351170	−	0.395426i
$75$		−	15657.6i		−	0.321418i
$76$	−36715.7	+	4368.14i	−0.729152	+	0.0867487i
$77$		−	76762.2i		−	1.47544i
$78$	−94525.5	−	83946.2i	−1.75919	−	1.56230i
$79$	30227.6			0.544925			0.272462	−	0.962166i	$-0.412162\pi$
$79$	30227.6			0.544925			0.272462	+	0.962166i	$0.412162\pi$
$80$	6006.35	+	24885.4i	0.104927	+	0.434730i
$81$	−4586.03			−0.0776648
$82$	15990.8	+	14201.1i	0.262625	+	0.233232i
$83$		−	93949.9i		−	1.49693i	−0.663175	−	0.748465i	$-0.730791\pi$
$83$		−	93949.9i		−	1.49693i	0.663175	−	0.748465i	$-0.269209\pi$
$84$	−82490.2	+	9814.03i	−1.27557	+	0.151757i
$85$		−	28470.3i		−	0.427410i
$86$	49088.5	−	55274.9i	0.715704	−	0.805901i
$87$	54074.1			0.765934
$88$	110081.	+	76573.8i	1.51533	+	1.05408i
$89$	1178.06			0.0157650			0.00788248	−	0.999969i	$-0.497491\pi$
$89$	1178.06			0.0157650			0.00788248	+	0.999969i	$0.497491\pi$
$90$	−36117.5	+	40669.1i	−0.470014	+	0.529247i
$91$			92439.5i			1.17018i
$92$	6058.44	+	50923.2i	0.0746262	+	0.627258i
$93$			124139.i			1.48834i
$94$	−33839.9	−	30052.6i	−0.395012	−	0.350802i
$95$	28886.4			0.328386
$96$	68213.9	−	128085.i	0.755431	−	1.41847i
$97$	74100.8			0.799638			0.399819	−	0.916594i	$-0.369073\pi$
$97$	74100.8			0.799638			0.399819	+	0.916594i	$0.369073\pi$
$98$	−25670.2	−	22797.2i	−0.270000	−	0.239782i
$99$			284908.i			2.92157i
$100$	−2362.78	−	19859.9i	−0.0236278	−	0.198599i
$101$		−	31104.3i		−	0.303401i	−0.988427	−	0.151700i	$-0.951525\pi$
$101$		−	31104.3i		−	0.303401i	0.988427	−	0.151700i	$-0.0484749\pi$
$102$	−107166.	+	120671.i	−1.01989	+	1.14843i
$103$	−140298.			−1.30305			−0.651523	−	0.758629i	$-0.725870\pi$
$103$	−140298.			−1.30305			−0.651523	+	0.758629i	$0.725870\pi$
$104$	−132563.	−	92212.7i	−1.20182	−	0.836002i
$105$	64900.0			0.574475
$106$	−128892.	+	145136.i	−1.11420	+	1.25461i
$107$			34792.6i			0.293784i	0.989153	+	0.146892i	$0.0469269\pi$
$107$			34792.6i			0.293784i	−0.989153	+	0.146892i	$0.953073\pi$
$108$	112727.	−	13411.3i	0.929965	−	0.110640i
$109$		−	83759.2i		−	0.675252i	−0.941280	−	0.337626i	$-0.890376\pi$
$109$		−	83759.2i		−	0.675252i	0.941280	−	0.337626i	$-0.109624\pi$
$110$	−78331.2	−	69564.4i	−0.617239	−	0.548157i
$111$	110327.			0.849910
$112$	−103149.	+	24896.1i	−0.776999	+	0.187537i
$113$	57262.1			0.421863			0.210931	−	0.977501i	$-0.432350\pi$
$113$	57262.1			0.421863			0.210931	+	0.977501i	$0.432350\pi$
$114$	−122435.	−	108732.i	−0.882355	−	0.783602i
$115$		−	40064.3i		−	0.282497i
$116$	68587.3	−	8159.97i	0.473259	−	0.0563046i
$117$		−	343095.i		−	2.31713i
$118$	82882.6	−	93327.9i	0.547972	−	0.617030i
$119$	118008.			0.763914
$120$	−64740.7	+	93070.1i	−0.410416	+	0.590007i
$121$	−387698.			−2.40730
$122$	10602.3	−	11938.4i	0.0644910	−	0.0726184i
$123$			94712.5i			0.564475i
$124$	18733.0	+	157457.i	0.109409	+	0.919621i
$125$			15625.0i			0.0894427i
$126$	−168572.	−	149705.i	−0.945930	−	0.840062i
$127$	−8848.12			−0.0486790			−0.0243395	−	0.999704i	$-0.507748\pi$
$127$	−8848.12			−0.0486790			−0.0243395	+	0.999704i	$0.507748\pi$
$128$	67193.5	−	172756.i	0.362495	−	0.931986i
$129$	327389.			1.73217
$130$	94329.0	+	83771.7i	0.489538	+	0.434749i
$131$		−	110458.i		−	0.562365i	−0.959654	−	0.281183i	$-0.909273\pi$
$131$		−	110458.i		−	0.562365i	0.959654	−	0.281183i	$-0.0907267\pi$
$132$	70157.4	+	589697.i	0.350460	+	2.94574i
$133$			119733.i			0.586929i
$134$	206527.	−	232554.i	0.993606	−	1.11882i
$135$	−88688.7			−0.418826
$136$	−117719.	+	169230.i	−0.545755	+	0.784568i
$137$	−304365.			−1.38546			−0.692728	−	0.721199i	$-0.743591\pi$
$137$	−304365.			−1.38546			−0.692728	+	0.721199i	$0.743591\pi$
$138$	−150807.	+	169813.i	−0.674100	+	0.759053i
$139$			59379.5i			0.260675i	0.991470	+	0.130338i	$0.0416061\pi$
$139$			59379.5i			0.260675i	−0.991470	+	0.130338i	$0.958394\pi$
$140$	82318.7	−	9793.63i	0.354959	−	0.0422302i
$141$		−	200431.i		−	0.849020i
$142$	181366.	+	161067.i	0.754804	+	0.670326i
$143$	660822.			2.70237
$144$	382844.	−	92403.4i	1.53856	−	0.371349i
$145$	−53961.7			−0.213140
$146$	−88371.8	−	78481.2i	−0.343108	−	0.304708i
$147$		−	152043.i		−	0.580326i
$148$	139938.	−	16648.7i	0.525146	−	0.0624777i
$149$			233744.i			0.862529i	0.902225	+	0.431265i	$0.141932\pi$
$149$			233744.i			0.862529i	−0.902225	+	0.431265i	$0.858068\pi$
$150$	58814.4	−	66226.5i	0.213430	−	0.240328i
$151$	−89068.4			−0.317893			−0.158947	−	0.987287i	$-0.550810\pi$
$151$	−89068.4			−0.317893			−0.158947	+	0.987287i	$0.550810\pi$
$152$	−171704.	−	119439.i	−0.602797	−	0.419313i
$153$	−437994.			−1.51266
$154$	288342.	−	324680.i	0.979728	−	1.10320i
$155$		−	123881.i		−	0.414167i
$156$	−84485.9	−	710132.i	−0.277954	−	2.33629i
$157$			608909.i			1.97153i	0.168132	+	0.985764i	$0.446227\pi$
$157$			608909.i			1.97153i	−0.168132	+	0.985764i	$0.553773\pi$
$158$	127853.	+	113544.i	0.407445	+	0.361844i
$159$	−859628.			−2.69661
$160$	−68072.1	+	127819.i	−0.210218	+	0.394726i
$161$	166065.			0.504910
$162$	−19397.4	−	17226.5i	−0.0580707	−	0.0515714i
$163$			172801.i			0.509421i	0.967017	+	0.254711i	$0.0819802\pi$
$163$			172801.i			0.509421i	−0.967017	+	0.254711i	$0.918020\pi$
$164$	14292.4	+	120133.i	0.0414951	+	0.348780i
$165$		−	463950.i		−	1.32666i
$166$	352904.	−	397378.i	0.994000	−	1.11927i
$167$	441506.			1.22503			0.612513	−	0.790461i	$-0.290159\pi$
$167$	441506.			1.22503			0.612513	+	0.790461i	$0.290159\pi$
$168$	−385772.	−	268348.i	−1.05453	−	0.733541i
$169$	−424490.			−1.14327
$170$	106943.	−	120420.i	0.283811	−	0.319578i
$171$		−	444397.i		−	1.16220i
$172$	415258.	−	49404.1i	1.07028	−	0.127333i
$173$		−	281414.i		−	0.714874i	−0.933937	−	0.357437i	$-0.883651\pi$
$173$		−	281414.i		−	0.714874i	0.933937	−	0.357437i	$-0.116349\pi$
$174$	228717.	+	203119.i	0.572696	+	0.508600i
$175$	−64765.0			−0.159862
$176$	177975.	+	737381.i	0.433088	+	1.79436i
$177$	552774.			1.32622
$178$	4982.83	+	4425.15i	0.0117876	+	0.0104683i
$179$			805768.i			1.87965i	0.341655	+	0.939825i	$0.389013\pi$
$179$			805768.i			1.87965i	−0.341655	+	0.939825i	$0.610987\pi$
$180$	−305531.	+	36349.6i	−0.702868	+	0.0836217i
$181$			610344.i			1.38477i	0.721528	+	0.692385i	$0.243440\pi$
$181$			610344.i			1.38477i	−0.721528	+	0.692385i	$0.756560\pi$
$182$	−347231.	+	390990.i	−0.777033	+	0.874958i
$183$	70710.3			0.156083
$184$	−165658.	+	238147.i	−0.360717	+	0.518561i
$185$	−110097.			−0.236509
$186$	−466304.	+	525070.i	−0.988295	+	1.11284i
$187$		−	843604.i		−	1.76415i
$188$	−30245.8	−	254226.i	−0.0624123	−	0.524596i
$189$		−	367611.i		−	0.748573i
$190$	122180.	+	108506.i	0.245538	+	0.218057i
$191$	−845737.			−1.67746			−0.838729	−	0.544549i	$-0.816701\pi$
$191$	−845737.			−1.67746			−0.838729	+	0.544549i	$0.816701\pi$
$192$	769650.	−	285529.i	1.50675	−	0.558981i
$193$	−184089.			−0.355742			−0.177871	−	0.984054i	$-0.556921\pi$
$193$	−184089.			−0.355742			−0.177871	+	0.984054i	$0.556921\pi$
$194$	313423.	+	278345.i	0.597897	+	0.530981i
$195$			558703.i			1.05219i
$196$	−22943.7	−	192850.i	−0.0426603	−	0.358574i
$197$		−	390522.i		−	0.716935i	−0.933542	−	0.358468i	$-0.883299\pi$
$197$		−	390522.i		−	0.716935i	0.933542	−	0.358468i	$-0.116701\pi$
$198$	−1.07020e6	+	1.20507e6i	−1.94000	+	2.18448i
$199$	−584263.			−1.04587			−0.522933	−	0.852374i	$-0.675162\pi$
$199$	−584263.			−1.04587			−0.522933	+	0.852374i	$0.675162\pi$
$200$	64606.1	−	92876.6i	0.114208	−	0.164184i
$201$	1.37740e6			2.40475
$202$	116837.	−	131561.i	0.201466	−	0.226856i
$203$		−	223669.i		−	0.380948i
$204$	−906553.	+	107855.i	−1.52517	+	0.181453i
$205$		−	94515.6i		−	0.157079i
$206$	−593418.	−	527003.i	−0.974300	−	0.865256i
$207$	−616361.			−0.999791
$208$	−214323.	−	887978.i	−0.343487	−	1.42313i
$209$	855935.			1.35542
$210$	274506.	+	243784.i	0.429540	+	0.381466i
$211$		−	428258.i		−	0.662215i	−0.943593	−	0.331107i	$-0.892578\pi$
$211$		−	428258.i		−	0.662215i	0.943593	−	0.331107i	$-0.107422\pi$
$212$	−1.09035e6	+	129721.i	−1.66619	+	0.198230i
$213$			1.07421e6i			1.62234i
$214$	−130691.	+	147162.i	−0.195080	+	0.219665i
$215$	−326708.			−0.482018
$216$	527174.	+	366709.i	0.768812	+	0.534795i
$217$	513482.			0.740246
$218$	314624.	−	354275.i	0.448385	−	0.504893i
$219$		−	523419.i		−	0.737461i
$220$	−70011.6	−	588471.i	−0.0975244	−	0.819725i
$221$			1.01590e6i			1.39916i
$222$	466647.	+	414420.i	0.635486	+	0.564362i
$223$	955618.			1.28683			0.643416	−	0.765517i	$-0.277516\pi$
$223$	955618.			1.28683			0.643416	+	0.765517i	$0.277516\pi$
$224$	−529805.	−	282156.i	−0.705499	−	0.375724i
$225$	240379.			0.316549
$226$	242201.	+	215094.i	0.315431	+	0.280128i
$227$			866233.i			1.11576i	0.829922	+	0.557879i	$0.188385\pi$
$227$			866233.i			1.11576i	−0.829922	+	0.557879i	$0.811615\pi$
$228$	−109431.	−	919805.i	−0.139413	−	1.17181i
$229$		−	654035.i		−	0.824161i	−0.911147	−	0.412080i	$-0.864802\pi$
$229$		−	654035.i		−	0.824161i	0.911147	−	0.412080i	$-0.135198\pi$
$230$	150494.	−	169460.i	0.187585	−	0.211226i
$231$	1.92305e6			2.37116
$232$	320754.	+	223120.i	0.391248	+	0.272157i
$233$	−820513.			−0.990138			−0.495069	−	0.868854i	$-0.664857\pi$
$233$	−820513.			−0.990138			−0.495069	+	0.868854i	$0.664857\pi$
$234$	1.28877e6	−	1.45118e6i	1.53863	−	1.73254i
$235$			200015.i			0.236261i
$236$	701135.	−	83415.4i	0.819448	−	0.0974914i
$237$			757265.i			0.875744i
$238$	499137.	+	443274.i	0.571186	+	0.507259i
$239$	867314.			0.982159			0.491079	−	0.871115i	$-0.336603\pi$
$239$	867314.			0.982159			0.491079	+	0.871115i	$0.336603\pi$
$240$	−623431.	+	150472.i	−0.698651	+	0.168627i
$241$	−1.65377e6			−1.83414			−0.917072	−	0.398722i	$-0.869454\pi$
$241$	−1.65377e6			−1.83414			−0.917072	+	0.398722i	$0.869454\pi$
$242$	−1.63984e6	−	1.45631e6i	−1.79996	−	1.59851i
$243$		−	976943.i		−	1.06134i
$244$	89688.5	−	10670.4i	0.0964411	−	0.0114738i
$245$			151726.i			0.161490i
$246$	−355768.	+	400604.i	−0.374826	+	0.422063i
$247$	−1.03075e6			−1.07500
$248$	−512222.	+	736362.i	−0.528846	+	0.760260i
$249$	2.35364e6			2.40570
$250$	−58692.2	+	66088.8i	−0.0593923	+	0.0668772i
$251$		−	860879.i		−	0.862497i	−0.902233	−	0.431249i	$-0.858073\pi$
$251$		−	860879.i		−	0.862497i	0.902233	−	0.431249i	$-0.141927\pi$
$252$	−150668.	−	1.26641e6i	−0.149458	−	1.25624i
$253$		−	1.18715e6i		−	1.16601i
$254$	−37424.7	−	33236.2i	−0.0363978	−	0.0323241i
$255$	713240.			0.686887
$256$	933132.	−	478306.i	0.889904	−	0.456148i
$257$	−765335.			−0.722801			−0.361401	−	0.932411i	$-0.617701\pi$
$257$	−765335.			−0.722801			−0.361401	+	0.932411i	$0.617701\pi$
$258$	1.38475e6	+	1.22977e6i	1.29516	+	1.15020i
$259$		−	456349.i		−	0.422715i
$260$	84310.2	+	708656.i	0.0773476	+	0.650133i
$261$			830162.i			0.754330i
$262$	414913.	−	467202.i	0.373425	−	0.420486i
$263$	260746.			0.232449			0.116225	−	0.993223i	$-0.462921\pi$
$263$	260746.			0.232449			0.116225	+	0.993223i	$0.462921\pi$
$264$	−1.91833e6	+	2.75776e6i	−1.69400	+	2.43527i
$265$	857841.			0.750399
$266$	−449754.	+	506433.i	−0.389736	+	0.438852i
$267$			29512.9i			0.0253357i
$268$	1.74709e6	−	207854.i	1.48586	−	0.176776i
$269$		−	1.12412e6i		−	0.947175i	−0.880747	−	0.473587i	$-0.842959\pi$
$269$		−	1.12412e6i		−	0.947175i	0.880747	−	0.473587i	$-0.157041\pi$
$270$	−375125.	−	333141.i	−0.313160	−	0.278111i
$271$	−1.07277e6			−0.887330			−0.443665	−	0.896193i	$-0.646322\pi$
$271$	−1.07277e6			−0.887330			−0.443665	+	0.896193i	$0.646322\pi$
$272$	−1.13359e6	+	273604.i	−0.929039	+	0.224233i
$273$	−2.31580e6			−1.88059
$274$	−1.28737e6	−	1.14328e6i	−1.03592	−	0.919979i
$275$			462985.i			0.369177i
$276$	−1.27573e6	+	151777.i	−1.00806	+	0.119931i
$277$			615080.i			0.481651i	0.970568	+	0.240825i	$0.0774181\pi$
$277$			615080.i			0.481651i	−0.970568	+	0.240825i	$0.922582\pi$
$278$	−223047.	+	251157.i	−0.173095	+	0.194909i
$279$	−1.90582e6			−1.46579
$280$	384970.	+	267790.i	0.293448	+	0.204126i
$281$	−652198.			−0.492736			−0.246368	−	0.969176i	$-0.579237\pi$
$281$	−652198.			−0.492736			−0.246368	+	0.969176i	$0.579237\pi$
$282$	752880.	−	847761.i	0.563771	−	0.634820i
$283$		−	908596.i		−	0.674380i	−0.941437	−	0.337190i	$-0.890524\pi$
$283$		−	908596.i		−	0.674380i	0.941437	−	0.337190i	$-0.109476\pi$
$284$	162103.	+	1.36253e6i	0.119260	+	1.00242i
$285$			723665.i			0.527747i
$286$	2.79507e6	+	2.48224e6i	2.02058	+	1.79444i
$287$	391763.			0.280750
$288$	1.96640e6	+	1.04724e6i	1.39698	+	0.743986i
$289$	−122967.			−0.0866050
$290$	−228241.	−	202696.i	−0.159367	−	0.141531i
$291$			1.85638e6i			1.28509i
$292$	−78985.7	−	663901.i	−0.0542115	−	0.455666i
$293$			514047.i			0.349811i	0.984585	+	0.174906i	$0.0559621\pi$
$293$			514047.i			0.349811i	−0.984585	+	0.174906i	$0.944038\pi$
$294$	571117.	−	643092.i	0.385351	−	0.433915i
$295$	−551624.			−0.369053
$296$	654429.	+	455229.i	0.434144	+	0.301996i
$297$	−2.62794e6			−1.72872
$298$	−878010.	+	988661.i	−0.572742	+	0.644921i
$299$			1.42960e6i			0.924778i
$300$	497533.	−	59192.5i	0.319168	−	0.0379720i
$301$		−	1.35419e6i		−	0.861517i
$302$	−376731.	−	334568.i	−0.237692	−	0.211089i
$303$	779227.			0.487593
$304$	−277604.	−	1.15016e6i	−0.172282	−	0.713797i
$305$	−70563.3			−0.0434339
$306$	−1.85258e6	−	1.64524e6i	−1.13103	−	1.00444i
$307$			1.46693e6i			0.888309i	0.895950	+	0.444155i	$0.146496\pi$
$307$			1.46693e6i			0.888309i	−0.895950	+	0.444155i	$0.853504\pi$
$308$	2.43919e6	−	290195.i	1.46510	−	0.174307i
$309$		−	3.51477e6i		−	2.09411i
$310$	465334.	−	523978.i	0.275018	−	0.309677i
$311$	547919.			0.321229			0.160615	−	0.987017i	$-0.448652\pi$
$311$	547919.			0.321229			0.160615	+	0.987017i	$0.448652\pi$
$312$	2.31012e6	−	3.32099e6i	1.34353	−	1.93144i
$313$	1.70857e6			0.985762			0.492881	−	0.870097i	$-0.335944\pi$
$313$	1.70857e6			0.985762			0.492881	+	0.870097i	$0.335944\pi$
$314$	−2.28724e6	+	2.57549e6i	−1.30915	+	1.47413i
$315$			996363.i			0.565772i
$316$	114274.	+	960510.i	0.0643768	+	0.541109i
$317$		−	978608.i		−	0.546966i	−0.961877	−	0.273483i	$-0.911824\pi$
$317$		−	978608.i		−	0.546966i	0.961877	−	0.273483i	$-0.0881758\pi$
$318$	−3.63596e6	−	3.22902e6i	−2.01628	−	1.79062i
$319$	−1.59894e6			−0.879743
$320$	−768050.	+	284935.i	−0.419290	+	0.155550i
$321$	−871627.			−0.472137
$322$	702403.	+	623790.i	0.377526	+	0.335273i
$323$			1.31585e6i			0.701777i
$324$	−17337.2	−	145725.i	−0.00917523	−	0.0771209i
$325$		−	557542.i		−	0.292799i
$326$	−649092.	+	730893.i	−0.338269	+	0.380899i
$327$	2.09834e6			1.08519
$328$	−390802.	+	561810.i	−0.200573	+	0.288340i
$329$	−829053.			−0.422272
$330$	1.74273e6	−	1.96236e6i	0.880939	−	0.991959i
$331$			345907.i			0.173536i	0.996229	+	0.0867679i	$0.0276539\pi$
$331$			345907.i			0.173536i	−0.996229	+	0.0867679i	$0.972346\pi$
$332$	2.98534e6	−	355173.i	1.48645	−	0.176846i
$333$			1.69377e6i			0.837034i
$334$	1.86743e6	+	1.65843e6i	0.915963	+	0.813449i
$335$	−1.37454e6			−0.669182
$336$	−623699.	−	2.58410e6i	−0.301389	−	1.24871i
$337$	376513.			0.180595			0.0902975	−	0.995915i	$-0.471218\pi$
$337$	376513.			0.180595			0.0902975	+	0.995915i	$0.471218\pi$
$338$	−1.79546e6	−	1.59451e6i	−0.854837	−	0.759164i
$339$			1.43454e6i			0.677972i
$340$	904669.	−	107630.i	0.424417	−	0.0504937i
$341$		−	3.67073e6i		−	1.70949i
$342$	1.66929e6	−	1.87966e6i	0.771731	−	0.868988i
$343$	−2.37051e6			−1.08794
$344$	1.94199e6	+	1.35087e6i	0.884810	+	0.615484i
$345$	1.00370e6			0.453998
$346$	1.05707e6	−	1.19029e6i	0.474695	−	0.534518i
$347$			164656.i			0.0734099i	0.999326	+	0.0367049i	$0.0116862\pi$
$347$			164656.i			0.0734099i	−0.999326	+	0.0367049i	$0.988314\pi$
$348$	204424.	+	1.71825e6i	0.0904867	+	0.760571i
$349$		−	35942.6i		−	0.0157959i	−0.999969	−	0.00789797i	$-0.997486\pi$
$349$		−	35942.6i		−	0.0157959i	0.999969	−	0.00789797i	$-0.00251403\pi$
$350$	−273936.	−	243277.i	−0.119530	−	0.106153i
$351$	3.16465e6			1.37106
$352$	−2.01705e6	+	3.78741e6i	−0.867679	+	1.62924i
$353$	1.39430e6			0.595550			0.297775	−	0.954636i	$-0.403756\pi$
$353$	1.39430e6			0.595550			0.297775	+	0.954636i	$0.403756\pi$
$354$	2.33806e6	+	2.07638e6i	0.991624	+	0.880642i
$355$		−	1.07198e6i		−	0.451457i
$356$	4453.60	+	37434.0i	0.00186246	+	0.0156546i
$357$			2.95635e6i			1.22768i
$358$	−3.02670e6	+	3.40814e6i	−1.24814	+	1.40543i
$359$	3.50589e6			1.43569			0.717847	−	0.696201i	$-0.245128\pi$
$359$	3.50589e6			1.43569			0.717847	+	0.696201i	$0.245128\pi$
$360$	−1.42884e6	−	993917.i	−0.581068	−	0.404198i
$361$	1.14102e6			0.460812
$362$	−2.29263e6	+	2.58156e6i	−0.919524	+	1.03541i
$363$		−	9.71265e6i		−	3.86875i
$364$	−2.93735e6	+	349463.i	−1.16199	+	0.138244i
$365$			522331.i			0.205217i
$366$	299082.	+	265609.i	0.116705	+	0.103643i
$367$	3.64440e6			1.41241			0.706206	−	0.708007i	$-0.250405\pi$
$367$	3.64440e6			1.41241			0.706206	+	0.708007i	$0.250405\pi$
$368$	−1.59523e6	+	385025.i	−0.614049	+	0.148207i
$369$	−1.45405e6			−0.555923
$370$	−465677.	−	413558.i	−0.176840	−	0.157048i
$371$			3.55572e6i			1.34120i
$372$	−3.94464e6	+	469302.i	−1.47792	+	0.175831i
$373$			4.19252e6i			1.56028i	0.625603	+	0.780142i	$0.284853\pi$
$373$			4.19252e6i			1.56028i	−0.625603	+	0.780142i	$0.715147\pi$
$374$	3.16883e6	−	3.56818e6i	1.17144	−	1.31907i
$375$	−391439.			−0.143743
$376$	827018.	−	1.18891e6i	0.301679	−	0.433689i
$377$	1.92550e6			0.697734
$378$	1.38086e6	−	1.55488e6i	0.497072	−	0.559715i
$379$		−	2.31089e6i		−	0.826384i	−0.910644	−	0.413192i	$-0.864414\pi$
$379$		−	2.31089e6i		−	0.826384i	0.910644	−	0.413192i	$-0.135586\pi$
$380$	109204.	+	917893.i	0.0387952	+	0.326087i
$381$		−	221664.i		−	0.0782316i
$382$	−3.57720e6	−	3.17684e6i	−1.25425	−	1.11388i
$383$	1.18240e6			0.411876			0.205938	−	0.978565i	$-0.433976\pi$
$383$	1.18240e6			0.411876			0.205938	+	0.978565i	$0.433976\pi$
$384$	4.32791e6	+	1.68334e6i	1.49779	+	0.582563i
$385$	−1.91906e6			−0.659835
$386$	−778639.	−	691494.i	−0.265992	−	0.236222i
$387$			5.02617e6i			1.70592i
$388$	280134.	+	2.35462e6i	0.0944684	+	0.794038i
$389$		−	5.09219e6i		−	1.70620i	−0.521745	−	0.853102i	$-0.674719\pi$
$389$		−	5.09219e6i		−	1.70620i	0.521745	−	0.853102i	$-0.325281\pi$
$390$	−2.09866e6	+	2.36314e6i	−0.698682	+	0.786733i
$391$	1.82503e6			0.603709
$392$	627357.	−	901877.i	0.206205	−	0.296437i
$393$	2.76720e6			0.903773
$394$	1.46692e6	−	1.65178e6i	0.476064	−	0.536059i
$395$		−	755691.i		−	0.243698i
$396$	−9.05320e6	+	1.07708e6i	−2.90111	+	0.345151i
$397$		−	63006.9i		−	0.0200637i	−0.999950	−	0.0100319i	$-0.996807\pi$
$397$		−	63006.9i		−	0.0200637i	0.999950	−	0.0100319i	$-0.00319330\pi$
$398$	−2.47125e6	−	2.19467e6i	−0.782004	−	0.694482i
$399$	−2.99957e6			−0.943248
$400$	622135.	−	150159.i	0.194417	−	0.0469246i
$401$	−4.48960e6			−1.39427			−0.697135	−	0.716940i	$-0.745542\pi$
$401$	−4.48960e6			−1.39427			−0.697135	+	0.716940i	$0.745542\pi$
$402$	5.82597e6	+	5.17392e6i	1.79805	+	1.59682i
$403$			4.42041e6i			1.35581i
$404$	988367.	−	117588.i	0.301276	−	0.0358434i
$405$			114651.i			0.0347327i
$406$	840169.	−	946050.i	0.252960	−	0.284839i
$407$	−3.26230e6			−0.976197
$408$	−4.23957e6	−	2.94909e6i	−1.26087	−	0.877078i
$409$	2.03416e6			0.601281			0.300641	−	0.953738i	$-0.402800\pi$
$409$	2.03416e6			0.601281			0.300641	+	0.953738i	$0.402800\pi$
$410$	355029.	−	399771.i	0.104305	−	0.117450i
$411$		−	7.62497e6i		−	2.22656i
$412$	−530391.	−	4.45811e6i	−0.153940	−	1.29392i
$413$		−	2.28646e6i		−	0.659612i
$414$	−2.60701e6	−	2.31524e6i	−0.747553	−	0.663887i
$415$	−2.34875e6			−0.669447
$416$	2.42899e6	−	4.56093e6i	0.688165	−	1.29217i
$417$	−1.48758e6			−0.418929
$418$	3.62034e6	+	3.21515e6i	1.01346	+	0.900037i
$419$			1.53143e6i			0.426150i	0.977036	+	0.213075i	$0.0683479\pi$
$419$			1.53143e6i			0.426150i	−0.977036	+	0.213075i	$0.931652\pi$
$420$	245351.	+	2.06225e6i	0.0678679	+	0.570452i
$421$			4.86857e6i			1.33874i	0.742929	+	0.669370i	$0.233436\pi$
$421$			4.86857e6i			1.33874i	−0.742929	+	0.669370i	$0.766564\pi$
$422$	1.60866e6	−	1.81139e6i	0.439728	−	0.495144i
$423$	3.07708e6			0.836157
$424$	−5.09909e6	−	3.54699e6i	−1.37746	−	0.958176i
$425$	−711757.			−0.191143
$426$	−4.03507e6	+	4.54359e6i	−1.07728	+	1.21304i
$427$		−	292482.i		−	0.0776300i
$428$	−1.10557e6	+	131532.i	−0.291726	+	0.0347073i
$429$			1.65550e7i			4.34295i
$430$	−1.38187e6	−	1.22721e6i	−0.360410	−	0.320073i
$431$	537754.			0.139441			0.0697204	−	0.997567i	$-0.477789\pi$
$431$	537754.			0.139441			0.0697204	+	0.997567i	$0.477789\pi$
$432$	852313.	+	3.53129e6i	0.219730	+	0.910382i
$433$	1.48235e6			0.379954			0.189977	−	0.981789i	$-0.439159\pi$
$433$	1.48235e6			0.379954			0.189977	+	0.981789i	$0.439159\pi$
$434$	2.17187e6	+	1.92879e6i	0.553489	+	0.491543i
$435$		−	1.35185e6i		−	0.342536i
$436$	2.66152e6	−	316647.i	0.670524	−	0.0797736i
$437$			1.85171e6i			0.463840i
$438$	1.96612e6	−	2.21390e6i	0.489693	−	0.551407i
$439$	−2.49966e6			−0.619041			−0.309520	−	0.950893i	$-0.600168\pi$
$439$	−2.49966e6			−0.619041			−0.309520	+	0.950893i	$0.600168\pi$
$440$	1.91434e6	−	2.75203e6i	0.471399	−	0.677675i
$441$	2.33420e6			0.571534
$442$	−3.81601e6	+	4.29692e6i	−0.929080	+	1.04617i
$443$			5.00804e6i			1.21244i	0.795299	+	0.606218i	$0.207314\pi$
$443$			5.00804e6i			1.21244i	−0.795299	+	0.606218i	$0.792686\pi$
$444$	417084.	+	3.50573e6i	0.100407	+	0.843958i
$445$		−	29451.5i		−	0.00705030i
$446$	4.04196e6	+	3.58959e6i	0.962177	+	0.854490i
$447$	−5.85576e6			−1.38616
$448$	−1.18105e6	−	3.18354e6i	−0.278017	−	0.749402i
$449$	3.04025e6			0.711694			0.355847	−	0.934544i	$-0.384192\pi$
$449$	3.04025e6			0.711694			0.355847	+	0.934544i	$0.384192\pi$
$450$	1.01673e6	+	902936.i	0.236687	+	0.210197i
$451$		−	2.80059e6i		−	0.648349i
$452$	216476.	+	1.81956e6i	0.0498384	+	0.418909i
$453$		−	2.23135e6i		−	0.510884i
$454$	−3.25383e6	+	3.66389e6i	−0.740892	+	0.834263i
$455$	2.31099e6			0.523322
$456$	2.99220e6	−	4.30154e6i	0.673874	−	0.968750i
$457$	7.20014e6			1.61269			0.806345	−	0.591446i	$-0.201443\pi$
$457$	7.20014e6			1.61269			0.806345	+	0.591446i	$0.201443\pi$
$458$	2.45675e6	−	2.76636e6i	0.547264	−	0.616233i
$459$		−	4.03999e6i		−	0.895052i
$460$	1.27308e6	−	151461.i	0.280518	−	0.0333739i
$461$		−	7.87732e6i		−	1.72634i	−0.504914	−	0.863170i	$-0.668476\pi$
$461$		−	7.87732e6i		−	1.72634i	0.504914	−	0.863170i	$-0.331524\pi$
$462$	8.13391e6	+	7.22356e6i	1.77294	+	1.57451i
$463$	−6.18812e6			−1.34155			−0.670774	−	0.741662i	$-0.734038\pi$
$463$	−6.18812e6			−1.34155			−0.670774	+	0.741662i	$0.734038\pi$
$464$	518581.	+	2.14858e6i	0.111821	+	0.463293i
$465$	3.10348e6			0.665605
$466$	−3.47051e6	−	3.08209e6i	−0.740336	−	0.657477i
$467$		−	7.21143e6i		−	1.53013i	−0.643952	−	0.765066i	$-0.722706\pi$
$467$		−	7.21143e6i		−	1.53013i	0.643952	−	0.765066i	$-0.277294\pi$
$468$	1.09022e7	−	1.29705e6i	2.30090	−	0.273743i
$469$		−	5.69740e6i		−	1.19604i
$470$	−751315.	+	845999.i	−0.156883	+	0.176655i
$471$	−1.52544e7			−3.16843
$472$	3.27891e6	+	2.28085e6i	0.677446	+	0.471239i
$473$	−9.68070e6			−1.98955
$474$	−2.84451e6	+	3.20299e6i	−0.581517	+	0.654802i
$475$		−	722161.i		−	0.146859i
$476$	446124.	+	3.74982e6i	0.0902480	+	0.758565i
$477$		−	1.31973e7i		−	2.65575i
$478$	3.66846e6	+	3.25789e6i	0.734369	+	0.652179i
$479$	4.05783e6			0.808081			0.404040	−	0.914741i	$-0.367605\pi$
$479$	4.05783e6			0.808081			0.404040	+	0.914741i	$0.367605\pi$
$480$	−3.20213e6	−	1.70535e6i	−0.634361	−	0.337839i
$481$	3.92856e6			0.774232
$482$	−6.99494e6	−	6.21206e6i	−1.37141	−	1.21792i
$483$			4.16028e6i			0.811437i
$484$	−1.46567e6	−	1.23195e7i	−0.284396	−	2.39044i
$485$		−	1.85252e6i		−	0.357609i
$486$	3.66969e6	−	4.13216e6i	0.704756	−	0.793573i
$487$	121792.			0.0232700			0.0116350	−	0.999932i	$-0.496296\pi$
$487$	121792.			0.0232700			0.0116350	+	0.999932i	$0.496296\pi$
$488$	419435.	+	291764.i	0.0797288	+	0.0554603i
$489$	−4.32902e6			−0.818687
$490$	−569930.	+	641755.i	−0.107234	+	0.120748i
$491$			2.80649e6i			0.525363i	0.964883	+	0.262682i	$0.0846069\pi$
$491$			2.80649e6i			0.525363i	−0.964883	+	0.262682i	$0.915393\pi$
$492$	−3.00957e6	+	358055.i	−0.560522	+	0.0666864i
$493$		−	2.45809e6i		−	0.455491i
$494$	−4.35973e6	−	3.87179e6i	−0.803789	−	0.713829i
$495$	7.12269e6			1.30656
$496$	−4.93253e6	+	1.19052e6i	−0.900255	+	0.217286i
$497$	4.44332e6			0.806894
$498$	9.95516e6	+	8.84098e6i	1.79877	+	1.59745i
$499$			2.59476e6i			0.466494i	0.972418	+	0.233247i	$0.0749351\pi$
$499$			2.59476e6i			0.466494i	−0.972418	+	0.233247i	$0.925065\pi$
$500$	−496499.	+	59069.5i	−0.0888164	+	0.0105667i
$501$			1.10606e7i			1.96873i
$502$	3.23372e6	−	3.64125e6i	0.572721	−	0.644897i
$503$	1.04638e6			0.184404			0.0922021	−	0.995740i	$-0.470609\pi$
$503$	1.04638e6			0.184404			0.0922021	+	0.995740i	$0.470609\pi$
$504$	4.11975e6	−	5.92248e6i	0.722428	−	1.03855i
$505$	−777607.			−0.135685
$506$	4.45928e6	−	5.02126e6i	0.774264	−	0.871840i
$507$		−	1.06344e7i		−	1.83735i
$508$	−33449.8	−	281157.i	−0.00575089	−	0.0483381i
$509$			8.38369e6i			1.43430i	0.696918	+	0.717151i	$0.254554\pi$
$509$			8.38369e6i			1.43430i	−0.696918	+	0.717151i	$0.745446\pi$
$510$	3.01678e6	+	2.67914e6i	0.513592	+	0.456111i
$511$	−2.16504e6			−0.366787
$512$	5.74351e6	+	1.48204e6i	0.968284	+	0.249853i
$513$	4.09904e6			0.687684
$514$	−3.23713e6	−	2.87483e6i	−0.540445	−	0.479959i
$515$			3.50746e6i			0.582740i
$516$	1.23767e6	+	1.04031e7i	0.204636	+	1.72004i
$517$			5.92664e6i			0.975174i
$518$	1.71418e6	−	1.93021e6i	0.280694	−	0.316068i
$519$	7.05000e6			1.14887
$520$	−2.30532e6	+	3.31408e6i	−0.373871	+	0.537471i
$521$	−4.38397e6			−0.707577			−0.353788	−	0.935325i	$-0.615107\pi$
$521$	−4.38397e6			−0.707577			−0.353788	+	0.935325i	$0.615107\pi$
$522$	−3.11834e6	+	3.51132e6i	−0.500895	+	0.564020i
$523$			915789.i			0.146400i	0.997317	+	0.0732000i	$0.0233211\pi$
$523$			915789.i			0.146400i	−0.997317	+	0.0732000i	$0.976679\pi$
$524$	3.50990e6	−	417580.i	0.558427	−	0.0664372i
$525$		−	1.62250e6i		−	0.256913i
$526$	1.10287e6	+	979439.i	0.173804	+	0.154352i
$527$	5.64309e6			0.885096
$528$	−1.84729e7	+	4.45863e6i	−2.88370	+	0.696012i
$529$	−3.86810e6			−0.600978
$530$	3.62840e6	+	3.22231e6i	0.561080	+	0.498284i
$531$			8.48634e6i			1.30612i
$532$	−3.80463e6	+	452645.i	−0.582819	+	0.0693391i
$533$			3.37257e6i			0.514212i
$534$	−110859.	+	124830.i	−0.0168236	+	0.0189438i
$535$	869815.			0.131384
$536$	8.17038e6	+	5.68342e6i	1.22837	+	0.854471i
$537$	−2.01862e7			−3.02077
$538$	4.22251e6	−	4.75465e6i	0.628949	−	0.708212i
$539$			4.49581e6i			0.666556i
$540$	−335283.	−	2.81816e6i	−0.0494797	−	0.415893i
$541$			6.98594e6i			1.02620i	0.858329	+	0.513100i	$0.171503\pi$
$541$			6.98594e6i			1.02620i	−0.858329	+	0.513100i	$0.828497\pi$
$542$	−4.53750e6	−	4.02966e6i	−0.663465	−	0.589210i
$543$	−1.52904e7			−2.22545
$544$	−5.82247e6	−	3.10085e6i	−0.843548	−	0.449245i
$545$	−2.09398e6			−0.301982
$546$	−9.79511e6	−	8.69885e6i	−1.40614	−	1.24876i
$547$		−	4.72947e6i		−	0.675841i	−0.941175	−	0.337920i	$-0.890277\pi$
$547$		−	4.72947e6i		−	0.675841i	0.941175	−	0.337920i	$-0.109723\pi$
$548$	−1.15063e6	−	9.67146e6i	−0.163676	−	1.37575i
$549$			1.08556e6i			0.153718i
$550$	−1.73911e6	+	1.95828e6i	−0.245143	+	0.276038i
$551$	2.49402e6			0.349962
$552$	−5.96607e6	−	4.15007e6i	−0.833375	−	0.579706i
$553$	3.13231e6			0.435564
$554$	−2.31042e6	+	2.60159e6i	−0.319829	+	0.360135i
$555$		−	2.75817e6i		−	0.380091i
$556$	−1.88684e6	+	224481.i	−0.258850	+	0.0307959i
$557$			3.26312e6i			0.445651i	0.974858	+	0.222825i	$0.0715280\pi$
$557$			3.26312e6i			0.445651i	−0.974858	+	0.222825i	$0.928472\pi$
$558$	−8.06102e6	−	7.15883e6i	−1.09598	−	0.973322i
$559$	1.16578e7			1.57793
$560$	622403.	+	2.57873e6i	0.0838690	+	0.347484i
$561$	2.11340e7			2.83514
$562$	−2.75859e6	−	2.44985e6i	−0.368423	−	0.327189i
$563$			5.81898e6i			0.773706i	0.922141	+	0.386853i	$0.126438\pi$
$563$			5.81898e6i			0.773706i	−0.922141	+	0.386853i	$0.873562\pi$
$564$	6.36889e6	−	757720.i	0.843074	−	0.100302i
$565$		−	1.43155e6i		−	0.188663i
$566$	3.41296e6	−	3.84307e6i	0.447806	−	0.504240i
$567$	−475223.			−0.0620782
$568$	−4.43241e6	+	6.37196e6i	−0.576461	+	0.828710i
$569$	−9.08770e6			−1.17672			−0.588360	−	0.808599i	$-0.700226\pi$
$569$	−9.08770e6			−1.17672			−0.588360	+	0.808599i	$0.700226\pi$
$570$	−2.71830e6	+	3.06088e6i	−0.350438	+	0.394601i
$571$			258870.i			0.0332270i	0.999862	+	0.0166135i	$0.00528849\pi$
$571$			258870.i			0.0332270i	−0.999862	+	0.0166135i	$0.994712\pi$
$572$	2.49820e6	+	2.09982e7i	0.319255	+	2.68344i
$573$		−	2.11875e7i		−	2.69583i
$574$	1.65704e6	+	1.47158e6i	0.209919	+	0.186425i
$575$	−1.00161e6			−0.126336
$576$	4.38352e6	+	1.18159e7i	0.550512	+	1.48392i
$577$	2.45070e6			0.306444			0.153222	−	0.988192i	$-0.451035\pi$
$577$	2.45070e6			0.306444			0.153222	+	0.988192i	$0.451035\pi$
$578$	−520110.	−	461900.i	−0.0647554	−	0.0575080i
$579$		−	4.61182e6i		−	0.571710i
$580$	−203999.	−	1.71468e6i	−0.0251802	−	0.211648i
$581$		−	9.73547e6i		−	1.19651i
$582$	−6.97311e6	+	7.85190e6i	−0.853334	+	0.960875i
$583$	2.54187e7			3.09729
$584$	2.15973e6	−	3.10479e6i	0.262039	−	0.376703i
$585$	−8.57737e6			−1.03625
$586$	−1.93091e6	+	2.17426e6i	−0.232284	+	0.261557i
$587$		−	3.61982e6i		−	0.433602i	−0.976216	−	0.216801i	$-0.930438\pi$
$587$		−	3.61982e6i		−	0.433602i	0.976216	−	0.216801i	$-0.0695623\pi$
$588$	4.83129e6	−	574789.i	0.576262	−	0.0685591i
$589$			5.72557e6i			0.680034i
$590$	−2.33320e6	−	2.07207e6i	−0.275944	−	0.245061i
$591$	9.78339e6			1.15218
$592$	1.05805e6	+	4.38371e6i	0.124080	+	0.514088i
$593$	−7.07347e6			−0.826030			−0.413015	−	0.910724i	$-0.635524\pi$
$593$	−7.07347e6			−0.826030			−0.413015	+	0.910724i	$0.635524\pi$
$594$	−1.11153e7	−	9.87132e6i	−1.29258	−	1.14791i
$595$		−	2.95020e6i		−	0.341633i
$596$	−7.42741e6	+	883655.i	−0.856489	+	0.101898i
$597$		−	1.46370e7i		−	1.68080i
$598$	−5.37001e6	+	6.04677e6i	−0.614077	+	0.691465i
$599$	−2.71813e6			−0.309530			−0.154765	−	0.987951i	$-0.549462\pi$
$599$	−2.71813e6			−0.309530			−0.154765	+	0.987951i	$0.549462\pi$
$600$	2.32675e6	+	1.61852e6i	0.263859	+	0.183543i
$601$	1.67171e6			0.188788			0.0943942	−	0.995535i	$-0.469909\pi$
$601$	1.67171e6			0.188788			0.0943942	+	0.995535i	$0.469909\pi$
$602$	5.08675e6	−	5.72780e6i	0.572070	−	0.644165i
$603$			2.11462e7i			2.36832i
$604$	−336718.	−	2.83023e6i	−0.0375556	−	0.315667i
$605$			9.69245e6i			1.07658i
$606$	3.29588e6	+	2.92701e6i	0.364578	+	0.323774i
$607$	−2.35562e6			−0.259498			−0.129749	−	0.991547i	$-0.541417\pi$
$607$	−2.35562e6			−0.259498			−0.129749	+	0.991547i	$0.541417\pi$
$608$	3.14617e6	−	5.90758e6i	0.345163	−	0.648113i
$609$	5.60338e6			0.612219
$610$	−298460.	−	265057.i	−0.0324760	−	0.0288413i
$611$		−	7.13705e6i		−	0.773421i
$612$	−1.65581e6	−	1.39177e7i	−0.178704	−	1.50206i
$613$			1.88749e6i			0.202877i	0.994842	+	0.101439i	$0.0323445\pi$
$613$			1.88749e6i			0.202877i	−0.994842	+	0.101439i	$0.967655\pi$
$614$	−5.51024e6	+	6.20466e6i	−0.589860	+	0.664197i
$615$	2.36781e6			0.252441
$616$	1.14071e7	+	7.93489e6i	1.21122	+	0.842537i
$617$	1.45446e7			1.53812			0.769058	−	0.639178i	$-0.220725\pi$
$617$	1.45446e7			1.53812			0.769058	+	0.639178i	$0.220725\pi$
$618$	1.32025e7	−	1.48664e7i	1.39055	−	1.56579i
$619$		−	1.08497e7i		−	1.13813i	−0.822292	−	0.569066i	$-0.807305\pi$
$619$		−	1.08497e7i		−	1.13813i	0.822292	−	0.569066i	$-0.192695\pi$
$620$	3.93643e6	−	468326.i	0.411267	−	0.0489293i
$621$		−	5.68521e6i		−	0.591585i
$622$	2.31752e6	+	2.05815e6i	0.240186	+	0.213305i
$623$	122075.			0.0126011
$624$	2.22457e7	−	5.36923e6i	2.28710	−	0.552015i
$625$	390625.			0.0400000
$626$	7.22671e6	+	6.41790e6i	0.737063	+	0.654571i
$627$			2.14430e7i			2.17829i
$628$	−1.93486e7	+	2.30195e6i	−1.95772	+	0.232914i
$629$		−	5.01520e6i		−	0.505431i
$630$	−3.74264e6	+	4.21430e6i	−0.375687	+	0.423033i
$631$	3.76561e6			0.376497			0.188249	−	0.982121i	$-0.439719\pi$
$631$	3.76561e6			0.376497			0.188249	+	0.982121i	$0.439719\pi$
$632$	−3.12462e6	+	4.49190e6i	−0.311175	+	0.447340i
$633$	1.07287e7			1.06424
$634$	3.67594e6	−	4.13920e6i	0.363200	−	0.408972i
$635$			221203.i			0.0217699i
$636$	−3.24978e6	−	2.73155e7i	−0.318574	−	2.67772i
$637$		−	5.41400e6i		−	0.528652i
$638$	−6.76302e6	−	6.00610e6i	−0.657792	−	0.584173i
$639$	−1.64917e7			−1.59776
$640$	−4.31891e6	−	1.67984e6i	−0.416797	−	0.162113i
$641$	−223711.			−0.0215052			−0.0107526	−	0.999942i	$-0.503423\pi$
$641$	−223711.			−0.0215052			−0.0107526	+	0.999942i	$0.503423\pi$
$642$	−3.68671e6	−	3.27409e6i	−0.353021	−	0.313511i
$643$			2.53011e6i			0.241330i	0.992693	+	0.120665i	$0.0385028\pi$
$643$			2.53011e6i			0.241330i	−0.992693	+	0.120665i	$0.961497\pi$
$644$	627800.	+	5.27687e6i	0.0596495	+	0.501374i
$645$		−	8.18472e6i		−	0.774648i
$646$	−4.94272e6	+	5.56562e6i	−0.465998	+	0.524726i
$647$	−8.44825e6			−0.793425			−0.396713	−	0.917943i	$-0.629849\pi$
$647$	−8.44825e6			−0.793425			−0.396713	+	0.917943i	$0.629849\pi$
$648$	474056.	−	681495.i	0.0443499	−	0.0637566i
$649$	−1.63452e7			−1.52328
$650$	2.09429e6	−	2.35822e6i	0.194426	−	0.218928i
$651$			1.28638e7i			1.18964i
$652$	−5.49091e6	+	653265.i	−0.505854	+	0.0601825i
$653$		−	1.72303e7i		−	1.58128i	−0.612280	−	0.790641i	$-0.709747\pi$
$653$		−	1.72303e7i		−	1.58128i	0.612280	−	0.790641i	$-0.290253\pi$
$654$	8.87532e6	+	7.88200e6i	0.811409	+	0.720596i
$655$	−2.76145e6			−0.251497
$656$	−3.76329e6	+	908310.i	−0.341435	+	0.0824090i
$657$	8.03568e6			0.726289
$658$	−3.50663e6	−	3.11417e6i	−0.315737	−	0.280400i
$659$			5.43243e6i			0.487282i	0.969865	+	0.243641i	$0.0783419\pi$
$659$			5.43243e6i			0.487282i	−0.969865	+	0.243641i	$0.921658\pi$
$660$	1.47424e7	−	1.75394e6i	1.31737	−	0.156731i
$661$			1.12770e7i			1.00390i	0.864897	+	0.501949i	$0.167384\pi$
$661$			1.12770e7i			1.00390i	−0.864897	+	0.501949i	$0.832616\pi$
$662$	−1.29933e6	+	1.46308e6i	−0.115232	+	0.129754i
$663$	−2.54503e7			−2.24858
$664$	1.39612e7	+	9.71158e6i	1.22886	+	0.854810i
$665$	2.99333e6			0.262483
$666$	−6.36229e6	+	7.16410e6i	−0.555812	+	0.625858i
$667$		−	3.45911e6i		−	0.301057i
$668$	1.66909e6	+	1.40292e7i	0.144723	+	1.21645i
$669$			2.39402e7i			2.06806i
$670$	−5.81385e6	−	5.16317e6i	−0.500354	−	0.444354i
$671$	−2.09086e6			−0.179275
$672$	7.06860e6	−	1.32727e7i	0.603823	−	1.13380i
$673$	1.15475e7			0.982769			0.491384	−	0.870943i	$-0.336491\pi$
$673$	1.15475e7			0.982769			0.491384	+	0.870943i	$0.336491\pi$
$674$	1.59253e6	+	1.41430e6i	0.135033	+	0.119920i
$675$			2.21722e6i			0.187305i
$676$	−1.60476e6	−	1.34886e7i	−0.135065	−	1.13527i
$677$		−	8.72804e6i		−	0.731889i	−0.930637	−	0.365944i	$-0.880746\pi$
$677$		−	8.72804e6i		−	0.731889i	0.930637	−	0.365944i	$-0.119254\pi$
$678$	−5.38854e6	+	6.06763e6i	−0.450191	+	0.506926i
$679$	7.67862e6			0.639159
$680$	4.23075e6	+	2.94296e6i	0.350869	+	0.244069i
$681$	−2.17009e7			−1.79313
$682$	1.37883e7	−	1.55260e7i	1.13514	−	1.27820i
$683$		−	5.37492e6i		−	0.440880i	−0.975401	−	0.220440i	$-0.929251\pi$
$683$		−	5.37492e6i		−	0.440880i	0.975401	−	0.220440i	$-0.0707493\pi$
$684$	1.41211e7	−	1.68002e6i	1.15406	−	0.137301i
$685$			7.60912e6i			0.619595i
$686$	−1.00265e7	−	8.90434e6i	−0.813466	−	0.722423i
$687$	1.63849e7			1.32450
$688$	3.13972e6	+	1.30084e7i	0.252883	+	1.04774i
$689$	−3.06101e7			−2.45650
$690$	4.24531e6	+	3.77018e6i	0.339459	+	0.301467i
$691$			1.03106e7i			0.821467i	0.911756	+	0.410733i	$0.134727\pi$
$691$			1.03106e7i			0.821467i	−0.911756	+	0.410733i	$0.865273\pi$
$692$	8.94217e6	−	1.06387e6i	0.709868	−	0.0844545i
$693$			2.95233e7i			2.33524i
$694$	−618498.	+	696444.i	−0.0487461	+	0.0548893i
$695$	1.48449e6			0.116577
$696$	−5.58963e6	+	8.03555e6i	−0.437381	+	0.628771i
$697$	4.30541e6			0.335686
$698$	135011.	−	152026.i	0.0104889	−	0.0118108i
$699$		−	2.05556e7i		−	1.59124i
$700$	−244841.	−	2.05797e6i	−0.0188859	−	0.158743i
$701$		−	7.87993e6i		−	0.605658i	−0.953045	−	0.302829i	$-0.902069\pi$
$701$		−	7.87993e6i		−	0.605658i	0.953045	−	0.302829i	$-0.0979311\pi$
$702$	1.33855e7	+	1.18874e7i	1.02516	+	0.910422i
$703$	5.08851e6			0.388331
$704$	−2.27581e7	+	8.44293e6i	−1.73063	+	0.642039i
$705$	−5.01078e6			−0.379693
$706$	5.89743e6	+	5.23739e6i	0.445298	+	0.395460i
$707$		−	3.22315e6i		−	0.242511i
$708$	2.08973e6	+	1.75649e7i	0.156678	+	1.31693i
$709$		−	2.06172e7i		−	1.54033i	−0.637846	−	0.770164i	$-0.720174\pi$
$709$		−	2.06172e7i		−	1.54033i	0.637846	−	0.770164i	$-0.279826\pi$
$710$	4.02668e6	−	4.53414e6i	0.299779	−	0.337559i
$711$	−1.16258e7			−0.862476
$712$	−121776.	+	175063.i	−0.00900246	+	0.0129418i
$713$	7.94115e6			0.585005
$714$	−1.11049e7	+	1.25044e7i	−0.815212	+	0.917949i
$715$		−	1.65205e7i		−	1.20853i
$716$	−2.56040e7	+	3.04616e6i	−1.86649	+	0.222060i
$717$			2.17280e7i			1.57842i
$718$	1.48288e7	+	1.31692e7i	1.07348	+	0.953338i
$719$	1.37162e7			0.989490			0.494745	−	0.869038i	$-0.335262\pi$
$719$	1.37162e7			0.989490			0.494745	+	0.869038i	$0.335262\pi$
$720$	−2.31009e6	−	9.57110e6i	−0.166072	−	0.688067i
$721$	−1.45383e7			−1.04154
$722$	4.82614e6	+	4.28600e6i	0.344554	+	0.305991i
$723$		−	4.14305e7i		−	2.94764i
$724$	−1.93942e7	+	2.30737e6i	−1.37507	+	0.163595i
$725$			1.34904e6i			0.0953193i
$726$	3.64836e7	−	4.10814e7i	2.56895	−	2.89270i
$727$	−2.33681e7			−1.63979			−0.819895	−	0.572514i	$-0.805968\pi$
$727$	−2.33681e7			−1.63979			−0.819895	+	0.572514i	$0.805968\pi$
$728$	−1.37367e7	−	9.55545e6i	−0.960629	−	0.668225i
$729$	2.33601e7			1.62800
$730$	−1.96203e6	+	2.20929e6i	−0.136269	+	0.153443i
$731$		−	1.48823e7i		−	1.03010i
$732$	267316.	+	2.24688e6i	0.0184394	+	0.154990i
$733$			2.94411e6i			0.202392i	0.994866	+	0.101196i	$0.0322670\pi$
$733$			2.94411e6i			0.202392i	−0.994866	+	0.101196i	$0.967733\pi$
$734$	1.54147e7	+	1.36895e7i	1.05607	+	0.937878i
$735$	−3.80106e6			−0.259530
$736$	−8.19358e6	−	4.36362e6i	−0.557544	−	0.296929i
$737$	−4.07289e7			−2.76207
$738$	−6.15019e6	−	5.46186e6i	−0.415669	−	0.369147i
$739$			3.66027e6i			0.246548i	0.992373	+	0.123274i	$0.0393395\pi$
$739$			3.66027e6i			0.246548i	−0.992373	+	0.123274i	$0.960661\pi$
$740$	−416217.	−	3.49844e6i	−0.0279409	−	0.234853i
$741$		−	2.58223e7i		−	1.72763i
$742$	−1.33563e7	+	1.50396e7i	−0.890590	+	1.00283i
$743$	−2.60824e7			−1.73331			−0.866653	−	0.498912i	$-0.833733\pi$
$743$	−2.60824e7			−1.73331			−0.866653	+	0.498912i	$0.833733\pi$
$744$	−1.84474e7	−	1.28322e7i	−1.22181	−	0.849904i
$745$	5.84359e6			0.385735
$746$	−1.57484e7	+	1.77331e7i	−1.03607	+	1.16664i
$747$			3.61338e7i			2.36926i
$748$	2.68063e7	−	3.18920e6i	1.75179	−	0.208414i
$749$			3.60535e6i			0.234824i
$750$	−1.65566e6	−	1.47036e6i	−0.107478	−	0.0954489i
$751$	−1.03196e7			−0.667673			−0.333836	−	0.942631i	$-0.608343\pi$
$751$	−1.03196e7			−0.667673			−0.333836	+	0.942631i	$0.608343\pi$
$752$	7.96391e6	−	1.92217e6i	0.513549	−	0.123950i
$753$	2.15668e7			1.38611
$754$	8.14425e6	+	7.23275e6i	0.521702	+	0.463313i
$755$			2.22671e6i			0.142166i
$756$	1.16812e7	−	1.38973e6i	0.743331	−	0.0884356i
$757$			2.70313e7i			1.71446i	0.514936	+	0.857228i	$0.327816\pi$
$757$			2.70313e7i			1.71446i	−0.514936	+	0.857228i	$0.672184\pi$
$758$	8.68040e6	−	9.77434e6i	0.548740	−	0.617895i
$759$	2.97405e7			1.87389
$760$	−2.98598e6	+	4.29260e6i	−0.187522	+	0.269579i
$761$	1.29548e7			0.810905			0.405452	−	0.914116i	$-0.367114\pi$
$761$	1.29548e7			0.810905			0.405452	+	0.914116i	$0.367114\pi$
$762$	832635.	−	937568.i	0.0519478	−	0.0584945i
$763$		−	8.67946e6i		−	0.539736i
$764$	−3.19726e6	−	2.68741e7i	−0.198173	−	1.66571i
$765$			1.09499e7i			0.676480i
$766$	5.00116e6	+	4.44143e6i	0.307963	+	0.273496i
$767$	1.96834e7			1.20813
$768$	1.19826e7	+	2.33769e7i	0.733072	+	1.43016i
$769$	8.35551e6			0.509515			0.254757	−	0.967005i	$-0.418004\pi$
$769$	8.35551e6			0.509515			0.254757	+	0.967005i	$0.418004\pi$
$770$	−8.11700e6	−	7.20854e6i	−0.493365	−	0.438148i
$771$		−	1.91732e7i		−	1.16161i
$772$	−695939.	−	5.84960e6i	−0.0420270	−	0.353251i
$773$			3.12215e7i			1.87934i	0.342087	+	0.939668i	$0.388866\pi$
$773$			3.12215e7i			1.87934i	−0.342087	+	0.939668i	$0.611134\pi$
$774$	−1.88798e7	+	2.12591e7i	−1.13278	+	1.27553i
$775$	−3.09703e6			−0.185221
$776$	−7.65978e6	+	1.10116e7i	−0.456627	+	0.656439i
$777$	1.14325e7			0.679342
$778$	1.91278e7	−	2.15384e7i	1.13296	−	1.27574i
$779$			4.36835e6i			0.257913i
$780$	−1.77533e7	+	2.11215e6i	−1.04482	+	0.124305i
$781$		−	3.17639e7i		−	1.86340i
$782$	7.71929e6	+	6.85535e6i	0.451399	+	0.400879i
$783$	−7.65727e6			−0.446344
$784$	6.04124e6	−	1.45812e6i	0.351023	−	0.0847232i
$785$	1.52227e7			0.881695
$786$	1.17044e7	+	1.03944e7i	0.675760	+	0.600129i
$787$		−	1.14664e7i		−	0.659920i	−0.943995	−	0.329960i	$-0.892965\pi$
$787$		−	1.14664e7i		−	0.659920i	0.943995	−	0.329960i	$-0.107035\pi$
$788$	1.24092e7	−	1.47635e6i	0.711915	−	0.0846980i
$789$			6.53222e6i			0.373567i
$790$	2.83860e6	−	3.19633e6i	0.161822	−	0.182215i
$791$	5.93373e6			0.337199
$792$	−4.23380e7	−	2.94508e7i	−2.39838	−	1.66834i
$793$	2.51789e6			0.142185
$794$	236673.	−	266499.i	0.0133228	−	0.0150018i
$795$			2.14907e7i			1.20596i
$796$	−2.20878e6	−	1.85655e7i	−0.123557	−	1.03854i
$797$			2.28998e7i			1.27699i	0.769628	+	0.638493i	$0.220442\pi$
$797$			2.28998e7i			1.27699i	−0.769628	+	0.638493i	$0.779558\pi$
$798$	−1.26872e7	−	1.12673e7i	−0.705276	−	0.626342i
$799$	−9.11115e6			−0.504901
$800$	3.19548e6	+	1.70180e6i	0.176527	+	0.0940121i
$801$	−453090.			−0.0249519
$802$	−1.89896e7	−	1.68643e7i	−1.04251	−	0.925831i
$803$			1.54772e7i			0.847040i
$804$	5.20719e6	+	4.37681e7i	0.284095	+	2.38791i
$805$		−	4.15163e6i		−	0.225803i
$806$	−1.66044e7	+	1.86969e7i	−0.900295	+	1.01375i
$807$	2.81614e7			1.52220
$808$	4.62217e6	+	3.21524e6i	0.249068	+	0.173255i
$809$	2.82761e7			1.51896			0.759482	−	0.650528i	$-0.225452\pi$
$809$	2.82761e7			1.51896			0.759482	+	0.650528i	$0.225452\pi$
$810$	−430662.	+	484936.i	−0.0230634	+	0.0259700i
$811$			2.97657e7i			1.58915i	0.607167	+	0.794574i	$0.292306\pi$
$811$			2.97657e7i			1.58915i	−0.607167	+	0.794574i	$0.707694\pi$
$812$	7.10729e6	−	845570.i	0.378281	−	0.0450048i
$813$		−	2.68752e7i		−	1.42602i
$814$	−1.37985e7	−	1.22542e7i	−0.729912	−	0.648220i
$815$	4.32002e6			0.227820
$816$	−6.85435e6	−	2.83988e7i	−0.360364	−	1.49305i
$817$	1.50999e7			0.791441
$818$	8.60387e6	+	7.64092e6i	0.449584	+	0.399266i
$819$		−	3.55529e7i		−	1.85210i
$820$	3.00332e6	−	357311.i	0.155979	−	0.0185572i
$821$			2.33663e7i			1.20985i	0.796282	+	0.604926i	$0.206797\pi$
$821$			2.33663e7i			1.20985i	−0.796282	+	0.604926i	$0.793203\pi$
$822$	2.86417e7	−	3.22512e7i	1.47849	−	1.66482i
$823$	−3.90864e6			−0.201153			−0.100576	−	0.994929i	$-0.532069\pi$
$823$	−3.90864e6			−0.201153			−0.100576	+	0.994929i	$0.532069\pi$
$824$	1.45026e7	−	2.08487e7i	0.744094	−	1.06970i
$825$	−1.15987e7			−0.593302
$826$	8.58863e6	−	9.67101e6i	0.438000	−	0.493198i
$827$			1.34407e7i			0.683371i	0.939814	+	0.341686i	$0.110998\pi$
$827$			1.34407e7i			0.683371i	−0.939814	+	0.341686i	$0.889002\pi$
$828$	−2.33012e6	−	1.95854e7i	−0.118114	−	0.992790i
$829$		−	2.39273e7i		−	1.20923i	−0.796519	−	0.604613i	$-0.793328\pi$
$829$		−	2.39273e7i		−	1.20923i	0.796519	−	0.604613i	$-0.206672\pi$
$830$	−9.93446e6	−	8.82260e6i	−0.500552	−	0.444530i
$831$	−1.54090e7			−0.774057
$832$	2.74061e7	−	1.01673e7i	1.37258	−	0.509208i
$833$	−6.91151e6			−0.345112
$834$	−6.29200e6	−	5.58780e6i	−0.313237	−	0.278180i
$835$		−	1.10376e7i		−	0.547848i
$836$	3.23582e6	+	2.71981e7i	0.160128	+	1.34593i
$837$		−	1.75790e7i		−	0.867320i
$838$	−5.75251e6	+	6.47747e6i	−0.282975	+	0.318636i
$839$	−4.44572e6			−0.218041			−0.109020	−	0.994040i	$-0.534771\pi$
$839$	−4.44572e6			−0.218041			−0.109020	+	0.994040i	$0.534771\pi$
$840$	−6.70869e6	+	9.64430e6i	−0.328050	+	0.471598i
$841$	1.58522e7			0.772856
$842$	−1.82878e7	+	2.05925e7i	−0.888958	+	1.00099i
$843$		−	1.63389e7i		−	0.791871i
$844$	1.36083e7	−	1.61900e6i	0.657577	−	0.0782334i
$845$			1.06122e7i			0.511288i
$846$	1.30151e7	+	1.15584e7i	0.625203	+	0.555230i
$847$	−4.01748e7			−1.92418
$848$	−8.24400e6	−	3.41564e7i	−0.393684	−	1.63111i
$849$	2.27622e7			1.08379
$850$	−3.01051e6	−	2.67357e6i	−0.142920	−	0.126924i
$851$		−	7.05756e6i		−	0.334065i
$852$	−3.41341e7	+	4.06101e6i	−1.61098	+	0.191662i
$853$		−	2.57954e7i		−	1.21386i	−0.794754	−	0.606931i	$-0.792400\pi$
$853$		−	2.57954e7i		−	1.21386i	0.794754	−	0.606931i	$-0.207600\pi$
$854$	1.09865e6	−	1.23711e6i	0.0515483	−	0.0580447i
$855$	−1.11099e7			−0.519752
$856$	−5.17027e6	−	3.59650e6i	−0.241173	−	0.167763i
$857$	1.79012e7			0.832590			0.416295	−	0.909230i	$-0.363328\pi$
$857$	1.79012e7			0.832590			0.416295	+	0.909230i	$0.363328\pi$
$858$	−6.21854e7	+	7.00222e7i	−2.88383	+	3.24727i
$859$			2.50747e7i			1.15945i	0.814811	+	0.579727i	$0.196841\pi$
$859$			2.50747e7i			1.15945i	−0.814811	+	0.579727i	$0.803159\pi$
$860$	−1.23510e6	−	1.03814e7i	−0.0569451	−	0.478643i
$861$			9.81449e6i			0.451190i
$862$	2.27453e6	+	2.01996e6i	0.104261	+	0.0925924i
$863$	8.98511e6			0.410673			0.205337	−	0.978691i	$-0.434171\pi$
$863$	8.98511e6			0.410673			0.205337	+	0.978691i	$0.434171\pi$
$864$	−9.65955e6	+	1.81378e7i	−0.440223	+	0.826608i
$865$	−7.03534e6			−0.319702
$866$	6.26988e6	+	5.56815e6i	0.284095	+	0.252300i
$867$		−	3.08057e6i		−	0.139182i
$868$	1.94119e6	+	1.63164e7i	0.0874519	+	0.735062i
$869$		−	2.23919e7i		−	1.00587i
$870$	5.07797e6	−	5.71791e6i	0.227453	−	0.256118i
$871$	4.90471e7			2.19063
$872$	1.24468e7	+	8.65816e6i	0.554329	+	0.385598i
$873$	−2.84997e7			−1.26562
$874$	−6.95556e6	+	7.83213e6i	−0.308002	+	0.346818i
$875$			1.61913e6i			0.0714925i
$876$	1.66321e7	−	1.97876e6i	0.732297	−	0.0871229i
$877$			1.08381e7i			0.475834i	0.971286	+	0.237917i	$0.0764646\pi$
$877$			1.08381e7i			0.475834i	−0.971286	+	0.237917i	$0.923535\pi$
$878$	−1.05728e7	−	9.38946e6i	−0.462863	−	0.411059i
$879$	−1.28780e7			−0.562179
$880$	1.84345e7	−	4.44936e6i	0.802463	−	0.193683i
$881$	−816876.			−0.0354582			−0.0177291	−	0.999843i	$-0.505644\pi$
$881$	−816876.			−0.0354582			−0.0177291	+	0.999843i	$0.505644\pi$
$882$	9.87293e6	+	8.76796e6i	0.427341	+	0.379513i
$883$			2.50842e6i			0.108268i	0.998534	+	0.0541339i	$0.0172398\pi$
$883$			2.50842e6i			0.108268i	−0.998534	+	0.0541339i	$0.982760\pi$
$884$	−3.22810e7	+	3.84054e6i	−1.38936	+	0.165296i
$885$		−	1.38193e7i		−	0.593102i
$886$	−1.88117e7	+	2.11824e7i	−0.805089	+	0.906550i
$887$	−1.58294e7			−0.675545			−0.337773	−	0.941228i	$-0.609673\pi$
$887$	−1.58294e7			−0.675545			−0.337773	+	0.941228i	$0.609673\pi$
$888$	−1.14044e7	+	1.63948e7i	−0.485335	+	0.697709i
$889$	−916878.			−0.0389096
$890$	110629.	−	124571.i	0.00468158	−	0.00527158i
$891$			3.39722e6i			0.143360i
$892$	3.61266e6	+	3.03656e7i	0.152025	+	1.27782i
$893$		−	9.24434e6i		−	0.387924i
$894$	−2.47680e7	−	2.19960e7i	−1.03645	−	0.920449i
$895$	2.01442e7			0.840605
$896$	6.96286e6	−	1.79017e7i	0.289746	−	0.744946i
$897$	−3.58145e7			−1.48620
$898$	1.28593e7	+	1.14201e7i	0.532140	+	0.472583i
$899$		−	1.06957e7i		−	0.441379i
$900$	908741.	+	7.63827e6i	0.0373967	+	0.314332i
$901$			3.90768e7i			1.60364i
$902$	1.05199e7	−	1.18456e7i	0.430521	−	0.484777i
$903$	3.39253e7			1.38454
$904$	−5.91917e6	+	8.50929e6i	−0.240902	+	0.346316i
$905$	1.52586e7			0.619288
$906$	8.38162e6	−	9.43790e6i	0.339240	−	0.381993i
$907$			2.36328e7i			0.953887i	0.878934	+	0.476944i	$0.158255\pi$
$907$			2.36328e7i			0.953887i	−0.878934	+	0.476944i	$0.841745\pi$
$908$	−2.75253e7	+	3.27475e6i	−1.10794	+	0.131814i
$909$			1.19629e7i			0.480206i
$910$	9.77475e6	+	8.68076e6i	0.391293	+	0.347500i
$911$	−9.17484e6			−0.366271			−0.183136	−	0.983088i	$-0.558625\pi$
$911$	−9.17484e6			−0.366271			−0.183136	+	0.983088i	$0.558625\pi$
$912$	2.88139e7	−	6.95455e6i	1.14714	−	0.276874i
$913$	−6.95959e7			−2.76316
$914$	3.04543e7	+	2.70459e7i	1.20582	+	1.07087i
$915$		−	1.76776e6i		−	0.0698023i
$916$	2.07825e7	−	2.47254e6i	0.818389	−	0.0973655i
$917$		−	1.14461e7i		−	0.449504i
$918$	1.51754e7	−	1.70879e7i	0.594338	−	0.669239i
$919$	−3.58059e7			−1.39851			−0.699255	−	0.714872i	$-0.746485\pi$
$919$	−3.58059e7			−1.39851			−0.699255	+	0.714872i	$0.746485\pi$
$920$	5.95366e6	+	4.14144e6i	0.231907	+	0.161318i
$921$	−3.67497e7			−1.42759
$922$	2.95896e7	−	3.33186e7i	1.14633	−	1.29080i
$923$			3.82511e7i			1.47788i
$924$	7.27000e6	+	6.11068e7i	0.280127	+	2.35456i
$925$			2.75243e6i			0.105770i
$926$	−2.61738e7	−	2.32444e7i	−1.00309	−	0.890823i
$927$	5.39597e7			2.06239
$928$	−5.87726e6	+	1.10357e7i	−0.224029	+	0.420660i
$929$	−2.41031e7			−0.916291			−0.458146	−	0.888877i	$-0.651486\pi$
$929$	−2.41031e7			−0.916291			−0.458146	+	0.888877i	$0.651486\pi$
$930$	1.31267e7	+	1.16576e7i	0.497679	+	0.441979i
$931$		−	7.01254e6i		−	0.265156i
$932$	−3.10191e6	−	2.60726e7i	−0.116974	−	0.983204i
$933$			1.37265e7i			0.516245i
$934$	2.70883e7	−	3.05021e7i	1.01605	−	1.14409i
$935$	−2.10901e7			−0.788950
$936$	5.09848e7	+	3.54656e7i	1.90218	+	1.32318i
$937$	−1.84615e7			−0.686938			−0.343469	−	0.939164i	$-0.611602\pi$
$937$	−1.84615e7			−0.686938			−0.343469	+	0.939164i	$0.611602\pi$
$938$	2.14011e7	−	2.40982e7i	0.794200	−	0.894288i
$939$			4.28032e7i			1.58421i
$940$	−6.35565e6	+	756144.i	−0.234607	+	0.0279116i
$941$			3.10319e6i			0.114244i	0.998367	+	0.0571220i	$0.0181924\pi$
$941$			3.10319e6i			0.114244i	−0.998367	+	0.0571220i	$0.981808\pi$
$942$	−6.45214e7	−	5.73002e7i	−2.36906	−	2.10392i
$943$	6.05873e6			0.221872
$944$	5.30120e6	+	2.19638e7i	0.193617	+	0.802192i
$945$	−9.19028e6			−0.334772
$946$	−4.09463e7	−	3.63636e7i	−1.48760	−	1.32111i
$947$		−	4.89572e7i		−	1.77395i	−0.461817	−	0.886975i	$-0.652802\pi$
$947$		−	4.89572e7i		−	1.77395i	0.461817	−	0.886975i	$-0.347198\pi$
$948$	−2.40628e7	+	2.86280e6i	−0.869611	+	0.103459i
$949$		−	1.86382e7i		−	0.671796i
$950$	2.71265e6	−	3.05451e6i	0.0975181	−	0.109808i
$951$	2.45162e7			0.879025
$952$	−1.21985e7	+	1.75363e7i	−0.436227	+	0.627113i
$953$	3.94753e7			1.40797			0.703984	−	0.710216i	$-0.251403\pi$
$953$	3.94753e7			1.40797			0.703984	+	0.710216i	$0.251403\pi$
$954$	4.95729e7	−	5.58203e7i	1.76349	−	1.98573i
$955$			2.11434e7i			0.750182i
$956$	3.27883e6	+	2.75597e7i	0.116031	+	0.975281i
$957$		−	4.00568e7i		−	1.41383i
$958$	1.71633e7	+	1.52424e7i	0.604210	+	0.536587i
$959$	−3.15395e7			−1.10741
$960$	−7.13822e6	−	1.92412e7i	−0.249984	−	0.673837i
$961$	−4.07470e6			−0.142327
$962$	1.66166e7	+	1.47569e7i	0.578901	+	0.514110i
$963$		−	1.33815e7i		−	0.464984i
$964$	−6.25200e6	−	5.25501e7i	−0.216684	−	1.82130i
$965$			4.60223e6i			0.159093i
$966$	−1.56272e7	+	1.75967e7i	−0.538815	+	0.606719i
$967$	−2.23447e7			−0.768438			−0.384219	−	0.923242i	$-0.625529\pi$
$967$	−2.23447e7			−0.768438			−0.384219	+	0.923242i	$0.625529\pi$
$968$	4.00762e7	−	5.76129e7i	1.37467	−	1.97620i
$969$	−3.29647e7			−1.12782
$970$	6.95862e6	−	7.83557e6i	0.237462	−	0.267388i
$971$		−	2.63033e7i		−	0.895288i	−0.894212	−	0.447644i	$-0.852263\pi$
$971$		−	2.63033e7i		−	0.895288i	0.894212	−	0.447644i	$-0.147737\pi$
$972$	3.10433e7	−	3.69328e6i	1.05391	−	0.125385i
$973$			6.15315e6i			0.208360i
$974$	515141.	+	457486.i	0.0173992	+	0.0154519i
$975$	1.39676e7			0.470554
$976$	678125.	+	2.80959e6i	0.0227869	+	0.0944102i
$977$	4.78338e7			1.60324			0.801619	−	0.597835i	$-0.203972\pi$
$977$	4.78338e7			1.60324			0.801619	+	0.597835i	$0.203972\pi$
$978$	−1.83104e7	−	1.62611e7i	−0.612140	−	0.543629i
$979$		−	872679.i		−	0.0291003i
$980$	−4.82125e6	+	573594.i	−0.160359	+	0.0190783i
$981$			3.22144e7i			1.06875i
$982$	−1.05420e7	+	1.18706e7i	−0.348855	+	0.392819i
$983$	4.88361e7			1.61197			0.805986	−	0.591935i	$-0.201636\pi$
$983$	4.88361e7			1.61197			0.805986	+	0.591935i	$0.201636\pi$
$984$	−1.40745e7	−	9.79040e6i	−0.463389	−	0.322339i
$985$	−9.76305e6			−0.320623
$986$	9.23331e6	−	1.03969e7i	0.302458	−	0.340575i
$987$		−	2.07695e7i		−	0.678630i
$988$	−3.89668e6	−	3.27529e7i	−0.126999	−	1.06747i
$989$		−	2.09429e7i		−	0.680843i
$990$	3.01267e7	+	2.67549e7i	0.976931	+	0.867593i
$991$	7.49231e6			0.242344			0.121172	−	0.992632i	$-0.461335\pi$
$991$	7.49231e6			0.242344			0.121172	+	0.992632i	$0.461335\pi$
$992$	−2.53350e7	−	1.34925e7i	−0.817413	−	0.435326i
$993$	−8.66569e6			−0.278888
$994$	1.87938e7	+	1.66904e7i	0.603323	+	0.535799i
$995$			1.46066e7i			0.467725i
$996$	8.89781e6	+	7.47891e7i	0.284207	+	2.38886i
$997$		−	1.46209e7i		−	0.465841i	−0.972496	−	0.232920i	$-0.925172\pi$
$997$		−	1.46209e7i		−	0.465841i	0.972496	−	0.232920i	$-0.0748281\pi$
$998$	−9.74670e6	+	1.09750e7i	−0.309764	+	0.348802i
$999$	−1.56230e7			−0.495280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.d.a.21.16	yes	20
3.2	odd	2		360.6.k.b.181.5		20
4.3	odd	2		160.6.d.a.81.3		20
5.2	odd	4		200.6.f.c.149.6		20
5.3	odd	4		200.6.f.b.149.15		20
5.4	even	2		200.6.d.b.101.5		20
8.3	odd	2		160.6.d.a.81.18		20
8.5	even	2	inner	40.6.d.a.21.15	✓	20
20.3	even	4		800.6.f.c.49.18		20
20.7	even	4		800.6.f.b.49.3		20
20.19	odd	2		800.6.d.c.401.18		20
24.5	odd	2		360.6.k.b.181.6		20
40.3	even	4		800.6.f.b.49.4		20
40.13	odd	4		200.6.f.c.149.5		20
40.19	odd	2		800.6.d.c.401.3		20
40.27	even	4		800.6.f.c.49.17		20
40.29	even	2		200.6.d.b.101.6		20
40.37	odd	4		200.6.f.b.149.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.15	✓	20	8.5	even	2	inner
40.6.d.a.21.16	yes	20	1.1	even	1	trivial
160.6.d.a.81.3		20	4.3	odd	2
160.6.d.a.81.18		20	8.3	odd	2
200.6.d.b.101.5		20	5.4	even	2
200.6.d.b.101.6		20	40.29	even	2
200.6.f.b.149.15		20	5.3	odd	4
200.6.f.b.149.16		20	40.37	odd	4
200.6.f.c.149.5		20	40.13	odd	4
200.6.f.c.149.6		20	5.2	odd	4
360.6.k.b.181.5		20	3.2	odd	2
360.6.k.b.181.6		20	24.5	odd	2
800.6.d.c.401.3		20	40.19	odd	2
800.6.d.c.401.18		20	20.19	odd	2
800.6.f.b.49.3		20	20.7	even	4
800.6.f.b.49.4		20	40.3	even	4
800.6.f.c.49.17		20	40.27	even	4
800.6.f.c.49.18		20	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.22968 + 3.75630i) q^{2} +25.0521i q^{3} +(3.78045 + 31.7759i) q^{4} -25.0000i q^{5} +(-94.1031 + 105.962i) q^{6} +103.624 q^{7} +(-103.370 + 148.603i) q^{8} -384.607 q^{9} +(93.9075 - 105.742i) q^{10} -740.776i q^{11} +(-796.053 + 94.7080i) q^{12} +892.067i q^{13} +(438.297 + 389.243i) q^{14} +626.302 q^{15} +(-995.416 + 240.254i) q^{16} +1138.81 q^{17} +(-1626.77 - 1444.70i) q^{18} +1155.46i q^{19} +(794.398 - 94.5111i) q^{20} +2596.00i q^{21} +(2782.58 - 3133.25i) q^{22} +1602.57 q^{23} +(-3722.80 - 2589.63i) q^{24} -625.000 q^{25} +(-3350.87 + 3773.16i) q^{26} -3547.55i q^{27} +(391.745 + 3292.75i) q^{28} -2158.47i q^{29} +(2649.06 + 2352.58i) q^{30} +4955.24 q^{31} +(-5112.76 - 2722.88i) q^{32} +18558.0 q^{33} +(4816.81 + 4277.71i) q^{34} -2590.60i q^{35} +(-1453.99 - 12221.2i) q^{36} -4403.89i q^{37} +(-4340.24 + 4887.22i) q^{38} -22348.1 q^{39} +(3715.06 + 2584.24i) q^{40} +3780.62 q^{41} +(-9751.34 + 10980.3i) q^{42} -13068.3i q^{43} +(23538.8 - 2800.46i) q^{44} +9615.17i q^{45} +(6778.38 + 6019.75i) q^{46} -8000.58 q^{47} +(-6018.87 - 24937.3i) q^{48} -6069.06 q^{49} +(-2643.55 - 2347.69i) q^{50} +28529.6i q^{51} +(-28346.2 + 3372.41i) q^{52} +34313.6i q^{53} +(13325.6 - 15005.0i) q^{54} -18519.4 q^{55} +(-10711.6 + 15398.8i) q^{56} -28946.6 q^{57} +(8107.85 - 9129.64i) q^{58} -22065.0i q^{59} +(2367.70 + 19901.3i) q^{60} -2822.53i q^{61} +(20959.1 + 18613.4i) q^{62} -39854.5 q^{63} +(-11397.4 - 30722.0i) q^{64} +22301.7 q^{65} +(78494.4 + 69709.3i) q^{66} -54981.5i q^{67} +(4305.21 + 36186.7i) q^{68} +40147.8i q^{69} +(9731.07 - 10957.4i) q^{70} +42879.2 q^{71} +(39756.7 - 57153.5i) q^{72} -20893.2 q^{73} +(16542.3 - 18627.1i) q^{74} -15657.6i q^{75} +(-36715.7 + 4368.14i) q^{76} -76762.2i q^{77} +(-94525.5 - 83946.2i) q^{78} +30227.6 q^{79} +(6006.35 + 24885.4i) q^{80} -4586.03 q^{81} +(15990.8 + 14201.1i) q^{82} -93949.9i q^{83} +(-82490.2 + 9814.03i) q^{84} -28470.3i q^{85} +(49088.5 - 55274.9i) q^{86} +54074.1 q^{87} +(110081. + 76573.8i) q^{88} +1178.06 q^{89} +(-36117.5 + 40669.1i) q^{90} +92439.5i q^{91} +(6058.44 + 50923.2i) q^{92} +124139. i q^{93} +(-33839.9 - 30052.6i) q^{94} +28886.4 q^{95} +(68213.9 - 128085. i) q^{96} +74100.8 q^{97} +(-25670.2 - 22797.2i) q^{98} +284908. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24}+ \cdots + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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