LMFDB - Embedded newform 200.6.f.b.149.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0767639626$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.16
Root			$0.236693 - 3.99299i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.b.149.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.75630 + 4.22968i) q^{2} -25.0521 q^{3} +(-3.78045 + 31.7759i) q^{4} +(-94.1031 - 105.962i) q^{6} +103.624i q^{7} +(-148.603 + 103.370i) q^{8} +384.607 q^{9} +O(q^{10})$	\(q+(3.75630 + 4.22968i) q^{2} -25.0521 q^{3} +(-3.78045 + 31.7759i) q^{4} +(-94.1031 - 105.962i) q^{6} +103.624i q^{7} +(-148.603 + 103.370i) q^{8} +384.607 q^{9} +740.776i q^{11} +(94.7080 - 796.053i) q^{12} -892.067 q^{13} +(-438.297 + 389.243i) q^{14} +(-995.416 - 240.254i) q^{16} +1138.81i q^{17} +(1444.70 + 1626.77i) q^{18} +1155.46i q^{19} -2596.00i q^{21} +(-3133.25 + 2782.58i) q^{22} -1602.57i q^{23} +(3722.80 - 2589.63i) q^{24} +(-3350.87 - 3773.16i) q^{26} -3547.55 q^{27} +(-3292.75 - 391.745i) q^{28} -2158.47i q^{29} +4955.24 q^{31} +(-2722.88 - 5112.76i) q^{32} -18558.0i q^{33} +(-4816.81 + 4277.71i) q^{34} +(-1453.99 + 12221.2i) q^{36} -4403.89 q^{37} +(-4887.22 + 4340.24i) q^{38} +22348.1 q^{39} +3780.62 q^{41} +(10980.3 - 9751.34i) q^{42} +13068.3 q^{43} +(-23538.8 - 2800.46i) q^{44} +(6778.38 - 6019.75i) q^{46} -8000.58i q^{47} +(24937.3 + 6018.87i) q^{48} +6069.06 q^{49} -28529.6i q^{51} +(3372.41 - 28346.2i) q^{52} -34313.6 q^{53} +(-13325.6 - 15005.0i) q^{54} +(-10711.6 - 15398.8i) q^{56} -28946.6i q^{57} +(9129.64 - 8107.85i) q^{58} -22065.0i q^{59} +2822.53i q^{61} +(18613.4 + 20959.1i) q^{62} +39854.5i q^{63} +(11397.4 - 30722.0i) q^{64} +(78494.4 - 69709.3i) q^{66} -54981.5 q^{67} +(-36186.7 - 4305.21i) q^{68} +40147.8i q^{69} +42879.2 q^{71} +(-57153.5 + 39756.7i) q^{72} +20893.2i q^{73} +(-16542.3 - 18627.1i) q^{74} +(-36715.7 - 4368.14i) q^{76} -76762.2 q^{77} +(83946.2 + 94525.5i) q^{78} -30227.6 q^{79} -4586.03 q^{81} +(14201.1 + 15990.8i) q^{82} +93949.9 q^{83} +(82490.2 + 9814.03i) q^{84} +(49088.5 + 55274.9i) q^{86} +54074.1i q^{87} +(-76573.8 - 110081. i) q^{88} -1178.06 q^{89} -92439.5i q^{91} +(50923.2 + 6058.44i) q^{92} -124139. q^{93} +(33839.9 - 30052.6i) q^{94} +(68213.9 + 128085. i) q^{96} +74100.8i q^{97} +(22797.2 + 25670.2i) q^{98} +284908. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9 - 1252 * q^12 - 2708 * q^14 + 3080 * q^16 - 2070 * q^18 - 8244 * q^22 - 1032 * q^24 - 8084 * q^26 - 11664 * q^27 - 22924 * q^28 + 7160 * q^31 - 14792 * q^32 - 21132 * q^34 + 18344 * q^36 + 3608 * q^37 + 16884 * q^38 + 44904 * q^39 + 11608 * q^41 + 49444 * q^42 + 51772 * q^43 - 72296 * q^44 - 28516 * q^46 + 85048 * q^48 - 18756 * q^49 + 111624 * q^52 - 928 * q^53 + 100584 * q^54 - 53624 * q^56 - 152344 * q^58 - 228648 * q^62 + 11264 * q^64 - 56688 * q^66 + 161604 * q^67 - 359040 * q^68 - 200312 * q^71 - 563448 * q^72 - 78876 * q^74 - 153872 * q^76 - 26008 * q^77 + 624640 * q^78 - 282080 * q^79 + 65172 * q^81 + 410576 * q^82 + 99092 * q^83 + 297128 * q^84 + 27452 * q^86 + 464496 * q^88 + 3160 * q^89 + 519244 * q^92 - 293472 * q^93 - 148820 * q^94 + 395168 * q^96 - 663674 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	3.75630	+	4.22968i	0.664026	+	0.747709i
$2$	3.75630	+	4.22968i	0.664026	+	0.747709i
$3$	−25.0521			−1.60709			−0.803546	−	0.595243i	$-0.797056\pi$
$3$	−25.0521			−1.60709			−0.803546	+	0.595243i	$0.797056\pi$
$4$	−3.78045	+	31.7759i	−0.118139	+	0.992997i
$5$		0			0
$5$		0			0
$6$	−94.1031	−	105.962i	−1.06715	−	1.20164i
$7$			103.624i			0.799310i	0.916666	+	0.399655i	$0.130870\pi$
$7$			103.624i			0.799310i	−0.916666	+	0.399655i	$0.869130\pi$
$8$	−148.603	+	103.370i	−0.820921	+	0.571042i
$9$	384.607			1.58274
$10$		0			0
$11$			740.776i			1.84589i	0.384935	+	0.922944i	$0.374224\pi$
$11$			740.776i			1.84589i	−0.384935	+	0.922944i	$0.625776\pi$
$12$	94.7080	−	796.053i	0.189860	−	1.59584i
$13$	−892.067			−1.46399			−0.731996	−	0.681309i	$-0.761411\pi$
$13$	−892.067			−1.46399			−0.731996	+	0.681309i	$0.761411\pi$
$14$	−438.297	+	389.243i	−0.597652	+	0.530763i
$15$		0			0
$16$	−995.416	−	240.254i	−0.972086	−	0.234623i
$17$			1138.81i			0.955717i	0.878437	+	0.477859i	$0.158587\pi$
$17$			1138.81i			0.955717i	−0.878437	+	0.477859i	$0.841413\pi$
$18$	1444.70	+	1626.77i	1.05098	+	1.18343i
$19$			1155.46i			0.734294i	0.930163	+	0.367147i	$0.119665\pi$
$19$			1155.46i			0.734294i	−0.930163	+	0.367147i	$0.880335\pi$
$20$		0			0
$21$		−	2596.00i		−	1.28457i
$22$	−3133.25	+	2782.58i	−1.38019	+	1.22572i
$23$		−	1602.57i		−	0.631682i	−0.948812	−	0.315841i	$-0.897713\pi$
$23$		−	1602.57i		−	0.631682i	0.948812	−	0.315841i	$-0.102287\pi$
$24$	3722.80	−	2589.63i	1.31929	−	0.917717i
$25$		0			0
$26$	−3350.87	−	3773.16i	−0.972129	−	1.09464i
$27$	−3547.55			−0.936524
$28$	−3292.75	−	391.745i	−0.793713	−	0.0944297i
$29$		−	2158.47i		−	0.476596i	−0.971192	−	0.238298i	$-0.923410\pi$
$29$		−	2158.47i		−	0.476596i	0.971192	−	0.238298i	$-0.0765896\pi$
$30$		0			0
$31$	4955.24			0.926106			0.463053	−	0.886331i	$-0.346754\pi$
$31$	4955.24			0.926106			0.463053	+	0.886331i	$0.346754\pi$
$32$	−2722.88	−	5112.76i	−0.470061	−	0.882634i
$33$		−	18558.0i		−	2.96651i
$34$	−4816.81	+	4277.71i	−0.714599	+	0.634621i
$35$		0			0
$36$	−1453.99	+	12221.2i	−0.186984	+	1.57166i
$37$	−4403.89			−0.528850			−0.264425	−	0.964406i	$-0.585182\pi$
$37$	−4403.89			−0.528850			−0.264425	+	0.964406i	$0.585182\pi$
$38$	−4887.22	+	4340.24i	−0.549039	+	0.487590i
$39$	22348.1			2.35277
$40$		0			0
$41$	3780.62			0.351240			0.175620	−	0.984458i	$-0.443807\pi$
$41$	3780.62			0.351240			0.175620	+	0.984458i	$0.443807\pi$
$42$	10980.3	−	9751.34i	0.960482	−	0.852985i
$43$	13068.3			1.07783			0.538913	−	0.842361i	$-0.318835\pi$
$43$	13068.3			1.07783			0.538913	+	0.842361i	$0.318835\pi$
$44$	−23538.8	−	2800.46i	−1.83296	−	0.218071i
$45$		0			0
$46$	6778.38	−	6019.75i	0.472315	−	0.419453i
$47$		−	8000.58i		−	0.528296i	−0.964482	−	0.264148i	$-0.914909\pi$
$47$		−	8000.58i		−	0.528296i	0.964482	−	0.264148i	$-0.0850907\pi$
$48$	24937.3	+	6018.87i	1.56223	+	0.377061i
$49$	6069.06			0.361103
$50$		0			0
$51$		−	28529.6i		−	1.53593i
$52$	3372.41	−	28346.2i	0.172955	−	1.45374i
$53$	−34313.6			−1.67794			−0.838971	−	0.544175i	$-0.816843\pi$
$53$	−34313.6			−1.67794			−0.838971	+	0.544175i	$0.816843\pi$
$54$	−13325.6	−	15005.0i	−0.621876	−	0.700248i
$55$		0			0
$56$	−10711.6	−	15398.8i	−0.456440	−	0.656170i
$57$		−	28946.6i		−	1.18008i
$58$	9129.64	−	8107.85i	0.356356	−	0.316472i
$59$		−	22065.0i		−	0.825227i	−0.910906	−	0.412613i	$-0.864616\pi$
$59$		−	22065.0i		−	0.825227i	0.910906	−	0.412613i	$-0.135384\pi$
$60$		0			0
$61$			2822.53i			0.0971212i	0.998820	+	0.0485606i	$0.0154634\pi$
$61$			2822.53i			0.0971212i	−0.998820	+	0.0485606i	$0.984537\pi$
$62$	18613.4	+	20959.1i	0.614959	+	0.692458i
$63$			39854.5i			1.26510i
$64$	11397.4	−	30722.0i	0.347821	−	0.937561i
$65$		0			0
$66$	78494.4	−	69709.3i	2.21809	−	1.96984i
$67$	−54981.5			−1.49634			−0.748168	−	0.663509i	$-0.769066\pi$
$67$	−54981.5			−1.49634			−0.748168	+	0.663509i	$0.769066\pi$
$68$	−36186.7	−	4305.21i	−0.949024	−	0.112907i
$69$			40147.8i			1.01517i
$70$		0			0
$71$	42879.2			1.00949			0.504744	−	0.863269i	$-0.331587\pi$
$71$	42879.2			1.00949			0.504744	+	0.863269i	$0.331587\pi$
$72$	−57153.5	+	39756.7i	−1.29931	+	0.903814i
$73$			20893.2i			0.458879i	0.973323	+	0.229440i	$0.0736894\pi$
$73$			20893.2i			0.458879i	−0.973323	+	0.229440i	$0.926311\pi$
$74$	−16542.3	−	18627.1i	−0.351170	−	0.395426i
$75$		0			0
$76$	−36715.7	−	4368.14i	−0.729152	−	0.0867487i
$77$	−76762.2			−1.47544
$78$	83946.2	+	94525.5i	1.56230	+	1.75919i
$79$	−30227.6			−0.544925			−0.272462	−	0.962166i	$-0.587838\pi$
$79$	−30227.6			−0.544925			−0.272462	+	0.962166i	$0.587838\pi$
$80$		0			0
$81$	−4586.03			−0.0776648
$82$	14201.1	+	15990.8i	0.233232	+	0.262625i
$83$	93949.9			1.49693			0.748465	−	0.663175i	$-0.230791\pi$
$83$	93949.9			1.49693			0.748465	+	0.663175i	$0.230791\pi$
$84$	82490.2	+	9814.03i	1.27557	+	0.151757i
$85$		0			0
$86$	49088.5	+	55274.9i	0.715704	+	0.805901i
$87$			54074.1i			0.765934i
$88$	−76573.8	−	110081.i	−1.05408	−	1.51533i
$89$	−1178.06			−0.0157650			−0.00788248	−	0.999969i	$-0.502509\pi$
$89$	−1178.06			−0.0157650			−0.00788248	+	0.999969i	$0.502509\pi$
$90$		0			0
$91$		−	92439.5i		−	1.17018i
$92$	50923.2	+	6058.44i	0.627258	+	0.0746262i
$93$	−124139.			−1.48834
$94$	33839.9	−	30052.6i	0.395012	−	0.350802i
$95$		0			0
$96$	68213.9	+	128085.i	0.755431	+	1.41847i
$97$			74100.8i			0.799638i	0.916594	+	0.399819i	$0.130927\pi$
$97$			74100.8i			0.799638i	−0.916594	+	0.399819i	$0.869073\pi$
$98$	22797.2	+	25670.2i	0.239782	+	0.270000i
$99$			284908.i			2.92157i
$100$		0			0
$101$			31104.3i			0.303401i	0.988427	+	0.151700i	$0.0484749\pi$
$101$			31104.3i			0.303401i	−0.988427	+	0.151700i	$0.951525\pi$
$102$	120671.	−	107166.i	1.14843	−	1.01989i
$103$			140298.i			1.30305i	0.758629	+	0.651523i	$0.225870\pi$
$103$			140298.i			1.30305i	−0.758629	+	0.651523i	$0.774130\pi$
$104$	132563.	−	92212.7i	1.20182	−	0.836002i
$105$		0			0
$106$	−128892.	−	145136.i	−1.11420	−	1.25461i
$107$	34792.6			0.293784			0.146892	−	0.989153i	$-0.453073\pi$
$107$	34792.6			0.293784			0.146892	+	0.989153i	$0.453073\pi$
$108$	13411.3	−	112727.i	0.110640	−	0.929965i
$109$		−	83759.2i		−	0.675252i	−0.941280	−	0.337626i	$-0.890376\pi$
$109$		−	83759.2i		−	0.675252i	0.941280	−	0.337626i	$-0.109624\pi$
$110$		0			0
$111$	110327.			0.849910
$112$	24896.1	−	103149.i	0.187537	−	0.776999i
$113$		−	57262.1i		−	0.421863i	−0.977501	−	0.210931i	$-0.932350\pi$
$113$		−	57262.1i		−	0.421863i	0.977501	−	0.210931i	$-0.0676497\pi$
$114$	122435.	−	108732.i	0.882355	−	0.783602i
$115$		0			0
$116$	68587.3	+	8159.97i	0.473259	+	0.0563046i
$117$	−343095.			−2.31713
$118$	93327.9	−	82882.6i	0.617030	−	0.547972i
$119$	−118008.			−0.763914
$120$		0			0
$121$	−387698.			−2.40730
$122$	−11938.4	+	10602.3i	−0.0726184	+	0.0644910i
$123$	−94712.5			−0.564475
$124$	−18733.0	+	157457.i	−0.109409	+	0.919621i
$125$		0			0
$126$	−168572.	+	149705.i	−0.945930	+	0.840062i
$127$		−	8848.12i		−	0.0486790i	−0.999704	−	0.0243395i	$-0.992252\pi$
$127$		−	8848.12i		−	0.0486790i	0.999704	−	0.0243395i	$-0.00774827\pi$
$128$	172756.	−	67193.5i	0.931986	−	0.362495i
$129$	−327389.			−1.73217
$130$		0			0
$131$			110458.i			0.562365i	0.959654	+	0.281183i	$0.0907267\pi$
$131$			110458.i			0.562365i	−0.959654	+	0.281183i	$0.909273\pi$
$132$	589697.	+	70157.4i	2.94574	+	0.350460i
$133$	−119733.			−0.586929
$134$	−206527.	−	232554.i	−0.993606	−	1.11882i
$135$		0			0
$136$	−117719.	−	169230.i	−0.545755	−	0.784568i
$137$		−	304365.i		−	1.38546i	−0.721199	−	0.692728i	$-0.756409\pi$
$137$		−	304365.i		−	1.38546i	0.721199	−	0.692728i	$-0.243591\pi$
$138$	−169813.	+	150807.i	−0.759053	+	0.674100i
$139$			59379.5i			0.260675i	0.991470	+	0.130338i	$0.0416061\pi$
$139$			59379.5i			0.260675i	−0.991470	+	0.130338i	$0.958394\pi$
$140$		0			0
$141$			200431.i			0.849020i
$142$	161067.	+	181366.i	0.670326	+	0.754804i
$143$		−	660822.i		−	2.70237i
$144$	−382844.	−	92403.4i	−1.53856	−	0.371349i
$145$		0			0
$146$	−88371.8	+	78481.2i	−0.343108	+	0.304708i
$147$	−152043.			−0.580326
$148$	16648.7	−	139938.i	0.0624777	−	0.525146i
$149$			233744.i			0.862529i	0.902225	+	0.431265i	$0.141932\pi$
$149$			233744.i			0.862529i	−0.902225	+	0.431265i	$0.858068\pi$
$150$		0			0
$151$	−89068.4			−0.317893			−0.158947	−	0.987287i	$-0.550810\pi$
$151$	−89068.4			−0.317893			−0.158947	+	0.987287i	$0.550810\pi$
$152$	−119439.	−	171704.i	−0.419313	−	0.602797i
$153$			437994.i			1.51266i
$154$	−288342.	−	324680.i	−0.979728	−	1.10320i
$155$		0			0
$156$	−84485.9	+	710132.i	−0.277954	+	2.33629i
$157$	608909.			1.97153			0.985764	−	0.168132i	$-0.0537735\pi$
$157$	608909.			1.97153			0.985764	+	0.168132i	$0.0537735\pi$
$158$	−113544.	−	127853.i	−0.361844	−	0.407445i
$159$	859628.			2.69661
$160$		0			0
$161$	166065.			0.504910
$162$	−17226.5	−	19397.4i	−0.0515714	−	0.0580707i
$163$	−172801.			−0.509421			−0.254711	−	0.967017i	$-0.581980\pi$
$163$	−172801.			−0.509421			−0.254711	+	0.967017i	$0.581980\pi$
$164$	−14292.4	+	120133.i	−0.0414951	+	0.348780i
$165$		0			0
$166$	352904.	+	397378.i	0.994000	+	1.11927i
$167$			441506.i			1.22503i	0.790461	+	0.612513i	$0.209841\pi$
$167$			441506.i			1.22503i	−0.790461	+	0.612513i	$0.790159\pi$
$168$	268348.	+	385772.i	0.733541	+	1.05453i
$169$	424490.			1.14327
$170$		0			0
$171$			444397.i			1.16220i
$172$	−49404.1	+	415258.i	−0.127333	+	1.07028i
$173$	281414.			0.714874			0.357437	−	0.933937i	$-0.383651\pi$
$173$	281414.			0.714874			0.357437	+	0.933937i	$0.383651\pi$
$174$	−228717.	+	203119.i	−0.572696	+	0.508600i
$175$		0			0
$176$	177975.	−	737381.i	0.433088	−	1.79436i
$177$			552774.i			1.32622i
$178$	−4425.15	−	4982.83i	−0.0104683	−	0.0117876i
$179$			805768.i			1.87965i	0.341655	+	0.939825i	$0.389013\pi$
$179$			805768.i			1.87965i	−0.341655	+	0.939825i	$0.610987\pi$
$180$		0			0
$181$		−	610344.i		−	1.38477i	−0.721528	−	0.692385i	$-0.756560\pi$
$181$		−	610344.i		−	1.38477i	0.721528	−	0.692385i	$-0.243440\pi$
$182$	390990.	−	347231.i	0.874958	−	0.777033i
$183$		−	70710.3i		−	0.156083i
$184$	165658.	+	238147.i	0.360717	+	0.518561i
$185$		0			0
$186$	−466304.	−	525070.i	−0.988295	−	1.11284i
$187$	−843604.			−1.76415
$188$	254226.	+	30245.8i	0.524596	+	0.0624123i
$189$		−	367611.i		−	0.748573i
$190$		0			0
$191$	−845737.			−1.67746			−0.838729	−	0.544549i	$-0.816701\pi$
$191$	−845737.			−1.67746			−0.838729	+	0.544549i	$0.816701\pi$
$192$	−285529.	+	769650.i	−0.558981	+	1.50675i
$193$			184089.i			0.355742i	0.984054	+	0.177871i	$0.0569210\pi$
$193$			184089.i			0.355742i	−0.984054	+	0.177871i	$0.943079\pi$
$194$	−313423.	+	278345.i	−0.597897	+	0.530981i
$195$		0			0
$196$	−22943.7	+	192850.i	−0.0426603	+	0.358574i
$197$	−390522.			−0.716935			−0.358468	−	0.933542i	$-0.616701\pi$
$197$	−390522.			−0.716935			−0.358468	+	0.933542i	$0.616701\pi$
$198$	−1.20507e6	+	1.07020e6i	−2.18448	+	1.94000i
$199$	584263.			1.04587			0.522933	−	0.852374i	$-0.324838\pi$
$199$	584263.			1.04587			0.522933	+	0.852374i	$0.324838\pi$
$200$		0			0
$201$	1.37740e6			2.40475
$202$	−131561.	+	116837.i	−0.226856	+	0.201466i
$203$	223669.			0.380948
$204$	906553.	+	107855.i	1.52517	+	0.181453i
$205$		0			0
$206$	−593418.	+	527003.i	−0.974300	+	0.865256i
$207$		−	616361.i		−	0.999791i
$208$	887978.	+	214323.i	1.42313	+	0.343487i
$209$	−855935.			−1.35542
$210$		0			0
$211$			428258.i			0.662215i	0.943593	+	0.331107i	$0.107422\pi$
$211$			428258.i			0.662215i	−0.943593	+	0.331107i	$0.892578\pi$
$212$	129721.	−	1.09035e6i	0.198230	−	1.66619i
$213$	−1.07421e6			−1.62234
$214$	130691.	+	147162.i	0.195080	+	0.219665i
$215$		0			0
$216$	527174.	−	366709.i	0.768812	−	0.534795i
$217$			513482.i			0.740246i
$218$	354275.	−	314624.i	0.504893	−	0.448385i
$219$		−	523419.i		−	0.737461i
$220$		0			0
$221$		−	1.01590e6i		−	1.39916i
$222$	414420.	+	466647.i	0.564362	+	0.635486i
$223$		−	955618.i		−	1.28683i	−0.765517	−	0.643416i	$-0.777516\pi$
$223$		−	955618.i		−	1.28683i	0.765517	−	0.643416i	$-0.222484\pi$
$224$	529805.	−	282156.i	0.705499	−	0.375724i
$225$		0			0
$226$	242201.	−	215094.i	0.315431	−	0.280128i
$227$	866233.			1.11576			0.557879	−	0.829922i	$-0.311615\pi$
$227$	866233.			1.11576			0.557879	+	0.829922i	$0.311615\pi$
$228$	919805.	+	109431.i	1.17181	+	0.139413i
$229$		−	654035.i		−	0.824161i	−0.911147	−	0.412080i	$-0.864802\pi$
$229$		−	654035.i		−	0.824161i	0.911147	−	0.412080i	$-0.135198\pi$
$230$		0			0
$231$	1.92305e6			2.37116
$232$	223120.	+	320754.i	0.272157	+	0.391248i
$233$			820513.i			0.990138i	0.868854	+	0.495069i	$0.164857\pi$
$233$			820513.i			0.990138i	−0.868854	+	0.495069i	$0.835143\pi$
$234$	−1.28877e6	−	1.45118e6i	−1.53863	−	1.73254i
$235$		0			0
$236$	701135.	+	83415.4i	0.819448	+	0.0974914i
$237$	757265.			0.875744
$238$	−443274.	−	499137.i	−0.507259	−	0.571186i
$239$	−867314.			−0.982159			−0.491079	−	0.871115i	$-0.663397\pi$
$239$	−867314.			−0.982159			−0.491079	+	0.871115i	$0.663397\pi$
$240$		0			0
$241$	−1.65377e6			−1.83414			−0.917072	−	0.398722i	$-0.869454\pi$
$241$	−1.65377e6			−1.83414			−0.917072	+	0.398722i	$0.869454\pi$
$242$	−1.45631e6	−	1.63984e6i	−1.59851	−	1.79996i
$243$	976943.			1.06134
$244$	−89688.5	−	10670.4i	−0.0964411	−	0.0114738i
$245$		0			0
$246$	−355768.	−	400604.i	−0.374826	−	0.422063i
$247$		−	1.03075e6i		−	1.07500i
$248$	−736362.	+	512222.i	−0.760260	+	0.528846i
$249$	−2.35364e6			−2.40570
$250$		0			0
$251$			860879.i			0.862497i	0.902233	+	0.431249i	$0.141927\pi$
$251$			860879.i			0.862497i	−0.902233	+	0.431249i	$0.858073\pi$
$252$	−1.26641e6	−	150668.i	−1.25624	−	0.149458i
$253$	1.18715e6			1.16601
$254$	37424.7	−	33236.2i	0.0363978	−	0.0323241i
$255$		0			0
$256$	933132.	+	478306.i	0.889904	+	0.456148i
$257$		−	765335.i		−	0.722801i	−0.932411	−	0.361401i	$-0.882299\pi$
$257$		−	765335.i		−	0.722801i	0.932411	−	0.361401i	$-0.117701\pi$
$258$	−1.22977e6	−	1.38475e6i	−1.15020	−	1.29516i
$259$		−	456349.i		−	0.422715i
$260$		0			0
$261$		−	830162.i		−	0.754330i
$262$	−467202.	+	414913.i	−0.420486	+	0.373425i
$263$		−	260746.i		−	0.232449i	−0.993223	−	0.116225i	$-0.962921\pi$
$263$		−	260746.i		−	0.232449i	0.993223	−	0.116225i	$-0.0370792\pi$
$264$	1.91833e6	+	2.75776e6i	1.69400	+	2.43527i
$265$		0			0
$266$	−449754.	−	506433.i	−0.389736	−	0.438852i
$267$	29512.9			0.0253357
$268$	207854.	−	1.74709e6i	0.176776	−	1.48586i
$269$		−	1.12412e6i		−	0.947175i	−0.880747	−	0.473587i	$-0.842959\pi$
$269$		−	1.12412e6i		−	0.947175i	0.880747	−	0.473587i	$-0.157041\pi$
$270$		0			0
$271$	−1.07277e6			−0.887330			−0.443665	−	0.896193i	$-0.646322\pi$
$271$	−1.07277e6			−0.887330			−0.443665	+	0.896193i	$0.646322\pi$
$272$	273604.	−	1.13359e6i	0.224233	−	0.929039i
$273$			2.31580e6i			1.88059i
$274$	1.28737e6	−	1.14328e6i	1.03592	−	0.919979i
$275$		0			0
$276$	−1.27573e6	−	151777.i	−1.00806	−	0.119931i
$277$	615080.			0.481651			0.240825	−	0.970568i	$-0.422582\pi$
$277$	615080.			0.481651			0.240825	+	0.970568i	$0.422582\pi$
$278$	−251157.	+	223047.i	−0.194909	+	0.173095i
$279$	1.90582e6			1.46579
$280$		0			0
$281$	−652198.			−0.492736			−0.246368	−	0.969176i	$-0.579237\pi$
$281$	−652198.			−0.492736			−0.246368	+	0.969176i	$0.579237\pi$
$282$	−847761.	+	752880.i	−0.634820	+	0.563771i
$283$	908596.			0.674380			0.337190	−	0.941437i	$-0.390524\pi$
$283$	908596.			0.674380			0.337190	+	0.941437i	$0.390524\pi$
$284$	−162103.	+	1.36253e6i	−0.119260	+	1.00242i
$285$		0			0
$286$	2.79507e6	−	2.48224e6i	2.02058	−	1.79444i
$287$			391763.i			0.280750i
$288$	−1.04724e6	−	1.96640e6i	−0.743986	−	1.39698i
$289$	122967.			0.0866050
$290$		0			0
$291$		−	1.85638e6i		−	1.28509i
$292$	−663901.	−	78985.7i	−0.455666	−	0.0542115i
$293$	−514047.			−0.349811			−0.174906	−	0.984585i	$-0.555962\pi$
$293$	−514047.			−0.349811			−0.174906	+	0.984585i	$0.555962\pi$
$294$	−571117.	−	643092.i	−0.385351	−	0.433915i
$295$		0			0
$296$	654429.	−	455229.i	0.434144	−	0.301996i
$297$		−	2.62794e6i		−	1.72872i
$298$	−988661.	+	878010.i	−0.644921	+	0.572742i
$299$			1.42960e6i			0.924778i
$300$		0			0
$301$			1.35419e6i			0.861517i
$302$	−334568.	−	376731.i	−0.211089	−	0.237692i
$303$		−	779227.i		−	0.487593i
$304$	277604.	−	1.15016e6i	0.172282	−	0.713797i
$305$		0			0
$306$	−1.85258e6	+	1.64524e6i	−1.13103	+	1.00444i
$307$	1.46693e6			0.888309			0.444155	−	0.895950i	$-0.353504\pi$
$307$	1.46693e6			0.888309			0.444155	+	0.895950i	$0.353504\pi$
$308$	290195.	−	2.43919e6i	0.174307	−	1.46510i
$309$		−	3.51477e6i		−	2.09411i
$310$		0			0
$311$	547919.			0.321229			0.160615	−	0.987017i	$-0.448652\pi$
$311$	547919.			0.321229			0.160615	+	0.987017i	$0.448652\pi$
$312$	−3.32099e6	+	2.31012e6i	−1.93144	+	1.34353i
$313$		−	1.70857e6i		−	0.985762i	−0.870097	−	0.492881i	$-0.835944\pi$
$313$		−	1.70857e6i		−	0.985762i	0.870097	−	0.492881i	$-0.164056\pi$
$314$	2.28724e6	+	2.57549e6i	1.30915	+	1.47413i
$315$		0			0
$316$	114274.	−	960510.i	0.0643768	−	0.541109i
$317$	−978608.			−0.546966			−0.273483	−	0.961877i	$-0.588176\pi$
$317$	−978608.			−0.546966			−0.273483	+	0.961877i	$0.588176\pi$
$318$	3.22902e6	+	3.63596e6i	1.79062	+	2.01628i
$319$	1.59894e6			0.879743
$320$		0			0
$321$	−871627.			−0.472137
$322$	623790.	+	702403.i	0.335273	+	0.377526i
$323$	−1.31585e6			−0.701777
$324$	17337.2	−	145725.i	0.00917523	−	0.0771209i
$325$		0			0
$326$	−649092.	−	730893.i	−0.338269	−	0.380899i
$327$			2.09834e6i			1.08519i
$328$	−561810.	+	390802.i	−0.288340	+	0.200573i
$329$	829053.			0.422272
$330$		0			0
$331$		−	345907.i		−	0.173536i	−0.996229	−	0.0867679i	$-0.972346\pi$
$331$		−	345907.i		−	0.173536i	0.996229	−	0.0867679i	$-0.0276539\pi$
$332$	−355173.	+	2.98534e6i	−0.176846	+	1.48645i
$333$	−1.69377e6			−0.837034
$334$	−1.86743e6	+	1.65843e6i	−0.915963	+	0.813449i
$335$		0			0
$336$	−623699.	+	2.58410e6i	−0.301389	+	1.24871i
$337$			376513.i			0.180595i	0.995915	+	0.0902975i	$0.0287818\pi$
$337$			376513.i			0.180595i	−0.995915	+	0.0902975i	$0.971218\pi$
$338$	1.59451e6	+	1.79546e6i	0.759164	+	0.854837i
$339$			1.43454e6i			0.677972i
$340$		0			0
$341$			3.67073e6i			1.70949i
$342$	−1.87966e6	+	1.66929e6i	−0.868988	+	0.771731i
$343$			2.37051e6i			1.08794i
$344$	−1.94199e6	+	1.35087e6i	−0.884810	+	0.615484i
$345$		0			0
$346$	1.05707e6	+	1.19029e6i	0.474695	+	0.534518i
$347$	164656.			0.0734099			0.0367049	−	0.999326i	$-0.488314\pi$
$347$	164656.			0.0734099			0.0367049	+	0.999326i	$0.488314\pi$
$348$	−1.71825e6	−	204424.i	−0.760571	−	0.0904867i
$349$		−	35942.6i		−	0.0157959i	−0.999969	−	0.00789797i	$-0.997486\pi$
$349$		−	35942.6i		−	0.0157959i	0.999969	−	0.00789797i	$-0.00251403\pi$
$350$		0			0
$351$	3.16465e6			1.37106
$352$	3.78741e6	−	2.01705e6i	1.62924	−	0.867679i
$353$		−	1.39430e6i		−	0.595550i	−0.954636	−	0.297775i	$-0.903756\pi$
$353$		−	1.39430e6i		−	0.595550i	0.954636	−	0.297775i	$-0.0962445\pi$
$354$	−2.33806e6	+	2.07638e6i	−0.991624	+	0.880642i
$355$		0			0
$356$	4453.60	−	37434.0i	0.00186246	−	0.0156546i
$357$	2.95635e6			1.22768
$358$	−3.40814e6	+	3.02670e6i	−1.40543	+	1.24814i
$359$	−3.50589e6			−1.43569			−0.717847	−	0.696201i	$-0.754872\pi$
$359$	−3.50589e6			−1.43569			−0.717847	+	0.696201i	$0.754872\pi$
$360$		0			0
$361$	1.14102e6			0.460812
$362$	2.58156e6	−	2.29263e6i	1.03541	−	0.919524i
$363$	9.71265e6			3.86875
$364$	2.93735e6	+	349463.i	1.16199	+	0.138244i
$365$		0			0
$366$	299082.	−	265609.i	0.116705	−	0.103643i
$367$			3.64440e6i			1.41241i	0.708007	+	0.706206i	$0.249595\pi$
$367$			3.64440e6i			1.41241i	−0.708007	+	0.706206i	$0.750405\pi$
$368$	−385025.	+	1.59523e6i	−0.148207	+	0.614049i
$369$	1.45405e6			0.555923
$370$		0			0
$371$		−	3.55572e6i		−	1.34120i
$372$	469302.	−	3.94464e6i	0.175831	−	1.47792i
$373$	−4.19252e6			−1.56028			−0.780142	−	0.625603i	$-0.784853\pi$
$373$	−4.19252e6			−1.56028			−0.780142	+	0.625603i	$0.784853\pi$
$374$	−3.16883e6	−	3.56818e6i	−1.17144	−	1.31907i
$375$		0			0
$376$	827018.	+	1.18891e6i	0.301679	+	0.433689i
$377$			1.92550e6i			0.697734i
$378$	1.55488e6	−	1.38086e6i	0.559715	−	0.497072i
$379$		−	2.31089e6i		−	0.826384i	−0.910644	−	0.413192i	$-0.864414\pi$
$379$		−	2.31089e6i		−	0.826384i	0.910644	−	0.413192i	$-0.135586\pi$
$380$		0			0
$381$			221664.i			0.0782316i
$382$	−3.17684e6	−	3.57720e6i	−1.11388	−	1.25425i
$383$		−	1.18240e6i		−	0.411876i	−0.978565	−	0.205938i	$-0.933976\pi$
$383$		−	1.18240e6i		−	0.411876i	0.978565	−	0.205938i	$-0.0660245\pi$
$384$	−4.32791e6	+	1.68334e6i	−1.49779	+	0.582563i
$385$		0			0
$386$	−778639.	+	691494.i	−0.265992	+	0.236222i
$387$	5.02617e6			1.70592
$388$	−2.35462e6	−	280134.i	−0.794038	−	0.0944684i
$389$		−	5.09219e6i		−	1.70620i	−0.521745	−	0.853102i	$-0.674719\pi$
$389$		−	5.09219e6i		−	1.70620i	0.521745	−	0.853102i	$-0.325281\pi$
$390$		0			0
$391$	1.82503e6			0.603709
$392$	−901877.	+	627357.i	−0.296437	+	0.206205i
$393$		−	2.76720e6i		−	0.903773i
$394$	−1.46692e6	−	1.65178e6i	−0.476064	−	0.536059i
$395$		0			0
$396$	−9.05320e6	−	1.07708e6i	−2.90111	−	0.345151i
$397$	−63006.9			−0.0200637			−0.0100319	−	0.999950i	$-0.503193\pi$
$397$	−63006.9			−0.0200637			−0.0100319	+	0.999950i	$0.503193\pi$
$398$	2.19467e6	+	2.47125e6i	0.694482	+	0.782004i
$399$	2.99957e6			0.943248
$400$		0			0
$401$	−4.48960e6			−1.39427			−0.697135	−	0.716940i	$-0.745542\pi$
$401$	−4.48960e6			−1.39427			−0.697135	+	0.716940i	$0.745542\pi$
$402$	5.17392e6	+	5.82597e6i	1.59682	+	1.79805i
$403$	−4.42041e6			−1.35581
$404$	−988367.	−	117588.i	−0.301276	−	0.0358434i
$405$		0			0
$406$	840169.	+	946050.i	0.252960	+	0.284839i
$407$		−	3.26230e6i		−	0.976197i
$408$	2.94909e6	+	4.23957e6i	0.877078	+	1.26087i
$409$	−2.03416e6			−0.601281			−0.300641	−	0.953738i	$-0.597200\pi$
$409$	−2.03416e6			−0.601281			−0.300641	+	0.953738i	$0.597200\pi$
$410$		0			0
$411$			7.62497e6i			2.22656i
$412$	−4.45811e6	−	530391.i	−1.29392	−	0.153940i
$413$	2.28646e6			0.659612
$414$	2.60701e6	−	2.31524e6i	0.747553	−	0.663887i
$415$		0			0
$416$	2.42899e6	+	4.56093e6i	0.688165	+	1.29217i
$417$		−	1.48758e6i		−	0.418929i
$418$	−3.21515e6	−	3.62034e6i	−0.900037	−	1.01346i
$419$			1.53143e6i			0.426150i	0.977036	+	0.213075i	$0.0683479\pi$
$419$			1.53143e6i			0.426150i	−0.977036	+	0.213075i	$0.931652\pi$
$420$		0			0
$421$		−	4.86857e6i		−	1.33874i	−0.742929	−	0.669370i	$-0.766564\pi$
$421$		−	4.86857e6i		−	1.33874i	0.742929	−	0.669370i	$-0.233436\pi$
$422$	−1.81139e6	+	1.60866e6i	−0.495144	+	0.439728i
$423$		−	3.07708e6i		−	0.836157i
$424$	5.09909e6	−	3.54699e6i	1.37746	−	0.958176i
$425$		0			0
$426$	−4.03507e6	−	4.54359e6i	−1.07728	−	1.21304i
$427$	−292482.			−0.0776300
$428$	−131532.	+	1.10557e6i	−0.0347073	+	0.291726i
$429$			1.65550e7i			4.34295i
$430$		0			0
$431$	537754.			0.139441			0.0697204	−	0.997567i	$-0.477789\pi$
$431$	537754.			0.139441			0.0697204	+	0.997567i	$0.477789\pi$
$432$	3.53129e6	+	852313.i	0.910382	+	0.219730i
$433$		−	1.48235e6i		−	0.379954i	−0.981789	−	0.189977i	$-0.939159\pi$
$433$		−	1.48235e6i		−	0.379954i	0.981789	−	0.189977i	$-0.0608414\pi$
$434$	−2.17187e6	+	1.92879e6i	−0.553489	+	0.491543i
$435$		0			0
$436$	2.66152e6	+	316647.i	0.670524	+	0.0797736i
$437$	1.85171e6			0.463840
$438$	2.21390e6	−	1.96612e6i	0.551407	−	0.489693i
$439$	2.49966e6			0.619041			0.309520	−	0.950893i	$-0.399832\pi$
$439$	2.49966e6			0.619041			0.309520	+	0.950893i	$0.399832\pi$
$440$		0			0
$441$	2.33420e6			0.571534
$442$	4.29692e6	−	3.81601e6i	1.04617	−	0.929080i
$443$	−5.00804e6			−1.21244			−0.606218	−	0.795299i	$-0.707314\pi$
$443$	−5.00804e6			−1.21244			−0.606218	+	0.795299i	$0.707314\pi$
$444$	−417084.	+	3.50573e6i	−0.100407	+	0.843958i
$445$		0			0
$446$	4.04196e6	−	3.58959e6i	0.962177	−	0.854490i
$447$		−	5.85576e6i		−	1.38616i
$448$	3.18354e6	+	1.18105e6i	0.749402	+	0.278017i
$449$	−3.04025e6			−0.711694			−0.355847	−	0.934544i	$-0.615808\pi$
$449$	−3.04025e6			−0.711694			−0.355847	+	0.934544i	$0.615808\pi$
$450$		0			0
$451$			2.80059e6i			0.648349i
$452$	1.81956e6	+	216476.i	0.418909	+	0.0498384i
$453$	2.23135e6			0.510884
$454$	3.25383e6	+	3.66389e6i	0.740892	+	0.834263i
$455$		0			0
$456$	2.99220e6	+	4.30154e6i	0.673874	+	0.968750i
$457$			7.20014e6i			1.61269i	0.591446	+	0.806345i	$0.298557\pi$
$457$			7.20014e6i			1.61269i	−0.591446	+	0.806345i	$0.701443\pi$
$458$	2.76636e6	−	2.45675e6i	0.616233	−	0.547264i
$459$		−	4.03999e6i		−	0.895052i
$460$		0			0
$461$			7.87732e6i			1.72634i	0.504914	+	0.863170i	$0.331524\pi$
$461$			7.87732e6i			1.72634i	−0.504914	+	0.863170i	$0.668476\pi$
$462$	7.22356e6	+	8.13391e6i	1.57451	+	1.77294i
$463$			6.18812e6i			1.34155i	0.741662	+	0.670774i	$0.234038\pi$
$463$			6.18812e6i			1.34155i	−0.741662	+	0.670774i	$0.765962\pi$
$464$	−518581.	+	2.14858e6i	−0.111821	+	0.463293i
$465$		0			0
$466$	−3.47051e6	+	3.08209e6i	−0.740336	+	0.657477i
$467$	−7.21143e6			−1.53013			−0.765066	−	0.643952i	$-0.777294\pi$
$467$	−7.21143e6			−1.53013			−0.765066	+	0.643952i	$0.777294\pi$
$468$	1.29705e6	−	1.09022e7i	0.273743	−	2.30090i
$469$		−	5.69740e6i		−	1.19604i
$470$		0			0
$471$	−1.52544e7			−3.16843
$472$	2.28085e6	+	3.27891e6i	0.471239	+	0.677446i
$473$			9.68070e6i			1.98955i
$474$	2.84451e6	+	3.20299e6i	0.581517	+	0.654802i
$475$		0			0
$476$	446124.	−	3.74982e6i	0.0902480	−	0.758565i
$477$	−1.31973e7			−2.65575
$478$	−3.25789e6	−	3.66846e6i	−0.652179	−	0.734369i
$479$	−4.05783e6			−0.808081			−0.404040	−	0.914741i	$-0.632395\pi$
$479$	−4.05783e6			−0.808081			−0.404040	+	0.914741i	$0.632395\pi$
$480$		0			0
$481$	3.92856e6			0.774232
$482$	−6.21206e6	−	6.99494e6i	−1.21792	−	1.37141i
$483$	−4.16028e6			−0.811437
$484$	1.46567e6	−	1.23195e7i	0.284396	−	2.39044i
$485$		0			0
$486$	3.66969e6	+	4.13216e6i	0.704756	+	0.793573i
$487$			121792.i			0.0232700i	0.999932	+	0.0116350i	$0.00370361\pi$
$487$			121792.i			0.0232700i	−0.999932	+	0.0116350i	$0.996296\pi$
$488$	−291764.	−	419435.i	−0.0554603	−	0.0797288i
$489$	4.32902e6			0.818687
$490$		0			0
$491$		−	2.80649e6i		−	0.525363i	−0.964883	−	0.262682i	$-0.915393\pi$
$491$		−	2.80649e6i		−	0.525363i	0.964883	−	0.262682i	$-0.0846069\pi$
$492$	358055.	−	3.00957e6i	0.0666864	−	0.560522i
$493$	2.45809e6			0.455491
$494$	4.35973e6	−	3.87179e6i	0.803789	−	0.713829i
$495$		0			0
$496$	−4.93253e6	−	1.19052e6i	−0.900255	−	0.217286i
$497$			4.44332e6i			0.806894i
$498$	−8.84098e6	−	9.95516e6i	−1.59745	−	1.79877i
$499$			2.59476e6i			0.466494i	0.972418	+	0.233247i	$0.0749351\pi$
$499$			2.59476e6i			0.466494i	−0.972418	+	0.233247i	$0.925065\pi$
$500$		0			0
$501$		−	1.10606e7i		−	1.96873i
$502$	−3.64125e6	+	3.23372e6i	−0.644897	+	0.572721i
$503$		−	1.04638e6i		−	0.184404i	−0.995740	−	0.0922021i	$-0.970609\pi$
$503$		−	1.04638e6i		−	0.184404i	0.995740	−	0.0922021i	$-0.0293906\pi$
$504$	−4.11975e6	−	5.92248e6i	−0.722428	−	1.03855i
$505$		0			0
$506$	4.45928e6	+	5.02126e6i	0.774264	+	0.871840i
$507$	−1.06344e7			−1.83735
$508$	281157.	+	33449.8i	0.0483381	+	0.00575089i
$509$			8.38369e6i			1.43430i	0.696918	+	0.717151i	$0.254554\pi$
$509$			8.38369e6i			1.43430i	−0.696918	+	0.717151i	$0.745446\pi$
$510$		0			0
$511$	−2.16504e6			−0.366787
$512$	1.48204e6	+	5.74351e6i	0.249853	+	0.968284i
$513$		−	4.09904e6i		−	0.687684i
$514$	3.23713e6	−	2.87483e6i	0.540445	−	0.479959i
$515$		0			0
$516$	1.23767e6	−	1.04031e7i	0.204636	−	1.72004i
$517$	5.92664e6			0.975174
$518$	1.93021e6	−	1.71418e6i	0.316068	−	0.280694i
$519$	−7.05000e6			−1.14887
$520$		0			0
$521$	−4.38397e6			−0.707577			−0.353788	−	0.935325i	$-0.615107\pi$
$521$	−4.38397e6			−0.707577			−0.353788	+	0.935325i	$0.615107\pi$
$522$	3.51132e6	−	3.11834e6i	0.564020	−	0.500895i
$523$	−915789.			−0.146400			−0.0732000	−	0.997317i	$-0.523321\pi$
$523$	−915789.			−0.146400			−0.0732000	+	0.997317i	$0.523321\pi$
$524$	−3.50990e6	−	417580.i	−0.558427	−	0.0664372i
$525$		0			0
$526$	1.10287e6	−	979439.i	0.173804	−	0.154352i
$527$			5.64309e6i			0.885096i
$528$	−4.45863e6	+	1.84729e7i	−0.696012	+	2.88370i
$529$	3.86810e6			0.600978
$530$		0			0
$531$		−	8.48634e6i		−	1.30612i
$532$	452645.	−	3.80463e6i	0.0693391	−	0.582819i
$533$	−3.37257e6			−0.514212
$534$	110859.	+	124830.i	0.0168236	+	0.0189438i
$535$		0			0
$536$	8.17038e6	−	5.68342e6i	1.22837	−	0.854471i
$537$		−	2.01862e7i		−	3.02077i
$538$	4.75465e6	−	4.22251e6i	0.708212	−	0.628949i
$539$			4.49581e6i			0.666556i
$540$		0			0
$541$		−	6.98594e6i		−	1.02620i	−0.858329	−	0.513100i	$-0.828497\pi$
$541$		−	6.98594e6i		−	1.02620i	0.858329	−	0.513100i	$-0.171503\pi$
$542$	−4.02966e6	−	4.53750e6i	−0.589210	−	0.663465i
$543$			1.52904e7i			2.22545i
$544$	5.82247e6	−	3.10085e6i	0.843548	−	0.449245i
$545$		0			0
$546$	−9.79511e6	+	8.69885e6i	−1.40614	+	1.24876i
$547$	−4.72947e6			−0.675841			−0.337920	−	0.941175i	$-0.609723\pi$
$547$	−4.72947e6			−0.675841			−0.337920	+	0.941175i	$0.609723\pi$
$548$	9.67146e6	+	1.15063e6i	1.37575	+	0.163676i
$549$			1.08556e6i			0.153718i
$550$		0			0
$551$	2.49402e6			0.349962
$552$	−4.15007e6	−	5.96607e6i	−0.579706	−	0.833375i
$553$		−	3.13231e6i		−	0.435564i
$554$	2.31042e6	+	2.60159e6i	0.319829	+	0.360135i
$555$		0			0
$556$	−1.88684e6	−	224481.i	−0.258850	−	0.0307959i
$557$	3.26312e6			0.445651			0.222825	−	0.974858i	$-0.428472\pi$
$557$	3.26312e6			0.445651			0.222825	+	0.974858i	$0.428472\pi$
$558$	7.15883e6	+	8.06102e6i	0.973322	+	1.09598i
$559$	−1.16578e7			−1.57793
$560$		0			0
$561$	2.11340e7			2.83514
$562$	−2.44985e6	−	2.75859e6i	−0.327189	−	0.368423i
$563$	−5.81898e6			−0.773706			−0.386853	−	0.922141i	$-0.626438\pi$
$563$	−5.81898e6			−0.773706			−0.386853	+	0.922141i	$0.626438\pi$
$564$	−6.36889e6	−	757720.i	−0.843074	−	0.100302i
$565$		0			0
$566$	3.41296e6	+	3.84307e6i	0.447806	+	0.504240i
$567$		−	475223.i		−	0.0620782i
$568$	−6.37196e6	+	4.43241e6i	−0.828710	+	0.576461i
$569$	9.08770e6			1.17672			0.588360	−	0.808599i	$-0.299774\pi$
$569$	9.08770e6			1.17672			0.588360	+	0.808599i	$0.299774\pi$
$570$		0			0
$571$		−	258870.i		−	0.0332270i	−0.999862	−	0.0166135i	$-0.994712\pi$
$571$		−	258870.i		−	0.0332270i	0.999862	−	0.0166135i	$-0.00528849\pi$
$572$	2.09982e7	+	2.49820e6i	2.68344	+	0.319255i
$573$	2.11875e7			2.69583
$574$	−1.65704e6	+	1.47158e6i	−0.209919	+	0.186425i
$575$		0			0
$576$	4.38352e6	−	1.18159e7i	0.550512	−	1.48392i
$577$			2.45070e6i			0.306444i	0.988192	+	0.153222i	$0.0489650\pi$
$577$			2.45070e6i			0.306444i	−0.988192	+	0.153222i	$0.951035\pi$
$578$	461900.	+	520110.i	0.0575080	+	0.0647554i
$579$		−	4.61182e6i		−	0.571710i
$580$		0			0
$581$			9.73547e6i			1.19651i
$582$	7.85190e6	−	6.97311e6i	0.960875	−	0.853334i
$583$		−	2.54187e7i		−	3.09729i
$584$	−2.15973e6	−	3.10479e6i	−0.262039	−	0.376703i
$585$		0			0
$586$	−1.93091e6	−	2.17426e6i	−0.232284	−	0.261557i
$587$	−3.61982e6			−0.433602			−0.216801	−	0.976216i	$-0.569562\pi$
$587$	−3.61982e6			−0.433602			−0.216801	+	0.976216i	$0.569562\pi$
$588$	574789.	−	4.83129e6i	0.0685591	−	0.576262i
$589$			5.72557e6i			0.680034i
$590$		0			0
$591$	9.78339e6			1.15218
$592$	4.38371e6	+	1.05805e6i	0.514088	+	0.124080i
$593$			7.07347e6i			0.826030i	0.910724	+	0.413015i	$0.135524\pi$
$593$			7.07347e6i			0.826030i	−0.910724	+	0.413015i	$0.864476\pi$
$594$	1.11153e7	−	9.87132e6i	1.29258	−	1.14791i
$595$		0			0
$596$	−7.42741e6	−	883655.i	−0.856489	−	0.101898i
$597$	−1.46370e7			−1.68080
$598$	−6.04677e6	+	5.37001e6i	−0.691465	+	0.614077i
$599$	2.71813e6			0.309530			0.154765	−	0.987951i	$-0.450538\pi$
$599$	2.71813e6			0.309530			0.154765	+	0.987951i	$0.450538\pi$
$600$		0			0
$601$	1.67171e6			0.188788			0.0943942	−	0.995535i	$-0.469909\pi$
$601$	1.67171e6			0.188788			0.0943942	+	0.995535i	$0.469909\pi$
$602$	−5.72780e6	+	5.08675e6i	−0.644165	+	0.572070i
$603$	−2.11462e7			−2.36832
$604$	336718.	−	2.83023e6i	0.0375556	−	0.315667i
$605$		0			0
$606$	3.29588e6	−	2.92701e6i	0.364578	−	0.323774i
$607$		−	2.35562e6i		−	0.259498i	−0.991547	−	0.129749i	$-0.958583\pi$
$607$		−	2.35562e6i		−	0.259498i	0.991547	−	0.129749i	$-0.0414171\pi$
$608$	5.90758e6	−	3.14617e6i	0.648113	−	0.345163i
$609$	−5.60338e6			−0.612219
$610$		0			0
$611$			7.13705e6i			0.773421i
$612$	−1.39177e7	−	1.65581e6i	−1.50206	−	0.178704i
$613$	−1.88749e6			−0.202877			−0.101439	−	0.994842i	$-0.532345\pi$
$613$	−1.88749e6			−0.202877			−0.101439	+	0.994842i	$0.532345\pi$
$614$	5.51024e6	+	6.20466e6i	0.589860	+	0.664197i
$615$		0			0
$616$	1.14071e7	−	7.93489e6i	1.21122	−	0.842537i
$617$			1.45446e7i			1.53812i	0.639178	+	0.769058i	$0.279275\pi$
$617$			1.45446e7i			1.53812i	−0.639178	+	0.769058i	$0.720725\pi$
$618$	1.48664e7	−	1.32025e7i	1.56579	−	1.39055i
$619$		−	1.08497e7i		−	1.13813i	−0.822292	−	0.569066i	$-0.807305\pi$
$619$		−	1.08497e7i		−	1.13813i	0.822292	−	0.569066i	$-0.192695\pi$
$620$		0			0
$621$			5.68521e6i			0.591585i
$622$	2.05815e6	+	2.31752e6i	0.213305	+	0.240186i
$623$		−	122075.i		−	0.0126011i
$624$	−2.22457e7	−	5.36923e6i	−2.28710	−	0.552015i
$625$		0			0
$626$	7.22671e6	−	6.41790e6i	0.737063	−	0.654571i
$627$	2.14430e7			2.17829
$628$	−2.30195e6	+	1.93486e7i	−0.232914	+	1.95772i
$629$		−	5.01520e6i		−	0.505431i
$630$		0			0
$631$	3.76561e6			0.376497			0.188249	−	0.982121i	$-0.439719\pi$
$631$	3.76561e6			0.376497			0.188249	+	0.982121i	$0.439719\pi$
$632$	4.49190e6	−	3.12462e6i	0.447340	−	0.311175i
$633$		−	1.07287e7i		−	1.06424i
$634$	−3.67594e6	−	4.13920e6i	−0.363200	−	0.408972i
$635$		0			0
$636$	−3.24978e6	+	2.73155e7i	−0.318574	+	2.67772i
$637$	−5.41400e6			−0.528652
$638$	6.00610e6	+	6.76302e6i	0.584173	+	0.657792i
$639$	1.64917e7			1.59776
$640$		0			0
$641$	−223711.			−0.0215052			−0.0107526	−	0.999942i	$-0.503423\pi$
$641$	−223711.			−0.0215052			−0.0107526	+	0.999942i	$0.503423\pi$
$642$	−3.27409e6	−	3.68671e6i	−0.313511	−	0.353021i
$643$	−2.53011e6			−0.241330			−0.120665	−	0.992693i	$-0.538503\pi$
$643$	−2.53011e6			−0.241330			−0.120665	+	0.992693i	$0.538503\pi$
$644$	−627800.	+	5.27687e6i	−0.0596495	+	0.501374i
$645$		0			0
$646$	−4.94272e6	−	5.56562e6i	−0.465998	−	0.524726i
$647$		−	8.44825e6i		−	0.793425i	−0.917943	−	0.396713i	$-0.870151\pi$
$647$		−	8.44825e6i		−	0.793425i	0.917943	−	0.396713i	$-0.129849\pi$
$648$	681495.	−	474056.i	0.0637566	−	0.0443499i
$649$	1.63452e7			1.52328
$650$		0			0
$651$		−	1.28638e7i		−	1.18964i
$652$	653265.	−	5.49091e6i	0.0601825	−	0.505854i
$653$	1.72303e7			1.58128			0.790641	−	0.612280i	$-0.209747\pi$
$653$	1.72303e7			1.58128			0.790641	+	0.612280i	$0.209747\pi$
$654$	−8.87532e6	+	7.88200e6i	−0.811409	+	0.720596i
$655$		0			0
$656$	−3.76329e6	−	908310.i	−0.341435	−	0.0824090i
$657$			8.03568e6i			0.726289i
$658$	3.11417e6	+	3.50663e6i	0.280400	+	0.315737i
$659$			5.43243e6i			0.487282i	0.969865	+	0.243641i	$0.0783419\pi$
$659$			5.43243e6i			0.487282i	−0.969865	+	0.243641i	$0.921658\pi$
$660$		0			0
$661$		−	1.12770e7i		−	1.00390i	−0.864897	−	0.501949i	$-0.832616\pi$
$661$		−	1.12770e7i		−	1.00390i	0.864897	−	0.501949i	$-0.167384\pi$
$662$	1.46308e6	−	1.29933e6i	0.129754	−	0.115232i
$663$			2.54503e7i			2.24858i
$664$	−1.39612e7	+	9.71158e6i	−1.22886	+	0.854810i
$665$		0			0
$666$	−6.36229e6	−	7.16410e6i	−0.555812	−	0.625858i
$667$	−3.45911e6			−0.301057
$668$	−1.40292e7	−	1.66909e6i	−1.21645	−	0.144723i
$669$			2.39402e7i			2.06806i
$670$		0			0
$671$	−2.09086e6			−0.179275
$672$	−1.32727e7	+	7.06860e6i	−1.13380	+	0.603823i
$673$		−	1.15475e7i		−	0.982769i	−0.870943	−	0.491384i	$-0.836491\pi$
$673$		−	1.15475e7i		−	0.982769i	0.870943	−	0.491384i	$-0.163509\pi$
$674$	−1.59253e6	+	1.41430e6i	−0.135033	+	0.119920i
$675$		0			0
$676$	−1.60476e6	+	1.34886e7i	−0.135065	+	1.13527i
$677$	−8.72804e6			−0.731889			−0.365944	−	0.930637i	$-0.619254\pi$
$677$	−8.72804e6			−0.731889			−0.365944	+	0.930637i	$0.619254\pi$
$678$	−6.06763e6	+	5.38854e6i	−0.506926	+	0.450191i
$679$	−7.67862e6			−0.639159
$680$		0			0
$681$	−2.17009e7			−1.79313
$682$	−1.55260e7	+	1.37883e7i	−1.27820	+	1.13514i
$683$	5.37492e6			0.440880			0.220440	−	0.975401i	$-0.429251\pi$
$683$	5.37492e6			0.440880			0.220440	+	0.975401i	$0.429251\pi$
$684$	−1.41211e7	−	1.68002e6i	−1.15406	−	0.137301i
$685$		0			0
$686$	−1.00265e7	+	8.90434e6i	−0.813466	+	0.722423i
$687$			1.63849e7i			1.32450i
$688$	−1.30084e7	−	3.13972e6i	−1.04774	−	0.252883i
$689$	3.06101e7			2.45650
$690$		0			0
$691$		−	1.03106e7i		−	0.821467i	−0.911756	−	0.410733i	$-0.865273\pi$
$691$		−	1.03106e7i		−	0.821467i	0.911756	−	0.410733i	$-0.134727\pi$
$692$	−1.06387e6	+	8.94217e6i	−0.0844545	+	0.709868i
$693$	−2.95233e7			−2.33524
$694$	618498.	+	696444.i	0.0487461	+	0.0548893i
$695$		0			0
$696$	−5.58963e6	−	8.03555e6i	−0.437381	−	0.628771i
$697$			4.30541e6i			0.335686i
$698$	152026.	−	135011.i	0.0118108	−	0.0104889i
$699$		−	2.05556e7i		−	1.59124i
$700$		0			0
$701$			7.87993e6i			0.605658i	0.953045	+	0.302829i	$0.0979311\pi$
$701$			7.87993e6i			0.605658i	−0.953045	+	0.302829i	$0.902069\pi$
$702$	1.18874e7	+	1.33855e7i	0.910422	+	1.02516i
$703$		−	5.08851e6i		−	0.388331i
$704$	2.27581e7	+	8.44293e6i	1.73063	+	0.642039i
$705$		0			0
$706$	5.89743e6	−	5.23739e6i	0.445298	−	0.395460i
$707$	−3.22315e6			−0.242511
$708$	−1.75649e7	−	2.08973e6i	−1.31693	−	0.156678i
$709$		−	2.06172e7i		−	1.54033i	−0.637846	−	0.770164i	$-0.720174\pi$
$709$		−	2.06172e7i		−	1.54033i	0.637846	−	0.770164i	$-0.279826\pi$
$710$		0			0
$711$	−1.16258e7			−0.862476
$712$	175063.	−	121776.i	0.0129418	−	0.00900246i
$713$		−	7.94115e6i		−	0.585005i
$714$	1.11049e7	+	1.25044e7i	0.815212	+	0.917949i
$715$		0			0
$716$	−2.56040e7	−	3.04616e6i	−1.86649	−	0.222060i
$717$	2.17280e7			1.57842
$718$	−1.31692e7	−	1.48288e7i	−0.953338	−	1.07348i
$719$	−1.37162e7			−0.989490			−0.494745	−	0.869038i	$-0.664738\pi$
$719$	−1.37162e7			−0.989490			−0.494745	+	0.869038i	$0.664738\pi$
$720$		0			0
$721$	−1.45383e7			−1.04154
$722$	4.28600e6	+	4.82614e6i	0.305991	+	0.344554i
$723$	4.14305e7			2.94764
$724$	1.93942e7	+	2.30737e6i	1.37507	+	0.163595i
$725$		0			0
$726$	3.64836e7	+	4.10814e7i	2.56895	+	2.89270i
$727$		−	2.33681e7i		−	1.63979i	−0.572514	−	0.819895i	$-0.694032\pi$
$727$		−	2.33681e7i		−	1.63979i	0.572514	−	0.819895i	$-0.305968\pi$
$728$	9.55545e6	+	1.37367e7i	0.668225	+	0.960629i
$729$	−2.33601e7			−1.62800
$730$		0			0
$731$			1.48823e7i			1.03010i
$732$	2.24688e6	+	267316.i	0.154990	+	0.0184394i
$733$	−2.94411e6			−0.202392			−0.101196	−	0.994866i	$-0.532267\pi$
$733$	−2.94411e6			−0.202392			−0.101196	+	0.994866i	$0.532267\pi$
$734$	−1.54147e7	+	1.36895e7i	−1.05607	+	0.937878i
$735$		0			0
$736$	−8.19358e6	+	4.36362e6i	−0.557544	+	0.296929i
$737$		−	4.07289e7i		−	2.76207i
$738$	5.46186e6	+	6.15019e6i	0.369147	+	0.415669i
$739$			3.66027e6i			0.246548i	0.992373	+	0.123274i	$0.0393395\pi$
$739$			3.66027e6i			0.246548i	−0.992373	+	0.123274i	$0.960661\pi$
$740$		0			0
$741$			2.58223e7i			1.72763i
$742$	1.50396e7	−	1.33563e7i	1.00283	−	0.890590i
$743$			2.60824e7i			1.73331i	0.498912	+	0.866653i	$0.333733\pi$
$743$			2.60824e7i			1.73331i	−0.498912	+	0.866653i	$0.666267\pi$
$744$	1.84474e7	−	1.28322e7i	1.22181	−	0.849904i
$745$		0			0
$746$	−1.57484e7	−	1.77331e7i	−1.03607	−	1.16664i
$747$	3.61338e7			2.36926
$748$	3.18920e6	−	2.68063e7i	0.208414	−	1.75179i
$749$			3.60535e6i			0.234824i
$750$		0			0
$751$	−1.03196e7			−0.667673			−0.333836	−	0.942631i	$-0.608343\pi$
$751$	−1.03196e7			−0.667673			−0.333836	+	0.942631i	$0.608343\pi$
$752$	−1.92217e6	+	7.96391e6i	−0.123950	+	0.513549i
$753$		−	2.15668e7i		−	1.38611i
$754$	−8.14425e6	+	7.23275e6i	−0.521702	+	0.463313i
$755$		0			0
$756$	1.16812e7	+	1.38973e6i	0.743331	+	0.0884356i
$757$	2.70313e7			1.71446			0.857228	−	0.514936i	$-0.172184\pi$
$757$	2.70313e7			1.71446			0.857228	+	0.514936i	$0.172184\pi$
$758$	9.77434e6	−	8.68040e6i	0.617895	−	0.548740i
$759$	−2.97405e7			−1.87389
$760$		0			0
$761$	1.29548e7			0.810905			0.405452	−	0.914116i	$-0.367114\pi$
$761$	1.29548e7			0.810905			0.405452	+	0.914116i	$0.367114\pi$
$762$	−937568.	+	832635.i	−0.0584945	+	0.0519478i
$763$	8.67946e6			0.539736
$764$	3.19726e6	−	2.68741e7i	0.198173	−	1.66571i
$765$		0			0
$766$	5.00116e6	−	4.44143e6i	0.307963	−	0.273496i
$767$			1.96834e7i			1.20813i
$768$	−2.33769e7	−	1.19826e7i	−1.43016	−	0.733072i
$769$	−8.35551e6			−0.509515			−0.254757	−	0.967005i	$-0.581996\pi$
$769$	−8.35551e6			−0.509515			−0.254757	+	0.967005i	$0.581996\pi$
$770$		0			0
$771$			1.91732e7i			1.16161i
$772$	−5.84960e6	−	695939.i	−0.353251	−	0.0420270i
$773$	−3.12215e7			−1.87934			−0.939668	−	0.342087i	$-0.888866\pi$
$773$	−3.12215e7			−1.87934			−0.939668	+	0.342087i	$0.888866\pi$
$774$	1.88798e7	+	2.12591e7i	1.13278	+	1.27553i
$775$		0			0
$776$	−7.65978e6	−	1.10116e7i	−0.456627	−	0.656439i
$777$			1.14325e7i			0.679342i
$778$	2.15384e7	−	1.91278e7i	1.27574	−	1.13296i
$779$			4.36835e6i			0.257913i
$780$		0			0
$781$			3.17639e7i			1.86340i
$782$	6.85535e6	+	7.71929e6i	0.400879	+	0.451399i
$783$			7.65727e6i			0.446344i
$784$	−6.04124e6	−	1.45812e6i	−0.351023	−	0.0847232i
$785$		0			0
$786$	1.17044e7	−	1.03944e7i	0.675760	−	0.600129i
$787$	−1.14664e7			−0.659920			−0.329960	−	0.943995i	$-0.607035\pi$
$787$	−1.14664e7			−0.659920			−0.329960	+	0.943995i	$0.607035\pi$
$788$	1.47635e6	−	1.24092e7i	0.0846980	−	0.711915i
$789$			6.53222e6i			0.373567i
$790$		0			0
$791$	5.93373e6			0.337199
$792$	−2.94508e7	−	4.23380e7i	−1.66834	−	2.39838i
$793$		−	2.51789e6i		−	0.142185i
$794$	−236673.	−	266499.i	−0.0133228	−	0.0150018i
$795$		0			0
$796$	−2.20878e6	+	1.85655e7i	−0.123557	+	1.03854i
$797$	2.28998e7			1.27699			0.638493	−	0.769628i	$-0.279558\pi$
$797$	2.28998e7			1.27699			0.638493	+	0.769628i	$0.279558\pi$
$798$	1.12673e7	+	1.26872e7i	0.626342	+	0.705276i
$799$	9.11115e6			0.504901
$800$		0			0
$801$	−453090.			−0.0249519
$802$	−1.68643e7	−	1.89896e7i	−0.925831	−	1.04251i
$803$	−1.54772e7			−0.847040
$804$	−5.20719e6	+	4.37681e7i	−0.284095	+	2.38791i
$805$		0			0
$806$	−1.66044e7	−	1.86969e7i	−0.900295	−	1.01375i
$807$			2.81614e7i			1.52220i
$808$	−3.21524e6	−	4.62217e6i	−0.173255	−	0.249068i
$809$	−2.82761e7			−1.51896			−0.759482	−	0.650528i	$-0.774548\pi$
$809$	−2.82761e7			−1.51896			−0.759482	+	0.650528i	$0.774548\pi$
$810$		0			0
$811$		−	2.97657e7i		−	1.58915i	−0.607167	−	0.794574i	$-0.707694\pi$
$811$		−	2.97657e7i		−	1.58915i	0.607167	−	0.794574i	$-0.292306\pi$
$812$	−845570.	+	7.10729e6i	−0.0450048	+	0.378281i
$813$	2.68752e7			1.42602
$814$	1.37985e7	−	1.22542e7i	0.729912	−	0.648220i
$815$		0			0
$816$	−6.85435e6	+	2.83988e7i	−0.360364	+	1.49305i
$817$			1.50999e7i			0.791441i
$818$	−7.64092e6	−	8.60387e6i	−0.399266	−	0.449584i
$819$		−	3.55529e7i		−	1.85210i
$820$		0			0
$821$		−	2.33663e7i		−	1.20985i	−0.796282	−	0.604926i	$-0.793203\pi$
$821$		−	2.33663e7i		−	1.20985i	0.796282	−	0.604926i	$-0.206797\pi$
$822$	−3.22512e7	+	2.86417e7i	−1.66482	+	1.47849i
$823$			3.90864e6i			0.201153i	0.994929	+	0.100576i	$0.0320687\pi$
$823$			3.90864e6i			0.201153i	−0.994929	+	0.100576i	$0.967931\pi$
$824$	−1.45026e7	−	2.08487e7i	−0.744094	−	1.06970i
$825$		0			0
$826$	8.58863e6	+	9.67101e6i	0.438000	+	0.493198i
$827$	1.34407e7			0.683371			0.341686	−	0.939814i	$-0.389002\pi$
$827$	1.34407e7			0.683371			0.341686	+	0.939814i	$0.389002\pi$
$828$	1.95854e7	+	2.33012e6i	0.992790	+	0.118114i
$829$		−	2.39273e7i		−	1.20923i	−0.796519	−	0.604613i	$-0.793328\pi$
$829$		−	2.39273e7i		−	1.20923i	0.796519	−	0.604613i	$-0.206672\pi$
$830$		0			0
$831$	−1.54090e7			−0.774057
$832$	−1.01673e7	+	2.74061e7i	−0.509208	+	1.37258i
$833$			6.91151e6i			0.345112i
$834$	6.29200e6	−	5.58780e6i	0.313237	−	0.278180i
$835$		0			0
$836$	3.23582e6	−	2.71981e7i	0.160128	−	1.34593i
$837$	−1.75790e7			−0.867320
$838$	−6.47747e6	+	5.75251e6i	−0.318636	+	0.282975i
$839$	4.44572e6			0.218041			0.109020	−	0.994040i	$-0.465229\pi$
$839$	4.44572e6			0.218041			0.109020	+	0.994040i	$0.465229\pi$
$840$		0			0
$841$	1.58522e7			0.772856
$842$	2.05925e7	−	1.82878e7i	1.00099	−	0.888958i
$843$	1.63389e7			0.791871
$844$	−1.36083e7	−	1.61900e6i	−0.657577	−	0.0782334i
$845$		0			0
$846$	1.30151e7	−	1.15584e7i	0.625203	−	0.555230i
$847$		−	4.01748e7i		−	1.92418i
$848$	3.41564e7	+	8.24400e6i	1.63111	+	0.393684i
$849$	−2.27622e7			−1.08379
$850$		0			0
$851$			7.05756e6i			0.334065i
$852$	4.06101e6	−	3.41341e7i	0.191662	−	1.61098i
$853$	2.57954e7			1.21386			0.606931	−	0.794754i	$-0.292400\pi$
$853$	2.57954e7			1.21386			0.606931	+	0.794754i	$0.292400\pi$
$854$	−1.09865e6	−	1.23711e6i	−0.0515483	−	0.0580447i
$855$		0			0
$856$	−5.17027e6	+	3.59650e6i	−0.241173	+	0.167763i
$857$			1.79012e7i			0.832590i	0.909230	+	0.416295i	$0.136672\pi$
$857$			1.79012e7i			0.832590i	−0.909230	+	0.416295i	$0.863328\pi$
$858$	−7.00222e7	+	6.21854e7i	−3.24727	+	2.88383i
$859$			2.50747e7i			1.15945i	0.814811	+	0.579727i	$0.196841\pi$
$859$			2.50747e7i			1.15945i	−0.814811	+	0.579727i	$0.803159\pi$
$860$		0			0
$861$		−	9.81449e6i		−	0.451190i
$862$	2.01996e6	+	2.27453e6i	0.0925924	+	0.104261i
$863$		−	8.98511e6i		−	0.410673i	−0.978691	−	0.205337i	$-0.934171\pi$
$863$		−	8.98511e6i		−	0.410673i	0.978691	−	0.205337i	$-0.0658289\pi$
$864$	9.65955e6	+	1.81378e7i	0.440223	+	0.826608i
$865$		0			0
$866$	6.26988e6	−	5.56815e6i	0.284095	−	0.252300i
$867$	−3.08057e6			−0.139182
$868$	−1.63164e7	−	1.94119e6i	−0.735062	−	0.0874519i
$869$		−	2.23919e7i		−	1.00587i
$870$		0			0
$871$	4.90471e7			2.19063
$872$	8.65816e6	+	1.24468e7i	0.385598	+	0.554329i
$873$			2.84997e7i			1.26562i
$874$	6.95556e6	+	7.83213e6i	0.308002	+	0.346818i
$875$		0			0
$876$	1.66321e7	+	1.97876e6i	0.732297	+	0.0871229i
$877$	1.08381e7			0.475834			0.237917	−	0.971286i	$-0.423535\pi$
$877$	1.08381e7			0.475834			0.237917	+	0.971286i	$0.423535\pi$
$878$	9.38946e6	+	1.05728e7i	0.411059	+	0.462863i
$879$	1.28780e7			0.562179
$880$		0			0
$881$	−816876.			−0.0354582			−0.0177291	−	0.999843i	$-0.505644\pi$
$881$	−816876.			−0.0354582			−0.0177291	+	0.999843i	$0.505644\pi$
$882$	8.76796e6	+	9.87293e6i	0.379513	+	0.427341i
$883$	−2.50842e6			−0.108268			−0.0541339	−	0.998534i	$-0.517240\pi$
$883$	−2.50842e6			−0.108268			−0.0541339	+	0.998534i	$0.517240\pi$
$884$	3.22810e7	+	3.84054e6i	1.38936	+	0.165296i
$885$		0			0
$886$	−1.88117e7	−	2.11824e7i	−0.805089	−	0.906550i
$887$		−	1.58294e7i		−	0.675545i	−0.941228	−	0.337773i	$-0.890327\pi$
$887$		−	1.58294e7i		−	0.675545i	0.941228	−	0.337773i	$-0.109673\pi$
$888$	−1.63948e7	+	1.14044e7i	−0.697709	+	0.485335i
$889$	916878.			0.0389096
$890$		0			0
$891$		−	3.39722e6i		−	0.143360i
$892$	3.03656e7	+	3.61266e6i	1.27782	+	0.152025i
$893$	9.24434e6			0.387924
$894$	2.47680e7	−	2.19960e7i	1.03645	−	0.920449i
$895$		0			0
$896$	6.96286e6	+	1.79017e7i	0.289746	+	0.744946i
$897$		−	3.58145e7i		−	1.48620i
$898$	−1.14201e7	−	1.28593e7i	−0.472583	−	0.532140i
$899$		−	1.06957e7i		−	0.441379i
$900$		0			0
$901$		−	3.90768e7i		−	1.60364i
$902$	−1.18456e7	+	1.05199e7i	−0.484777	+	0.430521i
$903$		−	3.39253e7i		−	1.38454i
$904$	5.91917e6	+	8.50929e6i	0.240902	+	0.346316i
$905$		0			0
$906$	8.38162e6	+	9.43790e6i	0.339240	+	0.381993i
$907$	2.36328e7			0.953887			0.476944	−	0.878934i	$-0.341745\pi$
$907$	2.36328e7			0.953887			0.476944	+	0.878934i	$0.341745\pi$
$908$	−3.27475e6	+	2.75253e7i	−0.131814	+	1.10794i
$909$			1.19629e7i			0.480206i
$910$		0			0
$911$	−9.17484e6			−0.366271			−0.183136	−	0.983088i	$-0.558625\pi$
$911$	−9.17484e6			−0.366271			−0.183136	+	0.983088i	$0.558625\pi$
$912$	−6.95455e6	+	2.88139e7i	−0.276874	+	1.14714i
$913$			6.95959e7i			2.76316i
$914$	−3.04543e7	+	2.70459e7i	−1.20582	+	1.07087i
$915$		0			0
$916$	2.07825e7	+	2.47254e6i	0.818389	+	0.0973655i
$917$	−1.14461e7			−0.449504
$918$	1.70879e7	−	1.51754e7i	0.669239	−	0.594338i
$919$	3.58059e7			1.39851			0.699255	−	0.714872i	$-0.253515\pi$
$919$	3.58059e7			1.39851			0.699255	+	0.714872i	$0.253515\pi$
$920$		0			0
$921$	−3.67497e7			−1.42759
$922$	−3.33186e7	+	2.95896e7i	−1.29080	+	1.14633i
$923$	−3.82511e7			−1.47788
$924$	−7.27000e6	+	6.11068e7i	−0.280127	+	2.35456i
$925$		0			0
$926$	−2.61738e7	+	2.32444e7i	−1.00309	+	0.890823i
$927$			5.39597e7i			2.06239i
$928$	−1.10357e7	+	5.87726e6i	−0.420660	+	0.224029i
$929$	2.41031e7			0.916291			0.458146	−	0.888877i	$-0.348514\pi$
$929$	2.41031e7			0.916291			0.458146	+	0.888877i	$0.348514\pi$
$930$		0			0
$931$			7.01254e6i			0.265156i
$932$	−2.60726e7	−	3.10191e6i	−0.983204	−	0.116974i
$933$	−1.37265e7			−0.516245
$934$	−2.70883e7	−	3.05021e7i	−1.01605	−	1.14409i
$935$		0			0
$936$	5.09848e7	−	3.54656e7i	1.90218	−	1.32318i
$937$		−	1.84615e7i		−	0.686938i	−0.939164	−	0.343469i	$-0.888398\pi$
$937$		−	1.84615e7i		−	0.686938i	0.939164	−	0.343469i	$-0.111602\pi$
$938$	2.40982e7	−	2.14011e7i	0.894288	−	0.794200i
$939$			4.28032e7i			1.58421i
$940$		0			0
$941$		−	3.10319e6i		−	0.114244i	−0.998367	−	0.0571220i	$-0.981808\pi$
$941$		−	3.10319e6i		−	0.114244i	0.998367	−	0.0571220i	$-0.0181924\pi$
$942$	−5.73002e7	−	6.45214e7i	−2.10392	−	2.36906i
$943$		−	6.05873e6i		−	0.221872i
$944$	−5.30120e6	+	2.19638e7i	−0.193617	+	0.802192i
$945$		0			0
$946$	−4.09463e7	+	3.63636e7i	−1.48760	+	1.32111i
$947$	−4.89572e7			−1.77395			−0.886975	−	0.461817i	$-0.847198\pi$
$947$	−4.89572e7			−1.77395			−0.886975	+	0.461817i	$0.847198\pi$
$948$	−2.86280e6	+	2.40628e7i	−0.103459	+	0.869611i
$949$		−	1.86382e7i		−	0.671796i
$950$		0			0
$951$	2.45162e7			0.879025
$952$	1.75363e7	−	1.21985e7i	0.627113	−	0.436227i
$953$		−	3.94753e7i		−	1.40797i	−0.710216	−	0.703984i	$-0.751403\pi$
$953$		−	3.94753e7i		−	1.40797i	0.710216	−	0.703984i	$-0.248597\pi$
$954$	−4.95729e7	−	5.58203e7i	−1.76349	−	1.98573i
$955$		0			0
$956$	3.27883e6	−	2.75597e7i	0.116031	−	0.975281i
$957$	−4.00568e7			−1.41383
$958$	−1.52424e7	−	1.71633e7i	−0.536587	−	0.604210i
$959$	3.15395e7			1.10741
$960$		0			0
$961$	−4.07470e6			−0.142327
$962$	1.47569e7	+	1.66166e7i	0.514110	+	0.578901i
$963$	1.33815e7			0.464984
$964$	6.25200e6	−	5.25501e7i	0.216684	−	1.82130i
$965$		0			0
$966$	−1.56272e7	−	1.75967e7i	−0.538815	−	0.606719i
$967$		−	2.23447e7i		−	0.768438i	−0.923242	−	0.384219i	$-0.874471\pi$
$967$		−	2.23447e7i		−	0.768438i	0.923242	−	0.384219i	$-0.125529\pi$
$968$	5.76129e7	−	4.00762e7i	1.97620	−	1.37467i
$969$	3.29647e7			1.12782
$970$		0			0
$971$			2.63033e7i			0.895288i	0.894212	+	0.447644i	$0.147737\pi$
$971$			2.63033e7i			0.895288i	−0.894212	+	0.447644i	$0.852263\pi$
$972$	−3.69328e6	+	3.10433e7i	−0.125385	+	1.05391i
$973$	−6.15315e6			−0.208360
$974$	−515141.	+	457486.i	−0.0173992	+	0.0154519i
$975$		0			0
$976$	678125.	−	2.80959e6i	0.0227869	−	0.0944102i
$977$			4.78338e7i			1.60324i	0.597835	+	0.801619i	$0.296028\pi$
$977$			4.78338e7i			1.60324i	−0.597835	+	0.801619i	$0.703972\pi$
$978$	1.62611e7	+	1.83104e7i	0.543629	+	0.612140i
$979$		−	872679.i		−	0.0291003i
$980$		0			0
$981$		−	3.22144e7i		−	1.06875i
$982$	1.18706e7	−	1.05420e7i	0.392819	−	0.348855i
$983$		−	4.88361e7i		−	1.61197i	−0.591935	−	0.805986i	$-0.701636\pi$
$983$		−	4.88361e7i		−	1.61197i	0.591935	−	0.805986i	$-0.298364\pi$
$984$	1.40745e7	−	9.79040e6i	0.463389	−	0.322339i
$985$		0			0
$986$	9.23331e6	+	1.03969e7i	0.302458	+	0.340575i
$987$	−2.07695e7			−0.678630
$988$	3.27529e7	+	3.89668e6i	1.06747	+	0.126999i
$989$		−	2.09429e7i		−	0.680843i
$990$		0			0
$991$	7.49231e6			0.242344			0.121172	−	0.992632i	$-0.461335\pi$
$991$	7.49231e6			0.242344			0.121172	+	0.992632i	$0.461335\pi$
$992$	−1.34925e7	−	2.53350e7i	−0.435326	−	0.817413i
$993$			8.66569e6i			0.278888i
$994$	−1.87938e7	+	1.66904e7i	−0.603323	+	0.535799i
$995$		0			0
$996$	8.89781e6	−	7.47891e7i	0.284207	−	2.38886i
$997$	−1.46209e7			−0.465841			−0.232920	−	0.972496i	$-0.574828\pi$
$997$	−1.46209e7			−0.465841			−0.232920	+	0.972496i	$0.574828\pi$
$998$	−1.09750e7	+	9.74670e6i	−0.348802	+	0.309764i
$999$	1.56230e7			0.495280

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.15	✓	20	5.3	odd	4
40.6.d.a.21.16	yes	20	40.13	odd	4
160.6.d.a.81.3		20	40.3	even	4
160.6.d.a.81.18		20	20.3	even	4
200.6.d.b.101.5		20	40.37	odd	4
200.6.d.b.101.6		20	5.2	odd	4
200.6.f.b.149.15		20	40.29	even	2	inner
200.6.f.b.149.16		20	1.1	even	1	trivial
200.6.f.c.149.5		20	5.4	even	2
200.6.f.c.149.6		20	8.5	even	2
360.6.k.b.181.5		20	120.53	even	4
360.6.k.b.181.6		20	15.8	even	4
800.6.d.c.401.3		20	20.7	even	4
800.6.d.c.401.18		20	40.27	even	4
800.6.f.b.49.3		20	8.3	odd	2
800.6.f.b.49.4		20	20.19	odd	2
800.6.f.c.49.17		20	4.3	odd	2
800.6.f.c.49.18		20	40.19	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.75630 + 4.22968i) q^{2} -25.0521 q^{3} +(-3.78045 + 31.7759i) q^{4} +(-94.1031 - 105.962i) q^{6} +103.624i q^{7} +(-148.603 + 103.370i) q^{8} +384.607 q^{9} +O(q^{10})\)	\(q+(3.75630 + 4.22968i) q^{2} -25.0521 q^{3} +(-3.78045 + 31.7759i) q^{4} +(-94.1031 - 105.962i) q^{6} +103.624i q^{7} +(-148.603 + 103.370i) q^{8} +384.607 q^{9} +740.776i q^{11} +(94.7080 - 796.053i) q^{12} -892.067 q^{13} +(-438.297 + 389.243i) q^{14} +(-995.416 - 240.254i) q^{16} +1138.81i q^{17} +(1444.70 + 1626.77i) q^{18} +1155.46i q^{19} -2596.00i q^{21} +(-3133.25 + 2782.58i) q^{22} -1602.57i q^{23} +(3722.80 - 2589.63i) q^{24} +(-3350.87 - 3773.16i) q^{26} -3547.55 q^{27} +(-3292.75 - 391.745i) q^{28} -2158.47i q^{29} +4955.24 q^{31} +(-2722.88 - 5112.76i) q^{32} -18558.0i q^{33} +(-4816.81 + 4277.71i) q^{34} +(-1453.99 + 12221.2i) q^{36} -4403.89 q^{37} +(-4887.22 + 4340.24i) q^{38} +22348.1 q^{39} +3780.62 q^{41} +(10980.3 - 9751.34i) q^{42} +13068.3 q^{43} +(-23538.8 - 2800.46i) q^{44} +(6778.38 - 6019.75i) q^{46} -8000.58i q^{47} +(24937.3 + 6018.87i) q^{48} +6069.06 q^{49} -28529.6i q^{51} +(3372.41 - 28346.2i) q^{52} -34313.6 q^{53} +(-13325.6 - 15005.0i) q^{54} +(-10711.6 - 15398.8i) q^{56} -28946.6i q^{57} +(9129.64 - 8107.85i) q^{58} -22065.0i q^{59} +2822.53i q^{61} +(18613.4 + 20959.1i) q^{62} +39854.5i q^{63} +(11397.4 - 30722.0i) q^{64} +(78494.4 - 69709.3i) q^{66} -54981.5 q^{67} +(-36186.7 - 4305.21i) q^{68} +40147.8i q^{69} +42879.2 q^{71} +(-57153.5 + 39756.7i) q^{72} +20893.2i q^{73} +(-16542.3 - 18627.1i) q^{74} +(-36715.7 - 4368.14i) q^{76} -76762.2 q^{77} +(83946.2 + 94525.5i) q^{78} -30227.6 q^{79} -4586.03 q^{81} +(14201.1 + 15990.8i) q^{82} +93949.9 q^{83} +(82490.2 + 9814.03i) q^{84} +(49088.5 + 55274.9i) q^{86} +54074.1i q^{87} +(-76573.8 - 110081. i) q^{88} -1178.06 q^{89} -92439.5i q^{91} +(50923.2 + 6058.44i) q^{92} -124139. q^{93} +(33839.9 - 30052.6i) q^{94} +(68213.9 + 128085. i) q^{96} +74100.8i q^{97} +(22797.2 + 25670.2i) q^{98} +284908. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9 - 1252 * q^12 - 2708 * q^14 + 3080 * q^16 - 2070 * q^18 - 8244 * q^22 - 1032 * q^24 - 8084 * q^26 - 11664 * q^27 - 22924 * q^28 + 7160 * q^31 - 14792 * q^32 - 21132 * q^34 + 18344 * q^36 + 3608 * q^37 + 16884 * q^38 + 44904 * q^39 + 11608 * q^41 + 49444 * q^42 + 51772 * q^43 - 72296 * q^44 - 28516 * q^46 + 85048 * q^48 - 18756 * q^49 + 111624 * q^52 - 928 * q^53 + 100584 * q^54 - 53624 * q^56 - 152344 * q^58 - 228648 * q^62 + 11264 * q^64 - 56688 * q^66 + 161604 * q^67 - 359040 * q^68 - 200312 * q^71 - 563448 * q^72 - 78876 * q^74 - 153872 * q^76 - 26008 * q^77 + 624640 * q^78 - 282080 * q^79 + 65172 * q^81 + 410576 * q^82 + 99092 * q^83 + 297128 * q^84 + 27452 * q^86 + 464496 * q^88 + 3160 * q^89 + 519244 * q^92 - 293472 * q^93 - 148820 * q^94 + 395168 * q^96 - 663674 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more