LMFDB - Embedded newform 200.6.f.c.149.5

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			149.5
Root			$0.236693 - 3.99299i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.c.149.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$-0.202944\pi$
$3$	25.0521			1.60709			0.803546	+	0.595243i	$0.202944\pi$
$4$	−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	$-0.869130\pi$
$7$		−	103.624i		−	0.799310i	0.916666	−	0.399655i	$-0.130870\pi$
$8$	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	$-0.238589\pi$
$13$	892.067			1.46399			0.731996	+	0.681309i	$0.238589\pi$
$14$	−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	$-0.841413\pi$
$17$		−	1138.81i		−	0.955717i	0.878437	−	0.477859i	$-0.158587\pi$
$18$	−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	$0.102287\pi$
$23$			1602.57i			0.631682i	−0.948812	+	0.315841i	$0.897713\pi$
$24$	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	$-0.414818\pi$
$37$	4403.89			0.528850			0.264425	+	0.964406i	$0.414818\pi$
$38$	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	$-0.681165\pi$
$43$	−13068.3			−1.07783			−0.538913	+	0.842361i	$0.681165\pi$
$44$	−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	$0.0850907\pi$
$47$			8000.58i			0.528296i	−0.964482	+	0.264148i	$0.914909\pi$
$48$	−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	$-0.183157\pi$
$53$	34313.6			1.67794			0.838971	+	0.544175i	$0.183157\pi$
$54$	−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	$-0.230934\pi$
$67$	54981.5			1.49634			0.748168	+	0.663509i	$0.230934\pi$
$68$	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	$-0.926311\pi$
$73$		−	20893.2i		−	0.458879i	0.973323	−	0.229440i	$-0.0736894\pi$
$74$	−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	$-0.769209\pi$
$83$	−93949.9			−1.49693			−0.748465	+	0.663175i	$0.769209\pi$
$84$	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	$-0.869073\pi$
$97$		−	74100.8i		−	0.799638i	0.916594	−	0.399819i	$-0.130927\pi$
$98$	−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	$-0.774130\pi$
$103$		−	140298.i		−	1.30305i	0.758629	−	0.651523i	$-0.225870\pi$
$104$	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	$-0.546927\pi$
$107$	−34792.6			−0.293784			−0.146892	+	0.989153i	$0.546927\pi$
$108$	−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	$0.0676497\pi$
$113$			57262.1i			0.421863i	−0.977501	+	0.210931i	$0.932350\pi$
$114$	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	$0.00774827\pi$
$127$			8848.12i			0.0486790i	−0.999704	+	0.0243395i	$0.992252\pi$
$128$	−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	$0.243591\pi$
$137$			304365.i			1.38546i	−0.721199	+	0.692728i	$0.756409\pi$
$138$	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	$-0.946227\pi$
$157$	−608909.			−1.97153			−0.985764	+	0.168132i	$0.946227\pi$
$158$	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	$-0.418020\pi$
$163$	172801.			0.509421			0.254711	+	0.967017i	$0.418020\pi$
$164$	−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	$-0.790159\pi$
$167$		−	441506.i		−	1.22503i	0.790461	−	0.612513i	$-0.209841\pi$
$168$	−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	$-0.616349\pi$
$173$	−281414.			−0.714874			−0.357437	+	0.933937i	$0.616349\pi$
$174$	−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	$-0.943079\pi$
$193$		−	184089.i		−	0.355742i	0.984054	−	0.177871i	$-0.0569210\pi$
$194$	−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	$-0.383299\pi$
$197$	390522.			0.716935			0.358468	+	0.933542i	$0.383299\pi$
$198$	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	$0.222484\pi$
$223$			955618.i			1.28683i	−0.765517	+	0.643416i	$0.777516\pi$
$224$	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	$-0.688385\pi$
$227$	−866233.			−1.11576			−0.557879	+	0.829922i	$0.688385\pi$
$228$	−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	$-0.835143\pi$
$233$		−	820513.i		−	0.990138i	0.868854	−	0.495069i	$-0.164857\pi$
$234$	−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	$0.117701\pi$
$257$			765335.i			0.722801i	−0.932411	+	0.361401i	$0.882299\pi$
$258$	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	$0.0370792\pi$
$263$			260746.i			0.232449i	−0.993223	+	0.116225i	$0.962921\pi$
$264$	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	$-0.577418\pi$
$277$	−615080.			−0.481651			−0.240825	+	0.970568i	$0.577418\pi$
$278$	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	$-0.609476\pi$
$283$	−908596.			−0.674380			−0.337190	+	0.941437i	$0.609476\pi$
$284$	−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	$-0.444038\pi$
$293$	514047.			0.349811			0.174906	+	0.984585i	$0.444038\pi$
$294$	−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	$-0.646496\pi$
$307$	−1.46693e6			−0.888309			−0.444155	+	0.895950i	$0.646496\pi$
$308$	−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	$0.164056\pi$
$313$			1.70857e6i			0.985762i	−0.870097	+	0.492881i	$0.835944\pi$
$314$	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	$-0.411824\pi$
$317$	978608.			0.546966			0.273483	+	0.961877i	$0.411824\pi$
$318$	−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	$-0.971218\pi$
$337$		−	376513.i		−	0.180595i	0.995915	−	0.0902975i	$-0.0287818\pi$
$338$	−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	$-0.511686\pi$
$347$	−164656.			−0.0734099			−0.0367049	+	0.999326i	$0.511686\pi$
$348$	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	$0.0962445\pi$
$353$			1.39430e6i			0.595550i	−0.954636	+	0.297775i	$0.903756\pi$
$354$	−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	$-0.750405\pi$
$367$		−	3.64440e6i		−	1.41241i	0.708007	−	0.706206i	$-0.249595\pi$
$368$	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	$-0.215147\pi$
$373$	4.19252e6			1.56028			0.780142	+	0.625603i	$0.215147\pi$
$374$	−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	$0.0660245\pi$
$383$			1.18240e6i			0.411876i	−0.978565	+	0.205938i	$0.933976\pi$
$384$	−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	$-0.496807\pi$
$397$	63006.9			0.0200637			0.0100319	+	0.999950i	$0.496807\pi$
$398$	−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	$0.0608414\pi$
$433$			1.48235e6i			0.379954i	−0.981789	+	0.189977i	$0.939159\pi$
$434$	−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	$-0.292686\pi$
$443$	5.00804e6			1.21244			0.606218	+	0.795299i	$0.292686\pi$
$444$	−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	$-0.701443\pi$
$457$		−	7.20014e6i		−	1.61269i	0.591446	−	0.806345i	$-0.298557\pi$
$458$	−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	$-0.765962\pi$
$463$		−	6.18812e6i		−	1.34155i	0.741662	−	0.670774i	$-0.234038\pi$
$464$	−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	$-0.222706\pi$
$467$	7.21143e6			1.53013			0.765066	+	0.643952i	$0.222706\pi$
$468$	−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	$-0.996296\pi$
$487$		−	121792.i		−	0.0232700i	0.999932	−	0.0116350i	$-0.00370361\pi$
$488$	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	$0.0293906\pi$
$503$			1.04638e6i			0.184404i	−0.995740	+	0.0922021i	$0.970609\pi$
$504$	−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	$-0.476679\pi$
$523$	915789.			0.146400			0.0732000	+	0.997317i	$0.476679\pi$
$524$	−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	$-0.390277\pi$
$547$	4.72947e6			0.675841			0.337920	+	0.941175i	$0.390277\pi$
$548$	−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	$-0.571528\pi$
$557$	−3.26312e6			−0.445651			−0.222825	+	0.974858i	$0.571528\pi$
$558$	−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	$-0.373562\pi$
$563$	5.81898e6			0.773706			0.386853	+	0.922141i	$0.373562\pi$
$564$	−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	$-0.951035\pi$
$577$		−	2.45070e6i		−	0.306444i	0.988192	−	0.153222i	$-0.0489650\pi$
$578$	−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	$-0.430438\pi$
$587$	3.61982e6			0.433602			0.216801	+	0.976216i	$0.430438\pi$
$588$	−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	$-0.864476\pi$
$593$		−	7.07347e6i		−	0.826030i	0.910724	−	0.413015i	$-0.135524\pi$
$594$	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	$0.0414171\pi$
$607$			2.35562e6i			0.259498i	−0.991547	+	0.129749i	$0.958583\pi$
$608$	−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	$-0.467655\pi$
$613$	1.88749e6			0.202877			0.101439	+	0.994842i	$0.467655\pi$
$614$	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	$-0.720725\pi$
$617$		−	1.45446e7i		−	1.53812i	0.639178	−	0.769058i	$-0.279275\pi$
$618$	−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	$-0.461497\pi$
$643$	2.53011e6			0.241330			0.120665	+	0.992693i	$0.461497\pi$
$644$	−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	$0.129849\pi$
$647$			8.44825e6i			0.793425i	−0.917943	+	0.396713i	$0.870151\pi$
$648$	−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	$-0.790253\pi$
$653$	−1.72303e7			−1.58128			−0.790641	+	0.612280i	$0.790253\pi$
$654$	−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	$0.163509\pi$
$673$			1.15475e7i			0.982769i	−0.870943	+	0.491384i	$0.836491\pi$
$674$	−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	$-0.380746\pi$
$677$	8.72804e6			0.731889			0.365944	+	0.930637i	$0.380746\pi$
$678$	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	$-0.570749\pi$
$683$	−5.37492e6			−0.440880			−0.220440	+	0.975401i	$0.570749\pi$
$684$	−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	$0.305968\pi$
$727$			2.33681e7i			1.63979i	−0.572514	+	0.819895i	$0.694032\pi$
$728$	−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	$-0.467733\pi$
$733$	2.94411e6			0.202392			0.101196	+	0.994866i	$0.467733\pi$
$734$	−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	$-0.666267\pi$
$743$		−	2.60824e7i		−	1.73331i	0.498912	−	0.866653i	$-0.333733\pi$
$744$	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	$-0.827816\pi$
$757$	−2.70313e7			−1.71446			−0.857228	+	0.514936i	$0.827816\pi$
$758$	−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	$-0.111134\pi$
$773$	3.12215e7			1.87934			0.939668	+	0.342087i	$0.111134\pi$
$774$	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	$-0.392965\pi$
$787$	1.14664e7			0.659920			0.329960	+	0.943995i	$0.392965\pi$
$788$	−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	$-0.720442\pi$
$797$	−2.28998e7			−1.27699			−0.638493	+	0.769628i	$0.720442\pi$
$798$	−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	$-0.967931\pi$
$823$		−	3.90864e6i		−	0.201153i	0.994929	−	0.100576i	$-0.0320687\pi$
$824$	−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	$-0.610998\pi$
$827$	−1.34407e7			−0.683371			−0.341686	+	0.939814i	$0.610998\pi$
$828$	−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	$-0.707600\pi$
$853$	−2.57954e7			−1.21386			−0.606931	+	0.794754i	$0.707600\pi$
$854$	−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	$-0.863328\pi$
$857$		−	1.79012e7i		−	0.832590i	0.909230	−	0.416295i	$-0.136672\pi$
$858$	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	$0.0658289\pi$
$863$			8.98511e6i			0.410673i	−0.978691	+	0.205337i	$0.934171\pi$
$864$	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	$-0.576465\pi$
$877$	−1.08381e7			−0.475834			−0.237917	+	0.971286i	$0.576465\pi$
$878$	−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	$-0.482760\pi$
$883$	2.50842e6			0.108268			0.0541339	+	0.998534i	$0.482760\pi$
$884$	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	$0.109673\pi$
$887$			1.58294e7i			0.675545i	−0.941228	+	0.337773i	$0.890327\pi$
$888$	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	$-0.658255\pi$
$907$	−2.36328e7			−0.953887			−0.476944	+	0.878934i	$0.658255\pi$
$908$	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	$0.111602\pi$
$937$			1.84615e7i			0.686938i	−0.939164	+	0.343469i	$0.888398\pi$
$938$	−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	$-0.152802\pi$
$947$	4.89572e7			1.77395			0.886975	+	0.461817i	$0.152802\pi$
$948$	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	$0.248597\pi$
$953$			3.94753e7i			1.40797i	−0.710216	+	0.703984i	$0.751403\pi$
$954$	−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	$0.125529\pi$
$967$			2.23447e7i			0.768438i	−0.923242	+	0.384219i	$0.874471\pi$
$968$	−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	$-0.703972\pi$
$977$		−	4.78338e7i		−	1.60324i	0.597835	−	0.801619i	$-0.296028\pi$
$978$	−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	$0.298364\pi$
$983$			4.88361e7i			1.61197i	−0.591935	+	0.805986i	$0.701636\pi$
$984$	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	$-0.425172\pi$
$997$	1.46209e7			0.465841			0.232920	+	0.972496i	$0.425172\pi$
$998$	1.09750e7	−	9.74670e6i	0.348802	−	0.309764i
$999$	1.56230e7			0.495280

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.c.149.5		20
4.3	odd	2		800.6.f.b.49.4		20
5.2	odd	4		40.6.d.a.21.15	✓	20
5.3	odd	4		200.6.d.b.101.6		20
5.4	even	2		200.6.f.b.149.16		20
8.3	odd	2		800.6.f.c.49.18		20
8.5	even	2		200.6.f.b.149.15		20
15.2	even	4		360.6.k.b.181.6		20
20.3	even	4		800.6.d.c.401.3		20
20.7	even	4		160.6.d.a.81.18		20
20.19	odd	2		800.6.f.c.49.17		20
40.3	even	4		800.6.d.c.401.18		20
40.13	odd	4		200.6.d.b.101.5		20
40.19	odd	2		800.6.f.b.49.3		20
40.27	even	4		160.6.d.a.81.3		20
40.29	even	2	inner	200.6.f.c.149.6		20
40.37	odd	4		40.6.d.a.21.16	yes	20
120.77	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	5.2	odd	4
40.6.d.a.21.16	yes	20	40.37	odd	4
160.6.d.a.81.3		20	40.27	even	4
160.6.d.a.81.18		20	20.7	even	4
200.6.d.b.101.5		20	40.13	odd	4
200.6.d.b.101.6		20	5.3	odd	4
200.6.f.b.149.15		20	8.5	even	2
200.6.f.b.149.16		20	5.4	even	2
200.6.f.c.149.5		20	1.1	even	1	trivial
200.6.f.c.149.6		20	40.29	even	2	inner
360.6.k.b.181.5		20	120.77	even	4
360.6.k.b.181.6		20	15.2	even	4
800.6.d.c.401.3		20	20.3	even	4
800.6.d.c.401.18		20	40.3	even	4
800.6.f.b.49.3		20	40.19	odd	2
800.6.f.b.49.4		20	4.3	odd	2
800.6.f.c.49.17		20	20.19	odd	2
800.6.f.c.49.18		20	8.3	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	200.6.f.c.149.5

Level	$200$
Weight	$6$
Character	200.149
Analytic conductor	$32.077$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$