LMFDB - Embedded newform 177.5.b.a.119.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.51
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68814i q^{2} +(6.36775 - 6.36017i) q^{3} +8.77388 q^{4} -40.9357i q^{5} +(17.0970 + 17.1174i) q^{6} +27.0431 q^{7} +66.5958i q^{8} +(0.0965568 - 80.9999i) q^{9} +O(q^{10})$	\(q+2.68814i q^{2} +(6.36775 - 6.36017i) q^{3} +8.77388 q^{4} -40.9357i q^{5} +(17.0970 + 17.1174i) q^{6} +27.0431 q^{7} +66.5958i q^{8} +(0.0965568 - 80.9999i) q^{9} +110.041 q^{10} +103.074i q^{11} +(55.8699 - 55.8034i) q^{12} +118.814 q^{13} +72.6957i q^{14} +(-260.358 - 260.669i) q^{15} -38.6368 q^{16} -49.6376i q^{17} +(217.739 + 0.259559i) q^{18} +76.7031 q^{19} -359.165i q^{20} +(172.204 - 171.999i) q^{21} -277.078 q^{22} -924.844i q^{23} +(423.560 + 424.065i) q^{24} -1050.73 q^{25} +319.388i q^{26} +(-514.558 - 516.402i) q^{27} +237.273 q^{28} -183.370i q^{29} +(700.714 - 699.880i) q^{30} -755.744 q^{31} +961.671i q^{32} +(655.570 + 656.352i) q^{33} +133.433 q^{34} -1107.03i q^{35} +(0.847178 - 710.684i) q^{36} -41.7055 q^{37} +206.189i q^{38} +(756.576 - 755.675i) q^{39} +2726.14 q^{40} -1404.41i q^{41} +(462.357 + 462.908i) q^{42} +2258.06 q^{43} +904.362i q^{44} +(-3315.79 - 3.95262i) q^{45} +2486.11 q^{46} +4238.13i q^{47} +(-246.030 + 245.736i) q^{48} -1669.67 q^{49} -2824.52i q^{50} +(-315.703 - 316.080i) q^{51} +1042.46 q^{52} -416.398i q^{53} +(1388.16 - 1383.21i) q^{54} +4219.42 q^{55} +1800.96i q^{56} +(488.426 - 487.845i) q^{57} +492.926 q^{58} +453.188i q^{59} +(-2284.35 - 2287.08i) q^{60} +3032.63 q^{61} -2031.55i q^{62} +(2.61119 - 2190.49i) q^{63} -3203.30 q^{64} -4863.72i q^{65} +(-1764.37 + 1762.27i) q^{66} +954.878 q^{67} -435.515i q^{68} +(-5882.16 - 5889.18i) q^{69} +2975.85 q^{70} +6293.85i q^{71} +(5394.25 + 6.43027i) q^{72} +5846.79 q^{73} -112.110i q^{74} +(-6690.81 + 6682.83i) q^{75} +672.984 q^{76} +2787.45i q^{77} +(2031.36 + 2033.79i) q^{78} +585.429 q^{79} +1581.62i q^{80} +(-6560.98 - 15.6422i) q^{81} +3775.26 q^{82} +12230.0i q^{83} +(1510.90 - 1509.10i) q^{84} -2031.95 q^{85} +6070.00i q^{86} +(-1166.27 - 1167.66i) q^{87} -6864.31 q^{88} +4079.55i q^{89} +(10.6252 - 8913.32i) q^{90} +3213.09 q^{91} -8114.47i q^{92} +(-4812.39 + 4806.66i) q^{93} -11392.7 q^{94} -3139.90i q^{95} +(6116.39 + 6123.68i) q^{96} -16180.1 q^{97} -4488.32i q^{98} +(8349.01 + 9.95252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.68814i			0.672036i	0.941856	+	0.336018i	$0.109080\pi$
$2$			2.68814i			0.672036i	−0.941856	+	0.336018i	$0.890920\pi$
$3$	6.36775	−	6.36017i	0.707528	−	0.706685i
$3$	6.36775	−	6.36017i	0.707528	−	0.706685i
$4$	8.77388			0.548368
$5$		−	40.9357i		−	1.63743i	−0.574201	−	0.818714i	$-0.694687\pi$
$5$		−	40.9357i		−	1.63743i	0.574201	−	0.818714i	$-0.305313\pi$
$6$	17.0970	+	17.1174i	0.474918	+	0.475484i
$7$	27.0431			0.551900			0.275950	−	0.961172i	$-0.411008\pi$
$7$	27.0431			0.551900			0.275950	+	0.961172i	$0.411008\pi$
$8$			66.5958i			1.04056i
$9$	0.0965568	−	80.9999i	0.00119206	−	0.999999i
$10$	110.041			1.10041
$11$			103.074i			0.851854i	0.904758	+	0.425927i	$0.140052\pi$
$11$			103.074i			0.851854i	−0.904758	+	0.425927i	$0.859948\pi$
$12$	55.8699	−	55.8034i	0.387986	−	0.387523i
$13$	118.814			0.703040			0.351520	−	0.936180i	$-0.385665\pi$
$13$	118.814			0.703040			0.351520	+	0.936180i	$0.385665\pi$
$14$			72.6957i			0.370897i
$15$	−260.358	−	260.669i	−1.15715	−	1.15853i
$16$	−38.6368			−0.150925
$17$		−	49.6376i		−	0.171756i	−0.996306	−	0.0858782i	$-0.972630\pi$
$17$		−	49.6376i		−	0.171756i	0.996306	−	0.0858782i	$-0.0273696\pi$
$18$	217.739	+	0.259559i	0.672035	+	0.000801107i
$19$	76.7031			0.212474			0.106237	−	0.994341i	$-0.466120\pi$
$19$	76.7031			0.212474			0.106237	+	0.994341i	$0.466120\pi$
$20$		−	359.165i		−	0.897913i
$21$	172.204	−	171.999i	0.390485	−	0.390019i
$22$	−277.078			−0.572476
$23$		−	924.844i		−	1.74829i	−0.485668	−	0.874143i	$-0.661424\pi$
$23$		−	924.844i		−	1.74829i	0.485668	−	0.874143i	$-0.338576\pi$
$24$	423.560	+	424.065i	0.735347	+	0.736225i
$25$	−1050.73			−1.68117
$26$			319.388i			0.472468i
$27$	−514.558	−	516.402i	−0.705841	−	0.708370i
$28$	237.273			0.302644
$29$		−	183.370i		−	0.218039i	−0.994040	−	0.109019i	$-0.965229\pi$
$29$		−	183.370i		−	0.218039i	0.994040	−	0.109019i	$-0.0347710\pi$
$30$	700.714	−	699.880i	0.778571	−	0.777644i
$31$	−755.744			−0.786414			−0.393207	−	0.919450i	$-0.628634\pi$
$31$	−755.744			−0.786414			−0.393207	+	0.919450i	$0.628634\pi$
$32$			961.671i			0.939132i
$33$	655.570	+	656.352i	0.601992	+	0.602710i
$34$	133.433			0.115426
$35$		−	1107.03i		−	0.903697i
$36$	0.847178	−	710.684i	0.000653687	−	0.548367i
$37$	−41.7055			−0.0304642			−0.0152321	−	0.999884i	$-0.504849\pi$
$37$	−41.7055			−0.0304642			−0.0152321	+	0.999884i	$0.504849\pi$
$38$			206.189i			0.142790i
$39$	756.576	−	755.675i	0.497420	−	0.496828i
$40$	2726.14			1.70384
$41$		−	1404.41i		−	0.835462i	−0.908571	−	0.417731i	$-0.862825\pi$
$41$		−	1404.41i		−	0.835462i	0.908571	−	0.417731i	$-0.137175\pi$
$42$	462.357	+	462.908i	0.262107	+	0.262420i
$43$	2258.06			1.22124			0.610618	−	0.791926i	$-0.290921\pi$
$43$	2258.06			1.22124			0.610618	+	0.791926i	$0.290921\pi$
$44$			904.362i			0.467129i
$45$	−3315.79	−	3.95262i	−1.63743	−	0.00195191i
$46$	2486.11			1.17491
$47$			4238.13i			1.91857i	0.282433	+	0.959287i	$0.408859\pi$
$47$			4238.13i			1.91857i	−0.282433	+	0.959287i	$0.591141\pi$
$48$	−246.030	+	245.736i	−0.106784	+	0.106656i
$49$	−1669.67			−0.695406
$50$		−	2824.52i		−	1.12981i
$51$	−315.703	−	316.080i	−0.121378	−	0.121522i
$52$	1042.46			0.385524
$53$		−	416.398i		−	0.148237i	−0.997249	−	0.0741185i	$-0.976386\pi$
$53$		−	416.398i		−	0.148237i	0.997249	−	0.0741185i	$-0.0236143\pi$
$54$	1388.16	−	1383.21i	0.476050	−	0.474351i
$55$	4219.42			1.39485
$56$			1800.96i			0.574284i
$57$	488.426	−	487.845i	0.150331	−	0.150152i
$58$	492.926			0.146530
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−2284.35	−	2287.08i	−0.634542	−	0.635299i
$61$	3032.63			0.815005			0.407503	−	0.913204i	$-0.366400\pi$
$61$	3032.63			0.815005			0.407503	+	0.913204i	$0.366400\pi$
$62$		−	2031.55i		−	0.528498i
$63$	2.61119	−	2190.49i	0.000657897	−	0.551900i
$64$	−3203.30			−0.782055
$65$		−	4863.72i		−	1.15118i
$66$	−1764.37	+	1762.27i	−0.405043	+	0.404560i
$67$	954.878			0.212715			0.106358	−	0.994328i	$-0.466081\pi$
$67$	954.878			0.212715			0.106358	+	0.994328i	$0.466081\pi$
$68$		−	435.515i		−	0.0941857i
$69$	−5882.16	−	5889.18i	−1.23549	−	1.23696i
$70$	2975.85			0.607317
$71$			6293.85i			1.24853i	0.781212	+	0.624266i	$0.214602\pi$
$71$			6293.85i			1.24853i	−0.781212	+	0.624266i	$0.785398\pi$
$72$	5394.25	+	6.43027i	1.04056	+	0.00124041i
$73$	5846.79			1.09716			0.548582	−	0.836097i	$-0.315168\pi$
$73$	5846.79			1.09716			0.548582	+	0.836097i	$0.315168\pi$
$74$		−	112.110i		−	0.0204731i
$75$	−6690.81	+	6682.83i	−1.18948	+	1.18806i
$76$	672.984			0.116514
$77$			2787.45i			0.470138i
$78$	2031.36	+	2033.79i	0.333886	+	0.334284i
$79$	585.429			0.0938037			0.0469019	−	0.998900i	$-0.485065\pi$
$79$	585.429			0.0938037			0.0469019	+	0.998900i	$0.485065\pi$
$80$			1581.62i			0.247129i
$81$	−6560.98	−	15.6422i	−0.999997	−	0.00238412i
$82$	3775.26			0.561461
$83$			12230.0i			1.77529i	0.460528	+	0.887645i	$0.347660\pi$
$83$			12230.0i			1.77529i	−0.460528	+	0.887645i	$0.652340\pi$
$84$	1510.90	−	1509.10i	0.214129	−	0.213874i
$85$	−2031.95			−0.281239
$86$			6070.00i			0.820714i
$87$	−1166.27	−	1167.66i	−0.154085	−	0.154268i
$88$	−6864.31			−0.886404
$89$			4079.55i			0.515029i	0.966274	+	0.257515i	$0.0829036\pi$
$89$			4079.55i			0.515029i	−0.966274	+	0.257515i	$0.917096\pi$
$90$	10.6252	−	8913.32i	0.00131175	−	1.10041i
$91$	3213.09			0.388007
$92$		−	8114.47i		−	0.958704i
$93$	−4812.39	+	4806.66i	−0.556410	+	0.555747i
$94$	−11392.7			−1.28935
$95$		−	3139.90i		−	0.347911i
$96$	6116.39	+	6123.68i	0.663670	+	0.664462i
$97$	−16180.1			−1.71964			−0.859822	−	0.510594i	$-0.829425\pi$
$97$	−16180.1			−1.71964			−0.859822	+	0.510594i	$0.829425\pi$
$98$		−	4488.32i		−	0.467338i
$99$	8349.01	+	9.95252i	0.851853	+	0.00101546i
$100$	−9219.01			−0.921901
$101$			2742.03i			0.268800i	0.990927	+	0.134400i	$0.0429107\pi$
$101$			2742.03i			0.268800i	−0.990927	+	0.134400i	$0.957089\pi$
$102$	849.668	−	848.656i	0.0816675	−	0.0815702i
$103$	−7324.02			−0.690359			−0.345180	−	0.938537i	$-0.612182\pi$
$103$	−7324.02			−0.690359			−0.345180	+	0.938537i	$0.612182\pi$
$104$			7912.49i			0.731554i
$105$	−7040.89	−	7049.28i	−0.638629	−	0.639391i
$106$	1119.34			0.0996206
$107$			3760.73i			0.328476i	0.986421	+	0.164238i	$0.0525166\pi$
$107$			3760.73i			0.328476i	−0.986421	+	0.164238i	$0.947483\pi$
$108$	−4514.68	−	4530.85i	−0.387061	−	0.388447i
$109$	107.989			0.00908921			0.00454461	−	0.999990i	$-0.498553\pi$
$109$	107.989			0.00908921			0.00454461	+	0.999990i	$0.498553\pi$
$110$			11342.4i			0.937389i
$111$	−265.571	+	265.254i	−0.0215543	+	0.0215286i
$112$	−1044.86			−0.0832955
$113$		−	9200.74i		−	0.720553i	−0.932846	−	0.360277i	$-0.882682\pi$
$113$		−	9200.74i		−	0.720553i	0.932846	−	0.360277i	$-0.117318\pi$
$114$	1311.40	+	1312.96i	0.100908	+	0.101028i
$115$	−37859.1			−2.86269
$116$		−	1608.87i		−	0.119565i
$117$	11.4723	−	9623.90i	0.000838065	−	0.703039i
$118$	−1218.23			−0.0874916
$119$		−	1342.35i		−	0.0947923i
$120$	17359.4	−	17338.7i	1.20552	−	1.20408i
$121$	4016.69			0.274345
$122$			8152.15i			0.547713i
$123$	−8932.30	−	8942.95i	−0.590409	−	0.591113i
$124$	−6630.81			−0.431244
$125$			17427.7i			1.11537i
$126$	5888.35	+	7.01927i	0.370896	+	0.000442131i
$127$	23490.3			1.45640			0.728201	−	0.685363i	$-0.240357\pi$
$127$	23490.3			1.45640			0.728201	+	0.685363i	$0.240357\pi$
$128$			6775.81i			0.413563i
$129$	14378.8	−	14361.7i	0.864058	−	0.863029i
$130$	13074.4			0.773632
$131$			24755.6i			1.44255i	0.692648	+	0.721275i	$0.256444\pi$
$131$			24755.6i			1.44255i	−0.692648	+	0.721275i	$0.743556\pi$
$132$	5751.89	+	5758.75i	0.330113	+	0.330507i
$133$	2074.29			0.117264
$134$			2566.85i			0.142952i
$135$	−21139.3	+	21063.8i	−1.15991	+	1.15576i
$136$	3305.65			0.178723
$137$		−	24333.7i		−	1.29649i	−0.761434	−	0.648243i	$-0.775504\pi$
$137$		−	24333.7i		−	1.29649i	0.761434	−	0.648243i	$-0.224496\pi$
$138$	15830.9	−	15812.1i	0.831283	−	0.830292i
$139$	−13893.6			−0.719095			−0.359547	−	0.933127i	$-0.617069\pi$
$139$	−13893.6			−0.719095			−0.359547	+	0.933127i	$0.617069\pi$
$140$		−	9712.94i		−	0.495558i
$141$	26955.2	+	26987.4i	1.35583	+	1.35745i
$142$	−16918.8			−0.839058
$143$			12246.6i			0.598887i
$144$	−3.73064	+	3129.58i	−0.000179912	+	0.150925i
$145$	−7506.40			−0.357023
$146$			15717.0i			0.737333i
$147$	−10632.1	+	10619.4i	−0.492020	+	0.491433i
$148$	−365.920			−0.0167056
$149$			30511.7i			1.37434i	0.726496	+	0.687171i	$0.241147\pi$
$149$			30511.7i			1.37434i	−0.726496	+	0.687171i	$0.758853\pi$
$150$	−17964.4	−	17985.8i	−0.798419	−	0.799371i
$151$	37570.7			1.64776			0.823882	−	0.566761i	$-0.191804\pi$
$151$	37570.7			1.64776			0.823882	+	0.566761i	$0.191804\pi$
$152$			5108.10i			0.221092i
$153$	−4020.64	−	4.79285i	−0.171756	−	0.000204744i
$154$	−7493.06			−0.315950
$155$			30936.9i			1.28770i
$156$	6638.11	−	6630.20i	0.272769	−	0.272444i
$157$	13046.6			0.529293			0.264647	−	0.964345i	$-0.414745\pi$
$157$	13046.6			0.529293			0.264647	+	0.964345i	$0.414745\pi$
$158$			1573.72i			0.0630395i
$159$	−2648.36	−	2651.52i	−0.104757	−	0.104882i
$160$	39366.7			1.53776
$161$		−	25010.6i		−	0.964879i
$162$	42.0485	−	17636.9i	0.00160221	−	0.672034i
$163$	44429.9			1.67225			0.836124	−	0.548541i	$-0.184816\pi$
$163$	44429.9			1.67225			0.836124	+	0.548541i	$0.184816\pi$
$164$		−	12322.2i		−	0.458141i
$165$	26868.2	−	26836.2i	0.986895	−	0.985720i
$166$	−32875.9			−1.19306
$167$		−	15168.7i		−	0.543895i	−0.962312	−	0.271948i	$-0.912332\pi$
$167$		−	15168.7i		−	0.543895i	0.962312	−	0.271948i	$-0.0876677\pi$
$168$	11454.4	+	11468.0i	0.405838	+	0.406322i
$169$	−14444.3			−0.505735
$170$		−	5462.17i		−	0.189003i
$171$	7.40621	−	6212.95i	0.000253282	−	0.212474i
$172$	19812.0			0.669686
$173$			18323.9i			0.612245i	0.951992	+	0.306122i	$0.0990317\pi$
$173$			18323.9i			0.612245i	−0.951992	+	0.306122i	$0.900968\pi$
$174$	3138.83	−	3135.09i	0.103674	−	0.103550i
$175$	−28415.1			−0.927839
$176$		−	3982.46i		−	0.128566i
$177$	2882.35	+	2885.79i	0.0920026	+	0.0921123i
$178$	−10966.4			−0.346118
$179$		−	30093.5i		−	0.939218i	−0.882875	−	0.469609i	$-0.844395\pi$
$179$		−	30093.5i		−	0.939218i	0.882875	−	0.469609i	$-0.155605\pi$
$180$	−29092.4	−	34.6798i	−0.897912	−	0.00107037i
$181$	28153.2			0.859351			0.429675	−	0.902983i	$-0.358628\pi$
$181$	28153.2			0.859351			0.429675	+	0.902983i	$0.358628\pi$
$182$			8637.25i			0.260755i
$183$	19311.1	−	19288.1i	0.576639	−	0.575952i
$184$	61590.7			1.81919
$185$			1707.25i			0.0498830i
$186$	−12921.0	−	12936.4i	−0.373482	−	0.373927i
$187$	5116.36			0.146311
$188$			37184.9i			1.05208i
$189$	−13915.2	−	13965.1i	−0.389554	−	0.390949i
$190$	8440.49			0.233809
$191$		−	37672.9i		−	1.03267i	−0.856386	−	0.516336i	$-0.827296\pi$
$191$		−	37672.9i		−	1.03267i	0.856386	−	0.516336i	$-0.172704\pi$
$192$	−20397.8	+	20373.5i	−0.553326	+	0.552667i
$193$	−24338.6			−0.653402			−0.326701	−	0.945128i	$-0.605937\pi$
$193$	−24338.6			−0.653402			−0.326701	+	0.945128i	$0.605937\pi$
$194$		−	43494.5i		−	1.15566i
$195$	−30934.1	−	30971.0i	−0.813520	−	0.814490i
$196$	−14649.5			−0.381339
$197$			34199.6i			0.881229i	0.897696	+	0.440614i	$0.145239\pi$
$197$			34199.6i			0.881229i	−0.897696	+	0.440614i	$0.854761\pi$
$198$	−26.7538	+	22443.3i	−0.000682426	+	0.572476i
$199$	27858.0			0.703466			0.351733	−	0.936100i	$-0.385592\pi$
$199$	27858.0			0.703466			0.351733	+	0.936100i	$0.385592\pi$
$200$		−	69974.3i		−	1.74936i
$201$	6080.43	−	6073.18i	0.150502	−	0.150323i
$202$	−7370.97			−0.180643
$203$		−	4958.90i		−	0.120335i
$204$	−2769.95	−	2773.25i	−0.0665596	−	0.0666390i
$205$	−57490.6			−1.36801
$206$		−	19688.0i		−	0.463946i
$207$	−74912.3	−	89.2999i	−1.74829	−	0.00208406i
$208$	−4590.58			−0.106106
$209$			7906.12i			0.180997i
$210$	18949.5	−	18926.9i	0.429694	−	0.429182i
$211$	−88085.2			−1.97851			−0.989255	−	0.146202i	$-0.953295\pi$
$211$	−88085.2			−1.97851			−0.989255	+	0.146202i	$0.953295\pi$
$212$		−	3653.43i		−	0.0812884i
$213$	40029.9	+	40077.7i	0.882319	+	0.883372i
$214$	−10109.4			−0.220748
$215$		−	92435.5i		−	1.99969i
$216$	34390.2	−	34267.4i	0.737101	−	0.734469i
$217$	−20437.6			−0.434022
$218$			290.290i			0.00610828i
$219$	37230.9	−	37186.5i	0.776274	−	0.775349i
$220$	37020.7			0.764891
$221$		−	5897.63i		−	0.120752i
$222$	−713.041	−	713.892i	−0.0144680	−	0.0144853i
$223$	−5907.75			−0.118799			−0.0593994	−	0.998234i	$-0.518919\pi$
$223$	−5907.75			−0.118799			−0.0593994	+	0.998234i	$0.518919\pi$
$224$			26006.6i			0.518307i
$225$	−101.455	+	85109.3i	−0.00200406	+	1.68117i
$226$	24732.9			0.484238
$227$		−	12182.5i		−	0.236420i	−0.992989	−	0.118210i	$-0.962284\pi$
$227$		−	12182.5i		−	0.236420i	0.992989	−	0.118210i	$-0.0377156\pi$
$228$	4285.40	−	4280.29i	0.0824369	−	0.0823386i
$229$	−28702.6			−0.547332			−0.273666	−	0.961825i	$-0.588236\pi$
$229$	−28702.6			−0.547332			−0.273666	+	0.961825i	$0.588236\pi$
$230$		−	101771.i		−	1.92383i
$231$	17728.6	+	17749.8i	0.332240	+	0.332636i
$232$	12211.7			0.226882
$233$			50516.8i			0.930516i	0.885175	+	0.465258i	$0.154038\pi$
$233$			50516.8i			0.930516i	−0.885175	+	0.465258i	$0.845962\pi$
$234$	25870.4	+	30.8391i	0.472467	+	0.000563210i
$235$	173491.			3.14153
$236$			3976.22i			0.0713914i
$237$	3727.87	−	3723.43i	0.0663688	−	0.0662897i
$238$	3608.44			0.0637039
$239$			112466.i			1.96890i	0.175663	+	0.984450i	$0.443793\pi$
$239$			112466.i			1.96890i	−0.175663	+	0.984450i	$0.556207\pi$
$240$	10059.4	+	10071.4i	0.174642	+	0.174851i
$241$	−46239.5			−0.796122			−0.398061	−	0.917359i	$-0.630317\pi$
$241$	−46239.5			−0.796122			−0.398061	+	0.917359i	$0.630317\pi$
$242$			10797.4i			0.184370i
$243$	−41878.2	+	41629.3i	−0.709211	+	0.704996i
$244$	26608.0			0.446923
$245$			68349.2i			1.13868i
$246$	24039.9	−	24011.3i	0.397249	−	0.396776i
$247$	9113.38			0.149378
$248$		−	50329.3i		−	0.818310i
$249$	77784.7	+	77877.4i	1.25457	+	1.25607i
$250$	−46848.1			−0.749569
$251$			75727.7i			1.20201i	0.799246	+	0.601004i	$0.205232\pi$
$251$			75727.7i			1.20201i	−0.799246	+	0.601004i	$0.794768\pi$
$252$	22.9103	−	19219.1i	0.000360770	−	0.302644i
$253$	95327.6			1.48928
$254$			63145.4i			0.978755i
$255$	−12939.0	+	12923.5i	−0.198984	+	0.198747i
$256$	−69467.1			−1.05998
$257$		−	1522.24i		−	0.0230472i	−0.999934	−	0.0115236i	$-0.996332\pi$
$257$		−	1522.24i		−	0.0230472i	0.999934	−	0.0115236i	$-0.00366816\pi$
$258$	38606.2	+	38652.3i	0.579986	+	0.580678i
$259$	−1127.85			−0.0168132
$260$		−	42673.7i		−	0.631268i
$261$	−14853.0	−	17.7057i	−0.218038	−	0.000259915i
$262$	−66546.6			−0.969446
$263$		−	26666.8i		−	0.385530i	−0.981245	−	0.192765i	$-0.938254\pi$
$263$		−	26666.8i		−	0.385530i	0.981245	−	0.192765i	$-0.0617456\pi$
$264$	−43710.2	+	43658.2i	−0.627156	+	0.626408i
$265$	−17045.5			−0.242728
$266$			5575.99i			0.0788059i
$267$	25946.6	+	25977.6i	0.363964	+	0.364398i
$268$	8377.99			0.116646
$269$		−	123702.i		−	1.70952i	−0.519027	−	0.854758i	$-0.673706\pi$
$269$		−	123702.i		−	1.70952i	0.519027	−	0.854758i	$-0.326294\pi$
$270$	−56622.5	−	56825.4i	−0.776715	−	0.779498i
$271$	−75081.3			−1.02233			−0.511167	−	0.859481i	$-0.670787\pi$
$271$	−75081.3			−1.02233			−0.511167	+	0.859481i	$0.670787\pi$
$272$			1917.84i			0.0259223i
$273$	20460.2	−	20435.8i	0.274526	−	0.274199i
$274$	65412.6			0.871284
$275$		−	108304.i		−	1.43211i
$276$	−51609.4	−	51670.9i	−0.677502	−	0.678310i
$277$	−135889.			−1.77103			−0.885514	−	0.464612i	$-0.846194\pi$
$277$	−135889.			−1.77103			−0.885514	+	0.464612i	$0.846194\pi$
$278$		−	37348.1i		−	0.483258i
$279$	−72.9722	+	61215.2i	−0.000937452	+	0.786413i
$280$	73723.4			0.940349
$281$		−	69801.6i		−	0.884000i	−0.897015	−	0.442000i	$-0.854269\pi$
$281$		−	69801.6i		−	0.884000i	0.897015	−	0.442000i	$-0.145731\pi$
$282$	−72545.9	+	72459.5i	−0.912252	+	0.911165i
$283$	−42484.7			−0.530469			−0.265234	−	0.964184i	$-0.585449\pi$
$283$	−42484.7			−0.530469			−0.265234	+	0.964184i	$0.585449\pi$
$284$			55221.5i			0.684655i
$285$	−19970.3	−	19994.1i	−0.245864	−	0.246157i
$286$	−32920.7			−0.402473
$287$		−	37979.7i		−	0.461092i
$288$	77895.3	+	92.8559i	0.939131	+	0.00111950i
$289$	81057.1			0.970500
$290$		−	20178.3i		−	0.239932i
$291$	−103031.	+	102908.i	−1.21670	+	1.21525i
$292$	51299.0			0.601649
$293$			154913.i			1.80448i	0.431229	+	0.902242i	$0.358080\pi$
$293$			154913.i			1.80448i	−0.431229	+	0.902242i	$0.641920\pi$
$294$	−28546.4	−	28580.5i	−0.330261	−	0.330655i
$295$	18551.6			0.213175
$296$		−	2777.41i		−	0.0316998i
$297$	53227.7	−	53037.7i	0.603428	−	0.601274i
$298$	−82020.0			−0.923607
$299$		−	109884.i		−	1.22911i
$300$	−58704.4	+	58634.4i	−0.652271	+	0.651494i
$301$	61065.0			0.674000
$302$			100995.i			1.10736i
$303$	17439.8	+	17460.6i	0.189957	+	0.190184i
$304$	−2963.56			−0.0320676
$305$		−	124143.i		−	1.33451i
$306$	12.8839	−	10808.1i	0.000137595	−	0.115426i
$307$	−85430.9			−0.906439			−0.453219	−	0.891399i	$-0.649725\pi$
$307$	−85430.9			−0.906439			−0.453219	+	0.891399i	$0.649725\pi$
$308$			24456.7i			0.257809i
$309$	−46637.6	+	46582.0i	−0.488449	+	0.487867i
$310$	−83162.8			−0.865378
$311$			7709.13i			0.0797048i	0.999206	+	0.0398524i	$0.0126888\pi$
$311$			7709.13i			0.0797048i	−0.999206	+	0.0398524i	$0.987311\pi$
$312$	50324.7	+	50384.8i	0.516978	+	0.517595i
$313$	88993.3			0.908382			0.454191	−	0.890904i	$-0.349928\pi$
$313$	88993.3			0.908382			0.454191	+	0.890904i	$0.349928\pi$
$314$			35071.0i			0.355704i
$315$	−89669.2	−	106.891i	−0.903696	−	0.00107726i
$316$	5136.49			0.0514389
$317$			54169.2i			0.539056i	0.962993	+	0.269528i	$0.0868677\pi$
$317$			54169.2i			0.539056i	−0.962993	+	0.269528i	$0.913132\pi$
$318$	7127.66	−	7119.17i	0.0704844	−	0.0704004i
$319$	18900.8			0.185737
$320$			131129.i			1.28056i
$321$	23918.8	+	23947.4i	0.232129	+	0.232406i
$322$	67232.2			0.648433
$323$		−	3807.36i		−	0.0364938i
$324$	−57565.3	−	137.243i	−0.548366	−	0.00130737i
$325$	−124841.			−1.18193
$326$			119434.i			1.12381i
$327$	687.647	−	686.828i	0.00643087	−	0.00642321i
$328$	93527.9			0.869348
$329$			114612.i			1.05886i
$330$	72139.6	+	72225.6i	0.662439	+	0.663229i
$331$	127337.			1.16225			0.581125	−	0.813814i	$-0.302613\pi$
$331$	127337.			1.16225			0.581125	+	0.813814i	$0.302613\pi$
$332$			107304.i			0.973512i
$333$	−4.02695	+	3378.15i	−3.63152e−5	+	0.0304642i
$334$	40775.6			0.365517
$335$		−	39088.6i		−	0.348306i
$336$	−6653.40	+	6645.47i	−0.0589339	+	0.0588637i
$337$	35955.2			0.316594			0.158297	−	0.987392i	$-0.449400\pi$
$337$	35955.2			0.316594			0.158297	+	0.987392i	$0.449400\pi$
$338$		−	38828.4i		−	0.339872i
$339$	−58518.3	−	58588.1i	−0.509204	−	0.509812i
$340$	−17828.1			−0.154222
$341$		−	77897.7i		−	0.669909i
$342$	16701.3	+	19.9089i	0.142790	+	0.000170214i
$343$	−110084.			−0.935695
$344$			150377.i			1.27077i
$345$	−241078.	+	240790.i	−2.02544	+	2.02302i
$346$	−49257.2			−0.411450
$347$		−	192952.i		−	1.60247i	−0.598351	−	0.801234i	$-0.704177\pi$
$347$		−	192952.i		−	1.60247i	0.598351	−	0.801234i	$-0.295823\pi$
$348$	−10232.7	−	10244.9i	−0.0844950	−	0.0845958i
$349$	−8373.26			−0.0687454			−0.0343727	−	0.999409i	$-0.510943\pi$
$349$	−8373.26			−0.0687454			−0.0343727	+	0.999409i	$0.510943\pi$
$350$		−	76383.8i		−	0.623541i
$351$	−61136.6	−	61355.6i	−0.496234	−	0.498012i
$352$	−99123.5			−0.800003
$353$		−	90515.6i		−	0.726397i	−0.931712	−	0.363198i	$-0.881685\pi$
$353$		−	90515.6i		−	0.726397i	0.931712	−	0.363198i	$-0.118315\pi$
$354$	−7757.41	+	7748.17i	−0.0619028	+	0.0618290i
$355$	257643.			2.04438
$356$			35793.5i			0.282426i
$357$	−8537.60	−	8547.78i	−0.0669883	−	0.0670683i
$358$	80895.6			0.631188
$359$			33358.3i			0.258830i	0.991591	+	0.129415i	$0.0413100\pi$
$359$			33358.3i			0.258830i	−0.991591	+	0.129415i	$0.958690\pi$
$360$	263.228	−	220818.i	0.00203108	−	1.70384i
$361$	−124438.			−0.954855
$362$			75679.8i			0.577514i
$363$	25577.3	−	25546.8i	0.194107	−	0.193876i
$364$	28191.3			0.212771
$365$		−	239342.i		−	1.79653i
$366$	51849.1	+	51910.9i	0.387060	+	0.387522i
$367$	−173393.			−1.28736			−0.643678	−	0.765297i	$-0.722592\pi$
$367$	−173393.			−1.28736			−0.643678	+	0.765297i	$0.722592\pi$
$368$			35733.0i			0.263860i
$369$	−113757.	−	135.606i	−0.835462	−	0.000995921i
$370$	−4589.32			−0.0335232
$371$		−	11260.7i		−	0.0818120i
$372$	−42223.3	+	42173.0i	−0.305117	+	0.304754i
$373$	212006.			1.52381			0.761906	−	0.647688i	$-0.224264\pi$
$373$	212006.			1.52381			0.761906	+	0.647688i	$0.224264\pi$
$374$			13753.5i			0.0983265i
$375$	110843.	+	110975.i	0.788216	+	0.789156i
$376$	−282241.			−1.99639
$377$		−	21786.9i		−	0.153290i
$378$	37540.2	−	37406.2i	0.262732	−	0.261794i
$379$	127813.			0.889807			0.444904	−	0.895578i	$-0.353238\pi$
$379$	127813.			0.889807			0.444904	+	0.895578i	$0.353238\pi$
$380$		−	27549.1i		−	0.190783i
$381$	149581.	−	149402.i	1.03045	−	1.02922i
$382$	101270.			0.693993
$383$		−	60318.9i		−	0.411202i	−0.978636	−	0.205601i	$-0.934085\pi$
$383$		−	60318.9i		−	0.411202i	0.978636	−	0.205601i	$-0.0659150\pi$
$384$	43095.3	+	43146.7i	0.292259	+	0.292607i
$385$	114106.			0.769817
$386$		−	65425.6i		−	0.439110i
$387$	218.031	−	182903.i	0.00145578	−	1.22123i
$388$	−141963.			−0.942997
$389$		−	215748.i		−	1.42576i	−0.701284	−	0.712882i	$-0.747389\pi$
$389$		−	215748.i		−	1.42576i	0.701284	−	0.712882i	$-0.252611\pi$
$390$	83254.5	−	83155.3i	0.547367	−	0.546714i
$391$	−45907.0			−0.300279
$392$		−	111193.i		−	0.723611i
$393$	157450.	+	157638.i	1.01943	+	1.02065i
$394$	−91933.4			−0.592217
$395$		−	23965.0i		−	0.153597i
$396$	73253.3	+	87.3223i	0.467129	+	0.000556846i
$397$	−269182.			−1.70791			−0.853954	−	0.520349i	$-0.825802\pi$
$397$	−269182.			−1.70791			−0.853954	+	0.520349i	$0.825802\pi$
$398$			74886.2i			0.472755i
$399$	13208.6	−	13192.8i	0.0829678	−	0.0828690i
$400$	40596.9			0.253731
$401$		−	79912.1i		−	0.496963i	−0.968637	−	0.248481i	$-0.920069\pi$
$401$		−	79912.1i		−	0.496963i	0.968637	−	0.248481i	$-0.0799315\pi$
$402$	16325.6	+	16345.1i	0.101022	+	0.101143i
$403$	−89792.7			−0.552880
$404$			24058.3i			0.147401i
$405$	−640.324	+	268578.i	−0.00390382	+	1.63742i
$406$	13330.2			0.0808697
$407$		−	4298.77i		−	0.0259511i
$408$	21049.6	−	21024.5i	0.126451	−	0.126301i
$409$	56708.3			0.339000			0.169500	−	0.985530i	$-0.445785\pi$
$409$	56708.3			0.339000			0.169500	+	0.985530i	$0.445785\pi$
$410$		−	154543.i		−	0.919352i
$411$	−154767.	−	154951.i	−0.916207	−	0.917300i
$412$	−64260.1			−0.378571
$413$			12255.6i			0.0718512i
$414$	240.051	−	201375.i	0.00140056	−	1.17491i
$415$	500643.			2.90691
$416$			114260.i			0.660247i
$417$	−88471.2	+	88365.8i	−0.508780	+	0.508174i
$418$	−21252.8			−0.121636
$419$		−	265845.i		−	1.51426i	−0.653265	−	0.757129i	$-0.726601\pi$
$419$		−	265845.i		−	1.51426i	0.653265	−	0.757129i	$-0.273399\pi$
$420$	−61775.9	−	61849.6i	−0.350204	−	0.350621i
$421$	−154820.			−0.873498			−0.436749	−	0.899583i	$-0.643870\pi$
$421$	−154820.			−0.873498			−0.436749	+	0.899583i	$0.643870\pi$
$422$		−	236786.i		−	1.32963i
$423$	343288.	+	409.220i	1.91857	+	0.00228705i
$424$	27730.3			0.154249
$425$			52155.8i			0.288752i
$426$	−107735.	+	107606.i	−0.593657	+	0.592950i
$427$	82011.8			0.449801
$428$			32996.2i			0.180126i
$429$	77890.7	+	77983.6i	0.423225	+	0.423729i
$430$	248480.			1.34386
$431$			73453.6i			0.395420i	0.980261	+	0.197710i	$0.0633504\pi$
$431$			73453.6i			0.395420i	−0.980261	+	0.197710i	$0.936650\pi$
$432$	19880.9	+	19952.1i	0.106529	+	0.106911i
$433$	198727.			1.05994			0.529971	−	0.848016i	$-0.322203\pi$
$433$	198727.			1.05994			0.529971	+	0.848016i	$0.322203\pi$
$434$		−	54939.3i		−	0.291678i
$435$	−47798.9	+	47741.9i	−0.252603	+	0.252303i
$436$	947.482			0.00498423
$437$		−	70938.4i		−	0.371465i
$438$	99962.7	+	100082.i	0.521063	+	0.521684i
$439$	106016.			0.550100			0.275050	−	0.961430i	$-0.411306\pi$
$439$	106016.			0.550100			0.275050	+	0.961430i	$0.411306\pi$
$440$			280995.i			1.45142i
$441$	−161.218	+	135243.i	−0.000828966	+	0.695406i
$442$	15853.7			0.0811494
$443$			214472.i			1.09286i	0.837505	+	0.546429i	$0.184013\pi$
$443$			214472.i			1.09286i	−0.837505	+	0.546429i	$0.815987\pi$
$444$	−2330.09	+	2327.31i	−0.0118197	+	0.0118056i
$445$	166999.			0.843324
$446$		−	15880.9i		−	0.0798371i
$447$	194060.	+	194291.i	0.971227	+	0.972385i
$448$	−86627.1			−0.431616
$449$		−	81179.4i		−	0.402673i	−0.979522	−	0.201337i	$-0.935471\pi$
$449$		−	81179.4i		−	0.402673i	0.979522	−	0.201337i	$-0.0645285\pi$
$450$	−228786.	−	272.727i	−1.12981	−	0.00134680i
$451$	144759.			0.711692
$452$		−	80726.3i		−	0.395128i
$453$	239241.	−	238956.i	1.16584	−	1.16445i
$454$	32748.3			0.158883
$455$		−	131530.i		−	0.635335i
$456$	32488.4	+	32527.1i	0.156242	+	0.156429i
$457$	−188136.			−0.900822			−0.450411	−	0.892821i	$-0.648723\pi$
$457$	−188136.			−0.900822			−0.450411	+	0.892821i	$0.648723\pi$
$458$		−	77156.8i		−	0.367827i
$459$	−25632.9	+	25541.4i	−0.121667	+	0.121233i
$460$	−332172.			−1.56981
$461$		−	312198.i		−	1.46902i	−0.678596	−	0.734512i	$-0.737411\pi$
$461$		−	312198.i		−	1.46902i	0.678596	−	0.734512i	$-0.262589\pi$
$462$	−47714.0	+	47657.1i	−0.223543	+	0.223277i
$463$	−294194.			−1.37237			−0.686187	−	0.727425i	$-0.740717\pi$
$463$	−294194.			−1.37237			−0.686187	+	0.727425i	$0.740717\pi$
$464$			7084.84i			0.0329075i
$465$	196764.	+	196999.i	0.909996	+	0.911081i
$466$	−135796.			−0.625340
$467$		−	205884.i		−	0.944039i	−0.881588	−	0.472019i	$-0.843525\pi$
$467$		−	205884.i		−	0.944039i	0.881588	−	0.472019i	$-0.156475\pi$
$468$	100.656	−	84439.0i	0.000459568	−	0.385524i
$469$	25822.9			0.117397
$470$			466368.i			2.11122i
$471$	83077.2	−	82978.3i	0.374490	−	0.374044i
$472$	−30180.4			−0.135469
$473$			232748.i			1.04031i
$474$	10009.1	+	10021.0i	0.0445491	+	0.0446022i
$475$	−80594.5			−0.357205
$476$		−	11777.7i		−	0.0519811i
$477$	−33728.2	−	40.2060i	−0.148237	−	0.000176707i
$478$	−302324.			−1.32317
$479$		−	162807.i		−	0.709583i	−0.934945	−	0.354791i	$-0.884552\pi$
$479$		−	162807.i		−	0.709583i	0.934945	−	0.354791i	$-0.115448\pi$
$480$	250677.	−	250379.i	1.08801	−	1.08671i
$481$	−4955.19			−0.0214176
$482$		−	124299.i		−	0.535022i
$483$	−159072.	−	159262.i	−0.681866	−	0.682679i
$484$	35242.0			0.150442
$485$			662345.i			2.81579i
$486$	−111906.	−	112575.i	−0.473783	−	0.476615i
$487$	247232.			1.04243			0.521216	−	0.853425i	$-0.325479\pi$
$487$	247232.			1.04243			0.521216	+	0.853425i	$0.325479\pi$
$488$			201961.i			0.848061i
$489$	282919.	−	282582.i	1.18316	−	1.18175i
$490$	−183732.			−0.765233
$491$		−	287137.i		−	1.19104i	−0.803340	−	0.595520i	$-0.796946\pi$
$491$		−	287137.i		−	1.19104i	0.803340	−	0.595520i	$-0.203054\pi$
$492$	−78370.9	−	78464.4i	−0.323761	−	0.324147i
$493$	−9102.07			−0.0374495
$494$			24498.1i			0.100387i
$495$	407.414	−	341773.i	0.00166274	−	1.39485i
$496$	29199.5			0.118689
$497$			170205.i			0.689065i
$498$	−209346.	+	209096.i	−0.844123	+	0.843117i
$499$	60111.9			0.241412			0.120706	−	0.992688i	$-0.461484\pi$
$499$	60111.9			0.241412			0.120706	+	0.992688i	$0.461484\pi$
$500$			152908.i			0.611633i
$501$	−96475.4	−	96590.5i	−0.384363	−	0.384821i
$502$	−203567.			−0.807792
$503$		−	113543.i		−	0.448771i	−0.974500	−	0.224386i	$-0.927962\pi$
$503$		−	113543.i		−	0.448771i	0.974500	−	0.224386i	$-0.0720375\pi$
$504$	145877.	+	173.894i	0.574284	+	0.000684581i
$505$	112247.			0.440141
$506$			256254.i			1.00085i
$507$	−91977.8	+	91868.2i	−0.357822	+	0.357396i
$508$	206101.			0.798644
$509$			134798.i			0.520293i	0.965569	+	0.260146i	$0.0837708\pi$
$509$			134798.i			0.520293i	−0.965569	+	0.260146i	$0.916229\pi$
$510$	−34740.3	−	34781.8i	−0.133565	−	0.133725i
$511$	158115.			0.605525
$512$		−	78324.6i		−	0.298785i
$513$	−39468.2	−	39609.6i	−0.149973	−	0.150510i
$514$	4092.01			0.0154885
$515$			299814.i			1.13041i
$516$	126158.	−	126008.i	0.473822	−	0.473257i
$517$	−436842.			−1.63434
$518$		−	3031.81i		−	0.0112991i
$519$	116543.	+	116682.i	0.432664	+	0.433180i
$520$	323903.			1.19787
$521$			371391.i			1.36822i	0.729379	+	0.684110i	$0.239809\pi$
$521$			371391.i			1.36822i	−0.729379	+	0.684110i	$0.760191\pi$
$522$	47.5954	−	39927.0i	0.000174672	−	0.146530i
$523$	−357941.			−1.30860			−0.654302	−	0.756234i	$-0.727037\pi$
$523$	−357941.			−1.30860			−0.654302	+	0.756234i	$0.727037\pi$
$524$			217203.i			0.791048i
$525$	−180940.	+	180725.i	−0.656472	+	0.655690i
$526$	71684.1			0.259090
$527$			37513.3i			0.135072i
$528$	−25329.1	−	25359.3i	−0.0908557	−	0.0909640i
$529$	−575495.			−2.05651
$530$		−	45820.9i		−	0.163122i
$531$	36708.2	+	43.7583i	0.130189	+	0.000155193i
$532$	18199.6			0.0643040
$533$		−	166863.i		−	0.587363i
$534$	−69831.4	+	69748.2i	−0.244888	+	0.244597i
$535$	153948.			0.537857
$536$			63590.8i			0.221343i
$537$	−191400.	−	191628.i	−0.663731	−	0.664523i
$538$	332529.			1.14886
$539$		−	172100.i		−	0.592385i
$540$	−185474.	+	184811.i	−0.636055	+	0.633784i
$541$	10655.7			0.0364071			0.0182036	−	0.999834i	$-0.494205\pi$
$541$	10655.7			0.0364071			0.0182036	+	0.999834i	$0.494205\pi$
$542$		−	201829.i		−	0.687046i
$543$	179273.	−	179059.i	0.608015	−	0.607290i
$544$	47735.0			0.161302
$545$		−	4420.60i		−	0.0148829i
$546$	54934.3	+	54999.9i	0.184272	+	0.184491i
$547$	−55656.0			−0.186011			−0.0930053	−	0.995666i	$-0.529647\pi$
$547$	−55656.0			−0.186011			−0.0930053	+	0.995666i	$0.529647\pi$
$548$		−	213501.i		−	0.710951i
$549$	292.821	−	245643.i	0.000971534	−	0.815004i
$550$	291135.			0.962431
$551$		−	14065.1i		−	0.0463275i
$552$	392194.	−	391727.i	1.28713	−	1.28560i
$553$	15831.8			0.0517703
$554$		−	365290.i		−	1.19019i
$555$	10858.4	+	10871.3i	0.0352516	+	0.0352936i
$556$	−121901.			−0.394328
$557$			83749.7i			0.269943i	0.990849	+	0.134972i	$0.0430944\pi$
$557$			83749.7i			0.269943i	−0.990849	+	0.134972i	$0.956906\pi$
$558$	−164555.	−	196.160i	−0.528498	−	0.000630001i
$559$	268289.			0.858577
$560$			42772.0i			0.136390i
$561$	32579.7	−	32540.9i	0.103519	−	0.103396i
$562$	187637.			0.594080
$563$		−	97847.0i		−	0.308696i	−0.988017	−	0.154348i	$-0.950672\pi$
$563$		−	97847.0i		−	0.308696i	0.988017	−	0.154348i	$-0.0493277\pi$
$564$	236502.	+	236784.i	0.743492	+	0.744379i
$565$	−376639.			−1.17985
$566$		−	114205.i		−	0.356494i
$567$	−177429.	−	423.013i	−0.551898	−	0.00131579i
$568$	−419144.			−1.29917
$569$			241508.i			0.745944i	0.927843	+	0.372972i	$0.121661\pi$
$569$			241508.i			0.745944i	−0.927843	+	0.372972i	$0.878339\pi$
$570$	53747.0	−	53682.9i	0.165426	−	0.165229i
$571$	624773.			1.91624			0.958120	−	0.286366i	$-0.0924473\pi$
$571$	624773.			1.91624			0.958120	+	0.286366i	$0.0924473\pi$
$572$			107451.i			0.328410i
$573$	−239606.	−	239892.i	−0.729774	−	0.730644i
$574$	102095.			0.309870
$575$			971763.i			2.93917i
$576$	−309.300	+	259467.i	−0.000932256	+	0.782055i
$577$	−217020.			−0.651852			−0.325926	−	0.945395i	$-0.605676\pi$
$577$	−217020.			−0.651852			−0.325926	+	0.945395i	$0.605676\pi$
$578$			217893.i			0.652211i
$579$	−154982.	+	154797.i	−0.462300	+	0.461750i
$580$	−65860.3			−0.195780
$581$			330736.i			0.979782i
$582$	−276632.	−	276962.i	−0.816689	−	0.817663i
$583$	42919.9			0.126276
$584$			389371.i			1.14166i
$585$	−393961.	−	469.626i	−1.15118	−	0.00137227i
$586$	−416429.			−1.21268
$587$		−	593750.i		−	1.72317i	−0.507615	−	0.861584i	$-0.669473\pi$
$587$		−	593750.i		−	1.72317i	0.507615	−	0.861584i	$-0.330527\pi$
$588$	−93284.4	+	93173.3i	−0.269808	+	0.269486i
$589$	−57967.9			−0.167092
$590$			49869.2i			0.143261i
$591$	217515.	+	217775.i	0.622751	+	0.623494i
$592$	1611.37			0.00459781
$593$			352380.i			1.00208i	0.865425	+	0.501039i	$0.167049\pi$
$593$			352380.i			1.00208i	−0.865425	+	0.501039i	$0.832951\pi$
$594$	142573.	+	143084.i	0.404077	+	0.405525i
$595$	−54950.2			−0.155216
$596$			267707.i			0.753644i
$597$	177393.	−	177181.i	0.497722	−	0.497129i
$598$	295384.			0.826009
$599$		−	457318.i		−	1.27457i	−0.770627	−	0.637286i	$-0.780057\pi$
$599$		−	457318.i		−	1.27457i	0.770627	−	0.637286i	$-0.219943\pi$
$600$	−445048.	−	445579.i	−1.23625	−	1.23772i
$601$	169949.			0.470511			0.235255	−	0.971934i	$-0.424407\pi$
$601$	169949.			0.470511			0.235255	+	0.971934i	$0.424407\pi$
$602$			164152.i			0.452952i
$603$	92.2000	−	77345.1i	0.000253569	−	0.212715i
$604$	329641.			0.903581
$605$		−	164426.i		−	0.449221i
$606$	−46936.5	+	46880.6i	−0.127810	+	0.127658i
$607$	−77491.0			−0.210317			−0.105158	−	0.994455i	$-0.533535\pi$
$607$	−77491.0			−0.210317			−0.105158	+	0.994455i	$0.533535\pi$
$608$			73763.1i			0.199541i
$609$	−31539.5	−	31577.1i	−0.0850393	−	0.0851407i
$610$	333714.			0.896840
$611$			503548.i			1.34883i
$612$	−35276.7	−	42.0519i	−0.0941856	−	0.000112275i
$613$	−523471.			−1.39307			−0.696533	−	0.717525i	$-0.745275\pi$
$613$	−523471.			−1.39307			−0.696533	+	0.717525i	$0.745275\pi$
$614$		−	229651.i		−	0.609159i
$615$	−366086.	+	365650.i	−0.967906	+	0.966752i
$616$	−185632.			−0.489206
$617$		−	518426.i		−	1.36181i	−0.732372	−	0.680905i	$-0.761587\pi$
$617$		−	518426.i		−	1.36181i	0.732372	−	0.680905i	$-0.238413\pi$
$618$	−125219.	−	125368.i	−0.327864	−	0.328255i
$619$	699994.			1.82689			0.913447	−	0.406958i	$-0.133411\pi$
$619$	699994.			1.82689			0.913447	+	0.406958i	$0.133411\pi$
$620$			271437.i			0.706131i
$621$	−477591.	+	475886.i	−1.23843	+	1.23401i
$622$	−20723.2			−0.0535645
$623$			110324.i			0.284245i
$624$	−29231.7	+	29196.9i	−0.0750731	+	0.0749837i
$625$	56706.1			0.145168
$626$			239227.i			0.610465i
$627$	50284.2	+	50344.2i	0.127908	+	0.128060i
$628$	114469.			0.290247
$629$			2070.16i			0.00523243i
$630$	287.339	−	241044.i	0.000723957	−	0.607316i
$631$	178942.			0.449422			0.224711	−	0.974425i	$-0.427856\pi$
$631$	178942.			0.449422			0.224711	+	0.974425i	$0.427856\pi$
$632$			38987.1i			0.0976083i
$633$	−560905.	+	560237.i	−1.39985	+	1.39818i
$634$	−145615.			−0.362265
$635$		−	961593.i		−	2.38476i
$636$	−23236.4	−	23264.1i	−0.0574453	−	0.0575138i
$637$	−198380.			−0.488898
$638$			50808.0i			0.124822i
$639$	509801.	+	607.714i	1.24853	+	0.00148832i
$640$	277373.			0.677179
$641$		−	57985.0i		−	0.141124i	−0.997507	−	0.0705618i	$-0.977521\pi$
$641$		−	57985.0i		−	0.141124i	0.997507	−	0.0705618i	$-0.0224792\pi$
$642$	−64374.0	+	64297.3i	−0.156185	+	0.155999i
$643$	−358015.			−0.865922			−0.432961	−	0.901413i	$-0.642531\pi$
$643$	−358015.			−0.865922			−0.432961	+	0.901413i	$0.642531\pi$
$644$		−	219440.i		−	0.529109i
$645$	−587905.	−	588606.i	−1.41315	−	1.41483i
$646$	10234.7			0.0245251
$647$			779724.i			1.86265i	0.364183	+	0.931327i	$0.381348\pi$
$647$			779724.i			1.86265i	−0.364183	+	0.931327i	$0.618652\pi$
$648$	1041.70	−	436934.i	0.00248081	−	1.04056i
$649$	−46712.0			−0.110902
$650$		−	335592.i		−	0.794300i
$651$	−130142.	+	129987.i	−0.307083	+	0.306717i
$652$	389823.			0.917007
$653$			479973.i			1.12562i	0.826588	+	0.562808i	$0.190279\pi$
$653$			479973.i			1.12562i	−0.826588	+	0.562808i	$0.809721\pi$
$654$	1846.29	+	1848.49i	0.00431663	+	0.00432178i
$655$	1.01339e6			2.36207
$656$			54262.0i			0.126092i
$657$	564.547	−	473589.i	0.00130788	−	1.09716i
$658$	−308094.			−0.711592
$659$		−	22445.0i		−	0.0516832i	−0.999666	−	0.0258416i	$-0.991773\pi$
$659$		−	22445.0i		−	0.0516832i	0.999666	−	0.0258416i	$-0.00822656\pi$
$660$	235739.	−	235458.i	0.541182	−	0.540537i
$661$	−415383.			−0.950705			−0.475352	−	0.879795i	$-0.657679\pi$
$661$	−415383.			−0.950705			−0.475352	+	0.879795i	$0.657679\pi$
$662$			342301.i			0.781073i
$663$	−37509.9	−	37554.6i	−0.0853333	−	0.0854351i
$664$	−814464.			−1.84729
$665$		−	84912.5i		−	0.192012i
$666$	−9080.94	−	10.8250i	−0.0204730	−	2.44051e-5i
$667$	−169589.			−0.381194
$668$		−	133088.i		−	0.298255i
$669$	−37619.1	+	37574.3i	−0.0840535	+	0.0839534i
$670$	105076.			0.234074
$671$			312587.i			0.694265i
$672$	165406.	+	165603.i	0.366280	+	0.366717i
$673$	−481165.			−1.06234			−0.531170	−	0.847265i	$-0.678247\pi$
$673$	−481165.			−1.06234			−0.531170	+	0.847265i	$0.678247\pi$
$674$			96652.8i			0.212762i
$675$	540663.	+	542600.i	1.18664	+	1.19089i
$676$	−126733.			−0.277329
$677$		−	327961.i		−	0.715559i	−0.933806	−	0.357780i	$-0.883534\pi$
$677$		−	327961.i		−	0.715559i	0.933806	−	0.357780i	$-0.116466\pi$
$678$	157493.	−	157305.i	0.342612	−	0.342203i
$679$	−437561.			−0.949071
$680$		−	135319.i		−	0.292646i
$681$	−77482.7	−	77575.1i	−0.167075	−	0.167274i
$682$	209400.			0.450203
$683$		−	692561.i		−	1.48462i	−0.670055	−	0.742312i	$-0.733729\pi$
$683$		−	692561.i		−	1.48462i	0.670055	−	0.742312i	$-0.266271\pi$
$684$	64.9812	−	54511.7i	0.000138891	−	0.116514i
$685$	−996119.			−2.12290
$686$		−	295920.i		−	0.628820i
$687$	−182771.	+	182553.i	−0.387253	+	0.386791i
$688$	−87244.3			−0.184315
$689$		−	49473.8i		−	0.104217i
$690$	−647279.	−	648051.i	−1.35954	−	1.36117i
$691$	−40721.0			−0.0852830			−0.0426415	−	0.999090i	$-0.513577\pi$
$691$	−40721.0			−0.0852830			−0.0426415	+	0.999090i	$0.513577\pi$
$692$			160772.i			0.335735i
$693$	225783.	+	269.147i	0.470138	+	0.000560432i
$694$	518681.			1.07692
$695$			568746.i			1.17747i
$696$	77761.0	−	77668.4i	0.160525	−	0.160334i
$697$	−69711.7			−0.143496
$698$		−	22508.5i		−	0.0461994i
$699$	321295.	+	321678.i	0.657582	+	0.658366i
$700$	−249310.			−0.508797
$701$			149272.i			0.303768i	0.988398	+	0.151884i	$0.0485341\pi$
$701$			149272.i			0.303768i	−0.988398	+	0.151884i	$0.951466\pi$
$702$	164933.	−	164344.i	0.334682	−	0.333487i
$703$	−3198.94			−0.00647286
$704$		−	330178.i		−	0.666197i
$705$	1.10475e6	−	1.10343e6i	2.22272	−	2.22007i
$706$	243319.			0.488165
$707$			74153.0i			0.148351i
$708$	25289.4	+	25319.6i	0.0504513	+	0.0505114i
$709$	480678.			0.956230			0.478115	−	0.878297i	$-0.341320\pi$
$709$	480678.			0.956230			0.478115	+	0.878297i	$0.341320\pi$
$710$			692582.i			1.37390i
$711$	56.5271	−	47419.7i	0.000111820	−	0.0938036i
$712$	−271681.			−0.535918
$713$			698945.i			1.37488i
$714$	22977.7	−	22950.3i	0.0450723	−	0.0450186i
$715$	501325.			0.980634
$716$		−	264037.i		−	0.515037i
$717$	715300.	+	716153.i	1.39139	+	1.39305i
$718$	−89671.9			−0.173943
$719$			185672.i			0.359161i	0.983743	+	0.179581i	$0.0574741\pi$
$719$			185672.i			0.359161i	−0.983743	+	0.179581i	$0.942526\pi$
$720$	128111.	+	152.717i	0.247129	+	0.000294592i
$721$	−198064.			−0.381009
$722$		−	334506.i		−	0.641697i
$723$	−294442.	+	294091.i	−0.563278	+	0.562607i
$724$	247013.			0.471240
$725$			192673.i			0.366560i
$726$	68673.5	+	68755.4i	0.130291	+	0.130447i
$727$	−624321.			−1.18124			−0.590621	−	0.806949i	$-0.701117\pi$
$727$	−624321.			−1.18124			−0.590621	+	0.806949i	$0.701117\pi$
$728$			213978.i			0.403745i
$729$	−1900.52	+	531438.i	−0.00357617	+	0.999994i
$730$	643387.			1.20733
$731$		−	112085.i		−	0.209755i
$732$	169433.	−	169231.i	0.316210	−	0.315834i
$733$	−625420.			−1.16403			−0.582014	−	0.813178i	$-0.697735\pi$
$733$	−625420.			−1.16403			−0.582014	+	0.813178i	$0.697735\pi$
$734$		−	466104.i		−	0.865149i
$735$	434712.	+	435231.i	0.804687	+	0.805647i
$736$	889395.			1.64187
$737$			98423.4i			0.181202i
$738$	364.527	−	305796.i	0.000669294	−	0.561460i
$739$	203495.			0.372619			0.186310	−	0.982491i	$-0.440347\pi$
$739$	203495.			0.372619			0.186310	+	0.982491i	$0.440347\pi$
$740$			14979.2i			0.0273542i
$741$	58031.8	−	57962.6i	0.105689	−	0.105563i
$742$	30270.3			0.0549806
$743$		−	406447.i		−	0.736251i	−0.929776	−	0.368125i	$-0.880000\pi$
$743$		−	406447.i		−	0.736251i	0.929776	−	0.368125i	$-0.120000\pi$
$744$	−320103.	−	320485.i	−0.578287	−	0.578977i
$745$	1.24902e6			2.25039
$746$			569904.i			1.02406i
$747$	990627.	+	1180.89i	1.77529	+	0.00211625i
$748$	44890.4			0.0802324
$749$			101702.i			0.181286i
$750$	−298317.	+	297962.i	−0.530341	+	0.529709i
$751$	305223.			0.541175			0.270587	−	0.962695i	$-0.412782\pi$
$751$	305223.			0.541175			0.270587	+	0.962695i	$0.412782\pi$
$752$		−	163748.i		−	0.289561i
$753$	481641.	+	482215.i	0.849441	+	0.850454i
$754$	58566.4			0.103016
$755$		−	1.53798e6i		−	2.69810i
$756$	−122091.	−	122528.i	−0.213619	−	0.214384i
$757$	316129.			0.551662			0.275831	−	0.961206i	$-0.411047\pi$
$757$	316129.			0.551662			0.275831	+	0.961206i	$0.411047\pi$
$758$			343579.i			0.597982i
$759$	607023.	−	606299.i	1.05371	−	1.05246i
$760$	209104.			0.362022
$761$		−	539926.i		−	0.932319i	−0.884701	−	0.466160i	$-0.845637\pi$
$761$		−	539926.i		−	0.932319i	0.884701	−	0.466160i	$-0.154363\pi$
$762$	401615.	+	402094.i	0.691672	+	0.692497i
$763$	2920.35			0.00501633
$764$		−	330538.i		−	0.566284i
$765$	−196.199	+	164588.i	−0.000335253	+	0.281239i
$766$	162146.			0.276343
$767$			53844.9i			0.0915280i
$768$	−442349.	+	441822.i	−0.749969	+	0.749075i
$769$	175981.			0.297586			0.148793	−	0.988868i	$-0.452461\pi$
$769$	175981.			0.297586			0.148793	+	0.988868i	$0.452461\pi$
$770$			306734.i			0.517345i
$771$	−9681.73	−	9693.28i	−0.0162871	−	0.0163065i
$772$	−213544.			−0.358305
$773$		−	64980.9i		−	0.108749i	−0.998521	−	0.0543747i	$-0.982683\pi$
$773$		−	64980.9i		−	0.108749i	0.998521	−	0.0543747i	$-0.0173165\pi$
$774$	491670.	+	586.100i	0.820713	+	0.000978340i
$775$	794084.			1.32210
$776$		−	1.07753e6i		−	1.78939i
$777$	−7181.85	+	7173.29i	−0.0118958	+	0.0118816i
$778$	579962.			0.958165
$779$		−	107723.i		−	0.177514i
$780$	−271412.	−	271736.i	−0.446108	−	0.446640i
$781$	−648734.			−1.06357
$782$		−	123405.i		−	0.201799i
$783$	−94692.8	+	94354.8i	−0.154452	+	0.153901i
$784$	64510.7			0.104954
$785$		−	534070.i		−	0.866680i
$786$	−423753.	+	423248.i	−0.685910	+	0.685093i
$787$	87675.0			0.141555			0.0707777	−	0.997492i	$-0.477452\pi$
$787$	87675.0			0.141555			0.0707777	+	0.997492i	$0.477452\pi$
$788$			300063.i			0.483237i
$789$	−169605.	−	169807.i	−0.272449	−	0.272774i
$790$	64421.2			0.103223
$791$		−	248817.i		−	0.397673i
$792$	−662.796	+	556009.i	−0.00105665	+	0.886403i
$793$	360318.			0.572981
$794$		−	723599.i		−	1.14777i
$795$	−108542.	+	108412.i	−0.171737	+	0.171532i
$796$	244423.			0.385758
$797$			1.12602e6i			1.77268i	0.463036	+	0.886339i	$0.346760\pi$
$797$			1.12602e6i			1.77268i	−0.463036	+	0.886339i	$0.653240\pi$
$798$	35464.2	+	35506.5i	0.0556909	+	0.0557574i
$799$	210371.			0.329527
$800$		−	1.01046e6i		−	1.57884i
$801$	330443.	+	393.908i	0.515029	+	0.000613946i
$802$	214815.			0.333977
$803$			602653.i			0.934623i
$804$	53349.0	−	53285.4i	0.0825304	−	0.0824321i
$805$	−1.02383e6			−1.57992
$806$		−	241376.i		−	0.371555i
$807$	−786767.	−	787705.i	−1.20809	−	1.20953i
$808$	−182608.			−0.279702
$809$		−	224415.i		−	0.342890i	−0.985194	−	0.171445i	$-0.945156\pi$
$809$		−	224415.i		−	0.342890i	0.985194	−	0.171445i	$-0.0548435\pi$
$810$	−721977.	−	1721.28i	−1.10041	−	0.00262351i
$811$	−1.22110e6			−1.85657			−0.928283	−	0.371875i	$-0.878715\pi$
$811$	−1.22110e6			−1.85657			−0.928283	+	0.371875i	$0.878715\pi$
$812$		−	43508.8i		−	0.0659881i
$813$	−478099.	+	477530.i	−0.723331	+	0.722469i
$814$	11555.7			0.0174401
$815$		−	1.81877e6i		−	2.73819i
$816$	12197.8	+	12212.3i	0.0183189	+	0.0183408i
$817$	173201.			0.259481
$818$			152440.i			0.227820i
$819$	310.246	−	260260.i	0.000462528	−	0.388007i
$820$	−504416.			−0.750173
$821$		−	484305.i		−	0.718510i	−0.933239	−	0.359255i	$-0.883031\pi$
$821$		−	484305.i		−	0.718510i	0.933239	−	0.359255i	$-0.116969\pi$
$822$	416531.	−	416035.i	0.616458	−	0.615724i
$823$	−435559.			−0.643053			−0.321527	−	0.946901i	$-0.604196\pi$
$823$	−435559.			−0.643053			−0.321527	+	0.946901i	$0.604196\pi$
$824$		−	487749.i		−	0.718359i
$825$	−688828.	−	689650.i	−1.01205	−	1.01326i
$826$	−32944.8			−0.0482866
$827$		−	1.28768e6i		−	1.88276i	−0.337346	−	0.941381i	$-0.609529\pi$
$827$		−	1.28768e6i		−	1.88276i	0.337346	−	0.941381i	$-0.390471\pi$
$828$	−657272.	−	783.507i	−0.958703	−	0.00114283i
$829$	250804.			0.364943			0.182471	−	0.983211i	$-0.441590\pi$
$829$	250804.			0.364943			0.182471	+	0.983211i	$0.441590\pi$
$830$			1.34580e6i			1.95355i
$831$	−865309.	+	864278.i	−1.25305	+	1.25156i
$832$	−380596.			−0.549816
$833$			82878.5i			0.119441i
$834$	−237540.	−	237823.i	−0.341511	−	0.341918i
$835$	−620941.			−0.890589
$836$			69367.4i			0.0992528i
$837$	388874.	+	390267.i	0.555083	+	0.557072i
$838$	714629.			1.01764
$839$			402394.i			0.571646i	0.958282	+	0.285823i	$0.0922669\pi$
$839$			402394.i			0.571646i	−0.958282	+	0.285823i	$0.907733\pi$
$840$	469452.	−	468893.i	0.665324	−	0.664531i
$841$	673656.			0.952459
$842$		−	416177.i		−	0.587022i
$843$	−443950.	−	444479.i	−0.624710	−	0.625455i
$844$	−772850.			−1.08495
$845$			591288.i			0.828105i
$846$	−1100.04	+	922808.i	−0.00153698	+	1.28935i
$847$	108624.			0.151411
$848$			16088.3i			0.0223727i
$849$	−270532.	+	270210.i	−0.375322	+	0.374875i
$850$	−140202.			−0.194052
$851$			38571.1i			0.0532602i
$852$	351218.	+	351637.i	0.483835	+	0.484412i
$853$	−882553.			−1.21295			−0.606475	−	0.795103i	$-0.707417\pi$
$853$	−882553.			−1.21295			−0.606475	+	0.795103i	$0.707417\pi$
$854$			220460.i			0.302283i
$855$	−254331.	−	303.178i	−0.347911	−	0.000414731i
$856$	−250448.			−0.341799
$857$			1.10133e6i			1.49954i	0.661701	+	0.749768i	$0.269835\pi$
$857$			1.10133e6i			1.49954i	−0.661701	+	0.749768i	$0.730165\pi$
$858$	−209631.	+	209381.i	−0.284761	+	0.284422i
$859$	−190437.			−0.258086			−0.129043	−	0.991639i	$-0.541191\pi$
$859$	−190437.			−0.258086			−0.129043	+	0.991639i	$0.541191\pi$
$860$		−	811018.i		−	1.09656i
$861$	−241557.	−	241845.i	−0.325847	−	0.326235i
$862$	−197454.			−0.265736
$863$			1.26740e6i			1.70173i	0.525383	+	0.850866i	$0.323922\pi$
$863$			1.26740e6i			1.70173i	−0.525383	+	0.850866i	$0.676078\pi$
$864$	496609.	−	494836.i	0.665253	−	0.662878i
$865$	750101.			1.00251
$866$			534207.i			0.712318i
$867$	516152.	−	515537.i	0.686656	−	0.685838i
$868$	−179318.			−0.238004
$869$			60342.7i			0.0799070i
$870$	−128337.	−	128490.i	−0.169556	−	0.169759i
$871$	113453.			0.149547
$872$			7191.60i			0.00945786i
$873$	−1562.30	+	1.31059e6i	−0.00204992	+	1.71964i
$874$	190693.			0.249638
$875$			471298.i			0.615573i
$876$	326660.	−	326270.i	0.425684	−	0.425177i
$877$	219156.			0.284940			0.142470	−	0.989799i	$-0.454496\pi$
$877$	219156.			0.284940			0.142470	+	0.989799i	$0.454496\pi$
$878$			284986.i			0.369687i
$879$	985274.	+	986449.i	1.27520	+	1.27672i
$880$	−163025.			−0.210518
$881$		−	158303.i		−	0.203956i	−0.994787	−	0.101978i	$-0.967483\pi$
$881$		−	158303.i		−	0.203956i	0.994787	−	0.101978i	$-0.0325172\pi$
$882$	−363553.	−	433.377i	−0.467338	−	0.000557095i
$883$	523888.			0.671920			0.335960	−	0.941876i	$-0.390939\pi$
$883$	523888.			0.671920			0.335960	+	0.941876i	$0.390939\pi$
$884$		−	51745.1i		−	0.0662163i
$885$	118132.	−	117991.i	0.150827	−	0.150648i
$886$	−576533.			−0.734440
$887$		−	342381.i		−	0.435173i	−0.976041	−	0.217587i	$-0.930182\pi$
$887$		−	342381.i		−	0.435173i	0.976041	−	0.217587i	$-0.0698185\pi$
$888$	−17664.8	−	17685.9i	−0.0224018	−	0.0224285i
$889$	635251.			0.803789
$890$			448918.i			0.566744i
$891$	1612.31	−	676269.i	0.00203092	−	0.851851i
$892$	−51833.9			−0.0651455
$893$			325078.i			0.407647i
$894$	−522283.	+	521661.i	−0.653478	+	0.652699i
$895$	−1.23190e6			−1.53790
$896$			183239.i			0.228245i
$897$	−698881.	−	699715.i	−0.868597	−	0.869633i
$898$	218222.			0.270611
$899$			138581.i			0.171468i
$900$	−890.158	+	746739.i	−0.00109896	+	0.921900i
$901$	−20669.0			−0.0254607
$902$			389132.i			0.478282i
$903$	388847.	−	388384.i	0.476874	−	0.476306i
$904$	612730.			0.749778
$905$		−	1.15247e6i		−	1.40713i
$906$	642347.	+	643114.i	0.782553	+	0.783486i
$907$	−1.04119e6			−1.26566			−0.632831	−	0.774290i	$-0.718107\pi$
$907$	−1.04119e6			−1.26566			−0.632831	+	0.774290i	$0.718107\pi$
$908$		−	106888.i		−	0.129645i
$909$	222104.	+	264.762i	0.268800	+	0.000320426i
$910$	353572.			0.426968
$911$		−	1.00350e6i		−	1.20915i	−0.796547	−	0.604577i	$-0.793342\pi$
$911$		−	1.00350e6i		−	1.20915i	0.796547	−	0.604577i	$-0.206658\pi$
$912$	−18871.2	+	18848.7i	−0.0226887	+	0.0226617i
$913$	−1.26060e6			−1.51229
$914$		−	505736.i		−	0.605385i
$915$	−789570.	−	790512.i	−0.943080	−	0.944205i
$916$	−251833.			−0.300139
$917$			669468.i			0.796144i
$918$	−68659.1	−	68905.0i	−0.0814728	−	0.0817647i
$919$	806292.			0.954688			0.477344	−	0.878717i	$-0.341600\pi$
$919$	806292.			0.954688			0.477344	+	0.878717i	$0.341600\pi$
$920$		−	2.52126e6i		−	2.97880i
$921$	−544003.	+	543355.i	−0.641331	+	0.640567i
$922$	839234.			0.987237
$923$			747796.i			0.877767i
$924$	155549.	+	155735.i	0.182189	+	0.182407i
$925$	43821.4			0.0512156
$926$		−	790837.i		−	0.922284i
$927$	−707.184	+	593245.i	−0.000822949	+	0.690359i
$928$	176342.			0.204767
$929$		−	119797.i		−	0.138808i	−0.997589	−	0.0694040i	$-0.977890\pi$
$929$		−	119797.i		−	0.138808i	0.997589	−	0.0694040i	$-0.0221097\pi$
$930$	−529560.	+	528929.i	−0.612279	+	0.611550i
$931$	−128069.			−0.147756
$932$			443228.i			0.510265i
$933$	49031.3	+	49089.8i	0.0563262	+	0.0563934i
$934$	553447.			0.634428
$935$		−	209442.i		−	0.239574i
$936$	640911.	+	764.005i	0.731553	+	0.000872056i
$937$	252847.			0.287991			0.143996	−	0.989578i	$-0.454005\pi$
$937$	252847.			0.287991			0.143996	+	0.989578i	$0.454005\pi$
$938$			69415.6i			0.0788953i
$939$	566687.	−	566012.i	0.642706	−	0.641940i
$940$	1.52219e6			1.72271
$941$			354100.i			0.399896i	0.979807	+	0.199948i	$0.0640773\pi$
$941$			354100.i			0.399896i	−0.979807	+	0.199948i	$0.935923\pi$
$942$	223057.	+	223324.i	0.251371	+	0.251671i
$943$	−1.29886e6			−1.46063
$944$		−	17509.7i		−	0.0196488i
$945$	−571671.	+	569631.i	−0.640152	+	0.637866i
$946$	−625661.			−0.699128
$947$		−	230565.i		−	0.257095i	−0.991703	−	0.128547i	$-0.958969\pi$
$947$		−	230565.i		−	0.257095i	0.991703	−	0.128547i	$-0.0410314\pi$
$948$	32707.9	−	32668.9i	0.0363945	−	0.0363511i
$949$	694678.			0.771350
$950$		−	216649.i		−	0.240055i
$951$	344525.	+	344936.i	0.380943	+	0.381397i
$952$	89395.1			0.0986370
$953$			1.56135e6i			1.71915i	0.511008	+	0.859576i	$0.329272\pi$
$953$			1.56135e6i			1.71915i	−0.511008	+	0.859576i	$0.670728\pi$
$954$	108.080	−	90666.2i	0.000118754	−	0.0996205i
$955$	−1.54217e6			−1.69093
$956$			986760.i			1.07968i
$957$	120355.	−	120212.i	0.131414	−	0.131258i
$958$	437650.			0.476865
$959$		−	658059.i		−	0.715530i
$960$	834004.	+	834999.i	0.904952	+	0.906032i
$961$	−352373.			−0.381553
$962$		−	13320.3i		−	0.0143934i
$963$	304619.	+	363.124i	0.328476	+	0.000391563i
$964$	−405700.			−0.436567
$965$			996317.i			1.06990i
$966$	428118.	−	427608.i	0.458785	−	0.458238i
$967$	−855705.			−0.915105			−0.457553	−	0.889183i	$-0.651274\pi$
$967$	−855705.			−0.915105			−0.457553	+	0.889183i	$0.651274\pi$
$968$			267494.i			0.285472i
$969$	−24215.4	−	24244.3i	−0.0257896	−	0.0258204i
$970$	−1.78048e6			−1.89231
$971$			1.66911e6i			1.77030i	0.465306	+	0.885150i	$0.345944\pi$
$971$			1.66911e6i			1.77030i	−0.465306	+	0.885150i	$0.654056\pi$
$972$	−367434.	+	365251.i	−0.388908	+	0.386597i
$973$	−375727.			−0.396868
$974$			664596.i			0.700552i
$975$	−794959.	+	794012.i	−0.836249	+	0.835253i
$976$	−117171.			−0.123005
$977$			1.31255e6i			1.37508i	0.726147	+	0.687540i	$0.241309\pi$
$977$			1.31255e6i			1.37508i	−0.726147	+	0.687540i	$0.758691\pi$
$978$	759621.	+	760527.i	0.794180	+	0.795127i
$979$	−420496.			−0.438730
$980$			599688.i			0.624415i
$981$	10.4271	−	8747.10i	1.08349e−5	−	0.00908920i
$982$	771866.			0.800422
$983$		−	1.68444e6i		−	1.74321i	−0.490210	−	0.871605i	$-0.663080\pi$
$983$		−	1.68444e6i		−	1.74321i	0.490210	−	0.871605i	$-0.336920\pi$
$984$	595563.	−	594853.i	0.615088	−	0.614355i
$985$	1.39999e6			1.44295
$986$		−	24467.7i		−	0.0251674i
$987$	728952.	+	729822.i	0.748281	+	0.749174i
$988$	79959.7			0.0819139
$989$		−	2.08836e6i		−	2.13507i
$990$	918734.	+	1095.19i	0.937388	+	0.00111742i
$991$	−76820.4			−0.0782220			−0.0391110	−	0.999235i	$-0.512453\pi$
$991$	−76820.4			−0.0782220			−0.0391110	+	0.999235i	$0.512453\pi$
$992$		−	726777.i		−	0.738546i
$993$	810852.	−	809886.i	0.822324	−	0.821345i
$994$	−457536.			−0.463076
$995$		−	1.14039e6i		−	1.15188i
$996$	682474.	+	683288.i	0.687966	+	0.688787i
$997$	−549557.			−0.552870			−0.276435	−	0.961033i	$-0.589153\pi$
$997$	−549557.			−0.552870			−0.276435	+	0.961033i	$0.589153\pi$
$998$			161589.i			0.162238i
$999$	21459.9	+	21536.8i	0.0215029	+	0.0215800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.51	yes	78
3.2	odd	2	inner	177.5.b.a.119.28	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.28	✓	78	3.2	odd	2	inner
177.5.b.a.119.51	yes	78	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.68814i q^{2} +(6.36775 - 6.36017i) q^{3} +8.77388 q^{4} -40.9357i q^{5} +(17.0970 + 17.1174i) q^{6} +27.0431 q^{7} +66.5958i q^{8} +(0.0965568 - 80.9999i) q^{9} +O(q^{10})\)	\(q+2.68814i q^{2} +(6.36775 - 6.36017i) q^{3} +8.77388 q^{4} -40.9357i q^{5} +(17.0970 + 17.1174i) q^{6} +27.0431 q^{7} +66.5958i q^{8} +(0.0965568 - 80.9999i) q^{9} +110.041 q^{10} +103.074i q^{11} +(55.8699 - 55.8034i) q^{12} +118.814 q^{13} +72.6957i q^{14} +(-260.358 - 260.669i) q^{15} -38.6368 q^{16} -49.6376i q^{17} +(217.739 + 0.259559i) q^{18} +76.7031 q^{19} -359.165i q^{20} +(172.204 - 171.999i) q^{21} -277.078 q^{22} -924.844i q^{23} +(423.560 + 424.065i) q^{24} -1050.73 q^{25} +319.388i q^{26} +(-514.558 - 516.402i) q^{27} +237.273 q^{28} -183.370i q^{29} +(700.714 - 699.880i) q^{30} -755.744 q^{31} +961.671i q^{32} +(655.570 + 656.352i) q^{33} +133.433 q^{34} -1107.03i q^{35} +(0.847178 - 710.684i) q^{36} -41.7055 q^{37} +206.189i q^{38} +(756.576 - 755.675i) q^{39} +2726.14 q^{40} -1404.41i q^{41} +(462.357 + 462.908i) q^{42} +2258.06 q^{43} +904.362i q^{44} +(-3315.79 - 3.95262i) q^{45} +2486.11 q^{46} +4238.13i q^{47} +(-246.030 + 245.736i) q^{48} -1669.67 q^{49} -2824.52i q^{50} +(-315.703 - 316.080i) q^{51} +1042.46 q^{52} -416.398i q^{53} +(1388.16 - 1383.21i) q^{54} +4219.42 q^{55} +1800.96i q^{56} +(488.426 - 487.845i) q^{57} +492.926 q^{58} +453.188i q^{59} +(-2284.35 - 2287.08i) q^{60} +3032.63 q^{61} -2031.55i q^{62} +(2.61119 - 2190.49i) q^{63} -3203.30 q^{64} -4863.72i q^{65} +(-1764.37 + 1762.27i) q^{66} +954.878 q^{67} -435.515i q^{68} +(-5882.16 - 5889.18i) q^{69} +2975.85 q^{70} +6293.85i q^{71} +(5394.25 + 6.43027i) q^{72} +5846.79 q^{73} -112.110i q^{74} +(-6690.81 + 6682.83i) q^{75} +672.984 q^{76} +2787.45i q^{77} +(2031.36 + 2033.79i) q^{78} +585.429 q^{79} +1581.62i q^{80} +(-6560.98 - 15.6422i) q^{81} +3775.26 q^{82} +12230.0i q^{83} +(1510.90 - 1509.10i) q^{84} -2031.95 q^{85} +6070.00i q^{86} +(-1166.27 - 1167.66i) q^{87} -6864.31 q^{88} +4079.55i q^{89} +(10.6252 - 8913.32i) q^{90} +3213.09 q^{91} -8114.47i q^{92} +(-4812.39 + 4806.66i) q^{93} -11392.7 q^{94} -3139.90i q^{95} +(6116.39 + 6123.68i) q^{96} -16180.1 q^{97} -4488.32i q^{98} +(8349.01 + 9.95252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more