LMFDB - Embedded newform 177.5.b.a.119.24

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			119.24
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.56380i q^{2} +(-1.54671 - 8.86610i) q^{3} +3.29930 q^{4} +32.9935i q^{5} +(-31.5970 + 5.51219i) q^{6} -48.4204 q^{7} -68.7789i q^{8} +(-76.2153 + 27.4266i) q^{9} +O(q^{10})$	\(q-3.56380i q^{2} +(-1.54671 - 8.86610i) q^{3} +3.29930 q^{4} +32.9935i q^{5} +(-31.5970 + 5.51219i) q^{6} -48.4204 q^{7} -68.7789i q^{8} +(-76.2153 + 27.4266i) q^{9} +117.582 q^{10} +143.870i q^{11} +(-5.10307 - 29.2519i) q^{12} +188.424 q^{13} +172.561i q^{14} +(292.524 - 51.0315i) q^{15} -192.326 q^{16} +314.784i q^{17} +(97.7432 + 271.617i) q^{18} -1.38992 q^{19} +108.855i q^{20} +(74.8926 + 429.300i) q^{21} +512.723 q^{22} +193.577i q^{23} +(-609.801 + 106.381i) q^{24} -463.571 q^{25} -671.508i q^{26} +(361.051 + 633.311i) q^{27} -159.753 q^{28} +1266.29i q^{29} +(-181.866 - 1042.50i) q^{30} +36.5072 q^{31} -415.051i q^{32} +(1275.56 - 222.525i) q^{33} +1121.83 q^{34} -1597.56i q^{35} +(-251.457 + 90.4886i) q^{36} +1485.40 q^{37} +4.95339i q^{38} +(-291.439 - 1670.59i) q^{39} +2269.26 q^{40} -1972.66i q^{41} +(1529.94 - 266.903i) q^{42} +203.989 q^{43} +474.668i q^{44} +(-904.901 - 2514.61i) q^{45} +689.872 q^{46} +934.292i q^{47} +(297.473 + 1705.18i) q^{48} -56.4629 q^{49} +1652.08i q^{50} +(2790.91 - 486.882i) q^{51} +621.668 q^{52} +3283.35i q^{53} +(2257.00 - 1286.71i) q^{54} -4746.76 q^{55} +3330.30i q^{56} +(2.14980 + 12.3231i) q^{57} +4512.83 q^{58} +453.188i q^{59} +(965.122 - 168.368i) q^{60} -5625.52 q^{61} -130.105i q^{62} +(3690.38 - 1328.01i) q^{63} -4556.37 q^{64} +6216.78i q^{65} +(-793.036 - 4545.85i) q^{66} -4794.66 q^{67} +1038.57i q^{68} +(1716.28 - 299.409i) q^{69} -5693.39 q^{70} -3643.38i q^{71} +(1886.38 + 5242.01i) q^{72} +2678.61 q^{73} -5293.67i q^{74} +(717.012 + 4110.07i) q^{75} -4.58574 q^{76} -6966.22i q^{77} +(-5953.66 + 1038.63i) q^{78} +7113.29 q^{79} -6345.50i q^{80} +(5056.56 - 4180.66i) q^{81} -7030.16 q^{82} +9846.88i q^{83} +(247.093 + 1416.39i) q^{84} -10385.8 q^{85} -726.977i q^{86} +(11227.1 - 1958.60i) q^{87} +9895.19 q^{88} +3149.01i q^{89} +(-8961.58 + 3224.89i) q^{90} -9123.59 q^{91} +638.669i q^{92} +(-56.4663 - 323.676i) q^{93} +3329.63 q^{94} -45.8582i q^{95} +(-3679.88 + 641.965i) q^{96} -13040.7 q^{97} +201.223i q^{98} +(-3945.86 - 10965.1i) 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 $

$2$		−	3.56380i		−	0.890951i	−0.895294	−	0.445476i	$-0.853035\pi$
$2$		−	3.56380i		−	0.890951i	0.895294	−	0.445476i	$-0.146965\pi$
$3$	−1.54671	−	8.86610i	−0.171857	−	0.985122i
$3$	−1.54671	−	8.86610i	−0.171857	−	0.985122i
$4$	3.29930			0.206206
$5$			32.9935i			1.31974i	0.751380	+	0.659870i	$0.229389\pi$
$5$			32.9935i			1.31974i	−0.751380	+	0.659870i	$0.770611\pi$
$6$	−31.5970	+	5.51219i	−0.877695	+	0.153116i
$7$	−48.4204			−0.988172			−0.494086	−	0.869413i	$-0.664497\pi$
$7$	−48.4204			−0.988172			−0.494086	+	0.869413i	$0.664497\pi$
$8$		−	68.7789i		−	1.07467i
$9$	−76.2153	+	27.4266i	−0.940930	+	0.338601i
$10$	117.582			1.17582
$11$			143.870i			1.18900i	0.804094	+	0.594502i	$0.202651\pi$
$11$			143.870i			1.18900i	−0.804094	+	0.594502i	$0.797349\pi$
$12$	−5.10307	−	29.2519i	−0.0354380	−	0.203138i
$13$	188.424			1.11494			0.557469	−	0.830198i	$-0.311773\pi$
$13$	188.424			1.11494			0.557469	+	0.830198i	$0.311773\pi$
$14$			172.561i			0.880413i
$15$	292.524	−	51.0315i	1.30010	−	0.226807i
$16$	−192.326			−0.751273
$17$			314.784i			1.08922i	0.838690	+	0.544610i	$0.183322\pi$
$17$			314.784i			1.08922i	−0.838690	+	0.544610i	$0.816678\pi$
$18$	97.7432	+	271.617i	0.301677	+	0.838323i
$19$	−1.38992			−0.00385018			−0.00192509	−	0.999998i	$-0.500613\pi$
$19$	−1.38992			−0.00385018			−0.00192509	+	0.999998i	$0.500613\pi$
$20$			108.855i			0.272138i
$21$	74.8926	+	429.300i	0.169824	+	0.973470i
$22$	512.723			1.05934
$23$			193.577i			0.365931i	0.983119	+	0.182965i	$0.0585697\pi$
$23$			193.577i			0.365931i	−0.983119	+	0.182965i	$0.941430\pi$
$24$	−609.801	+	106.381i	−1.05868	+	0.184690i
$25$	−463.571			−0.741714
$26$		−	671.508i		−	0.993355i
$27$	361.051	+	633.311i	0.495268	+	0.868740i
$28$	−159.753			−0.203767
$29$			1266.29i			1.50570i	0.658191	+	0.752851i	$0.271322\pi$
$29$			1266.29i			1.50570i	−0.658191	+	0.752851i	$0.728678\pi$
$30$	−181.866	−	1042.50i	−0.202074	−	1.15833i
$31$	36.5072			0.0379888			0.0189944	−	0.999820i	$-0.493954\pi$
$31$	36.5072			0.0379888			0.0189944	+	0.999820i	$0.493954\pi$
$32$		−	415.051i		−	0.405323i
$33$	1275.56	−	222.525i	1.17131	−	0.204339i
$34$	1121.83			0.970441
$35$		−	1597.56i		−	1.30413i
$36$	−251.457	+	90.4886i	−0.194025	+	0.0698215i
$37$	1485.40			1.08502			0.542512	−	0.840048i	$-0.317473\pi$
$37$	1485.40			1.08502			0.542512	+	0.840048i	$0.317473\pi$
$38$			4.95339i			0.00343032i
$39$	−291.439	−	1670.59i	−0.191610	−	1.09835i
$40$	2269.26			1.41829
$41$		−	1972.66i		−	1.17350i	−0.809768	−	0.586750i	$-0.800407\pi$
$41$		−	1972.66i		−	1.17350i	0.809768	−	0.586750i	$-0.199593\pi$
$42$	1529.94	−	266.903i	0.867314	−	0.151305i
$43$	203.989			0.110324			0.0551620	−	0.998477i	$-0.482432\pi$
$43$	203.989			0.110324			0.0551620	+	0.998477i	$0.482432\pi$
$44$			474.668i			0.245180i
$45$	−904.901	−	2514.61i	−0.446865	−	1.24178i
$46$	689.872			0.326027
$47$			934.292i			0.422948i	0.977384	+	0.211474i	$0.0678263\pi$
$47$			934.292i			0.422948i	−0.977384	+	0.211474i	$0.932174\pi$
$48$	297.473	+	1705.18i	0.129112	+	0.740096i
$49$	−56.4629			−0.0235164
$50$			1652.08i			0.660831i
$51$	2790.91	−	486.882i	1.07301	−	0.187190i
$52$	621.668			0.229907
$53$			3283.35i			1.16887i	0.811442	+	0.584433i	$0.198683\pi$
$53$			3283.35i			1.16887i	−0.811442	+	0.584433i	$0.801317\pi$
$54$	2257.00	−	1286.71i	0.774005	−	0.441260i
$55$	−4746.76			−1.56918
$56$			3330.30i			1.06196i
$57$	2.14980	+	12.3231i	0.000661682	+	0.00379290i
$58$	4512.83			1.34151
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	965.122	−	168.368i	0.268089	−	0.0467689i
$61$	−5625.52			−1.51183			−0.755914	−	0.654670i	$-0.772807\pi$
$61$	−5625.52			−1.51183			−0.755914	+	0.654670i	$0.772807\pi$
$62$		−	130.105i		−	0.0338461i
$63$	3690.38	−	1328.01i	0.929801	−	0.334596i
$64$	−4556.37			−1.11240
$65$			6216.78i			1.47143i
$66$	−793.036	−	4545.85i	−0.182056	−	1.04358i
$67$	−4794.66			−1.06809			−0.534045	−	0.845456i	$-0.679329\pi$
$67$	−4794.66			−1.06809			−0.534045	+	0.845456i	$0.679329\pi$
$68$			1038.57i			0.224604i
$69$	1716.28	−	299.409i	0.360487	−	0.0628879i
$70$	−5693.39			−1.16192
$71$		−	3643.38i		−	0.722749i	−0.932421	−	0.361375i	$-0.882308\pi$
$71$		−	3643.38i		−	0.722749i	0.932421	−	0.361375i	$-0.117692\pi$
$72$	1886.38	+	5242.01i	0.363884	+	1.01119i
$73$	2678.61			0.502649			0.251324	−	0.967903i	$-0.419134\pi$
$73$	2678.61			0.502649			0.251324	+	0.967903i	$0.419134\pi$
$74$		−	5293.67i		−	0.966704i
$75$	717.012	+	4110.07i	0.127469	+	0.730678i
$76$	−4.58574			−0.000793931
$77$		−	6966.22i		−	1.17494i
$78$	−5953.66	+	1038.63i	−0.978576	+	0.170715i
$79$	7113.29			1.13977			0.569884	−	0.821725i	$-0.306988\pi$
$79$	7113.29			1.13977			0.569884	+	0.821725i	$0.306988\pi$
$80$		−	6345.50i		−	0.991485i
$81$	5056.56	−	4180.66i	0.770699	−	0.637199i
$82$	−7030.16			−1.04553
$83$			9846.88i			1.42936i	0.699450	+	0.714681i	$0.253428\pi$
$83$			9846.88i			1.42936i	−0.699450	+	0.714681i	$0.746572\pi$
$84$	247.093	+	1416.39i	0.0350188	+	0.200735i
$85$	−10385.8			−1.43749
$86$		−	726.977i		−	0.0982932i
$87$	11227.1	−	1958.60i	1.48330	−	0.258766i
$88$	9895.19			1.27779
$89$			3149.01i			0.397552i	0.980045	+	0.198776i	$0.0636967\pi$
$89$			3149.01i			0.397552i	−0.980045	+	0.198776i	$0.936303\pi$
$90$	−8961.58	+	3224.89i	−1.10637	+	0.398135i
$91$	−9123.59			−1.10175
$92$			638.669i			0.0754572i
$93$	−56.4663	−	323.676i	−0.00652864	−	0.0374236i
$94$	3329.63			0.376826
$95$		−	45.8582i		−	0.00508124i
$96$	−3679.88	+	641.965i	−0.399293	+	0.0696577i
$97$	−13040.7			−1.38598			−0.692990	−	0.720947i	$-0.743707\pi$
$97$	−13040.7			−1.38598			−0.692990	+	0.720947i	$0.743707\pi$
$98$			201.223i			0.0209520i
$99$	−3945.86	−	10965.1i	−0.402598	−	1.11877i
$100$	−1529.46			−0.152946
$101$			18350.4i			1.79888i	0.437042	+	0.899441i	$0.356026\pi$
$101$			18350.4i			1.79888i	−0.437042	+	0.899441i	$0.643974\pi$
$102$	−1735.15	−	9946.25i	−0.166777	−	0.956003i
$103$	5773.21			0.544180			0.272090	−	0.962272i	$-0.412285\pi$
$103$	5773.21			0.544180			0.272090	+	0.962272i	$0.412285\pi$
$104$		−	12959.6i		−	1.19819i
$105$	−14164.1	+	2470.97i	−1.28473	+	0.224124i
$106$	11701.2			1.04140
$107$			1010.41i			0.0882531i	0.999026	+	0.0441265i	$0.0140505\pi$
$107$			1010.41i			0.0882531i	−0.999026	+	0.0441265i	$0.985950\pi$
$108$	1191.21	+	2089.48i	0.102127	+	0.179139i
$109$	3241.62			0.272841			0.136420	−	0.990651i	$-0.456440\pi$
$109$	3241.62			0.272841			0.136420	+	0.990651i	$0.456440\pi$
$110$			16916.5i			1.39806i
$111$	−2297.49	−	13169.7i	−0.186469	−	1.06888i
$112$	9312.50			0.742387
$113$			14844.0i			1.16250i	0.813724	+	0.581252i	$0.197437\pi$
$113$			14844.0i			1.16250i	−0.813724	+	0.581252i	$0.802563\pi$
$114$	43.9172	−	7.66148i	0.00337929	−	0.000589526i
$115$	−6386.80			−0.482934
$116$			4177.88i			0.310485i
$117$	−14360.8	+	5167.85i	−1.04908	+	0.377519i
$118$	1615.07			0.115992
$119$		−	15242.0i		−	1.07634i
$120$	−3509.89	−	20119.5i	−0.243743	−	1.39718i
$121$	−6057.45			−0.413732
$122$			20048.2i			1.34697i
$123$	−17489.8	+	3051.13i	−1.15604	+	0.201675i
$124$	120.448			0.00783351
$125$			5326.10i			0.340871i
$126$	−4732.77	−	13151.8i	−0.298108	−	0.828407i
$127$	−8624.34			−0.534710			−0.267355	−	0.963598i	$-0.586150\pi$
$127$	−8624.34			−0.534710			−0.267355	+	0.963598i	$0.586150\pi$
$128$			9597.22i			0.585768i
$129$	−315.513	−	1808.59i	−0.0189600	−	0.108683i
$130$	22155.4			1.31097
$131$		−	32219.3i		−	1.87747i	−0.344635	−	0.938737i	$-0.611997\pi$
$131$		−	32219.3i		−	1.87747i	0.344635	−	0.938737i	$-0.388003\pi$
$132$	4208.45	−	734.176i	0.241532	−	0.0421359i
$133$	67.3003			0.00380464
$134$			17087.2i			0.951617i
$135$	−20895.2	+	11912.3i	−1.14651	+	0.653626i
$136$	21650.5			1.17055
$137$		−	8355.56i		−	0.445179i	−0.974912	−	0.222589i	$-0.928549\pi$
$137$		−	8355.56i		−	0.445179i	0.974912	−	0.222589i	$-0.0714509\pi$
$138$	−1067.04	−	6116.47i	−0.0560300	−	0.321176i
$139$	−6883.91			−0.356292			−0.178146	−	0.984004i	$-0.557010\pi$
$139$	−6883.91			−0.356292			−0.178146	+	0.984004i	$0.557010\pi$
$140$		−	5270.82i		−	0.268919i
$141$	8283.52	−	1445.08i	0.416655	−	0.0726866i
$142$	−12984.3			−0.643934
$143$			27108.5i			1.32567i
$144$	14658.2	−	5274.85i	0.706896	−	0.254382i
$145$	−41779.5			−1.98713
$146$		−	9546.06i		−	0.447835i
$147$	87.3320	+	500.606i	0.00404147	+	0.0231665i
$148$	4900.77			0.223739
$149$			31197.8i			1.40524i	0.711564	+	0.702622i	$0.247987\pi$
$149$			31197.8i			1.40524i	−0.711564	+	0.702622i	$0.752013\pi$
$150$	14647.5	−	2555.29i	0.650999	−	0.113569i
$151$	10047.5			0.440661			0.220330	−	0.975425i	$-0.429286\pi$
$151$	10047.5			0.440661			0.220330	+	0.975425i	$0.429286\pi$
$152$			95.5969i			0.00413768i
$153$	−8633.48	−	23991.4i	−0.368810	−	1.02488i
$154$	−24826.3			−1.04681
$155$			1204.50i			0.0501353i
$156$	−961.544	−	5511.77i	−0.0395112	−	0.226486i
$157$	33206.3			1.34717			0.673584	−	0.739111i	$-0.264754\pi$
$157$	33206.3			1.34717			0.673584	+	0.739111i	$0.264754\pi$
$158$		−	25350.4i		−	1.01548i
$159$	29110.5	−	5078.40i	1.15148	−	0.200878i
$160$	13694.0			0.534921
$161$		−	9373.10i		−	0.361603i
$162$	−14899.1	−	18020.6i	−0.567713	−	0.686655i
$163$	16842.0			0.633895			0.316947	−	0.948443i	$-0.397342\pi$
$163$	16842.0			0.633895			0.316947	+	0.948443i	$0.397342\pi$
$164$		−	6508.37i		−	0.241983i
$165$	7341.88	+	42085.2i	0.269674	+	1.54583i
$166$	35092.4			1.27349
$167$		−	47210.2i		−	1.69279i	−0.532556	−	0.846395i	$-0.678768\pi$
$167$		−	47210.2i		−	1.69279i	0.532556	−	0.846395i	$-0.321232\pi$
$168$	29526.8	−	5151.03i	1.04616	−	0.182505i
$169$	6942.79			0.243086
$170$			37013.1i			1.28073i
$171$	105.933	−	38.1207i	0.00362275	−	0.00130367i
$172$	673.020			0.0227495
$173$			44614.6i			1.49068i	0.666683	+	0.745341i	$0.267713\pi$
$173$			44614.6i			1.49068i	−0.666683	+	0.745341i	$0.732287\pi$
$174$	−6980.06	−	40011.2i	−0.230548	−	1.32155i
$175$	22446.3			0.732941
$176$		−	27669.8i		−	0.893267i
$177$	4018.01	−	700.952i	0.128252	−	0.0223739i
$178$	11222.5			0.354200
$179$		−	42181.9i		−	1.31650i	−0.752800	−	0.658249i	$-0.771297\pi$
$179$		−	42181.9i		−	1.31650i	0.752800	−	0.658249i	$-0.228703\pi$
$180$	−2985.54	−	8296.45i	−0.0921462	−	0.256063i
$181$	−60384.5			−1.84318			−0.921592	−	0.388160i	$-0.873111\pi$
$181$	−60384.5			−1.84318			−0.921592	+	0.388160i	$0.873111\pi$
$182$			32514.7i			0.981606i
$183$	8701.07	+	49876.4i	0.259819	+	1.48934i
$184$	13314.1			0.393255
$185$			49008.5i			1.43195i
$186$	−1153.52	+	201.235i	−0.0333426	+	0.00581670i
$187$	−45287.9			−1.29509
$188$			3082.50i			0.0872144i
$189$	−17482.2	−	30665.2i	−0.489410	−	0.858464i
$190$	−163.430			−0.00452714
$191$		−	51191.6i		−	1.40324i	−0.712551	−	0.701621i	$-0.752460\pi$
$191$		−	51191.6i		−	1.40324i	0.712551	−	0.701621i	$-0.247540\pi$
$192$	7047.41	+	40397.3i	0.191173	+	1.09585i
$193$	−22027.7			−0.591364			−0.295682	−	0.955286i	$-0.595547\pi$
$193$	−22027.7			−0.591364			−0.295682	+	0.955286i	$0.595547\pi$
$194$			46474.5i			1.23484i
$195$	55118.6	−	9615.59i	1.44954	−	0.252876i
$196$	−186.288			−0.00484923
$197$		−	22961.1i		−	0.591644i	−0.955243	−	0.295822i	$-0.904406\pi$
$197$		−	22961.1i		−	0.591644i	0.955243	−	0.295822i	$-0.0955936\pi$
$198$	−39077.4	+	14062.3i	−0.996770	+	0.358695i
$199$	38265.0			0.966263			0.483132	−	0.875548i	$-0.339499\pi$
$199$	38265.0			0.966263			0.483132	+	0.875548i	$0.339499\pi$
$200$			31883.9i			0.797098i
$201$	7415.97	+	42509.9i	0.183559	+	1.05220i
$202$	65397.2			1.60272
$203$		−	61314.5i		−	1.48789i
$204$	9208.03	−	1606.37i	0.221262	−	0.0385997i
$205$	65084.8			1.54872
$206$		−	20574.6i		−	0.484838i
$207$	−5309.18	−	14753.6i	−0.123904	−	0.344315i
$208$	−36238.9			−0.837623
$209$		−	199.967i		−	0.00457788i
$210$	8806.05	+	50478.1i	0.199684	+	1.14463i
$211$	34607.7			0.777335			0.388668	−	0.921378i	$-0.372935\pi$
$211$	34607.7			0.777335			0.388668	+	0.921378i	$0.372935\pi$
$212$			10832.7i			0.241027i
$213$	−32302.6	+	5635.27i	−0.711996	+	0.124210i
$214$	3600.90			0.0786292
$215$			6730.31i			0.145599i
$216$	43558.5	−	24832.7i	0.933609	−	0.532251i
$217$	−1767.69			−0.0375394
$218$		−	11552.5i		−	0.243088i
$219$	−4143.05	−	23748.9i	−0.0863838	−	0.495170i
$220$	−15661.0			−0.323574
$221$			59313.1i			1.21441i
$222$	−46934.2	+	8187.80i	−0.952321	+	0.166135i
$223$	58364.2			1.17364			0.586822	−	0.809716i	$-0.300379\pi$
$223$	58364.2			1.17364			0.586822	+	0.809716i	$0.300379\pi$
$224$			20096.9i			0.400529i
$225$	35331.2	−	12714.2i	0.697901	−	0.251145i
$226$	52901.2			1.03573
$227$			18653.8i			0.362005i	0.983483	+	0.181003i	$0.0579343\pi$
$227$			18653.8i			0.362005i	−0.983483	+	0.181003i	$0.942066\pi$
$228$	7.09284	+	40.6577i	0.000136443	+	0.000782119i
$229$	−71930.2			−1.37164			−0.685820	−	0.727771i	$-0.740556\pi$
$229$	−71930.2			−1.37164			−0.685820	+	0.727771i	$0.740556\pi$
$230$			22761.3i			0.430270i
$231$	−61763.2	+	10774.8i	−1.15746	+	0.201922i
$232$	87094.4			1.61813
$233$		−	72712.2i		−	1.33935i	−0.742653	−	0.669677i	$-0.766433\pi$
$233$		−	72712.2i		−	1.33935i	0.742653	−	0.669677i	$-0.233567\pi$
$234$	18417.2	+	51179.2i	0.336351	+	0.934678i
$235$	−30825.6			−0.558181
$236$			1495.20i			0.0268457i
$237$	−11002.2	−	63067.2i	−0.195877	−	1.12281i
$238$	−54319.5			−0.958963
$239$			27801.0i			0.486703i	0.969938	+	0.243352i	$0.0782469\pi$
$239$			27801.0i			0.486703i	−0.969938	+	0.243352i	$0.921753\pi$
$240$	−56259.9	+	9814.69i	−0.976734	+	0.170394i
$241$	48259.9			0.830907			0.415454	−	0.909614i	$-0.363623\pi$
$241$	48259.9			0.830907			0.415454	+	0.909614i	$0.363623\pi$
$242$			21587.6i			0.368615i
$243$	−44887.2	−	38365.6i	−0.760169	−	0.649725i
$244$	−18560.2			−0.311748
$245$		−	1862.91i		−	0.0310356i
$246$	10873.6	+	62330.1i	0.179682	+	1.02998i
$247$	−261.894			−0.00429271
$248$		−	2510.93i		−	0.0408254i
$249$	87303.4	−	15230.3i	1.40810	−	0.245646i
$250$	18981.2			0.303699
$251$			53937.3i			0.856134i	0.903747	+	0.428067i	$0.140805\pi$
$251$			53937.3i			0.856134i	−0.903747	+	0.428067i	$0.859195\pi$
$252$	12175.7	−	4381.50i	0.191731	−	0.0689956i
$253$	−27849.9			−0.435094
$254$			30735.5i			0.476401i
$255$	16063.9	+	92081.8i	0.247042	+	1.41610i
$256$	−38699.4			−0.590506
$257$		−	69434.7i		−	1.05126i	−0.850713	−	0.525630i	$-0.823830\pi$
$257$		−	69434.7i		−	1.05126i	0.850713	−	0.525630i	$-0.176170\pi$
$258$	−6445.45	+	1124.43i	−0.0968308	+	0.0168924i
$259$	−71923.6			−1.07219
$260$			20511.0i			0.303417i
$261$	−34730.2	−	96511.1i	−0.509831	−	1.41676i
$262$	−114823.			−1.67274
$263$		−	96388.7i		−	1.39352i	−0.717302	−	0.696762i	$-0.754623\pi$
$263$		−	96388.7i		−	1.39352i	0.717302	−	0.696762i	$-0.245377\pi$
$264$	−15305.0	−	87731.7i	−0.219597	−	1.25878i
$265$	−108329.			−1.54260
$266$		−	239.845i		−	0.00338975i
$267$	27919.5	−	4870.63i	0.391638	−	0.0683223i
$268$	−15819.0			−0.220247
$269$		−	62174.8i		−	0.859230i	−0.903012	−	0.429615i	$-0.858649\pi$
$269$		−	62174.8i		−	0.859230i	0.903012	−	0.429615i	$-0.141351\pi$
$270$	42453.2	+	74466.3i	0.582349	+	1.02149i
$271$	31459.2			0.428360			0.214180	−	0.976794i	$-0.431292\pi$
$271$	31459.2			0.428360			0.214180	+	0.976794i	$0.431292\pi$
$272$		−	60541.2i		−	0.818301i
$273$	14111.6	+	80890.7i	0.189344	+	1.08536i
$274$	−29777.6			−0.396632
$275$		−	66693.8i		−	0.881901i
$276$	5662.51	−	987.840i	0.0743345	−	0.0129679i
$277$	92427.3			1.20459			0.602297	−	0.798272i	$-0.294252\pi$
$277$	92427.3			1.20459			0.602297	+	0.798272i	$0.294252\pi$
$278$			24532.9i			0.317438i
$279$	−2782.41	+	1001.27i	−0.0357448	+	0.0128630i
$280$	−109878.			−1.40151
$281$		−	27532.2i		−	0.348681i	−0.984685	−	0.174341i	$-0.944221\pi$
$281$		−	27532.2i		−	0.348681i	0.984685	−	0.174341i	$-0.0557794\pi$
$282$	−5149.99	−	29520.8i	−0.0647602	−	0.371219i
$283$	−93843.8			−1.17174			−0.585872	−	0.810404i	$-0.699248\pi$
$283$	−93843.8			−1.17174			−0.585872	+	0.810404i	$0.699248\pi$
$284$		−	12020.6i		−	0.149035i
$285$	−406.583	+	70.9296i	−0.00500564	+	0.000873248i
$286$	96609.6			1.18110
$287$			95516.8i			1.15962i
$288$	11383.5	+	31633.2i	0.137243	+	0.381381i
$289$	−15568.2			−0.186399
$290$			148894.i			1.77044i
$291$	20170.2	+	115620.i	0.238191	+	1.36536i
$292$	8837.54			0.103649
$293$			95388.5i			1.11112i	0.831477	+	0.555560i	$0.187496\pi$
$293$			95388.5i			1.11112i	−0.831477	+	0.555560i	$0.812504\pi$
$294$	1784.06	−	311.234i	0.0206403	−	0.00360075i
$295$	−14952.2			−0.171816
$296$		−	102164.i		−	1.16604i
$297$	−91114.2	+	51944.2i	−1.03294	+	0.588876i
$298$	111183.			1.25200
$299$			36474.7i			0.407990i
$300$	2365.64	+	13560.3i	0.0262848	+	0.150670i
$301$	−9877.23			−0.109019
$302$		−	35807.4i		−	0.392607i
$303$	162696.	−	28382.8i	1.77212	−	0.309151i
$304$	267.317			0.00289254
$305$		−	185605.i		−	1.99522i
$306$	−85500.7	+	30768.0i	−0.913117	+	0.328592i
$307$	−34270.2			−0.363613			−0.181807	−	0.983334i	$-0.558194\pi$
$307$	−34270.2			−0.363613			−0.181807	+	0.983334i	$0.558194\pi$
$308$		−	22983.6i		−	0.242280i
$309$	−8929.50	−	51185.8i	−0.0935213	−	0.536084i
$310$	4292.61			0.0446681
$311$		−	137459.i		−	1.42119i	−0.703602	−	0.710594i	$-0.748426\pi$
$311$		−	137459.i		−	1.42119i	0.703602	−	0.710594i	$-0.251574\pi$
$312$	−114901.	+	20044.9i	−1.18036	+	0.205918i
$313$	147882.			1.50948			0.754739	−	0.656026i	$-0.227764\pi$
$313$	147882.			1.50948			0.754739	+	0.656026i	$0.227764\pi$
$314$		−	118341.i		−	1.20026i
$315$	43815.7	+	121759.i	0.441579	+	1.22710i
$316$	23468.9			0.235027
$317$		−	105626.i		−	1.05112i	−0.850758	−	0.525558i	$-0.823857\pi$
$317$		−	105626.i		−	1.05112i	0.850758	−	0.525558i	$-0.176143\pi$
$318$	−18098.4	−	103744.i	−0.178973	−	1.02591i
$319$	−182181.			−1.79029
$320$		−	150331.i		−	1.46807i
$321$	8958.39	−	1562.82i	0.0869400	−	0.0151669i
$322$	−33403.9			−0.322170
$323$		−	437.524i		−	0.00419369i
$324$	16683.1	−	13793.2i	0.158923	−	0.131394i
$325$	−87348.2			−0.826965
$326$		−	60021.4i		−	0.564769i
$327$	−5013.87	−	28740.5i	−0.0468897	−	0.268782i
$328$	−135677.			−1.26113
$329$		−	45238.8i		−	0.417945i
$330$	149984.	−	26165.0i	1.37726	−	0.240267i
$331$	−142699.			−1.30246			−0.651230	−	0.758880i	$-0.725747\pi$
$331$	−142699.			−1.30246			−0.651230	+	0.758880i	$0.725747\pi$
$332$			32487.8i			0.294743i
$333$	−113210.	+	40739.5i	−1.02093	+	0.367390i
$334$	−168248.			−1.50819
$335$		−	158193.i		−	1.40960i
$336$	−14403.8	−	82565.5i	−0.127585	−	0.731342i
$337$	−100324.			−0.883377			−0.441689	−	0.897168i	$-0.645620\pi$
$337$	−100324.			−0.883377			−0.441689	+	0.897168i	$0.645620\pi$
$338$		−	24742.8i		−	0.216578i
$339$	131608.	−	22959.5i	1.14521	−	0.199785i
$340$	−34266.0			−0.296418
$341$			5252.28i			0.0451688i
$342$	−135.855	−	377.524i	−0.00116151	−	0.00322770i
$343$	118991.			1.01141
$344$		−	14030.1i		−	0.118562i
$345$	9878.56	+	56626.0i	0.0829956	+	0.475749i
$346$	158998.			1.32813
$347$			181469.i			1.50710i	0.657388	+	0.753552i	$0.271661\pi$
$347$			181469.i			1.50710i	−0.657388	+	0.753552i	$0.728339\pi$
$348$	37041.5	−	6461.99i	0.305865	−	0.0533590i
$349$	149731.			1.22931			0.614656	−	0.788795i	$-0.289295\pi$
$349$	149731.			1.22931			0.614656	+	0.788795i	$0.289295\pi$
$350$		−	79994.3i		−	0.653014i
$351$	68030.8	+	119331.i	0.552194	+	0.968591i
$352$	59713.2			0.481931
$353$			29293.1i			0.235080i	0.993068	+	0.117540i	$0.0375008\pi$
$353$			29293.1i			0.235080i	−0.993068	+	0.117540i	$0.962499\pi$
$354$	−2498.06	−	14319.4i	−0.0199341	−	0.114266i
$355$	120208.			0.953841
$356$			10389.5i			0.0819777i
$357$	−135137.	+	23575.0i	−1.06032	+	0.184976i
$358$	−150328.			−1.17294
$359$			10042.8i			0.0779227i	0.999241	+	0.0389614i	$0.0124049\pi$
$359$			10042.8i			0.0779227i	−0.999241	+	0.0389614i	$0.987595\pi$
$360$	−172952.	+	62238.1i	−1.33451	+	0.480232i
$361$	−130319.			−0.999985
$362$			215199.i			1.64219i
$363$	9369.14	+	53705.9i	0.0711028	+	0.407576i
$364$	−30101.4			−0.227188
$365$			88376.9i			0.663366i
$366$	177750.	−	31008.9i	1.32693	−	0.231486i
$367$	139800.			1.03795			0.518974	−	0.854790i	$-0.326314\pi$
$367$	139800.			1.03795			0.518974	+	0.854790i	$0.326314\pi$
$368$		−	37230.0i		−	0.274914i
$369$	54103.3	+	150347.i	0.397348	+	1.10418i
$370$	174657.			1.27580
$371$		−	158981.i		−	1.15504i
$372$	−186.299	−	1067.90i	−0.00134625	−	0.00771697i
$373$	−120658.			−0.867238			−0.433619	−	0.901096i	$-0.642764\pi$
$373$	−120658.			−0.867238			−0.433619	+	0.901096i	$0.642764\pi$
$374$			161397.i			1.15386i
$375$	47221.8	−	8237.97i	0.335799	−	0.0585811i
$376$	64259.6			0.454530
$377$			238601.i			1.67876i
$378$	−109285.	+	62303.2i	−0.764850	+	0.436041i
$379$	160981.			1.12072			0.560358	−	0.828251i	$-0.310664\pi$
$379$	160981.			1.12072			0.560358	+	0.828251i	$0.310664\pi$
$380$		−	151.300i		−	0.00104778i
$381$	13339.4	+	76464.2i	0.0918938	+	0.526755i
$382$	−182437.			−1.25022
$383$			267800.i			1.82563i	0.408374	+	0.912815i	$0.366096\pi$
$383$			267800.i			1.82563i	−0.408374	+	0.912815i	$0.633904\pi$
$384$	85089.8	−	14844.2i	0.577052	−	0.100668i
$385$	229840.			1.55062
$386$			78502.4i			0.526876i
$387$	−15547.1	+	5594.73i	−0.103807	+	0.0373558i
$388$	−43025.1			−0.285797
$389$		−	2697.04i		−	0.0178233i	−0.999960	−	0.00891165i	$-0.997163\pi$
$389$		−	2697.04i		−	0.0178233i	0.999960	−	0.00891165i	$-0.00283670\pi$
$390$	−34268.1	−	196432.i	−0.225300	−	1.29147i
$391$	−60935.2			−0.398579
$392$			3883.46i			0.0252724i
$393$	−285660.	+	49834.1i	−1.84954	+	0.322657i
$394$	−81829.0			−0.527126
$395$			234692.i			1.50420i
$396$	−13018.6	−	36177.0i	−0.0830181	−	0.230697i
$397$	−34899.8			−0.221433			−0.110716	−	0.993852i	$-0.535314\pi$
$397$	−34899.8			−0.221433			−0.110716	+	0.993852i	$0.535314\pi$
$398$		−	136369.i		−	0.860893i
$399$	−104.094	−	596.691i	−0.000653855	−	0.00374804i
$400$	89156.7			0.557230
$401$			61105.8i			0.380009i	0.981783	+	0.190004i	$0.0608503\pi$
$401$			61105.8i			0.380009i	−0.981783	+	0.190004i	$0.939150\pi$
$402$	151497.	−	26429.1i	0.937459	−	0.163542i
$403$	6878.85			0.0423551
$404$			60543.4i			0.370940i
$405$	137935.	+	166834.i	0.840937	+	1.01712i
$406$	−218513.			−1.32564
$407$			213704.i			1.29010i
$408$	−33487.2	−	191956.i	−0.201168	−	1.15314i
$409$	245183.			1.46569			0.732847	−	0.680394i	$-0.238191\pi$
$409$	245183.			1.46569			0.732847	+	0.680394i	$0.238191\pi$
$410$		−	231949.i		−	1.37983i
$411$	−74081.2	+	12923.7i	−0.438555	+	0.0765071i
$412$	19047.5			0.112213
$413$		−	21943.5i		−	0.128649i
$414$	−52578.9	+	18920.9i	−0.306768	+	0.110393i
$415$	−324883.			−1.88639
$416$		−	78205.7i		−	0.451910i
$417$	10647.4	+	61033.4i	0.0612313	+	0.350991i
$418$	−712.642			−0.00407867
$419$		−	89352.9i		−	0.508956i	−0.967079	−	0.254478i	$-0.918096\pi$
$419$		−	89352.9i		−	0.508956i	0.967079	−	0.254478i	$-0.0819037\pi$
$420$	−46731.6	+	8152.46i	−0.264918	+	0.0462157i
$421$	−137615.			−0.776431			−0.388215	−	0.921569i	$-0.626908\pi$
$421$	−137615.			−0.776431			−0.388215	+	0.921569i	$0.626908\pi$
$422$		−	123335.i		−	0.692568i
$423$	−25624.5	−	71207.4i	−0.143210	−	0.397964i
$424$	225825.			1.25615
$425$		−	145925.i		−	0.807889i
$426$	20083.0	+	115120.i	0.110665	+	0.634354i
$427$	272390.			1.49395
$428$			3333.64i			0.0181983i
$429$	240347.	−	41929.2i	1.30594	−	0.227825i
$430$	23985.5			0.129722
$431$		−	260720.i		−	1.40353i	−0.712411	−	0.701763i	$-0.752397\pi$
$431$		−	260720.i		−	1.40353i	0.712411	−	0.701763i	$-0.247603\pi$
$432$	−69439.4	−	121802.i	−0.372082	−	0.652661i
$433$	223240.			1.19068			0.595341	−	0.803473i	$-0.297017\pi$
$433$	223240.			1.19068			0.595341	+	0.803473i	$0.297017\pi$
$434$			6299.72i			0.0334458i
$435$	64621.0	+	370421.i	0.341503	+	1.95757i
$436$	10695.1			0.0562614
$437$		−	269.056i		−	0.00140890i
$438$	−84636.3	+	14765.0i	−0.441172	+	0.0769637i
$439$	210890.			1.09428			0.547138	−	0.837042i	$-0.315717\pi$
$439$	210890.			1.09428			0.547138	+	0.837042i	$0.315717\pi$
$440$			326477.i			1.68635i
$441$	4303.34	−	1548.59i	0.0221273	−	0.00796267i
$442$	211380.			1.08198
$443$			94013.2i			0.479051i	0.970890	+	0.239525i	$0.0769918\pi$
$443$			94013.2i			0.479051i	−0.970890	+	0.239525i	$0.923008\pi$
$444$	−7580.09	−	43450.7i	−0.0384511	−	0.220410i
$445$	−103897.			−0.524666
$446$		−	207999.i		−	1.04566i
$447$	276603.	−	48254.1i	1.38434	−	0.241501i
$448$	220622.			1.09924
$449$		−	251762.i		−	1.24881i	−0.781100	−	0.624406i	$-0.785341\pi$
$449$		−	251762.i		−	1.24881i	0.781100	−	0.624406i	$-0.214659\pi$
$450$	−45310.9	−	125914.i	−0.223758	−	0.621796i
$451$	283805.			1.39530
$452$			48974.8i			0.239715i
$453$	−15540.6	−	89082.2i	−0.0757308	−	0.434105i
$454$	66478.4			0.322529
$455$		−	301019.i		−	1.45402i
$456$	847.572	−	147.861i	0.00407612	−	0.000711090i
$457$	202155.			0.967946			0.483973	−	0.875083i	$-0.339193\pi$
$457$	202155.			0.967946			0.483973	+	0.875083i	$0.339193\pi$
$458$			256345.i			1.22206i
$459$	−199357.	+	113653.i	−0.946248	+	0.539456i
$460$	−21071.9			−0.0995838
$461$		−	180886.i		−	0.851143i	−0.904925	−	0.425572i	$-0.860073\pi$
$461$		−	180886.i		−	0.851143i	0.904925	−	0.425572i	$-0.139927\pi$
$462$	38399.1	+	220112.i	0.179903	+	1.03124i
$463$	−121417.			−0.566394			−0.283197	−	0.959062i	$-0.591395\pi$
$463$	−121417.			−0.566394			−0.283197	+	0.959062i	$0.591395\pi$
$464$		−	243541.i		−	1.13119i
$465$	10679.2	−	1863.02i	0.0493894	−	0.00861611i
$466$	−259132.			−1.19330
$467$			220885.i			1.01282i	0.862293	+	0.506409i	$0.169027\pi$
$467$			220885.i			1.01282i	−0.862293	+	0.506409i	$0.830973\pi$
$468$	−47380.7	+	17050.3i	−0.216326	+	0.0778466i
$469$	232159.			1.05546
$470$			109856.i			0.497312i
$471$	−51360.7	−	294411.i	−0.231520	−	1.32712i
$472$	31169.8			0.139910
$473$			29347.8i			0.131176i
$474$	−224759.	+	39209.8i	−1.00037	+	0.174517i
$475$	644.325			0.00285573
$476$		−	50287.8i		−	0.221947i
$477$	−90051.2	−	250241.i	−0.395779	−	1.09982i
$478$	99077.2			0.433629
$479$		−	9680.62i		−	0.0421922i	−0.999777	−	0.0210961i	$-0.993284\pi$
$479$		−	9680.62i		−	0.0421922i	0.999777	−	0.0210961i	$-0.00671559\pi$
$480$	−21180.7	−	121412.i	−0.0919300	−	0.526962i
$481$	279885.			1.20973
$482$		−	171989.i		−	0.740298i
$483$	−83102.8	+	14497.5i	−0.356223	+	0.0621440i
$484$	−19985.3			−0.0853140
$485$		−	430258.i		−	1.82913i
$486$	−136728.	+	159969.i	−0.578874	+	0.677273i
$487$	431822.			1.82074			0.910368	−	0.413799i	$-0.135798\pi$
$487$	431822.			1.82074			0.910368	+	0.413799i	$0.135798\pi$
$488$			386917.i			1.62472i
$489$	−26049.7	−	149322.i	−0.108939	−	0.624464i
$490$	−6639.04			−0.0276512
$491$			25060.0i			0.103948i	0.998648	+	0.0519742i	$0.0165514\pi$
$491$			25060.0i			0.103948i	−0.998648	+	0.0519742i	$0.983449\pi$
$492$	−57703.9	+	10066.6i	−0.238383	+	0.0415865i
$493$	−398610.			−1.64004
$494$			933.340i			0.00382460i
$495$	361776.	−	130188.i	1.47649	−	0.531324i
$496$	−7021.28			−0.0285399
$497$			176414.i			0.714201i
$498$	−54277.9	−	311132.i	−0.218859	−	1.25455i
$499$	172187.			0.691511			0.345755	−	0.938325i	$-0.387623\pi$
$499$	172187.			0.691511			0.345755	+	0.938325i	$0.387623\pi$
$500$			17572.4i			0.0702896i
$501$	−418570.	+	73020.8i	−1.66760	+	0.290918i
$502$	192222.			0.762773
$503$		−	451517.i		−	1.78459i	−0.451455	−	0.892294i	$-0.649095\pi$
$503$		−	451517.i		−	1.78459i	0.451455	−	0.892294i	$-0.350905\pi$
$504$	−91339.1	−	253820.i	−0.359580	−	0.999230i
$505$	−605444.			−2.37406
$506$			99251.6i			0.387647i
$507$	−10738.5	−	61555.5i	−0.0417762	−	0.239470i
$508$	−28454.2			−0.110260
$509$		−	171453.i		−	0.661773i	−0.943670	−	0.330887i	$-0.892652\pi$
$509$		−	171453.i		−	0.661773i	0.943670	−	0.330887i	$-0.107348\pi$
$510$	328162.	−	57248.7i	1.26168	−	0.220103i
$511$	−129700.			−0.496703
$512$			291473.i			1.11188i
$513$	−501.830	−	880.250i	−0.00190687	−	0.00334481i
$514$	−247452.			−0.936622
$515$			190478.i			0.718176i
$516$	−1040.97	−	5967.06i	−0.00390966	−	0.0224110i
$517$	−134416.			−0.502887
$518$			256322.i			0.955270i
$519$	395558.	−	69006.1i	1.46850	−	0.256185i
$520$	427584.			1.58130
$521$			497867.i			1.83416i	0.398701	+	0.917081i	$0.369461\pi$
$521$			497867.i			1.83416i	−0.398701	+	0.917081i	$0.630539\pi$
$522$	−343947.	+	123772.i	−1.26226	+	0.454235i
$523$	93268.9			0.340984			0.170492	−	0.985359i	$-0.445464\pi$
$523$	93268.9			0.340984			0.170492	+	0.985359i	$0.445464\pi$
$524$		−	106301.i		−	0.387146i
$525$	−34718.0	−	199011.i	−0.125961	−	0.722036i
$526$	−343511.			−1.24156
$527$			11491.9i			0.0413781i
$528$	−245323.	+	42797.4i	−0.879977	+	0.153514i
$529$	242369.			0.866095
$530$			386064.i			1.37438i
$531$	−12429.4	−	34539.8i	−0.0440820	−	0.122499i
$532$	222.044			0.000784540
$533$		−	371697.i		−	1.30838i
$534$	−17358.0	−	99499.5i	−0.0608718	−	0.348930i
$535$	−33336.9			−0.116471
$536$			329772.i			1.14785i
$537$	−373989.	+	65243.4i	−1.29691	+	0.226250i
$538$	−221579.			−0.765532
$539$		−	8123.29i		−	0.0279611i
$540$	−68939.3	+	39302.3i	−0.236417	+	0.134782i
$541$	−239967.			−0.819891			−0.409946	−	0.912110i	$-0.634452\pi$
$541$	−239967.			−0.819891			−0.409946	+	0.912110i	$0.634452\pi$
$542$		−	112114.i		−	0.381648i
$543$	93397.7	+	535375.i	0.316764	+	1.81576i
$544$	130652.			0.441486
$545$			106953.i			0.360079i
$546$	288279.	−	50291.0i	0.967001	−	0.168696i
$547$	−305510.			−1.02106			−0.510529	−	0.859860i	$-0.670551\pi$
$547$	−305510.			−1.02106			−0.510529	+	0.859860i	$0.670551\pi$
$548$		−	27567.5i		−	0.0917985i
$549$	428751.	−	154289.i	1.42253	−	0.511906i
$550$	−237684.			−0.785731
$551$		−	1760.04i		−	0.00579723i
$552$	−20593.0	−	118044.i	−0.0675838	−	0.387404i
$553$	−344429.			−1.12629
$554$		−	329393.i		−	1.07323i
$555$	434514.	−	75802.2i	1.41065	−	0.246091i
$556$	−22712.1			−0.0734695
$557$			351391.i			1.13261i	0.824196	+	0.566305i	$0.191627\pi$
$557$			351391.i			1.13261i	−0.824196	+	0.566305i	$0.808373\pi$
$558$	3568.33	+	9915.97i	0.0114603	+	0.0318469i
$559$	38436.5			0.123004
$560$			307252.i			0.979758i
$561$	70047.4	+	401527.i	0.222570	+	1.27582i
$562$	−98119.5			−0.310658
$563$			234536.i			0.739934i	0.929045	+	0.369967i	$0.120631\pi$
$563$			234536.i			0.739934i	−0.929045	+	0.369967i	$0.879369\pi$
$564$	27329.8	−	4767.76i	0.0859168	−	0.0149884i
$565$	−489756.			−1.53420
$566$			334441.i			1.04397i
$567$	−244841.	+	202429.i	−0.761583	+	0.629662i
$568$	−250588.			−0.776718
$569$			111484.i			0.344340i	0.985067	+	0.172170i	$0.0550778\pi$
$569$			111484.i			0.344340i	−0.985067	+	0.172170i	$0.944922\pi$
$570$	252.779	+	1448.98i	0.000778021	+	0.00445978i
$571$	12151.4			0.0372696			0.0186348	−	0.999826i	$-0.494068\pi$
$571$	12151.4			0.0372696			0.0186348	+	0.999826i	$0.494068\pi$
$572$			89439.1i			0.273360i
$573$	−453870.	+	79178.9i	−1.38236	+	0.241157i
$574$	340403.			1.03317
$575$		−	89736.9i		−	0.271416i
$576$	347266.	−	124966.i	1.04669	−	0.376658i
$577$	414975.			1.24644			0.623218	−	0.782048i	$-0.285825\pi$
$577$	414975.			1.24644			0.623218	+	0.782048i	$0.285825\pi$
$578$			55482.0i			0.166072i
$579$	34070.6	+	195300.i	0.101630	+	0.582565i
$580$	−137843.			−0.409759
$581$		−	476790.i		−	1.41246i
$582$	412047.	−	71882.7i	1.21647	−	0.212216i
$583$	−472374.			−1.38979
$584$		−	184232.i		−	0.540182i
$585$	−170506.	−	473814.i	−0.498226	−	1.38451i
$586$	339946.			0.989953
$587$			325482.i			0.944606i	0.881436	+	0.472303i	$0.156577\pi$
$587$			325482.i			0.944606i	−0.881436	+	0.472303i	$0.843423\pi$
$588$	288.134	+	1651.65i	0.000833375	+	0.00477708i
$589$	−50.7420			−0.000146264
$590$			53286.9i			0.153079i
$591$	−203576.	+	35514.3i	−0.582842	+	0.101678i
$592$	−285681.			−0.815150
$593$			208866.i			0.593962i	0.954883	+	0.296981i	$0.0959798\pi$
$593$			208866.i			0.593962i	−0.954883	+	0.296981i	$0.904020\pi$
$594$	185119.	+	324713.i	0.524660	+	0.920295i
$595$	502887.			1.42048
$596$			102931.i			0.289770i
$597$	−59185.0	−	339261.i	−0.166059	−	0.951887i
$598$	129989.			0.363499
$599$			199894.i			0.557116i	0.960419	+	0.278558i	$0.0898565\pi$
$599$			199894.i			0.557116i	−0.960419	+	0.278558i	$0.910144\pi$
$600$	282686.	−	49315.3i	0.785239	−	0.136987i
$601$	110370.			0.305565			0.152782	−	0.988260i	$-0.451177\pi$
$601$	110370.			0.305565			0.152782	+	0.988260i	$0.451177\pi$
$602$			35200.5i			0.0971306i
$603$	365427.	−	131501.i	1.00500	−	0.361656i
$604$	33149.7			0.0908669
$605$		−	199856.i		−	0.546018i
$606$	−101151.	−	579818.i	−0.275438	−	1.57887i
$607$	−671627.			−1.82285			−0.911425	−	0.411466i	$-0.865017\pi$
$607$	−671627.			−1.82285			−0.911425	+	0.411466i	$0.865017\pi$
$608$			576.886i			0.00156057i
$609$	−543621.	+	94836.1i	−1.46575	+	0.255705i
$610$	−661462.			−1.77764
$611$			176043.i			0.471560i
$612$	−28484.4	−	79154.7i	−0.0760509	−	0.211336i
$613$	400715.			1.06639			0.533193	−	0.845993i	$-0.320992\pi$
$613$	400715.			1.06639			0.533193	+	0.845993i	$0.320992\pi$
$614$			122132.i			0.323961i
$615$	−100668.	−	577048.i	−0.266158	−	1.52567i
$616$	−479129.			−1.26267
$617$		−	353491.i		−	0.928556i	−0.885690	−	0.464278i	$-0.846314\pi$
$617$		−	353491.i		−	0.928556i	0.885690	−	0.464278i	$-0.153686\pi$
$618$	−182416.	+	31823.0i	−0.477624	+	0.0833229i
$619$	106626.			0.278279			0.139139	−	0.990273i	$-0.455566\pi$
$619$	106626.			0.278279			0.139139	+	0.990273i	$0.455566\pi$
$620$			3974.00i			0.0103382i
$621$	−122595.	+	69891.3i	−0.317899	+	0.181234i
$622$	−489876.			−1.26621
$623$		−	152477.i		−	0.392850i
$624$	56051.3	+	321298.i	0.143952	+	0.825161i
$625$	−465459.			−1.19157
$626$		−	527022.i		−	1.34487i
$627$	−1772.92	+	309.291i	−0.00450977	+	0.000786742i
$628$	109558.			0.277794
$629$			467580.i			1.18183i
$630$	433924.	−	156151.i	1.09328	−	0.393425i
$631$	−699848.			−1.75770			−0.878851	−	0.477097i	$-0.841689\pi$
$631$	−699848.			−1.75770			−0.878851	+	0.477097i	$0.841689\pi$
$632$		−	489245.i		−	1.22488i
$633$	−53528.3	−	306836.i	−0.133591	−	0.765770i
$634$	−376429.			−0.936492
$635$		−	284547.i		−	0.705678i
$636$	96044.1	−	16755.2i	0.237441	−	0.0414223i
$637$	−10639.0			−0.0262193
$638$			649258.i			1.59506i
$639$	99925.7	+	277681.i	0.244723	+	0.680057i
$640$	−316646.			−0.773061
$641$		−	300253.i		−	0.730754i	−0.930860	−	0.365377i	$-0.880940\pi$
$641$		−	300253.i		−	0.730754i	0.930860	−	0.365377i	$-0.119060\pi$
$642$	−5569.57	−	31925.9i	−0.0135130	−	0.0774593i
$643$	466427.			1.12814			0.564069	−	0.825728i	$-0.309235\pi$
$643$	466427.			1.12814			0.564069	+	0.825728i	$0.309235\pi$
$644$		−	30924.6i		−	0.0745646i
$645$	59671.6	−	10409.9i	0.143433	−	0.0250222i
$646$	−1559.25			−0.00373638
$647$			107628.i			0.257109i	0.991702	+	0.128554i	$0.0410336\pi$
$647$			107628.i			0.257109i	−0.991702	+	0.128554i	$0.958966\pi$
$648$	−287541.	−	347785.i	−0.684779	−	0.828248i
$649$	−65199.9			−0.154795
$650$			311292.i			0.736785i
$651$	2734.12	+	15672.6i	0.00645142	+	0.0369809i
$652$	55566.6			0.130713
$653$		−	509956.i		−	1.19593i	−0.801522	−	0.597966i	$-0.795976\pi$
$653$		−	509956.i		−	1.19593i	0.801522	−	0.597966i	$-0.204024\pi$
$654$	−102426.	+	17868.4i	−0.239471	+	0.0417764i
$655$	1.06303e6			2.47778
$656$			379393.i			0.881620i
$657$	−204152.	+	73465.4i	−0.472957	+	0.170197i
$658$	−161222.			−0.372369
$659$			547617.i			1.26097i	0.776200	+	0.630486i	$0.217145\pi$
$659$			547617.i			1.26097i	−0.776200	+	0.630486i	$0.782855\pi$
$660$	24223.1	+	138852.i	0.0556085	+	0.318760i
$661$	341882.			0.782480			0.391240	−	0.920289i	$-0.372046\pi$
$661$	341882.			0.782480			0.391240	+	0.920289i	$0.372046\pi$
$662$			508551.i			1.16043i
$663$	525876.	−	91740.4i	1.19634	−	0.208705i
$664$	677258.			1.53609
$665$			2220.47i			0.00502114i
$666$	145188.	+	403459.i	0.327326	+	0.909601i
$667$	−245126.			−0.550983
$668$		−	155761.i		−	0.349064i
$669$	−90272.7	−	517462.i	−0.201699	−	1.15618i
$670$	−563768.			−1.25589
$671$		−	809340.i		−	1.79757i
$672$	178181.	−	31084.2i	0.394570	−	0.0688338i
$673$	−318066.			−0.702244			−0.351122	−	0.936330i	$-0.614200\pi$
$673$	−318066.			−0.702244			−0.351122	+	0.936330i	$0.614200\pi$
$674$			357536.i			0.787046i
$675$	−167373.	−	293585.i	−0.367347	−	0.644356i
$676$	22906.3			0.0501259
$677$			793472.i			1.73123i	0.500711	+	0.865615i	$0.333072\pi$
$677$			793472.i			1.73123i	−0.500711	+	0.865615i	$0.666928\pi$
$678$	−81823.0	−	469027.i	−0.177998	−	1.02032i
$679$	631435.			1.36959
$680$			714327.i			1.54482i
$681$	165386.	−	28852.1i	0.356619	−	0.0622132i
$682$	18718.1			0.0402432
$683$		−	208408.i		−	0.446759i	−0.974732	−	0.223379i	$-0.928291\pi$
$683$		−	208408.i		−	0.446759i	0.974732	−	0.223379i	$-0.0717089\pi$
$684$	349.504	−	125.772i	0.000747034	−	0.000268825i
$685$	275679.			0.587520
$686$		−	424062.i		−	0.901117i
$687$	111255.	+	637740.i	0.235726	+	1.35123i
$688$	−39232.4			−0.0828834
$689$			618663.i			1.30321i
$690$	201804.	−	35205.2i	0.423869	−	0.0739451i
$691$	543662.			1.13860			0.569302	−	0.822128i	$-0.307213\pi$
$691$	543662.			1.13860			0.569302	+	0.822128i	$0.307213\pi$
$692$			147197.i			0.307388i
$693$	191060.	+	530933.i	0.397836	+	1.10554i
$694$	646720.			1.34276
$695$		−	227124.i		−	0.470212i
$696$	−134710.	−	772187.i	−0.278088	−	1.59406i
$697$	620961.			1.27820
$698$		−	533614.i		−	1.09526i
$699$	−644673.	+	112465.i	−1.31943	+	0.230178i
$700$	74057.0			0.151137
$701$		−	72520.4i		−	0.147579i	−0.997274	−	0.0737894i	$-0.976491\pi$
$701$		−	72520.4i		−	0.147579i	0.997274	−	0.0737894i	$-0.0235093\pi$
$702$	425274.	−	242448.i	0.862967	−	0.491978i
$703$	−2064.58			−0.00417754
$704$		−	655524.i		−	1.32264i
$705$	47678.3	+	273302.i	0.0959274	+	0.549876i
$706$	104395.			0.209445
$707$		−	888534.i		−	1.77761i
$708$	13256.6	−	2312.65i	0.0264463	−	0.00461363i
$709$	112277.			0.223356			0.111678	−	0.993744i	$-0.464378\pi$
$709$	112277.			0.223356			0.111678	+	0.993744i	$0.464378\pi$
$710$		−	428397.i		−	0.849826i
$711$	−542142.	+	195094.i	−1.07244	+	0.385926i
$712$	216586.			0.427238
$713$			7066.97i			0.0139013i
$714$	84016.7	+	481602.i	0.164805	+	0.944695i
$715$	−894406.			−1.74953
$716$		−	139171.i		−	0.271470i
$717$	246486.	−	43000.2i	0.479462	−	0.0836434i
$718$	35790.4			0.0694254
$719$		−	315016.i		−	0.609361i	−0.952455	−	0.304681i	$-0.901450\pi$
$719$		−	315016.i		−	0.609361i	0.952455	−	0.304681i	$-0.0985498\pi$
$720$	174036.	+	483625.i	0.335717	+	0.932918i
$721$	−279541.			−0.537743
$722$			464432.i			0.890938i
$723$	−74644.3	−	427877.i	−0.142797	−	0.818545i
$724$	−199226.			−0.380076
$725$		−	587018.i		−	1.11680i
$726$	191397.	−	33389.8i	0.363130	−	0.0633491i
$727$	−886179.			−1.67669			−0.838345	−	0.545141i	$-0.816476\pi$
$727$	−886179.			−1.67669			−0.838345	+	0.545141i	$0.816476\pi$
$728$			627511.i			1.18402i
$729$	−270726.	+	457315.i	−0.509418	+	0.860519i
$730$	314958.			0.591026
$731$			64212.5i			0.120167i
$732$	28707.4	+	164557.i	0.0535762	+	0.307110i
$733$	530184.			0.986775			0.493388	−	0.869810i	$-0.335758\pi$
$733$	530184.			0.986775			0.493388	+	0.869810i	$0.335758\pi$
$734$		−	498220.i		−	0.924760i
$735$	−16516.7	+	2881.39i	−0.0305738	+	0.00533368i
$736$	80344.5			0.148320
$737$		−	689806.i		−	1.26996i
$738$	535806.	−	192814.i	0.983773	−	0.354018i
$739$	703143.			1.28752			0.643761	−	0.765226i	$-0.277373\pi$
$739$	703143.			1.28752			0.643761	+	0.765226i	$0.277373\pi$
$740$			161694.i			0.295277i
$741$	405.076	+	2321.98i	0.000737734	+	0.00422885i
$742$	−566577.			−1.02909
$743$			201327.i			0.364690i	0.983235	+	0.182345i	$0.0583688\pi$
$743$			201327.i			0.364690i	−0.983235	+	0.182345i	$0.941631\pi$
$744$	−22262.1	+	3883.69i	−0.0402180	+	0.00701614i
$745$	−1.02932e6			−1.85456
$746$			430001.i			0.772666i
$747$	−270067.	−	750483.i	−0.483983	−	1.34493i
$748$	−149418.			−0.267055
$749$		−	48924.4i		−	0.0872092i
$750$	−29358.5	−	168289.i	−0.0521929	−	0.299181i
$751$	362775.			0.643217			0.321609	−	0.946873i	$-0.395776\pi$
$751$	362775.			0.643217			0.321609	+	0.946873i	$0.395776\pi$
$752$		−	179688.i		−	0.317749i
$753$	478213.	−	83425.6i	0.843396	−	0.147133i
$754$	850327.			1.49570
$755$			331503.i			0.581558i
$756$	−57679.0	−	101174.i	−0.100919	−	0.177021i
$757$	494359.			0.862682			0.431341	−	0.902189i	$-0.358041\pi$
$757$	494359.			0.862682			0.431341	+	0.902189i	$0.358041\pi$
$758$		−	573704.i		−	0.998503i
$759$	43075.9	+	246920.i	0.0747740	+	0.428620i
$760$	−3154.08			−0.00546066
$761$			1.04816e6i			1.80992i	0.425498	+	0.904959i	$0.360099\pi$
$761$			1.04816e6i			1.80992i	−0.425498	+	0.904959i	$0.639901\pi$
$762$	272504.	−	47539.0i	0.469313	−	0.0818729i
$763$	−156961.			−0.269614
$764$		−	168896.i		−	0.289357i
$765$	791560.	−	284849.i	1.35257	−	0.486734i
$766$	954386.			1.62655
$767$			85391.6i			0.145153i
$768$	59856.9	+	343113.i	0.101483	+	0.581720i
$769$	−145986.			−0.246865			−0.123432	−	0.992353i	$-0.539390\pi$
$769$	−145986.			−0.246865			−0.123432	+	0.992353i	$0.539390\pi$
$770$		−	819105.i		−	1.38152i
$771$	−615615.	+	107396.i	−1.03562	+	0.180667i
$772$	−72675.9			−0.121943
$773$		−	929338.i		−	1.55530i	−0.628696	−	0.777651i	$-0.716411\pi$
$773$		−	929338.i		−	1.55530i	0.628696	−	0.777651i	$-0.283589\pi$
$774$	19938.5	+	55406.8i	0.0332822	+	0.0924871i
$775$	−16923.7			−0.0281768
$776$			896924.i			1.48947i
$777$	111245.	+	637682.i	0.184264	+	1.05624i
$778$	−9611.72			−0.0158797
$779$			2741.82i			0.00451819i
$780$	181853.	−	31724.7i	0.298903	−	0.0521445i
$781$	524171.			0.859352
$782$			217161.i			0.355114i
$783$	−801959.	+	457197.i	−1.30806	+	0.745726i
$784$	10859.3			0.0176672
$785$			1.09559e6i			1.77791i
$786$	177599.	+	1.01804e6i	0.287472	+	1.64785i
$787$	1.09920e6			1.77470			0.887352	−	0.461092i	$-0.152542\pi$
$787$	1.09920e6			1.77470			0.887352	+	0.461092i	$0.152542\pi$
$788$		−	75755.6i		−	0.122001i
$789$	−854592.	+	149086.i	−1.37279	+	0.239487i
$790$	836398.			1.34017
$791$		−	718753.i		−	1.14875i
$792$	−754166.	+	271392.i	−1.20231	+	0.432660i
$793$	−1.05998e6			−1.68560
$794$			124376.i			0.197286i
$795$	167554.	+	960456.i	0.265107	+	1.51965i
$796$	126248.			0.199249
$797$		−	871729.i		−	1.37235i	−0.727437	−	0.686175i	$-0.759289\pi$
$797$		−	871729.i		−	1.37235i	0.727437	−	0.686175i	$-0.240711\pi$
$798$	−2126.49	+	370.972i	−0.00333932	+	0.000582553i
$799$	−294100.			−0.460683
$800$			192406.i			0.300634i
$801$	−86366.9	−	240003.i	−0.134612	−	0.374069i
$802$	217769.			0.338569
$803$			385371.i			0.597651i
$804$	24467.5	+	140253.i	0.0378510	+	0.216970i
$805$	309251.			0.477222
$806$		−	24514.9i		−	0.0377363i
$807$	−551248.	+	96166.6i	−0.846447	+	0.147665i
$808$	1.26212e6			1.93321
$809$		−	631887.i		−	0.965478i	−0.875764	−	0.482739i	$-0.839642\pi$
$809$		−	631887.i		−	0.965478i	0.875764	−	0.482739i	$-0.160358\pi$
$810$	594562.	−	491572.i	0.906207	−	0.749234i
$811$	−1.25367e6			−1.90608			−0.953042	−	0.302839i	$-0.902065\pi$
$811$	−1.25367e6			−1.90608			−0.953042	+	0.302839i	$0.902065\pi$
$812$		−	202295.i		−	0.306812i
$813$	−48658.4	−	278920.i	−0.0736168	−	0.421987i
$814$	761598.			1.14942
$815$			555675.i			0.836576i
$816$	−536764.	+	93640.0i	−0.806126	+	0.140631i
$817$	−283.528			−0.000424767
$818$		−	873783.i		−	1.30586i
$819$	695358.	−	250230.i	1.03667	−	0.373053i
$820$	214734.			0.319355
$821$			891043.i			1.32194i	0.750411	+	0.660971i	$0.229855\pi$
$821$			891043.i			1.32194i	−0.750411	+	0.660971i	$0.770145\pi$
$822$	46057.4	+	264011.i	0.0681641	+	0.390731i
$823$	−577380.			−0.852436			−0.426218	−	0.904620i	$-0.640154\pi$
$823$	−577380.			−0.852436			−0.426218	+	0.904620i	$0.640154\pi$
$824$		−	397075.i		−	0.584814i
$825$	−591313.	+	103156.i	−0.868780	+	0.151561i
$826$	−78202.5			−0.114620
$827$			978522.i			1.43074i	0.698747	+	0.715368i	$0.253741\pi$
$827$			978522.i			1.43074i	−0.698747	+	0.715368i	$0.746259\pi$
$828$	−17516.6	−	48676.4i	−0.0255498	−	0.0709999i
$829$	−1.22664e6			−1.78488			−0.892439	−	0.451169i	$-0.851007\pi$
$829$	−1.22664e6			−1.78488			−0.892439	+	0.451169i	$0.851007\pi$
$830$			1.15782e6i			1.68068i
$831$	−142959.	−	819469.i	−0.207018	−	1.18667i
$832$	−858533.			−1.24025
$833$		−	17773.6i		−	0.0256145i
$834$	217511.	−	37945.4i	0.312715	−	0.0545541i
$835$	1.55763e6			2.23404
$836$		−	659.749i		−	0.000943987i
$837$	13181.0	+	23120.4i	0.0188146	+	0.0330024i
$838$	−318436.			−0.453455
$839$		−	221493.i		−	0.314657i	−0.987546	−	0.157328i	$-0.949712\pi$
$839$		−	221493.i		−	0.314657i	0.987546	−	0.157328i	$-0.0502881\pi$
$840$	169951.	+	974193.i	0.240860	+	1.38066i
$841$	−896222.			−1.26714
$842$			490434.i			0.691762i
$843$	−244103.	+	42584.5i	−0.343494	+	0.0599234i
$844$	114181.			0.160291
$845$			229067.i			0.320811i
$846$	−253769.	+	91320.7i	−0.354567	+	0.127593i
$847$	293304.			0.408838
$848$		−	631473.i		−	0.878138i
$849$	145150.	+	832028.i	0.201373	+	1.15431i
$850$	−520048.			−0.719790
$851$			287540.i			0.397044i
$852$	−106576.	+	18592.4i	−0.146818	+	0.0256128i
$853$	1.07567e6			1.47836			0.739179	−	0.673509i	$-0.235214\pi$
$853$	1.07567e6			1.47836			0.739179	+	0.673509i	$0.235214\pi$
$854$		−	970744.i		−	1.33103i
$855$	1257.74	+	3495.10i	0.00172051	+	0.00478109i
$856$	69494.9			0.0948430
$857$			967907.i			1.31787i	0.752200	+	0.658934i	$0.228993\pi$
$857$			967907.i			1.31787i	−0.752200	+	0.658934i	$0.771007\pi$
$858$	−149427.	−	856550.i	−0.202981	−	1.16353i
$859$	476618.			0.645928			0.322964	−	0.946411i	$-0.395321\pi$
$859$	476618.			0.645928			0.322964	+	0.946411i	$0.395321\pi$
$860$			22205.3i			0.0300234i
$861$	846861.	−	147737.i	1.14237	−	0.199289i
$862$	−929156.			−1.25047
$863$			682724.i			0.916692i	0.888774	+	0.458346i	$0.151558\pi$
$863$			682724.i			0.916692i	−0.888774	+	0.458346i	$0.848442\pi$
$864$	262856.	−	149854.i	0.352120	−	0.200744i
$865$	−1.47199e6			−1.96731
$866$		−	795584.i		−	1.06084i
$867$	24079.6	+	138029.i	0.0320340	+	0.183625i
$868$	−5832.15			−0.00774086
$869$			1.02339e6i			1.35519i
$870$	1.32011e6	−	230297.i	1.74410	−	0.304263i
$871$	−903431.			−1.19085
$872$		−	222955.i		−	0.293214i
$873$	993900.	−	357662.i	1.30411	−	0.469294i
$874$	−958.865			−0.00125526
$875$		−	257892.i		−	0.336839i
$876$	−13669.2	−	78354.5i	−0.0178129	−	0.102107i
$877$	−716340.			−0.931365			−0.465683	−	0.884952i	$-0.654191\pi$
$877$	−716340.			−0.931365			−0.465683	+	0.884952i	$0.654191\pi$
$878$		−	751571.i		−	0.974947i
$879$	845724.	−	147539.i	1.09459	−	0.190954i
$880$	912925.			1.17888
$881$			304540.i			0.392367i	0.980567	+	0.196183i	$0.0628548\pi$
$881$			304540.i			0.392367i	−0.980567	+	0.196183i	$0.937145\pi$
$882$	−5518.87	−	15336.3i	−0.00709435	−	0.0197143i
$883$	408396.			0.523794			0.261897	−	0.965096i	$-0.415652\pi$
$883$	408396.			0.523794			0.261897	+	0.965096i	$0.415652\pi$
$884$			195691.i			0.250419i
$885$	23126.9	+	132568.i	0.0295277	+	0.169259i
$886$	335045.			0.426811
$887$		−	657288.i		−	0.835427i	−0.908579	−	0.417713i	$-0.862832\pi$
$887$		−	657288.i		−	0.835427i	0.908579	−	0.417713i	$-0.137168\pi$
$888$	−905797.	+	158019.i	−1.14870	+	0.200393i
$889$	417594.			0.528385
$890$			370269.i			0.467452i
$891$	601470.	+	727485.i	0.757633	+	0.916365i
$892$	192561.			0.242013
$893$		−	1298.59i		−	0.00162843i
$894$	−171968.	−	985758.i	−0.215166	−	1.23338i
$895$	1.39173e6			1.73744
$896$		−	464701.i		−	0.578839i
$897$	323389.	−	56416.0i	0.401920	−	0.0701161i
$898$	−897229.			−1.11263
$899$			46228.9i			0.0571998i
$900$	116568.	−	41947.9i	0.143911	−	0.0517876i
$901$	−1.03355e6			−1.27315
$902$		−	1.01143e6i		−	1.24314i
$903$	15277.3	+	87572.5i	0.0187357	+	0.107397i
$904$	1.02096e6			1.24931
$905$		−	1.99230e6i		−	2.43252i
$906$	−317472.	+	55383.8i	−0.386766	+	0.0674724i
$907$	1.35437e6			1.64636			0.823179	−	0.567783i	$-0.192199\pi$
$907$	1.35437e6			1.64636			0.823179	+	0.567783i	$0.192199\pi$
$908$			61544.3i			0.0746477i
$909$	−503290.	−	1.39858e6i	−0.609103	−	1.69262i
$910$	−1.07277e6			−1.29546
$911$		−	29604.9i		−	0.0356719i	−0.999841	−	0.0178360i	$-0.994322\pi$
$911$		−	29604.9i		−	0.0356719i	0.999841	−	0.0178360i	$-0.00567766\pi$
$912$	−413.463	−	2370.06i	−0.000497104	−	0.00284950i
$913$	−1.41667e6			−1.69952
$914$		−	720439.i		−	0.862393i
$915$	−1.64560e6	+	287079.i	−1.96554	+	0.342893i
$916$	−237319.			−0.282840
$917$			1.56007e6i			1.85527i
$918$	405038.	+	710468.i	0.480629	+	0.843061i
$919$	−792378.			−0.938213			−0.469106	−	0.883142i	$-0.655424\pi$
$919$	−792378.			−0.938213			−0.469106	+	0.883142i	$0.655424\pi$
$920$			439277.i			0.518995i
$921$	53006.2	+	303843.i	0.0624895	+	0.358203i
$922$	−644642.			−0.758327
$923$		−	686502.i		−	0.805821i
$924$	−203775.	+	35549.1i	−0.238675	+	0.0416375i
$925$	−688588.			−0.804778
$926$			432708.i			0.504630i
$927$	−440007.	+	158340.i	−0.512035	+	0.184260i
$928$	525577.			0.610295
$929$		−	678039.i		−	0.785639i	−0.919616	−	0.392820i	$-0.871500\pi$
$929$		−	678039.i		−	0.785639i	0.919616	−	0.392820i	$-0.128500\pi$
$930$	−6639.44	−	38058.7i	−0.00767654	−	0.0440035i
$931$	78.4787			9.05425e−5
$932$		−	239899.i		−	0.276183i
$933$	−1.21872e6	+	212610.i	−1.40004	+	0.244242i
$934$	787189.			0.902372
$935$		−	1.49421e6i		−	1.70918i
$936$	355439.	+	987723.i	0.405708	+	1.12741i
$937$	−1.48025e6			−1.68599			−0.842996	−	0.537920i	$-0.819210\pi$
$937$	−1.48025e6			−1.68599			−0.842996	+	0.537920i	$0.819210\pi$
$938$		−	827371.i		−	0.940361i
$939$	−228731.	−	1.31114e6i	−0.259415	−	1.48702i
$940$	−101703.			−0.115100
$941$		−	149475.i		−	0.168807i	−0.996432	−	0.0844034i	$-0.973102\pi$
$941$		−	149475.i		−	0.168807i	0.996432	−	0.0844034i	$-0.0268984\pi$
$942$	−1.04922e6	+	183040.i	−1.18240	+	0.206273i
$943$	381862.			0.429420
$944$		−	87159.7i		−	0.0978074i
$945$	1.01175e6	−	576800.i	1.13295	−	0.645894i
$946$	104590.			0.116871
$947$		−	533086.i		−	0.594425i	−0.954811	−	0.297213i	$-0.903943\pi$
$947$		−	533086.i		−	0.594425i	0.954811	−	0.297213i	$-0.0960570\pi$
$948$	−36299.6	−	208077.i	−0.0403911	−	0.231530i
$949$	504717.			0.560422
$950$		−	2296.25i		−	0.00254432i
$951$	−936486.	+	163373.i	−1.03548	+	0.180642i
$952$	−1.04833e6			−1.15671
$953$			551784.i			0.607552i	0.952743	+	0.303776i	$0.0982475\pi$
$953$			551784.i			0.607552i	−0.952743	+	0.303776i	$0.901753\pi$
$954$	−891812.	+	320925.i	−0.979888	+	0.352620i
$955$	1.68899e6			1.85191
$956$			91723.6i			0.100361i
$957$	281782.	+	1.61524e6i	0.307674	+	1.76365i
$958$	−34499.8			−0.0375912
$959$			404580.i			0.439913i
$960$	−1.33285e6	+	232519.i	−1.44623	+	0.252299i
$961$	−922188.			−0.998557
$962$		−	997457.i		−	1.07781i
$963$	−27712.1	−	77008.7i	−0.0298825	−	0.0830400i
$964$	159224.			0.171338
$965$		−	726771.i		−	0.780446i
$966$	51666.3	+	296162.i	0.0553673	+	0.317377i
$967$	436427.			0.466723			0.233361	−	0.972390i	$-0.425027\pi$
$967$	436427.			0.466723			0.233361	+	0.972390i	$0.425027\pi$
$968$			416625.i			0.444625i
$969$	−3879.13	+	676.725i	−0.00413130	+	0.000720716i
$970$	−1.53335e6			−1.62967
$971$			61610.5i			0.0653456i	0.999466	+	0.0326728i	$0.0104019\pi$
$971$			61610.5i			0.0653456i	−0.999466	+	0.0326728i	$0.989598\pi$
$972$	−148096.	−	126580.i	−0.156751	−	0.133977i
$973$	333322.			0.352077
$974$		−	1.53893e6i		−	1.62219i
$975$	135103.	+	774437.i	0.142120	+	0.814661i
$976$	1.08193e6			1.13580
$977$		−	432087.i		−	0.452671i	−0.974049	−	0.226335i	$-0.927325\pi$
$977$		−	432087.i		−	0.452671i	0.974049	−	0.226335i	$-0.0726745\pi$
$978$	−532156.	+	92836.0i	−0.556367	+	0.0970597i
$979$	−453047.			−0.472692
$980$		−	6146.29i		−	0.00639972i
$981$	−247061.	+	88906.9i	−0.256724	+	0.0923841i
$982$	89308.9			0.0926130
$983$			901970.i			0.933437i	0.884406	+	0.466718i	$0.154564\pi$
$983$			901970.i			0.933437i	−0.884406	+	0.466718i	$0.845436\pi$
$984$	209854.	+	1.20293e6i	0.216734	+	1.24236i
$985$	757568.			0.780817
$986$			1.42057e6i			1.46119i
$987$	−401092.	+	69971.5i	−0.411727	+	0.0718269i
$988$	−864.067			−0.000885184
$989$			39487.7i			0.0403709i
$990$	−463964.	−	1.28930e6i	−0.473384	−	1.31548i
$991$	310140.			0.315799			0.157899	−	0.987455i	$-0.449528\pi$
$991$	310140.			0.315799			0.157899	+	0.987455i	$0.449528\pi$
$992$		−	15152.3i		−	0.0153977i
$993$	220714.	+	1.26518e6i	0.223837	+	1.28308i
$994$	628705.			0.636318
$995$			1.26250e6i			1.27522i
$996$	288040.	−	50249.3i	0.290358	−	0.0506537i
$997$	922449.			0.928008			0.464004	−	0.885833i	$-0.346412\pi$
$997$	922449.			0.928008			0.464004	+	0.885833i	$0.346412\pi$
$998$		−	613641.i		−	0.616103i
$999$	536304.	+	940720.i	0.537378	+	0.942604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.24	✓	78
3.2	odd	2	inner	177.5.b.a.119.55	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.24	✓	78	1.1	even	1	trivial
177.5.b.a.119.55	yes	78	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-3.56380i q^{2} +(-1.54671 - 8.86610i) q^{3} +3.29930 q^{4} +32.9935i q^{5} +(-31.5970 + 5.51219i) q^{6} -48.4204 q^{7} -68.7789i q^{8} +(-76.2153 + 27.4266i) q^{9} +O(q^{10})\)	\(q-3.56380i q^{2} +(-1.54671 - 8.86610i) q^{3} +3.29930 q^{4} +32.9935i q^{5} +(-31.5970 + 5.51219i) q^{6} -48.4204 q^{7} -68.7789i q^{8} +(-76.2153 + 27.4266i) q^{9} +117.582 q^{10} +143.870i q^{11} +(-5.10307 - 29.2519i) q^{12} +188.424 q^{13} +172.561i q^{14} +(292.524 - 51.0315i) q^{15} -192.326 q^{16} +314.784i q^{17} +(97.7432 + 271.617i) q^{18} -1.38992 q^{19} +108.855i q^{20} +(74.8926 + 429.300i) q^{21} +512.723 q^{22} +193.577i q^{23} +(-609.801 + 106.381i) q^{24} -463.571 q^{25} -671.508i q^{26} +(361.051 + 633.311i) q^{27} -159.753 q^{28} +1266.29i q^{29} +(-181.866 - 1042.50i) q^{30} +36.5072 q^{31} -415.051i q^{32} +(1275.56 - 222.525i) q^{33} +1121.83 q^{34} -1597.56i q^{35} +(-251.457 + 90.4886i) q^{36} +1485.40 q^{37} +4.95339i q^{38} +(-291.439 - 1670.59i) q^{39} +2269.26 q^{40} -1972.66i q^{41} +(1529.94 - 266.903i) q^{42} +203.989 q^{43} +474.668i q^{44} +(-904.901 - 2514.61i) q^{45} +689.872 q^{46} +934.292i q^{47} +(297.473 + 1705.18i) q^{48} -56.4629 q^{49} +1652.08i q^{50} +(2790.91 - 486.882i) q^{51} +621.668 q^{52} +3283.35i q^{53} +(2257.00 - 1286.71i) q^{54} -4746.76 q^{55} +3330.30i q^{56} +(2.14980 + 12.3231i) q^{57} +4512.83 q^{58} +453.188i q^{59} +(965.122 - 168.368i) q^{60} -5625.52 q^{61} -130.105i q^{62} +(3690.38 - 1328.01i) q^{63} -4556.37 q^{64} +6216.78i q^{65} +(-793.036 - 4545.85i) q^{66} -4794.66 q^{67} +1038.57i q^{68} +(1716.28 - 299.409i) q^{69} -5693.39 q^{70} -3643.38i q^{71} +(1886.38 + 5242.01i) q^{72} +2678.61 q^{73} -5293.67i q^{74} +(717.012 + 4110.07i) q^{75} -4.58574 q^{76} -6966.22i q^{77} +(-5953.66 + 1038.63i) q^{78} +7113.29 q^{79} -6345.50i q^{80} +(5056.56 - 4180.66i) q^{81} -7030.16 q^{82} +9846.88i q^{83} +(247.093 + 1416.39i) q^{84} -10385.8 q^{85} -726.977i q^{86} +(11227.1 - 1958.60i) q^{87} +9895.19 q^{88} +3149.01i q^{89} +(-8961.58 + 3224.89i) q^{90} -9123.59 q^{91} +638.669i q^{92} +(-56.4663 - 323.676i) q^{93} +3329.63 q^{94} -45.8582i q^{95} +(-3679.88 + 641.965i) q^{96} -13040.7 q^{97} +201.223i q^{98} +(-3945.86 - 10965.1i) 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