LMFDB - Embedded newform 177.5.b.a.119.53

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			119.53
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.43329i q^{2} +(0.889192 - 8.95597i) q^{3} +4.21249 q^{4} -18.6227i q^{5} +(30.7485 + 3.05286i) q^{6} -68.5956 q^{7} +69.3954i q^{8} +(-79.4187 - 15.9271i) q^{9} +O(q^{10})$	\(q+3.43329i q^{2} +(0.889192 - 8.95597i) q^{3} +4.21249 q^{4} -18.6227i q^{5} +(30.7485 + 3.05286i) q^{6} -68.5956 q^{7} +69.3954i q^{8} +(-79.4187 - 15.9271i) q^{9} +63.9371 q^{10} -69.0487i q^{11} +(3.74571 - 37.7269i) q^{12} -25.1488 q^{13} -235.509i q^{14} +(-166.784 - 16.5591i) q^{15} -170.855 q^{16} +489.540i q^{17} +(54.6826 - 272.668i) q^{18} -352.583 q^{19} -78.4478i q^{20} +(-60.9946 + 614.340i) q^{21} +237.065 q^{22} +736.679i q^{23} +(621.503 + 61.7058i) q^{24} +278.196 q^{25} -86.3432i q^{26} +(-213.261 + 697.109i) q^{27} -288.958 q^{28} -166.138i q^{29} +(56.8524 - 572.619i) q^{30} -776.957 q^{31} +523.731i q^{32} +(-618.398 - 61.3976i) q^{33} -1680.74 q^{34} +1277.43i q^{35} +(-334.550 - 67.0929i) q^{36} -432.452 q^{37} -1210.52i q^{38} +(-22.3621 + 225.232i) q^{39} +1292.33 q^{40} -3199.69i q^{41} +(-2109.21 - 209.412i) q^{42} -2342.99 q^{43} -290.867i q^{44} +(-296.606 + 1478.99i) q^{45} -2529.24 q^{46} +1231.19i q^{47} +(-151.923 + 1530.17i) q^{48} +2304.35 q^{49} +955.129i q^{50} +(4384.31 + 435.295i) q^{51} -105.939 q^{52} -4424.01i q^{53} +(-2393.38 - 732.189i) q^{54} -1285.87 q^{55} -4760.22i q^{56} +(-313.514 + 3157.72i) q^{57} +570.400 q^{58} -453.188i q^{59} +(-702.576 - 69.7551i) q^{60} -499.323 q^{61} -2667.52i q^{62} +(5447.77 + 1092.53i) q^{63} -4531.80 q^{64} +468.338i q^{65} +(210.796 - 2123.14i) q^{66} -1405.62 q^{67} +2062.18i q^{68} +(6597.67 + 655.049i) q^{69} -4385.80 q^{70} +578.843i q^{71} +(1105.27 - 5511.29i) q^{72} -9315.74 q^{73} -1484.74i q^{74} +(247.370 - 2491.51i) q^{75} -1485.25 q^{76} +4736.44i q^{77} +(-773.287 - 76.7757i) q^{78} -3813.63 q^{79} +3181.78i q^{80} +(6053.65 + 2529.82i) q^{81} +10985.5 q^{82} -4628.81i q^{83} +(-256.939 + 2587.90i) q^{84} +9116.55 q^{85} -8044.18i q^{86} +(-1487.92 - 147.728i) q^{87} +4791.67 q^{88} +1932.73i q^{89} +(-5077.80 - 1018.34i) q^{90} +1725.10 q^{91} +3103.25i q^{92} +(-690.864 + 6958.40i) q^{93} -4227.04 q^{94} +6566.04i q^{95} +(4690.51 + 465.697i) q^{96} +5695.17 q^{97} +7911.52i q^{98} +(-1099.75 + 5483.76i) 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 $

$2$			3.43329i			0.858324i	0.903228	+	0.429162i	$0.141191\pi$
$2$			3.43329i			0.858324i	−0.903228	+	0.429162i	$0.858809\pi$
$3$	0.889192	−	8.95597i	0.0987991	−	0.995107i
$3$	0.889192	−	8.95597i	0.0987991	−	0.995107i
$4$	4.21249			0.263280
$5$		−	18.6227i		−	0.744907i	−0.928051	−	0.372453i	$-0.878517\pi$
$5$		−	18.6227i		−	0.744907i	0.928051	−	0.372453i	$-0.121483\pi$
$6$	30.7485	+	3.05286i	0.854124	+	0.0848016i
$7$	−68.5956			−1.39991			−0.699955	−	0.714187i	$-0.746797\pi$
$7$	−68.5956			−1.39991			−0.699955	+	0.714187i	$0.746797\pi$
$8$			69.3954i			1.08430i
$9$	−79.4187	−	15.9271i	−0.980477	−	0.196631i
$10$	63.9371			0.639371
$11$		−	69.0487i		−	0.570651i	−0.958431	−	0.285325i	$-0.907898\pi$
$11$		−	69.0487i		−	0.570651i	0.958431	−	0.285325i	$-0.0921017\pi$
$12$	3.74571	−	37.7269i	0.0260119	−	0.261992i
$13$	−25.1488			−0.148809			−0.0744047	−	0.997228i	$-0.523706\pi$
$13$	−25.1488			−0.148809			−0.0744047	+	0.997228i	$0.523706\pi$
$14$		−	235.509i		−	1.20158i
$15$	−166.784	−	16.5591i	−0.741262	−	0.0735961i
$16$	−170.855			−0.667403
$17$			489.540i			1.69391i	0.531664	+	0.846956i	$0.321567\pi$
$17$			489.540i			1.69391i	−0.531664	+	0.846956i	$0.678433\pi$
$18$	54.6826	−	272.668i	0.168773	−	0.841567i
$19$	−352.583			−0.976684			−0.488342	−	0.872652i	$-0.662398\pi$
$19$	−352.583			−0.976684			−0.488342	+	0.872652i	$0.662398\pi$
$20$		−	78.4478i		−	0.196119i
$21$	−60.9946	+	614.340i	−0.138310	+	1.39306i
$22$	237.065			0.489803
$23$			736.679i			1.39259i	0.717757	+	0.696294i	$0.245169\pi$
$23$			736.679i			1.39259i	−0.717757	+	0.696294i	$0.754831\pi$
$24$	621.503	+	61.7058i	1.07900	+	0.107128i
$25$	278.196			0.445114
$26$		−	86.3432i		−	0.127727i
$27$	−213.261	+	697.109i	−0.292540	+	0.956253i
$28$	−288.958			−0.368569
$29$		−	166.138i		−	0.197548i	−0.995110	−	0.0987740i	$-0.968508\pi$
$29$		−	166.138i		−	0.197548i	0.995110	−	0.0987740i	$-0.0314921\pi$
$30$	56.8524	−	572.619i	0.0631693	−	0.636243i
$31$	−776.957			−0.808488			−0.404244	−	0.914651i	$-0.632465\pi$
$31$	−776.957			−0.808488			−0.404244	+	0.914651i	$0.632465\pi$
$32$			523.731i			0.511456i
$33$	−618.398	−	61.3976i	−0.567859	−	0.0563798i
$34$	−1680.74			−1.45392
$35$			1277.43i			1.04280i
$36$	−334.550	−	67.0929i	−0.258141	−	0.0517692i
$37$	−432.452			−0.315889			−0.157945	−	0.987448i	$-0.550487\pi$
$37$	−432.452			−0.315889			−0.157945	+	0.987448i	$0.550487\pi$
$38$		−	1210.52i		−	0.838311i
$39$	−22.3621	+	225.232i	−0.0147022	+	0.148081i
$40$	1292.33			0.807705
$41$		−	3199.69i		−	1.90344i	−0.306963	−	0.951721i	$-0.599313\pi$
$41$		−	3199.69i		−	1.90344i	0.306963	−	0.951721i	$-0.400687\pi$
$42$	−2109.21	−	209.412i	−1.19570	−	0.118715i
$43$	−2342.99			−1.26717			−0.633584	−	0.773674i	$-0.718417\pi$
$43$	−2342.99			−1.26717			−0.633584	+	0.773674i	$0.718417\pi$
$44$		−	290.867i		−	0.150241i
$45$	−296.606	+	1478.99i	−0.146472	+	0.730364i
$46$	−2529.24			−1.19529
$47$			1231.19i			0.557352i	0.960385	+	0.278676i	$0.0898955\pi$
$47$			1231.19i			0.557352i	−0.960385	+	0.278676i	$0.910104\pi$
$48$	−151.923	+	1530.17i	−0.0659388	+	0.664138i
$49$	2304.35			0.959747
$50$			955.129i			0.382052i
$51$	4384.31	+	435.295i	1.68562	+	0.167357i
$52$	−105.939			−0.0391786
$53$		−	4424.01i		−	1.57494i	−0.616352	−	0.787471i	$-0.711390\pi$
$53$		−	4424.01i		−	1.57494i	0.616352	−	0.787471i	$-0.288610\pi$
$54$	−2393.38	−	732.189i	−0.820775	−	0.251094i
$55$	−1285.87			−0.425082
$56$		−	4760.22i		−	1.51793i
$57$	−313.514	+	3157.72i	−0.0964955	+	0.971906i
$58$	570.400			0.169560
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	−702.576	−	69.7551i	−0.195160	−	0.0193764i
$61$	−499.323			−0.134191			−0.0670953	−	0.997747i	$-0.521373\pi$
$61$	−499.323			−0.134191			−0.0670953	+	0.997747i	$0.521373\pi$
$62$		−	2667.52i		−	0.693945i
$63$	5447.77	+	1092.53i	1.37258	+	0.275266i
$64$	−4531.80			−1.10640
$65$			468.338i			0.110849i
$66$	210.796	−	2123.14i	0.0483921	−	0.487407i
$67$	−1405.62			−0.313126			−0.156563	−	0.987668i	$-0.550041\pi$
$67$	−1405.62			−0.313126			−0.156563	+	0.987668i	$0.550041\pi$
$68$			2062.18i			0.445974i
$69$	6597.67	+	655.049i	1.38577	+	0.137586i
$70$	−4385.80			−0.895062
$71$			578.843i			0.114827i	0.998350	+	0.0574135i	$0.0182853\pi$
$71$			578.843i			0.114827i	−0.998350	+	0.0574135i	$0.981715\pi$
$72$	1105.27	−	5511.29i	0.213208	−	1.06314i
$73$	−9315.74			−1.74812			−0.874061	−	0.485816i	$-0.838523\pi$
$73$	−9315.74			−1.74812			−0.874061	+	0.485816i	$0.838523\pi$
$74$		−	1484.74i		−	0.271135i
$75$	247.370	−	2491.51i	0.0439768	−	0.442936i
$76$	−1485.25			−0.257142
$77$			4736.44i			0.798859i
$78$	−773.287	−	76.7757i	−0.127102	−	0.0126193i
$79$	−3813.63			−0.611061			−0.305530	−	0.952182i	$-0.598834\pi$
$79$	−3813.63			−0.611061			−0.305530	+	0.952182i	$0.598834\pi$
$80$			3181.78i			0.497153i
$81$	6053.65	+	2529.82i	0.922672	+	0.385585i
$82$	10985.5			1.63377
$83$		−	4628.81i		−	0.671913i	−0.941877	−	0.335957i	$-0.890940\pi$
$83$		−	4628.81i		−	0.671913i	0.941877	−	0.335957i	$-0.109060\pi$
$84$	−256.939	+	2587.90i	−0.0364142	+	0.366766i
$85$	9116.55			1.26181
$86$		−	8044.18i		−	1.08764i
$87$	−1487.92	−	147.728i	−0.196581	−	0.0195175i
$88$	4791.67			0.618759
$89$			1932.73i			0.244001i	0.992530	+	0.122001i	$0.0389310\pi$
$89$			1932.73i			0.244001i	−0.992530	+	0.122001i	$0.961069\pi$
$90$	−5077.80	−	1018.34i	−0.626889	−	0.125720i
$91$	1725.10			0.208320
$92$			3103.25i			0.366641i
$93$	−690.864	+	6958.40i	−0.0798779	+	0.804533i
$94$	−4227.04			−0.478388
$95$			6566.04i			0.727539i
$96$	4690.51	+	465.697i	0.508953	+	0.0505313i
$97$	5695.17			0.605290			0.302645	−	0.953103i	$-0.402130\pi$
$97$	5695.17			0.605290			0.302645	+	0.953103i	$0.402130\pi$
$98$			7911.52i			0.823774i
$99$	−1099.75	+	5483.76i	−0.112208	+	0.559510i
$100$	1171.90			0.117190
$101$			1935.83i			0.189769i	0.995488	+	0.0948845i	$0.0302482\pi$
$101$			1935.83i			0.189769i	−0.995488	+	0.0948845i	$0.969752\pi$
$102$	−1494.50	+	15052.6i	−0.143646	+	1.44681i
$103$	21023.8			1.98169			0.990847	−	0.134987i	$-0.0430993\pi$
$103$	21023.8			1.98169			0.990847	+	0.134987i	$0.0430993\pi$
$104$		−	1745.21i		−	0.161355i
$105$	11440.6	+	1135.88i	1.03770	+	0.103028i
$106$	15188.9			1.35181
$107$		−	1239.15i		−	0.108232i	−0.998535	−	0.0541162i	$-0.982766\pi$
$107$		−	1239.15i		−	0.108232i	0.998535	−	0.0541162i	$-0.0172341\pi$
$108$	−898.361	+	2936.56i	−0.0770199	+	0.251763i
$109$	−19223.7			−1.61802			−0.809012	−	0.587792i	$-0.799997\pi$
$109$	−19223.7			−1.61802			−0.809012	+	0.587792i	$0.799997\pi$
$110$		−	4414.78i		−	0.364858i
$111$	−384.533	+	3873.03i	−0.0312096	+	0.314344i
$112$	11719.9			0.934304
$113$			10069.8i			0.788613i	0.918979	+	0.394306i	$0.129015\pi$
$113$			10069.8i			0.788613i	−0.918979	+	0.394306i	$0.870985\pi$
$114$	−10841.4	−	1076.39i	−0.834210	−	0.0828244i
$115$	13718.9			1.03735
$116$		−	699.853i		−	0.0520105i
$117$	1997.28	+	400.548i	0.145904	+	0.0292606i
$118$	1555.93			0.111744
$119$		−	33580.3i		−	2.37132i
$120$	1149.13	−	11574.0i	0.0798005	−	0.803753i
$121$	9873.27			0.674358
$122$		−	1714.32i		−	0.115179i
$123$	−28656.3	−	2845.13i	−1.89413	−	0.188058i
$124$	−3272.92			−0.212859
$125$		−	16819.9i		−	1.07648i
$126$	−3750.98	+	18703.8i	−0.236267	+	1.17812i
$127$	−523.608			−0.0324638			−0.0162319	−	0.999868i	$-0.505167\pi$
$127$	−523.608			−0.0324638			−0.0162319	+	0.999868i	$0.505167\pi$
$128$		−	7179.33i		−	0.438192i
$129$	−2083.37	+	20983.8i	−0.125195	+	1.26097i
$130$	−1607.94			−0.0951445
$131$			9744.40i			0.567822i	0.958851	+	0.283911i	$0.0916321\pi$
$131$			9744.40i			0.567822i	−0.958851	+	0.283911i	$0.908368\pi$
$132$	−2604.99	−	258.636i	−0.149506	−	0.0148437i
$133$	24185.6			1.36727
$134$		−	4825.92i		−	0.268764i
$135$	12982.0	+	3971.50i	0.712320	+	0.217915i
$136$	−33971.9			−1.83671
$137$		−	35694.8i		−	1.90179i	−0.309508	−	0.950897i	$-0.600164\pi$
$137$		−	35694.8i		−	1.90179i	0.309508	−	0.950897i	$-0.399836\pi$
$138$	−2248.98	+	22651.8i	−0.118094	+	1.18944i
$139$	1483.96			0.0768056			0.0384028	−	0.999262i	$-0.487773\pi$
$139$	1483.96			0.0768056			0.0384028	+	0.999262i	$0.487773\pi$
$140$			5381.17i			0.274549i
$141$	11026.5	+	1094.76i	0.554625	+	0.0550658i
$142$	−1987.34			−0.0985587
$143$			1736.49i			0.0849182i
$144$	13569.1	+	2721.23i	0.654374	+	0.131232i
$145$	−3093.93			−0.147155
$146$		−	31983.7i		−	1.50045i
$147$	2049.01	−	20637.7i	0.0948221	−	0.955051i
$148$	−1821.70			−0.0831675
$149$			8446.68i			0.380464i	0.981739	+	0.190232i	$0.0609240\pi$
$149$			8446.68i			0.380464i	−0.981739	+	0.190232i	$0.939076\pi$
$150$	8554.10	+	849.293i	0.380182	+	0.0377463i
$151$	−31006.4			−1.35987			−0.679935	−	0.733272i	$-0.737992\pi$
$151$	−31006.4			−1.35987			−0.679935	+	0.733272i	$0.737992\pi$
$152$		−	24467.6i		−	1.05902i
$153$	7796.98	−	38878.6i	0.333076	−	1.66084i
$154$	−16261.6			−0.685680
$155$			14469.0i			0.602249i
$156$	−94.2000	+	948.786i	−0.00387081	+	0.0389869i
$157$	22789.4			0.924558			0.462279	−	0.886734i	$-0.347032\pi$
$157$	22789.4			0.924558			0.462279	+	0.886734i	$0.347032\pi$
$158$		−	13093.3i		−	0.524488i
$159$	−39621.3	−	3933.79i	−1.56724	−	0.155603i
$160$	9753.26			0.380987
$161$		−	50532.9i		−	1.94950i
$162$	−8685.63	+	20784.0i	−0.330957	+	0.791951i
$163$	39542.2			1.48829			0.744143	−	0.668021i	$-0.232858\pi$
$163$	39542.2			1.48829			0.744143	+	0.668021i	$0.232858\pi$
$164$		−	13478.6i		−	0.501139i
$165$	−1143.39	+	11516.2i	−0.0419977	+	0.423002i
$166$	15892.1			0.576719
$167$			5538.18i			0.198579i	0.995059	+	0.0992897i	$0.0316571\pi$
$167$			5538.18i			0.198579i	−0.995059	+	0.0992897i	$0.968343\pi$
$168$	−42632.4	−	4232.75i	−1.51050	−	0.149970i
$169$	−27928.5			−0.977856
$170$			31299.8i			1.08304i
$171$	28001.7	+	5615.64i	0.957617	+	0.192047i
$172$	−9869.82			−0.333620
$173$			21328.1i			0.712622i	0.934367	+	0.356311i	$0.115966\pi$
$173$			21328.1i			0.712622i	−0.934367	+	0.356311i	$0.884034\pi$
$174$	507.195	−	5108.48i	0.0167524	−	0.168730i
$175$	−19083.0			−0.623119
$176$			11797.3i			0.380854i
$177$	−4058.73	−	402.971i	−0.129552	−	0.0128625i
$178$	−6635.65			−0.209432
$179$			23635.0i			0.737649i	0.929499	+	0.368825i	$0.120240\pi$
$179$			23635.0i			0.737649i	−0.929499	+	0.368825i	$0.879760\pi$
$180$	−1249.45	+	6230.22i	−0.0385632	+	0.192291i
$181$	43001.6			1.31259			0.656293	−	0.754506i	$-0.272124\pi$
$181$	43001.6			1.31259			0.656293	+	0.754506i	$0.272124\pi$
$182$			5922.76i			0.178806i
$183$	−443.994	+	4471.92i	−0.0132579	+	0.133534i
$184$	−51122.2			−1.50999
$185$			8053.42i			0.235308i
$186$	−23890.2	−	2371.94i	−0.690549	−	0.0685611i
$187$	33802.1			0.966632
$188$			5186.37i			0.146740i
$189$	14628.8	−	47818.6i	0.409529	−	1.33867i
$190$	−22543.1			−0.624464
$191$			25711.7i			0.704796i	0.935850	+	0.352398i	$0.114634\pi$
$191$			25711.7i			0.704796i	−0.935850	+	0.352398i	$0.885366\pi$
$192$	−4029.64	+	40586.7i	−0.109311	+	1.10098i
$193$	−39417.9			−1.05823			−0.529113	−	0.848551i	$-0.677475\pi$
$193$	−39417.9			−1.05823			−0.529113	+	0.848551i	$0.677475\pi$
$194$			19553.2i			0.519534i
$195$	4194.42	+	416.442i	0.110307	+	0.0109518i
$196$	9707.05			0.252683
$197$			4221.38i			0.108773i	0.998520	+	0.0543866i	$0.0173203\pi$
$197$			4221.38i			0.108773i	−0.998520	+	0.0543866i	$0.982680\pi$
$198$	−18827.4	−	3775.76i	−0.480241	−	0.0963106i
$199$	−17411.5			−0.439674			−0.219837	−	0.975537i	$-0.570553\pi$
$199$	−17411.5			−0.439674			−0.219837	+	0.975537i	$0.570553\pi$
$200$			19305.5i			0.482638i
$201$	−1249.87	+	12588.7i	−0.0309366	+	0.311594i
$202$	−6646.29			−0.162883
$203$			11396.3i			0.276549i
$204$	18468.8	+	1833.67i	0.443792	+	0.0440618i
$205$	−59586.7			−1.41789
$206$			72180.9i			1.70094i
$207$	11733.2	−	58506.1i	0.273827	−	1.36540i
$208$	4296.80			0.0993159
$209$			24345.4i			0.557346i
$210$	−3899.82	+	39279.1i	−0.0884313	+	0.890683i
$211$	−85262.2			−1.91510			−0.957551	−	0.288266i	$-0.906921\pi$
$211$	−85262.2			−1.91510			−0.957551	+	0.288266i	$0.906921\pi$
$212$		−	18636.1i		−	0.414651i
$213$	5184.10	+	514.702i	0.114265	+	0.0113448i
$214$	4254.38			0.0928984
$215$			43632.8i			0.943922i
$216$	−48376.2	−	14799.4i	−1.03687	−	0.317202i
$217$	53295.8			1.13181
$218$		−	66000.8i		−	1.38879i
$219$	−8283.48	+	83431.5i	−0.172713	+	1.73957i
$220$	−5416.72			−0.111916
$221$		−	12311.4i		−	0.252070i
$222$	−13297.3	−	1320.22i	−0.269809	−	0.0267879i
$223$	17295.8			0.347802			0.173901	−	0.984763i	$-0.444363\pi$
$223$	17295.8			0.347802			0.173901	+	0.984763i	$0.444363\pi$
$224$		−	35925.6i		−	0.715992i
$225$	−22094.0	−	4430.87i	−0.436424	−	0.0875233i
$226$	−34572.6			−0.676885
$227$			69409.8i			1.34700i	0.739185	+	0.673502i	$0.235211\pi$
$227$			69409.8i			1.34700i	−0.739185	+	0.673502i	$0.764789\pi$
$228$	−1320.67	+	13301.9i	−0.0254054	+	0.255884i
$229$	−5324.85			−0.101540			−0.0507699	−	0.998710i	$-0.516168\pi$
$229$	−5324.85			−0.101540			−0.0507699	+	0.998710i	$0.516168\pi$
$230$			47101.2i			0.890381i
$231$	42419.4	+	4211.60i	0.794951	+	0.0789266i
$232$	11529.2			0.214202
$233$		−	103952.i		−	1.91479i	−0.288782	−	0.957395i	$-0.593250\pi$
$233$		−	103952.i		−	1.91479i	0.288782	−	0.957395i	$-0.406750\pi$
$234$	−1375.20	+	6857.27i	−0.0251151	+	0.125233i
$235$	22928.0			0.415175
$236$		−	1909.05i		−	0.0342762i
$237$	−3391.05	+	34154.7i	−0.0603722	+	0.608071i
$238$	115291.			2.03536
$239$		−	81609.9i		−	1.42872i	−0.699779	−	0.714360i	$-0.746718\pi$
$239$		−	81609.9i		−	1.42872i	0.699779	−	0.714360i	$-0.253282\pi$
$240$	28495.9	+	2829.21i	0.494721	+	0.0491183i
$241$	55398.8			0.953819			0.476910	−	0.878952i	$-0.341757\pi$
$241$	55398.8			0.953819			0.476910	+	0.878952i	$0.341757\pi$
$242$			33897.9i			0.578817i
$243$	28039.9	−	51966.8i	0.474858	−	0.880062i
$244$	−2103.39			−0.0353297
$245$		−	42913.2i		−	0.714922i
$246$	9768.19	−	98385.5i	0.161415	−	1.62578i
$247$	8867.04			0.145340
$248$		−	53917.3i		−	0.876647i
$249$	−41455.5	−	4115.90i	−0.668626	−	0.0663844i
$250$	57747.8			0.923964
$251$			56736.7i			0.900568i	0.892885	+	0.450284i	$0.148677\pi$
$251$			56736.7i			0.900568i	−0.892885	+	0.450284i	$0.851323\pi$
$252$	22948.7	+	4602.27i	0.361373	+	0.0724722i
$253$	50866.8			0.794682
$254$		−	1797.70i		−	0.0278644i
$255$	8106.36	−	81647.5i	0.124665	−	1.25563i
$256$	−47860.1			−0.730287
$257$		−	15674.5i		−	0.237315i	−0.992935	−	0.118658i	$-0.962141\pi$
$257$		−	15674.5i		−	0.237315i	0.992935	−	0.118658i	$-0.0378591\pi$
$258$	−72043.4	−	7152.82i	−1.08232	−	0.107458i
$259$	29664.3			0.442216
$260$			1972.87i			0.0291844i
$261$	−2646.10	+	13194.4i	−0.0388441	+	0.193691i
$262$	−33455.4			−0.487375
$263$		−	74973.4i		−	1.08392i	−0.840405	−	0.541958i	$-0.817683\pi$
$263$		−	74973.4i		−	1.08392i	0.840405	−	0.541958i	$-0.182317\pi$
$264$	4260.71	−	42914.0i	0.0611328	−	0.615731i
$265$	−82386.9			−1.17318
$266$			83036.4i			1.17356i
$267$	17309.5	+	1718.57i	0.242808	+	0.0241071i
$268$	−5921.17			−0.0824400
$269$			38118.0i			0.526775i	0.964690	+	0.263388i	$0.0848398\pi$
$269$			38118.0i			0.526775i	−0.964690	+	0.263388i	$0.915160\pi$
$270$	−13635.3	+	44571.1i	−0.187041	+	0.611401i
$271$	−39309.6			−0.535254			−0.267627	−	0.963523i	$-0.586239\pi$
$271$	−39309.6			−0.535254			−0.267627	+	0.963523i	$0.586239\pi$
$272$		−	83640.5i		−	1.13052i
$273$	1533.94	−	15449.9i	0.0205818	−	0.207301i
$274$	122551.			1.63235
$275$		−	19209.1i		−	0.254004i
$276$	27792.6	+	2759.38i	0.364847	+	0.0362238i
$277$	24748.5			0.322544			0.161272	−	0.986910i	$-0.448440\pi$
$277$	24748.5			0.322544			0.161272	+	0.986910i	$0.448440\pi$
$278$			5094.88i			0.0659241i
$279$	61704.9	+	12374.7i	0.792705	+	0.158974i
$280$	−88648.0			−1.13071
$281$			84569.8i			1.07103i	0.844525	+	0.535516i	$0.179883\pi$
$281$			84569.8i			1.07103i	−0.844525	+	0.535516i	$0.820117\pi$
$282$	−3758.65	+	37857.2i	−0.0472643	+	0.476048i
$283$	−112366.			−1.40302			−0.701510	−	0.712660i	$-0.747490\pi$
$283$	−112366.			−1.40302			−0.701510	+	0.712660i	$0.747490\pi$
$284$			2438.37i			0.0302317i
$285$	58805.2	+	5838.47i	0.723979	+	0.0718802i
$286$	−5961.89			−0.0728873
$287$			219484.i			2.66465i
$288$	8341.53	−	41594.0i	0.100568	−	0.501471i
$289$	−156129.			−1.86934
$290$		−	10622.4i		−	0.126306i
$291$	5064.10	−	51005.7i	0.0598020	−	0.602328i
$292$	−39242.4			−0.460246
$293$		−	9165.98i		−	0.106769i	−0.998574	−	0.0533843i	$-0.982999\pi$
$293$		−	9165.98i		−	0.106769i	0.998574	−	0.0533843i	$-0.0170008\pi$
$294$	70855.3	+	7034.86i	0.819743	+	0.0813881i
$295$	−8439.56			−0.0969786
$296$		−	30010.2i		−	0.342520i
$297$	48134.5	+	14725.4i	0.545687	+	0.166938i
$298$	−28999.9			−0.326561
$299$		−	18526.6i		−	0.207230i
$300$	1042.04	−	10495.5i	0.0115782	−	0.116616i
$301$	160719.			1.77392
$302$		−	106454.i		−	1.16721i
$303$	17337.3	+	1721.33i	0.188841	+	0.0187490i
$304$	60240.6			0.651842
$305$			9298.73i			0.0999595i
$306$	133482.	+	26769.3i	1.42554	+	0.285887i
$307$	15619.4			0.165725			0.0828624	−	0.996561i	$-0.473594\pi$
$307$	15619.4			0.165725			0.0828624	+	0.996561i	$0.473594\pi$
$308$			19952.2i			0.210324i
$309$	18694.2	−	188288.i	0.195790	−	1.97200i
$310$	−49676.4			−0.516924
$311$			98034.3i			1.01358i	0.862070	+	0.506789i	$0.169168\pi$
$311$			98034.3i			1.01358i	−0.862070	+	0.506789i	$0.830832\pi$
$312$	−15630.1	−	1551.83i	−0.160565	−	0.0159417i
$313$	−89112.2			−0.909596			−0.454798	−	0.890595i	$-0.650289\pi$
$313$	−89112.2			−0.909596			−0.454798	+	0.890595i	$0.650289\pi$
$314$			78242.9i			0.793570i
$315$	20345.9	−	101452.i	0.205048	−	1.02244i
$316$	−16064.9			−0.160880
$317$			91487.0i			0.910418i	0.890385	+	0.455209i	$0.150436\pi$
$317$			91487.0i			0.910418i	−0.890385	+	0.455209i	$0.849564\pi$
$318$	13505.9	−	136032.i	0.133558	−	1.34520i
$319$	−11471.6			−0.112731
$320$			84394.3i			0.824163i
$321$	−11097.8	−	1101.84i	−0.107703	−	0.0106933i
$322$	173494.			1.67330
$323$		−	172604.i		−	1.65442i
$324$	25500.9	+	10656.9i	0.242922	+	0.101517i
$325$	−6996.30			−0.0662371
$326$			135760.i			1.27743i
$327$	−17093.6	+	172167.i	−0.159859	+	1.61011i
$328$	222044.			2.06391
$329$		−	84454.2i		−	0.780242i
$330$	−39538.6	−	3925.58i	−0.363073	−	0.0360476i
$331$	150627.			1.37482			0.687411	−	0.726269i	$-0.258747\pi$
$331$	150627.			1.37482			0.687411	+	0.726269i	$0.258747\pi$
$332$		−	19498.8i		−	0.176902i
$333$	34344.8	+	6887.73i	0.309722	+	0.0621137i
$334$	−19014.2			−0.170445
$335$			26176.5i			0.233250i
$336$	10421.2	−	104963.i	0.0923084	−	0.929733i
$337$	8388.71			0.0738644			0.0369322	−	0.999318i	$-0.488241\pi$
$337$	8388.71			0.0738644			0.0369322	+	0.999318i	$0.488241\pi$
$338$		−	95886.9i		−	0.839317i
$339$	90184.7	+	8953.98i	0.784754	+	0.0779142i
$340$	38403.3			0.332209
$341$			53647.9i			0.461364i
$342$	−19280.1	+	96138.0i	−0.164838	+	0.821945i
$343$	6629.61			0.0563507
$344$		−	162593.i		−	1.37399i
$345$	12198.8	−	122866.i	0.102489	−	1.03227i
$346$	−73225.6			−0.611661
$347$			209055.i			1.73621i	0.496385	+	0.868103i	$0.334661\pi$
$347$			209055.i			1.73621i	−0.496385	+	0.868103i	$0.665339\pi$
$348$	−6267.86	−	622.304i	−0.0517560	−	0.00513859i
$349$	188860.			1.55056			0.775280	−	0.631617i	$-0.217609\pi$
$349$	188860.			1.55056			0.775280	+	0.631617i	$0.217609\pi$
$350$		−	65517.6i		−	0.534838i
$351$	5363.27	−	17531.4i	0.0435327	−	0.142300i
$352$	36162.9			0.291863
$353$		−	40958.6i		−	0.328697i	−0.986402	−	0.164348i	$-0.947448\pi$
$353$		−	40958.6i		−	0.328697i	0.986402	−	0.164348i	$-0.0525521\pi$
$354$	1383.52	−	13934.8i	0.0110402	−	0.111198i
$355$	10779.6			0.0855354
$356$			8141.62i			0.0642408i
$357$	−300744.	−	29859.3i	−2.35972	−	0.234284i
$358$	−81146.0			−0.633142
$359$		−	10400.6i		−	0.0806992i	−0.999186	−	0.0403496i	$-0.987153\pi$
$359$		−	10400.6i		−	0.0806992i	0.999186	−	0.0403496i	$-0.0128472\pi$
$360$	−102635.	−	20583.1i	−0.791937	−	0.158820i
$361$	−6006.21			−0.0460878
$362$			147637.i			1.12662i
$363$	8779.23	−	88424.7i	0.0666259	−	0.671058i
$364$	7266.94			0.0548465
$365$			173484.i			1.30219i
$366$	−15353.4	−	1524.36i	−0.114615	−	0.0113796i
$367$	−196509.			−1.45898			−0.729491	−	0.683990i	$-0.760243\pi$
$367$	−196509.			−1.45898			−0.729491	+	0.683990i	$0.760243\pi$
$368$		−	125865.i		−	0.929418i
$369$	−50961.9	+	254115.i	−0.374277	+	1.86628i
$370$	−27649.8			−0.201971
$371$			303468.i			2.20478i
$372$	−2910.25	+	29312.2i	−0.0210303	+	0.211818i
$373$	−48100.6			−0.345727			−0.172863	−	0.984946i	$-0.555302\pi$
$373$	−48100.6			−0.345727			−0.172863	+	0.984946i	$0.555302\pi$
$374$			116053.i			0.829683i
$375$	−150639.	−	14956.1i	−1.07121	−	0.106355i
$376$	−85438.9			−0.604338
$377$			4178.17i			0.0293970i
$378$	164175.	+	50224.9i	1.14901	+	0.351508i
$379$	−169252.			−1.17830			−0.589149	−	0.808025i	$-0.700537\pi$
$379$	−169252.			−1.17830			−0.589149	+	0.808025i	$0.700537\pi$
$380$			27659.3i			0.191547i
$381$	−465.588	+	4689.42i	−0.00320739	+	0.0323049i
$382$	−88275.7			−0.604943
$383$			69172.7i			0.471560i	0.971806	+	0.235780i	$0.0757645\pi$
$383$			69172.7i			0.471560i	−0.971806	+	0.235780i	$0.924236\pi$
$384$	−64297.8	−	6383.80i	−0.436048	−	0.0432929i
$385$	88205.1			0.595076
$386$		−	135333.i		−	0.908300i
$387$	186077.	+	37317.2i	1.24243	+	0.249165i
$388$	23990.8			0.159361
$389$		−	264446.i		−	1.74758i	−0.486301	−	0.873791i	$-0.661654\pi$
$389$		−	264446.i		−	1.74758i	0.486301	−	0.873791i	$-0.338346\pi$
$390$	−1429.77	+	14400.7i	−0.00940019	+	0.0946790i
$391$	−360634.			−2.35892
$392$			159912.i			1.04066i
$393$	87270.5	+	8664.64i	0.565044	+	0.0561003i
$394$	−14493.2			−0.0933626
$395$			71020.0i			0.455183i
$396$	−4632.68	+	23100.3i	−0.0295421	+	0.147308i
$397$	114863.			0.728782			0.364391	−	0.931246i	$-0.381277\pi$
$397$	114863.			0.728782			0.364391	+	0.931246i	$0.381277\pi$
$398$		−	59779.0i		−	0.377383i
$399$	21505.7	−	216606.i	0.135085	−	1.36058i
$400$	−47531.2			−0.297070
$401$		−	196797.i		−	1.22386i	−0.790913	−	0.611929i	$-0.790394\pi$
$401$		−	196797.i		−	1.22386i	0.790913	−	0.611929i	$-0.209606\pi$
$402$	−43220.8	−	4291.17i	−0.267449	−	0.0265536i
$403$	19539.5			0.120311
$404$			8154.68i			0.0499625i
$405$	47112.1	−	112735.i	0.287225	−	0.687305i
$406$	−39126.9			−0.237369
$407$			29860.3i			0.180262i
$408$	−30207.5	+	304251.i	−0.181466	+	1.82773i
$409$	−48193.5			−0.288099			−0.144050	−	0.989570i	$-0.546012\pi$
$409$	−48193.5			−0.288099			−0.144050	+	0.989570i	$0.546012\pi$
$410$		−	204579.i		−	1.21701i
$411$	−319681.	−	31739.5i	−1.89249	−	0.187895i
$412$	88562.5			0.521741
$413$			31086.7i			0.182253i
$414$	200869.	+	40283.5i	1.17196	+	0.235032i
$415$	−86200.8			−0.500513
$416$		−	13171.2i		−	0.0761094i
$417$	1319.53	−	13290.3i	0.00758833	−	0.0764299i
$418$	−83585.0			−0.478383
$419$			8146.04i			0.0464001i	0.999731	+	0.0232000i	$0.00738546\pi$
$419$			8146.04i			0.0464001i	−0.999731	+	0.0232000i	$0.992615\pi$
$420$	48193.6	+	4784.89i	0.273206	+	0.0271252i
$421$	308500.			1.74057			0.870283	−	0.492552i	$-0.163936\pi$
$421$	308500.			1.74057			0.870283	+	0.492552i	$0.163936\pi$
$422$		−	292730.i		−	1.64378i
$423$	19609.3	−	97779.5i	0.109593	−	0.546471i
$424$	307006.			1.70771
$425$			136188.i			0.753983i
$426$	−1767.12	+	17798.5i	−0.00973751	+	0.0980765i
$427$	34251.4			0.187855
$428$		−	5219.91i		−	0.0284955i
$429$	15552.0	+	1544.07i	0.0845027	+	0.00838984i
$430$	−149804.			−0.810190
$431$			157993.i			0.850517i	0.905072	+	0.425258i	$0.139817\pi$
$431$			157993.i			0.850517i	−0.905072	+	0.425258i	$0.860183\pi$
$432$	36436.8	−	119105.i	0.195242	−	0.638206i
$433$	101256.			0.540061			0.270031	−	0.962852i	$-0.412966\pi$
$433$	101256.			0.540061			0.270031	+	0.962852i	$0.412966\pi$
$434$			182980.i			0.971460i
$435$	−2751.10	+	27709.1i	−0.0145388	+	0.146435i
$436$	−80979.8			−0.425994
$437$		−	259741.i		−	1.36012i
$438$	−286445.	−	28439.6i	−1.49311	−	0.148244i
$439$	−138902.			−0.720743			−0.360371	−	0.932809i	$-0.617350\pi$
$439$	−138902.			−0.720743			−0.360371	+	0.932809i	$0.617350\pi$
$440$		−	89233.6i		−	0.460918i
$441$	−183009.	−	36701.7i	−0.941010	−	0.188716i
$442$	42268.5			0.216358
$443$			105430.i			0.537226i	0.963248	+	0.268613i	$0.0865653\pi$
$443$			105430.i			0.537226i	−0.963248	+	0.268613i	$0.913435\pi$
$444$	−1619.84	+	16315.1i	−0.00821687	+	0.0827605i
$445$	35992.7			0.181758
$446$			59381.7i			0.298526i
$447$	75648.2	+	7510.72i	0.378602	+	0.0375895i
$448$	310862.			1.54886
$449$			101376.i			0.502854i	0.967876	+	0.251427i	$0.0808999\pi$
$449$			101376.i			0.502854i	−0.967876	+	0.251427i	$0.919100\pi$
$450$	15212.5	−	75855.1i	0.0751233	−	0.374593i
$451$	−220934.			−1.08620
$452$			42418.9i			0.207626i
$453$	−27570.6	+	277692.i	−0.134354	+	1.35322i
$454$	−238304.			−1.15617
$455$		−	32125.9i		−	0.155179i
$456$	−219131.	−	21756.4i	−1.05384	−	0.104630i
$457$	−210938.			−1.01000			−0.505001	−	0.863119i	$-0.668508\pi$
$457$	−210938.			−1.01000			−0.505001	+	0.863119i	$0.668508\pi$
$458$		−	18281.8i		−	0.0871540i
$459$	−341263.	−	104400.i	−1.61981	−	0.495536i
$460$	57790.8			0.273114
$461$			176047.i			0.828375i	0.910191	+	0.414188i	$0.135934\pi$
$461$			176047.i			0.828375i	−0.910191	+	0.414188i	$0.864066\pi$
$462$	−14459.7	+	145638.i	−0.0677445	+	0.682325i
$463$	−341759.			−1.59426			−0.797128	−	0.603810i	$-0.793649\pi$
$463$	−341759.			−1.59426			−0.797128	+	0.603810i	$0.793649\pi$
$464$			28385.5i			0.131844i
$465$	129584.	+	12865.7i	0.599302	+	0.0595016i
$466$	356898.			1.64351
$467$		−	180141.i		−	0.825999i	−0.910731	−	0.412999i	$-0.864481\pi$
$467$		−	180141.i		−	0.825999i	0.910731	−	0.412999i	$-0.135519\pi$
$468$	8413.53	+	1687.30i	0.0384137	+	0.00770374i
$469$	96419.6			0.438349
$470$			78718.7i			0.356355i
$471$	20264.2	−	204101.i	0.0913455	−	0.920035i
$472$	31449.1			0.141164
$473$			161781.i			0.723110i
$474$	−117263.	−	11642.5i	−0.521922	−	0.0518189i
$475$	−98087.2			−0.434736
$476$		−	141457.i		−	0.624323i
$477$	−70461.8	+	351349.i	−0.309683	+	1.54419i
$478$	280191.			1.22630
$479$		−	379267.i		−	1.65301i	−0.562933	−	0.826503i	$-0.690327\pi$
$479$		−	379267.i		−	1.65301i	0.562933	−	0.826503i	$-0.309673\pi$
$480$	8672.52	−	87349.9i	0.0376411	−	0.379123i
$481$	10875.7			0.0470073
$482$			190200.i			0.818686i
$483$	−452571.	−	44933.5i	−1.93996	−	0.192609i
$484$	41591.0			0.177545
$485$		−	106059.i		−	0.450884i
$486$	178417.	+	96269.2i	0.755379	+	0.407582i
$487$	−422272.			−1.78047			−0.890234	−	0.455504i	$-0.849459\pi$
$487$	−422272.			−1.78047			−0.890234	+	0.455504i	$0.849459\pi$
$488$		−	34650.7i		−	0.145503i
$489$	35160.6	−	354139.i	0.147041	−	1.48100i
$490$	147334.			0.613635
$491$			11215.0i			0.0465197i	0.999729	+	0.0232599i	$0.00740451\pi$
$491$			11215.0i			0.0465197i	−0.999729	+	0.0232599i	$0.992595\pi$
$492$	−120714.	−	11985.1i	−0.498687	−	0.0495121i
$493$	81331.2			0.334629
$494$			30443.2i			0.124749i
$495$	102122.	+	20480.3i	0.416783	+	0.0835844i
$496$	132747.			0.539588
$497$		−	39706.1i		−	0.160747i
$498$	14131.1	−	142329.i	0.0569793	−	0.573897i
$499$	−221551.			−0.889761			−0.444880	−	0.895590i	$-0.646754\pi$
$499$	−221551.			−0.889761			−0.444880	+	0.895590i	$0.646754\pi$
$500$		−	70853.7i		−	0.283415i
$501$	49599.8	+	4924.51i	0.197608	+	0.0196195i
$502$	−194794.			−0.772979
$503$			97397.4i			0.384956i	0.981301	+	0.192478i	$0.0616525\pi$
$503$			97397.4i			0.384956i	−0.981301	+	0.192478i	$0.938348\pi$
$504$	−75816.7	+	378050.i	−0.298472	+	1.48829i
$505$	36050.4			0.141360
$506$			174641.i			0.682094i
$507$	−24833.8	+	250127.i	−0.0966112	+	0.973071i
$508$	−2205.69			−0.00854708
$509$			110106.i			0.424988i	0.977162	+	0.212494i	$0.0681585\pi$
$509$			110106.i			0.424988i	−0.977162	+	0.212494i	$0.931841\pi$
$510$	280320.	+	27831.5i	1.07774	+	0.107003i
$511$	639019.			2.44721
$512$		−	279187.i		−	1.06501i
$513$	75192.3	−	245789.i	0.285719	−	0.933958i
$514$	53815.0			0.203694
$515$		−	391519.i		−	1.47618i
$516$	−8776.16	+	88393.8i	−0.0329614	+	0.331988i
$517$	85012.1			0.318053
$518$			101846.i			0.379565i
$519$	191013.	+	18964.7i	0.709136	+	0.0704064i
$520$	−32500.5			−0.120194
$521$			196979.i			0.725679i	0.931852	+	0.362839i	$0.118193\pi$
$521$			196979.i			0.725679i	−0.931852	+	0.362839i	$0.881807\pi$
$522$	−45300.4	−	9084.84i	−0.166250	−	0.0333408i
$523$	190680.			0.697111			0.348556	−	0.937288i	$-0.386672\pi$
$523$	190680.			0.697111			0.348556	+	0.937288i	$0.386672\pi$
$524$			41048.2i			0.149497i
$525$	−16968.5	+	170907.i	−0.0615636	+	0.620070i
$526$	257406.			0.930351
$527$		−	380352.i		−	1.36951i
$528$	105657.	+	10490.1i	0.378991	+	0.0376280i
$529$	−262855.			−0.939302
$530$		−	282859.i		−	1.00697i
$531$	−7217.98	+	35991.6i	−0.0255992	+	0.127647i
$532$	101882.			0.359975
$533$			80468.3i			0.283250i
$534$	−5900.36	+	59428.6i	−0.0206917	+	0.208407i
$535$	−23076.3			−0.0806231
$536$		−	97543.9i		−	0.339524i
$537$	211674.	+	21016.1i	0.734040	+	0.0728791i
$538$	−130870.			−0.452144
$539$		−	159113.i		−	0.547680i
$540$	54686.6	+	16729.9i	0.187540	+	0.0573727i
$541$	213359.			0.728981			0.364490	−	0.931207i	$-0.381243\pi$
$541$	213359.			0.728981			0.364490	+	0.931207i	$0.381243\pi$
$542$		−	134961.i		−	0.459421i
$543$	38236.7	−	385121.i	0.129682	−	1.30616i
$544$	−256387.			−0.866361
$545$			357998.i			1.20528i
$546$	53044.1	+	5266.47i	0.177931	+	0.0176658i
$547$	−105742.			−0.353407			−0.176703	−	0.984264i	$-0.556543\pi$
$547$	−105742.			−0.353407			−0.176703	+	0.984264i	$0.556543\pi$
$548$		−	150364.i		−	0.500705i
$549$	39655.6	+	7952.79i	0.131571	+	0.0263861i
$550$	65950.5			0.218018
$551$			58577.4i			0.192942i
$552$	−45457.4	+	457848.i	−0.149185	+	1.50260i
$553$	261598.			0.855430
$554$			84968.9i			0.276847i
$555$	72126.2	+	7161.03i	0.234157	+	0.0232482i
$556$	6251.17			0.0202214
$557$			470787.i			1.51745i	0.651412	+	0.758724i	$0.274177\pi$
$557$			470787.i			1.51745i	−0.651412	+	0.758724i	$0.725823\pi$
$558$	−42486.0	+	211851.i	−0.136451	+	0.680397i
$559$	58923.4			0.188566
$560$		−	218256.i		−	0.695969i
$561$	30056.6	−	302731.i	0.0955023	−	0.961902i
$562$	−290353.			−0.919292
$563$		−	61231.4i		−	0.193178i	−0.995324	−	0.0965890i	$-0.969207\pi$
$563$		−	61231.4i		−	0.193178i	0.995324	−	0.0965890i	$-0.0307932\pi$
$564$	46449.0	+	4611.68i	0.146022	+	0.0144978i
$565$	187526.			0.587443
$566$		−	385787.i		−	1.20424i
$567$	−415254.	−	173535.i	−1.29166	−	0.539784i
$568$	−40169.0			−0.124507
$569$		−	160875.i		−	0.496894i	−0.968645	−	0.248447i	$-0.920080\pi$
$569$		−	160875.i		−	0.496894i	0.968645	−	0.248447i	$-0.0799202\pi$
$570$	−20045.2	+	201896.i	−0.0616964	+	0.621409i
$571$	393550.			1.20706			0.603529	−	0.797341i	$-0.293761\pi$
$571$	393550.			1.20706			0.603529	+	0.797341i	$0.293761\pi$
$572$			7314.95i			0.0223573i
$573$	230273.	+	22862.6i	0.701348	+	0.0696332i
$574$	−753555.			−2.28713
$575$			204941.i			0.619860i
$576$	359910.	+	72178.7i	1.08480	+	0.217552i
$577$	430633.			1.29347			0.646734	−	0.762715i	$-0.276134\pi$
$577$	430633.			1.29347			0.646734	+	0.762715i	$0.276134\pi$
$578$		−	536036.i		−	1.60449i
$579$	−35050.0	+	353025.i	−0.104552	+	1.05305i
$580$	−13033.1			−0.0387430
$581$			317516.i			0.940618i
$582$	175118.	+	17386.5i	0.516993	+	0.0513295i
$583$	−305472.			−0.898742
$584$		−	646470.i		−	1.89550i
$585$	7459.28	−	37194.8i	0.0217964	−	0.108685i
$586$	31469.5			0.0916420
$587$			413425.i			1.19983i	0.800063	+	0.599916i	$0.204800\pi$
$587$			413425.i			1.19983i	−0.800063	+	0.599916i	$0.795200\pi$
$588$	8631.43	−	86936.0i	0.0249648	−	0.251446i
$589$	273942.			0.789638
$590$		−	28975.5i		−	0.0832391i
$591$	37806.5	+	3753.61i	0.108241	+	0.0107467i
$592$	73886.7			0.210825
$593$		−	267773.i		−	0.761478i	−0.924683	−	0.380739i	$-0.875670\pi$
$593$		−	267773.i		−	0.761478i	0.924683	−	0.380739i	$-0.124330\pi$
$594$	−50556.7	+	165260.i	−0.143287	+	0.468376i
$595$	−625355.			−1.76641
$596$			35581.5i			0.100169i
$597$	−15482.2	+	155937.i	−0.0434394	+	0.437523i
$598$	63607.3			0.177871
$599$			365723.i			1.01929i	0.860384	+	0.509646i	$0.170224\pi$
$599$			365723.i			1.01929i	−0.860384	+	0.509646i	$0.829776\pi$
$600$	172900.	+	17166.3i	0.480277	+	0.0476842i
$601$	−71516.9			−0.197998			−0.0989988	−	0.995088i	$-0.531564\pi$
$601$	−71516.9			−0.197998			−0.0989988	+	0.995088i	$0.531564\pi$
$602$			551795.i			1.52260i
$603$	111633.	+	22387.6i	0.307013	+	0.0615705i
$604$	−130614.			−0.358027
$605$		−	183867.i		−	0.502334i
$606$	−5909.83	+	59524.0i	−0.0160927	+	0.162086i
$607$	520735.			1.41332			0.706658	−	0.707556i	$-0.250202\pi$
$607$	520735.			1.41332			0.706658	+	0.707556i	$0.250202\pi$
$608$		−	184659.i		−	0.499531i
$609$	102065.	+	10133.5i	0.275196	+	0.0273228i
$610$	−31925.3			−0.0857976
$611$		−	30962.9i		−	0.0829392i
$612$	32844.7	−	163776.i	0.0876924	−	0.437267i
$613$	478823.			1.27425			0.637125	−	0.770761i	$-0.280124\pi$
$613$	478823.			1.27425			0.637125	+	0.770761i	$0.280124\pi$
$614$			53626.0i			0.142246i
$615$	−52984.0	+	533657.i	−0.140086	+	1.41095i
$616$	−328687.			−0.866206
$617$		−	64255.4i		−	0.168787i	−0.996433	−	0.0843935i	$-0.973105\pi$
$617$		−	64255.4i		−	0.168787i	0.996433	−	0.0843935i	$-0.0268953\pi$
$618$	646450.	+	64182.6i	1.69261	+	0.168051i
$619$	283519.			0.739948			0.369974	−	0.929042i	$-0.379367\pi$
$619$	283519.			0.739948			0.369974	+	0.929042i	$0.379367\pi$
$620$			60950.6i			0.158560i
$621$	−513546.	−	157105.i	−1.33167	−	0.407387i
$622$	−336581.			−0.869978
$623$		−	132577.i		−	0.341580i
$624$	3820.68	−	38482.0i	0.00981232	−	0.0988300i
$625$	−139359.			−0.356760
$626$		−	305948.i		−	0.780728i
$627$	218037.	+	21647.7i	0.554619	+	0.0550652i
$628$	96000.2			0.243418
$629$		−	211703.i		−	0.535088i
$630$	348315.	+	69853.3i	0.877588	+	0.175997i
$631$	462469.			1.16151			0.580756	−	0.814077i	$-0.302757\pi$
$631$	462469.			1.16151			0.580756	+	0.814077i	$0.302757\pi$
$632$		−	264648.i		−	0.662575i
$633$	−75814.4	+	763606.i	−0.189210	+	1.90573i
$634$	−314102.			−0.781434
$635$			9750.99i			0.0241825i
$636$	−166904.	−	16571.1i	−0.412623	−	0.0409672i
$637$	−57951.7			−0.142819
$638$		−	39385.4i		−	0.0967596i
$639$	9219.31	−	45970.9i	0.0225786	−	0.112585i
$640$	−133698.			−0.326412
$641$		−	490204.i		−	1.19305i	−0.802593	−	0.596527i	$-0.796547\pi$
$641$		−	490204.i		−	1.19305i	0.802593	−	0.596527i	$-0.203453\pi$
$642$	3782.96	−	38102.0i	0.00917828	−	0.0924439i
$643$	−656990.			−1.58905			−0.794524	−	0.607233i	$-0.792280\pi$
$643$	−656990.			−1.58905			−0.794524	+	0.607233i	$0.792280\pi$
$644$		−	212869.i		−	0.513265i
$645$	390774.	+	38797.9i	0.939303	+	0.0932586i
$646$	592599.			1.42002
$647$		−	398191.i		−	0.951225i	−0.879655	−	0.475612i	$-0.842227\pi$
$647$		−	398191.i		−	0.951225i	0.879655	−	0.475612i	$-0.157773\pi$
$648$	−175558.	+	420096.i	−0.418091	+	1.00046i
$649$	−31292.0			−0.0742924
$650$		−	24020.3i		−	0.0568529i
$651$	47390.2	−	477316.i	0.111822	−	1.12627i
$652$	166571.			0.391836
$653$			543404.i			1.27437i	0.770710	+	0.637187i	$0.219902\pi$
$653$			543404.i			1.27437i	−0.770710	+	0.637187i	$0.780098\pi$
$654$	−591101.	−	58687.4i	−1.38199	−	0.137211i
$655$	181467.			0.422975
$656$			546683.i			1.27036i
$657$	739844.	+	148373.i	1.71399	+	0.343736i
$658$	289956.			0.669700
$659$		−	345618.i		−	0.795840i	−0.917420	−	0.397920i	$-0.869732\pi$
$659$		−	345618.i		−	0.795840i	0.917420	−	0.397920i	$-0.130268\pi$
$660$	−4816.50	+	48512.0i	−0.0110572	+	0.111368i
$661$	−213452.			−0.488536			−0.244268	−	0.969708i	$-0.578548\pi$
$661$	−213452.			−0.488536			−0.244268	+	0.969708i	$0.578548\pi$
$662$			517146.i			1.18004i
$663$	−110260.	−	10947.1i	−0.250837	−	0.0249043i
$664$	321218.			0.728558
$665$		−	450401.i		−	1.01849i
$666$	−23647.6	+	117916.i	−0.0533137	+	0.265842i
$667$	122390.			0.275103
$668$			23329.5i			0.0522821i
$669$	15379.3	−	154901.i	0.0343625	−	0.346100i
$670$	−89871.6			−0.200204
$671$			34477.6i			0.0765759i
$672$	−321748.	−	31944.7i	−0.712489	−	0.0707393i
$673$	−570231.			−1.25899			−0.629493	−	0.777006i	$-0.716737\pi$
$673$	−570231.			−1.25899			−0.629493	+	0.777006i	$0.716737\pi$
$674$			28800.9i			0.0633996i
$675$	−59328.5	+	193933.i	−0.130213	+	0.425641i
$676$	−117649.			−0.257450
$677$			709222.i			1.54741i	0.633547	+	0.773704i	$0.281598\pi$
$677$			709222.i			1.54741i	−0.633547	+	0.773704i	$0.718402\pi$
$678$	−30741.6	+	309631.i	−0.0668756	+	0.673573i
$679$	−390663.			−0.847351
$680$			632647.i			1.36818i
$681$	621632.	+	61718.6i	1.34041	+	0.133083i
$682$	−184189.			−0.396000
$683$		−	208512.i		−	0.446981i	−0.974706	−	0.223490i	$-0.928255\pi$
$683$		−	208512.i		−	0.446981i	0.974706	−	0.223490i	$-0.0717451\pi$
$684$	117957.	+	23655.8i	0.252122	+	0.0505621i
$685$	−664732.			−1.41666
$686$			22761.4i			0.0483672i
$687$	−4734.81	+	47689.2i	−0.0100320	+	0.101043i
$688$	400312.			0.845711
$689$			111259.i			0.234366i
$690$	421836.	+	41882.0i	0.886025	+	0.0879688i
$691$	86295.4			0.180731			0.0903653	−	0.995909i	$-0.471197\pi$
$691$	86295.4			0.180731			0.0903653	+	0.995909i	$0.471197\pi$
$692$			89844.2i			0.187619i
$693$	75437.9	−	376162.i	0.157081	−	0.783264i
$694$	−717747.			−1.49023
$695$		−	27635.3i		−	0.0572131i
$696$	10251.7	−	103255.i	0.0211629	−	0.213154i
$697$	1.56638e6			3.22426
$698$			648411.i			1.33088i
$699$	−930991.	−	92433.3i	−1.90542	−	0.189179i
$700$	−80386.9			−0.164055
$701$		−	240845.i		−	0.490119i	−0.969508	−	0.245059i	$-0.921193\pi$
$701$		−	240845.i		−	0.490119i	0.969508	−	0.245059i	$-0.0788074\pi$
$702$	60190.6	+	18413.7i	0.122139	+	0.0373651i
$703$	152475.			0.308524
$704$			312915.i			0.631367i
$705$	20387.4	−	205343.i	0.0410189	−	0.413144i
$706$	140623.			0.282128
$707$		−	132790.i		−	0.265660i
$708$	−17097.4	−	1697.51i	−0.0341085	−	0.00338646i
$709$	−83637.4			−0.166383			−0.0831913	−	0.996534i	$-0.526511\pi$
$709$	−83637.4			−0.166383			−0.0831913	+	0.996534i	$0.526511\pi$
$710$			37009.5i			0.0734171i
$711$	302873.	+	60740.2i	0.599131	+	0.120154i
$712$	−134123.			−0.264572
$713$		−	572368.i		−	1.12589i
$714$	102516.	−	1.03254e6i	0.201092	−	2.02540i
$715$	32338.1			0.0632562
$716$			99562.2i			0.194209i
$717$	−730896.	−	72566.8i	−1.42173	−	0.141156i
$718$	35708.3			0.0692660
$719$		−	312232.i		−	0.603976i	−0.953312	−	0.301988i	$-0.902350\pi$
$719$		−	312232.i		−	0.603976i	0.953312	−	0.301988i	$-0.0976503\pi$
$720$	50676.7	−	252693.i	0.0977559	−	0.487447i
$721$	−1.44214e6			−2.77419
$722$		−	20621.1i		−	0.0395582i
$723$	49260.1	−	496150.i	0.0942364	−	0.949152i
$724$	181144.			0.345578
$725$		−	46218.9i		−	0.0879313i
$726$	303588.	+	30141.7i	0.575985	+	0.0571866i
$727$	823879.			1.55881			0.779407	−	0.626518i	$-0.215520\pi$
$727$	823879.			1.55881			0.779407	+	0.626518i	$0.215520\pi$
$728$			119714.i			0.225882i
$729$	−440480.	−	297333.i	−0.828841	−	0.559484i
$730$	−595622.			−1.11770
$731$		−	1.14699e6i		−	2.14647i
$732$	−1870.32	+	18837.9i	−0.00349055	+	0.0351569i
$733$	−89422.5			−0.166433			−0.0832164	−	0.996532i	$-0.526519\pi$
$733$	−89422.5			−0.166433			−0.0832164	+	0.996532i	$0.526519\pi$
$734$		−	674673.i		−	1.25228i
$735$	−384329.	−	38158.1i	−0.711424	−	0.0706336i
$736$	−385821.			−0.712247
$737$			97056.6i			0.178686i
$738$	−872451.	−	174967.i	−1.60187	−	0.321250i
$739$	−713132.			−1.30581			−0.652907	−	0.757438i	$-0.726451\pi$
$739$	−713132.			−1.30581			−0.652907	+	0.757438i	$0.726451\pi$
$740$			33924.9i			0.0619520i
$741$	7884.50	−	79412.9i	0.0143594	−	0.144629i
$742$	−1.04189e6			−1.89241
$743$		−	86450.5i		−	0.156599i	−0.996930	−	0.0782997i	$-0.975051\pi$
$743$		−	86450.5i		−	0.156599i	0.996930	−	0.0782997i	$-0.0249491\pi$
$744$	−482881.	−	47942.8i	−0.872358	−	0.0866119i
$745$	157300.			0.283410
$746$		−	165144.i		−	0.296745i
$747$	−73723.7	+	367614.i	−0.132119	+	0.658796i
$748$	142391.			0.254495
$749$			85000.4i			0.151516i
$750$	51348.8	−	517187.i	0.0912868	−	0.919444i
$751$	−674506.			−1.19593			−0.597966	−	0.801522i	$-0.704024\pi$
$751$	−674506.			−1.19593			−0.597966	+	0.801522i	$0.704024\pi$
$752$		−	210355.i		−	0.371978i
$753$	508132.	+	50449.8i	0.896161	+	0.0889752i
$754$	−14344.9			−0.0252321
$755$			577422.i			1.01298i
$756$	61623.6	−	201435.i	0.107821	−	0.352445i
$757$	996053.			1.73816			0.869082	−	0.494668i	$-0.164710\pi$
$757$	996053.			1.73816			0.869082	+	0.494668i	$0.164710\pi$
$758$		−	581091.i		−	1.01136i
$759$	45230.3	−	455561.i	0.0785138	−	0.790793i
$760$	−455653.			−0.788873
$761$			472162.i			0.815308i	0.913136	+	0.407654i	$0.133653\pi$
$761$			472162.i			0.815308i	−0.913136	+	0.407654i	$0.866347\pi$
$762$	−16100.2	−	1598.50i	−0.0277281	−	0.00275298i
$763$	1.31866e6			2.26509
$764$			108310.i			0.185559i
$765$	−724024.	−	145201.i	−1.23717	−	0.248111i
$766$	−237490.			−0.404751
$767$			11397.1i			0.0193733i
$768$	−42556.8	+	428634.i	−0.0721517	+	0.726714i
$769$	−38649.4			−0.0653566			−0.0326783	−	0.999466i	$-0.510404\pi$
$769$	−38649.4			−0.0653566			−0.0326783	+	0.999466i	$0.510404\pi$
$770$			302834.i			0.510768i
$771$	−140380.	−	13937.6i	−0.236154	−	0.0234465i
$772$	−166047.			−0.278610
$773$			831779.i			1.39203i	0.718027	+	0.696015i	$0.245045\pi$
$773$			831779.i			1.39203i	−0.718027	+	0.696015i	$0.754955\pi$
$774$	−128121.	+	638858.i	−0.213864	+	1.06641i
$775$	−216146.			−0.359869
$776$			395219.i			0.656318i
$777$	26377.3	−	265673.i	0.0436906	−	0.440053i
$778$	907921.			1.49999
$779$			1.12816e6i			1.85906i
$780$	17668.9	+	1754.26i	0.0290416	+	0.00288339i
$781$	39968.4			0.0655261
$782$		−	1.23816e6i		−	2.02472i
$783$	115816.	+	35430.8i	0.188906	+	0.0577906i
$784$	−393711.			−0.640538
$785$		−	424400.i		−	0.688710i
$786$	−29748.3	+	299625.i	−0.0481522	+	0.484991i
$787$	373492.			0.603021			0.301510	−	0.953463i	$-0.402509\pi$
$787$	373492.			0.603021			0.301510	+	0.953463i	$0.402509\pi$
$788$			17782.5i			0.0286378i
$789$	−671460.	−	66665.7i	−1.07861	−	0.107090i
$790$	−243833.			−0.390695
$791$		−	690743.i		−	1.10399i
$792$	−380548.	−	76317.5i	−0.606679	−	0.121667i
$793$	12557.4			0.0199688
$794$			394357.i			0.625531i
$795$	−73257.7	+	737854.i	−0.115910	+	1.16744i
$796$	−73345.9			−0.115758
$797$			420465.i			0.661931i	0.943643	+	0.330966i	$0.107374\pi$
$797$			420465.i			0.661931i	−0.943643	+	0.330966i	$0.892626\pi$
$798$	743671.	+	73835.3i	1.16782	+	0.115947i
$799$	−602717.			−0.944104
$800$			145700.i			0.227656i
$801$	30782.9	−	153495.i	0.0479783	−	0.239238i
$802$	675664.			1.05047
$803$			643240.i			0.997567i
$804$	−5265.06	+	53029.8i	−0.00814500	+	0.0820367i
$805$	−941058.			−1.45219
$806$			67085.0i			0.103266i
$807$	341383.	+	33894.2i	0.524198	+	0.0520449i
$808$	−134338.			−0.205767
$809$		−	379081.i		−	0.579209i	−0.957146	−	0.289605i	$-0.906476\pi$
$809$		−	379081.i		−	0.579209i	0.957146	−	0.289605i	$-0.0935238\pi$
$810$	387053.	+	161750.i	0.589930	+	0.246532i
$811$	−514619.			−0.782428			−0.391214	−	0.920300i	$-0.627945\pi$
$811$	−514619.			−0.782428			−0.391214	+	0.920300i	$0.627945\pi$
$812$			48006.8i			0.0728100i
$813$	−34953.7	+	352055.i	−0.0528826	+	0.532635i
$814$	−102519.			−0.154724
$815$		−	736382.i		−	1.10863i
$816$	−749082.	−	74372.4i	−1.12499	−	0.111694i
$817$	826099.			1.23762
$818$		−	165462.i		−	0.247282i
$819$	−137005.	−	27475.8i	−0.204253	−	0.0409622i
$820$	−251008.			−0.373302
$821$		−	1.26707e6i		−	1.87981i	−0.341433	−	0.939906i	$-0.610912\pi$
$821$		−	1.26707e6i		−	1.87981i	0.341433	−	0.939906i	$-0.389088\pi$
$822$	108971.	−	1.09756e6i	0.161275	−	1.62437i
$823$	868555.			1.28232			0.641162	−	0.767406i	$-0.278453\pi$
$823$	868555.			1.28232			0.641162	+	0.767406i	$0.278453\pi$
$824$			1.45896e6i			2.14876i
$825$	−172036.	−	17080.6i	−0.252762	−	0.0250954i
$826$	−106730.			−0.156432
$827$			169043.i			0.247164i	0.992334	+	0.123582i	$0.0394382\pi$
$827$			169043.i			0.247164i	−0.992334	+	0.123582i	$0.960562\pi$
$828$	49425.9	−	246456.i	0.0720932	−	0.359483i
$829$	621329.			0.904092			0.452046	−	0.891995i	$-0.350694\pi$
$829$	621329.			0.904092			0.452046	+	0.891995i	$0.350694\pi$
$830$		−	295953.i		−	0.429602i
$831$	22006.2	−	221647.i	0.0318671	−	0.320966i
$832$	113969.			0.164642
$833$			1.12807e6i			1.62573i
$834$	45629.6	+	4530.32i	0.0656016	+	0.00651324i
$835$	103136.			0.147923
$836$			102555.i			0.146738i
$837$	165695.	−	541624.i	0.236515	−	0.773120i
$838$	−27967.8			−0.0398263
$839$			794681.i			1.12894i	0.825455	+	0.564468i	$0.190918\pi$
$839$			794681.i			1.12894i	−0.825455	+	0.564468i	$0.809082\pi$
$840$	−78825.1	+	793929.i	−0.111714	+	1.12518i
$841$	679679.			0.960975
$842$			1.05917e6i			1.49397i
$843$	757404.	+	75198.7i	1.06579	+	0.105817i
$844$	−359166.			−0.504209
$845$			520104.i			0.728412i
$846$	335706.	+	67324.6i	0.469049	+	0.0940661i
$847$	−677263.			−0.944040
$848$			755865.i			1.05112i
$849$	−99915.3	+	1.00635e6i	−0.138617	+	1.39616i
$850$	−467574.			−0.647162
$851$		−	318579.i		−	0.439904i
$852$	21837.9	+	2168.18i	0.0300838	+	0.00298686i
$853$	543677.			0.747210			0.373605	−	0.927588i	$-0.378122\pi$
$853$	543677.			0.747210			0.373605	+	0.927588i	$0.378122\pi$
$854$			117595.i			0.161240i
$855$	104578.	−	521466.i	0.143057	−	0.713336i
$856$	85991.5			0.117357
$857$		−	951795.i		−	1.29593i	−0.761670	−	0.647965i	$-0.775620\pi$
$857$		−	951795.i		−	1.29593i	0.761670	−	0.647965i	$-0.224380\pi$
$858$	−5301.26	+	53394.5i	−0.00720120	+	0.0725307i
$859$	−264788.			−0.358850			−0.179425	−	0.983772i	$-0.557424\pi$
$859$	−264788.			−0.358850			−0.179425	+	0.983772i	$0.557424\pi$
$860$			183802.i			0.248516i
$861$	1.96569e6	+	195164.i	2.65161	+	0.263265i
$862$	−542436.			−0.730019
$863$			559759.i			0.751587i	0.926703	+	0.375794i	$0.122630\pi$
$863$			559759.i			0.751587i	−0.926703	+	0.375794i	$0.877370\pi$
$864$	−365097.	−	111691.i	−0.489081	−	0.149621i
$865$	397186.			0.530837
$866$			347640.i			0.463547i
$867$	−138828.	+	1.39828e6i	−0.184689	+	1.86019i
$868$	224508.			0.297984
$869$			263326.i			0.348702i
$870$	−95133.6	−	9445.33i	−0.125689	−	0.0124790i
$871$	35349.8			0.0465962
$872$		−	1.33404e6i		−	1.75443i
$873$	−452303.	−	90707.8i	−0.593473	−	0.119019i
$874$	891766.			1.16742
$875$			1.15377e6i			1.50697i
$876$	−34894.0	+	351454.i	−0.0454719	+	0.457995i
$877$	−392260.			−0.510006			−0.255003	−	0.966940i	$-0.582076\pi$
$877$	−392260.			−0.510006			−0.255003	+	0.966940i	$0.582076\pi$
$878$		−	476893.i		−	0.618631i
$879$	−82090.2	−	8150.31i	−0.106246	−	0.0105486i
$880$	219698.			0.283701
$881$			1.29957e6i			1.67436i	0.546926	+	0.837181i	$0.315798\pi$
$881$			1.29957e6i			1.67436i	−0.546926	+	0.837181i	$0.684202\pi$
$882$	126008.	−	628323.i	0.161980	−	0.807691i
$883$	−1.11614e6			−1.43152			−0.715758	−	0.698348i	$-0.753919\pi$
$883$	−1.11614e6			−1.43152			−0.715758	+	0.698348i	$0.753919\pi$
$884$		−	51861.4i		−	0.0663651i
$885$	−7504.39	+	75584.5i	−0.00958140	+	0.0965041i
$886$	−361973.			−0.461114
$887$			468740.i			0.595778i	0.954600	+	0.297889i	$0.0962826\pi$
$887$			468740.i			0.595778i	−0.954600	+	0.297889i	$0.903717\pi$
$888$	−268771.	−	26684.8i	−0.340844	−	0.0338406i
$889$	35917.2			0.0454464
$890$			123574.i			0.156007i
$891$	174681.	−	417997.i	0.220034	−	0.526524i
$892$	72858.4			0.0915693
$893$		−	434097.i		−	0.544357i
$894$	−25786.5	+	259722.i	−0.0322639	+	0.324963i
$895$	440147.			0.549480
$896$			492470.i			0.613429i
$897$	−165924.	−	16473.7i	−0.206216	−	0.0204742i
$898$	−348054.			−0.431612
$899$			129082.i			0.159715i
$900$	−93070.5	−	18665.0i	−0.114902	−	0.0230432i
$901$	2.16573e6			2.66781
$902$		−	758533.i		−	0.932312i
$903$	142910.	−	1.43939e6i	0.175262	−	1.76524i
$904$	−698798.			−0.855095
$905$		−	800805.i		−	0.977754i
$906$	−953400.	−	94658.2i	−1.16150	−	0.115319i
$907$	−601525.			−0.731205			−0.365602	−	0.930771i	$-0.619137\pi$
$907$	−601525.			−0.731205			−0.365602	+	0.930771i	$0.619137\pi$
$908$			292388.i			0.354640i
$909$	30832.3	−	153741.i	0.0373146	−	0.186064i
$910$	110298.			0.133194
$911$		−	1.24972e6i		−	1.50583i	−0.658118	−	0.752915i	$-0.728647\pi$
$911$		−	1.24972e6i		−	1.50583i	0.658118	−	0.752915i	$-0.271353\pi$
$912$	53565.5	−	539513.i	0.0644014	−	0.648653i
$913$	−319613.			−0.383428
$914$		−	724212.i		−	0.866909i
$915$	83279.1	+	8268.35i	0.0994704	+	0.00987590i
$916$	−22430.9			−0.0267334
$917$		−	668423.i		−	0.794900i
$918$	358436.	−	1.17166e6i	0.425330	−	1.39032i
$919$	840586.			0.995294			0.497647	−	0.867380i	$-0.334198\pi$
$919$	840586.			0.995294			0.497647	+	0.867380i	$0.334198\pi$
$920$			952031.i			1.12480i
$921$	13888.6	−	139887.i	0.0163735	−	0.164914i
$922$	−604422.			−0.711014
$923$		−	14557.2i		−	0.0170873i
$924$	178691.	+	17741.3i	0.209295	+	0.0207798i
$925$	−120307.			−0.140607
$926$		−	1.17336e6i		−	1.36839i
$927$	−1.66968e6	−	334849.i	−1.94301	−	0.389663i
$928$	87011.5			0.101037
$929$			190932.i			0.221232i	0.993863	+	0.110616i	$0.0352823\pi$
$929$			190932.i			0.221232i	−0.993863	+	0.110616i	$0.964718\pi$
$930$	−44171.9	+	444900.i	−0.0510716	+	0.514395i
$931$	−812476.			−0.937370
$932$		−	437897.i		−	0.504127i
$933$	877992.	+	87171.3i	1.00862	+	0.100141i
$934$	618478.			0.708974
$935$		−	629486.i		−	0.720051i
$936$	−27796.2	+	138602.i	−0.0317274	+	0.158205i
$937$	470602.			0.536012			0.268006	−	0.963417i	$-0.413635\pi$
$937$	470602.			0.536012			0.268006	+	0.963417i	$0.413635\pi$
$938$			331037.i			0.376245i
$939$	−79237.8	+	798086.i	−0.0898672	+	0.905146i
$940$	96584.1			0.109307
$941$			386286.i			0.436244i	0.975922	+	0.218122i	$0.0699930\pi$
$941$			386286.i			0.436244i	−0.975922	+	0.218122i	$0.930007\pi$
$942$	700740.	+	69572.9i	0.789688	+	0.0784040i
$943$	2.35714e6			2.65071
$944$			77429.4i			0.0868885i
$945$	−890510.	−	272427.i	−0.997183	−	0.305061i
$946$	−555441.			−0.620662
$947$			1.18787e6i			1.32456i	0.749258	+	0.662278i	$0.230410\pi$
$947$			1.18787e6i			1.32456i	−0.749258	+	0.662278i	$0.769590\pi$
$948$	−14284.7	+	143876.i	−0.0158948	+	0.160093i
$949$	234280.			0.260137
$950$		−	336762.i		−	0.373144i
$951$	819355.	+	81349.5i	0.905964	+	0.0899485i
$952$	2.33032e6			2.57123
$953$			727291.i			0.800797i	0.916341	+	0.400399i	$0.131128\pi$
$953$			727291.i			0.800797i	−0.916341	+	0.400399i	$0.868872\pi$
$954$	−1.20629e6	−	241916.i	−1.32542	−	0.265808i
$955$	478820.			0.525007
$956$		−	343781.i		−	0.376154i
$957$	−10200.5	+	102739.i	−0.0111377	+	0.112179i
$958$	1.30214e6			1.41881
$959$			2.44850e6i			2.66234i
$960$	755833.	+	75042.7i	0.820131	+	0.0814266i
$961$	−319858.			−0.346347
$962$			37339.3i			0.0403475i
$963$	−19736.2	+	98411.9i	−0.0212819	+	0.106119i
$964$	233367.			0.251122
$965$			734066.i			0.788280i
$966$	154270.	−	1.55381e6i	0.165320	−	1.66511i
$967$	−557679.			−0.596391			−0.298196	−	0.954505i	$-0.596385\pi$
$967$	−557679.			−0.596391			−0.298196	+	0.954505i	$0.596385\pi$
$968$			685160.i			0.731209i
$969$	−1.54583e6	−	153478.i	−1.64632	−	0.163455i
$970$	364133.			0.387005
$971$			214923.i			0.227953i	0.993483	+	0.113976i	$0.0363588\pi$
$971$			214923.i			0.227953i	−0.993483	+	0.113976i	$0.963641\pi$
$972$	118118.	−	218909.i	0.125021	−	0.231703i
$973$	−101793.			−0.107521
$974$		−	1.44978e6i		−	1.52822i
$975$	−6221.05	+	62658.6i	−0.00654416	+	0.0659130i
$976$	85311.9			0.0895592
$977$		−	1.52555e6i		−	1.59823i	−0.601181	−	0.799113i	$-0.705303\pi$
$977$		−	1.52555e6i		−	1.59823i	0.601181	−	0.799113i	$-0.294697\pi$
$978$	1.21586e6	+	120717.i	1.27118	+	0.126209i
$979$	133453.			0.139240
$980$		−	180771.i		−	0.188225i
$981$	1.52672e6	+	306179.i	1.58644	+	0.318154i
$982$	−38504.5			−0.0399290
$983$		−	346401.i		−	0.358486i	−0.983805	−	0.179243i	$-0.942635\pi$
$983$		−	346401.i		−	0.358486i	0.983805	−	0.179243i	$-0.0573648\pi$
$984$	197439.	−	1.98862e6i	0.203912	−	2.05381i
$985$	78613.3			0.0810259
$986$			279234.i			0.287220i
$987$	−756369.	−	75095.9i	−0.776425	−	0.0770872i
$988$	37352.3			0.0382651
$989$		−	1.72603e6i		−	1.76464i
$990$	−70314.8	+	350616.i	−0.0717425	+	0.357735i
$991$	−891442.			−0.907707			−0.453853	−	0.891076i	$-0.649951\pi$
$991$	−891442.			−0.907707			−0.453853	+	0.891076i	$0.649951\pi$
$992$		−	406916.i		−	0.413506i
$993$	133936.	−	1.34901e6i	0.135831	−	1.36809i
$994$	136323.			0.137973
$995$			324249.i			0.327516i
$996$	−174631.	−	17338.2i	−0.176036	−	0.0174777i
$997$	−1.92977e6			−1.94140			−0.970702	−	0.240288i	$-0.922758\pi$
$997$	−1.92977e6			−1.94140			−0.970702	+	0.240288i	$0.922758\pi$
$998$		−	760651.i		−	0.763703i
$999$	92225.4	−	301466.i	0.0924101	−	0.302070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.53	yes	78
3.2	odd	2	inner	177.5.b.a.119.26	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.26	✓	78	3.2	odd	2	inner
177.5.b.a.119.53	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)

\(f(q)\)	\(=\)	\(q+3.43329i q^{2} +(0.889192 - 8.95597i) q^{3} +4.21249 q^{4} -18.6227i q^{5} +(30.7485 + 3.05286i) q^{6} -68.5956 q^{7} +69.3954i q^{8} +(-79.4187 - 15.9271i) q^{9} +O(q^{10})\)	\(q+3.43329i q^{2} +(0.889192 - 8.95597i) q^{3} +4.21249 q^{4} -18.6227i q^{5} +(30.7485 + 3.05286i) q^{6} -68.5956 q^{7} +69.3954i q^{8} +(-79.4187 - 15.9271i) q^{9} +63.9371 q^{10} -69.0487i q^{11} +(3.74571 - 37.7269i) q^{12} -25.1488 q^{13} -235.509i q^{14} +(-166.784 - 16.5591i) q^{15} -170.855 q^{16} +489.540i q^{17} +(54.6826 - 272.668i) q^{18} -352.583 q^{19} -78.4478i q^{20} +(-60.9946 + 614.340i) q^{21} +237.065 q^{22} +736.679i q^{23} +(621.503 + 61.7058i) q^{24} +278.196 q^{25} -86.3432i q^{26} +(-213.261 + 697.109i) q^{27} -288.958 q^{28} -166.138i q^{29} +(56.8524 - 572.619i) q^{30} -776.957 q^{31} +523.731i q^{32} +(-618.398 - 61.3976i) q^{33} -1680.74 q^{34} +1277.43i q^{35} +(-334.550 - 67.0929i) q^{36} -432.452 q^{37} -1210.52i q^{38} +(-22.3621 + 225.232i) q^{39} +1292.33 q^{40} -3199.69i q^{41} +(-2109.21 - 209.412i) q^{42} -2342.99 q^{43} -290.867i q^{44} +(-296.606 + 1478.99i) q^{45} -2529.24 q^{46} +1231.19i q^{47} +(-151.923 + 1530.17i) q^{48} +2304.35 q^{49} +955.129i q^{50} +(4384.31 + 435.295i) q^{51} -105.939 q^{52} -4424.01i q^{53} +(-2393.38 - 732.189i) q^{54} -1285.87 q^{55} -4760.22i q^{56} +(-313.514 + 3157.72i) q^{57} +570.400 q^{58} -453.188i q^{59} +(-702.576 - 69.7551i) q^{60} -499.323 q^{61} -2667.52i q^{62} +(5447.77 + 1092.53i) q^{63} -4531.80 q^{64} +468.338i q^{65} +(210.796 - 2123.14i) q^{66} -1405.62 q^{67} +2062.18i q^{68} +(6597.67 + 655.049i) q^{69} -4385.80 q^{70} +578.843i q^{71} +(1105.27 - 5511.29i) q^{72} -9315.74 q^{73} -1484.74i q^{74} +(247.370 - 2491.51i) q^{75} -1485.25 q^{76} +4736.44i q^{77} +(-773.287 - 76.7757i) q^{78} -3813.63 q^{79} +3181.78i q^{80} +(6053.65 + 2529.82i) q^{81} +10985.5 q^{82} -4628.81i q^{83} +(-256.939 + 2587.90i) q^{84} +9116.55 q^{85} -8044.18i q^{86} +(-1487.92 - 147.728i) q^{87} +4791.67 q^{88} +1932.73i q^{89} +(-5077.80 - 1018.34i) q^{90} +1725.10 q^{91} +3103.25i q^{92} +(-690.864 + 6958.40i) q^{93} -4227.04 q^{94} +6566.04i q^{95} +(4690.51 + 465.697i) q^{96} +5695.17 q^{97} +7911.52i q^{98} +(-1099.75 + 5483.76i) 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

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