LMFDB - Embedded newform 177.5.b.a.119.63

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			119.63
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.41049i q^{2} +(7.81854 + 4.45762i) q^{3} -13.2734 q^{4} -41.9044i q^{5} +(-24.1179 + 42.3021i) q^{6} -64.0047 q^{7} +14.7525i q^{8} +(41.2592 + 69.7042i) q^{9} +O(q^{10})$	\(q+5.41049i q^{2} +(7.81854 + 4.45762i) q^{3} -13.2734 q^{4} -41.9044i q^{5} +(-24.1179 + 42.3021i) q^{6} -64.0047 q^{7} +14.7525i q^{8} +(41.2592 + 69.7042i) q^{9} +226.723 q^{10} +161.993i q^{11} +(-103.778 - 59.1676i) q^{12} -266.705 q^{13} -346.297i q^{14} +(186.794 - 327.631i) q^{15} -292.192 q^{16} -98.3026i q^{17} +(-377.134 + 223.232i) q^{18} -447.364 q^{19} +556.211i q^{20} +(-500.424 - 285.309i) q^{21} -876.458 q^{22} -28.8687i q^{23} +(-65.7610 + 115.343i) q^{24} -1130.98 q^{25} -1443.00i q^{26} +(11.8714 + 728.903i) q^{27} +849.558 q^{28} -337.070i q^{29} +(1772.64 + 1010.65i) q^{30} +1735.49 q^{31} -1344.86i q^{32} +(-722.102 + 1266.55i) q^{33} +531.865 q^{34} +2682.08i q^{35} +(-547.648 - 925.209i) q^{36} -328.761 q^{37} -2420.46i q^{38} +(-2085.24 - 1188.87i) q^{39} +618.194 q^{40} +606.752i q^{41} +(1543.66 - 2707.54i) q^{42} -2506.79 q^{43} -2150.18i q^{44} +(2920.91 - 1728.94i) q^{45} +156.194 q^{46} +2517.63i q^{47} +(-2284.51 - 1302.48i) q^{48} +1695.61 q^{49} -6119.13i q^{50} +(438.196 - 768.583i) q^{51} +3540.06 q^{52} +1760.77i q^{53} +(-3943.72 + 64.2303i) q^{54} +6788.20 q^{55} -944.229i q^{56} +(-3497.73 - 1994.18i) q^{57} +1823.71 q^{58} +453.188i q^{59} +(-2479.38 + 4348.76i) q^{60} +1300.26 q^{61} +9389.82i q^{62} +(-2640.78 - 4461.40i) q^{63} +2601.27 q^{64} +11176.1i q^{65} +(-6852.63 - 3906.92i) q^{66} +5806.28 q^{67} +1304.80i q^{68} +(128.686 - 225.711i) q^{69} -14511.3 q^{70} -7039.96i q^{71} +(-1028.31 + 608.676i) q^{72} +3733.10 q^{73} -1778.75i q^{74} +(-8842.58 - 5041.47i) q^{75} +5938.02 q^{76} -10368.3i q^{77} +(6432.36 - 11282.2i) q^{78} -4184.54 q^{79} +12244.1i q^{80} +(-3156.36 + 5751.88i) q^{81} -3282.82 q^{82} -6012.45i q^{83} +(6642.30 + 3787.01i) q^{84} -4119.31 q^{85} -13562.9i q^{86} +(1502.53 - 2635.40i) q^{87} -2389.79 q^{88} +13337.9i q^{89} +(9354.41 + 15803.6i) q^{90} +17070.4 q^{91} +383.184i q^{92} +(13569.0 + 7736.14i) q^{93} -13621.6 q^{94} +18746.5i q^{95} +(5994.88 - 10514.8i) q^{96} -7745.75 q^{97} +9174.06i q^{98} +(-11291.6 + 6683.68i) 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 $

$2$			5.41049i			1.35262i	0.736617	+	0.676311i	$0.236422\pi$
$2$			5.41049i			1.35262i	−0.736617	+	0.676311i	$0.763578\pi$
$3$	7.81854	+	4.45762i	0.868727	+	0.495291i
$3$	7.81854	+	4.45762i	0.868727	+	0.495291i
$4$	−13.2734			−0.829584
$5$		−	41.9044i		−	1.67617i	−0.545536	−	0.838087i	$-0.683674\pi$
$5$		−	41.9044i		−	1.67617i	0.545536	−	0.838087i	$-0.316326\pi$
$6$	−24.1179	+	42.3021i	−0.669942	+	1.17506i
$7$	−64.0047			−1.30622			−0.653110	−	0.757263i	$-0.726536\pi$
$7$	−64.0047			−1.30622			−0.653110	+	0.757263i	$0.726536\pi$
$8$			14.7525i			0.230508i
$9$	41.2592	+	69.7042i	0.509373	+	0.860546i
$10$	226.723			2.26723
$11$			161.993i			1.33878i	0.742911	+	0.669391i	$0.233445\pi$
$11$			161.993i			1.33878i	−0.742911	+	0.669391i	$0.766555\pi$
$12$	−103.778	−	59.1676i	−0.720682	−	0.410886i
$13$	−266.705			−1.57813			−0.789067	−	0.614308i	$-0.789435\pi$
$13$	−266.705			−1.57813			−0.789067	+	0.614308i	$0.789435\pi$
$14$		−	346.297i		−	1.76682i
$15$	186.794	−	327.631i	0.830195	−	1.45614i
$16$	−292.192			−1.14137
$17$		−	98.3026i		−	0.340147i	−0.985431	−	0.170074i	$-0.945599\pi$
$17$		−	98.3026i		−	0.340147i	0.985431	−	0.170074i	$-0.0544006\pi$
$18$	−377.134	+	223.232i	−1.16399	+	0.688988i
$19$	−447.364			−1.23924			−0.619618	−	0.784904i	$-0.712712\pi$
$19$	−447.364			−1.23924			−0.619618	+	0.784904i	$0.712712\pi$
$20$			556.211i			1.39053i
$21$	−500.424	−	285.309i	−1.13475	−	0.646959i
$22$	−876.458			−1.81086
$23$		−	28.8687i		−	0.0545722i	−0.999628	−	0.0272861i	$-0.991313\pi$
$23$		−	28.8687i		−	0.0545722i	0.999628	−	0.0272861i	$-0.00868651\pi$
$24$	−65.7610	+	115.343i	−0.114168	+	0.200248i
$25$	−1130.98			−1.80956
$26$		−	1443.00i		−	2.13462i
$27$	11.8714	+	728.903i	0.0162846	+	0.999867i
$28$	849.558			1.08362
$29$		−	337.070i		−	0.400797i	−0.979715	−	0.200398i	$-0.935776\pi$
$29$		−	337.070i		−	0.400797i	0.979715	−	0.200398i	$-0.0642236\pi$
$30$	1772.64	+	1010.65i	1.96960	+	1.12294i
$31$	1735.49			1.80592			0.902958	−	0.429728i	$-0.141390\pi$
$31$	1735.49			1.80592			0.902958	+	0.429728i	$0.141390\pi$
$32$		−	1344.86i		−	1.31334i
$33$	−722.102	+	1266.55i	−0.663087	+	1.16304i
$34$	531.865			0.460090
$35$			2682.08i			2.18945i
$36$	−547.648	−	925.209i	−0.422568	−	0.713896i
$37$	−328.761			−0.240146			−0.120073	−	0.992765i	$-0.538313\pi$
$37$	−328.761			−0.240146			−0.120073	+	0.992765i	$0.538313\pi$
$38$		−	2420.46i		−	1.67622i
$39$	−2085.24	−	1188.87i	−1.37097	−	0.781636i
$40$	618.194			0.386371
$41$			606.752i			0.360947i	0.983580	+	0.180473i	$0.0577630\pi$
$41$			606.752i			0.360947i	−0.983580	+	0.180473i	$0.942237\pi$
$42$	1543.66	−	2707.54i	0.875091	−	1.53488i
$43$	−2506.79			−1.35575			−0.677876	−	0.735176i	$-0.737099\pi$
$43$	−2506.79			−1.35575			−0.677876	+	0.735176i	$0.737099\pi$
$44$		−	2150.18i		−	1.11063i
$45$	2920.91	−	1728.94i	1.44243	−	0.853798i
$46$	156.194			0.0738155
$47$			2517.63i			1.13971i	0.821744	+	0.569857i	$0.193001\pi$
$47$			2517.63i			1.13971i	−0.821744	+	0.569857i	$0.806999\pi$
$48$	−2284.51	−	1302.48i	−0.991542	−	0.565313i
$49$	1695.61			0.706209
$50$		−	6119.13i		−	2.44765i
$51$	438.196	−	768.583i	0.168472	−	0.295495i
$52$	3540.06			1.30919
$53$			1760.77i			0.626832i	0.949616	+	0.313416i	$0.101473\pi$
$53$			1760.77i			0.626832i	−0.949616	+	0.313416i	$0.898527\pi$
$54$	−3943.72	+	64.2303i	−1.35244	+	0.0220269i
$55$	6788.20			2.24403
$56$		−	944.229i		−	0.301094i
$57$	−3497.73	−	1994.18i	−1.07656	−	0.613783i
$58$	1823.71			0.542126
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−2479.38	+	4348.76i	−0.688717	+	1.20799i
$61$	1300.26			0.349437			0.174719	−	0.984618i	$-0.444098\pi$
$61$	1300.26			0.349437			0.174719	+	0.984618i	$0.444098\pi$
$62$			9389.82i			2.44272i
$63$	−2640.78	−	4461.40i	−0.665352	−	1.12406i
$64$	2601.27			0.635077
$65$			11176.1i			2.64523i
$66$	−6852.63	−	3906.92i	−1.57315	−	0.896906i
$67$	5806.28			1.29345			0.646723	−	0.762725i	$-0.276139\pi$
$67$	5806.28			1.29345			0.646723	+	0.762725i	$0.276139\pi$
$68$			1304.80i			0.282181i
$69$	128.686	−	225.711i	0.0270291	−	0.0474083i
$70$	−14511.3			−2.96150
$71$		−	7039.96i		−	1.39654i	−0.715834	−	0.698270i	$-0.753953\pi$
$71$		−	7039.96i		−	1.39654i	0.715834	−	0.698270i	$-0.246047\pi$
$72$	−1028.31	+	608.676i	−0.198362	+	0.117414i
$73$	3733.10			0.700526			0.350263	−	0.936651i	$-0.386092\pi$
$73$	3733.10			0.700526			0.350263	+	0.936651i	$0.386092\pi$
$74$		−	1778.75i		−	0.324827i
$75$	−8842.58	−	5041.47i	−1.57201	−	0.896261i
$76$	5938.02			1.02805
$77$		−	10368.3i		−	1.74874i
$78$	6432.36	−	11282.2i	1.05726	−	1.85440i
$79$	−4184.54			−0.670493			−0.335246	−	0.942131i	$-0.608820\pi$
$79$	−4184.54			−0.670493			−0.335246	+	0.942131i	$0.608820\pi$
$80$			12244.1i			1.91314i
$81$	−3156.36	+	5751.88i	−0.481079	+	0.876677i
$82$	−3282.82			−0.488225
$83$		−	6012.45i		−	0.872762i	−0.899762	−	0.436381i	$-0.856260\pi$
$83$		−	6012.45i		−	0.872762i	0.899762	−	0.436381i	$-0.143740\pi$
$84$	6642.30	+	3787.01i	0.941369	+	0.536707i
$85$	−4119.31			−0.570146
$86$		−	13562.9i		−	1.83382i
$87$	1502.53	−	2635.40i	0.198511	−	0.348183i
$88$	−2389.79			−0.308599
$89$			13337.9i			1.68387i	0.539579	+	0.841935i	$0.318584\pi$
$89$			13337.9i			1.68387i	−0.539579	+	0.841935i	$0.681416\pi$
$90$	9354.41	+	15803.6i	1.15486	+	1.95106i
$91$	17070.4			2.06139
$92$			383.184i			0.0452722i
$93$	13569.0	+	7736.14i	1.56885	+	0.894455i
$94$	−13621.6			−1.54160
$95$			18746.5i			2.07717i
$96$	5994.88	−	10514.8i	0.650486	−	1.14093i
$97$	−7745.75			−0.823228			−0.411614	−	0.911358i	$-0.635035\pi$
$97$	−7745.75			−0.823228			−0.411614	+	0.911358i	$0.635035\pi$
$98$			9174.06i			0.955233i
$99$	−11291.6	+	6683.68i	−1.15208	+	0.681939i
$100$	15011.8			1.50118
$101$		−	1454.56i		−	0.142590i	−0.997455	−	0.0712951i	$-0.977287\pi$
$101$		−	1454.56i		−	0.142590i	0.997455	−	0.0712951i	$-0.0227132\pi$
$102$	4158.41	+	2370.85i	0.399693	+	0.227879i
$103$	11377.7			1.07245			0.536227	−	0.844074i	$-0.319849\pi$
$103$	11377.7			1.07245			0.536227	+	0.844074i	$0.319849\pi$
$104$		−	3934.56i		−	0.363772i
$105$	−11955.7	+	20969.9i	−1.08442	+	1.90204i
$106$	−9526.63			−0.847867
$107$			6247.21i			0.545656i	0.962063	+	0.272828i	$0.0879590\pi$
$107$			6247.21i			0.545656i	−0.962063	+	0.272828i	$0.912041\pi$
$108$	−157.574	−	9674.99i	−0.0135094	−	0.829474i
$109$	−8355.95			−0.703304			−0.351652	−	0.936131i	$-0.614380\pi$
$109$	−8355.95			−0.703304			−0.351652	+	0.936131i	$0.614380\pi$
$110$			36727.4i			3.03533i
$111$	−2570.43	−	1465.49i	−0.208622	−	0.118943i
$112$	18701.7			1.49088
$113$		−	2933.39i		−	0.229727i	−0.993381	−	0.114864i	$-0.963357\pi$
$113$		−	2933.39i		−	0.229727i	0.993381	−	0.114864i	$-0.0366431\pi$
$114$	10789.5	−	18924.4i	0.830215	−	1.45617i
$115$	−1209.72			−0.0914725
$116$			4474.05i			0.332495i
$117$	−11004.0	−	18590.4i	−0.803858	−	1.35806i
$118$	−2451.96			−0.176096
$119$			6291.83i			0.444307i
$120$	4833.37	+	2755.68i	0.335651	+	0.191366i
$121$	−11600.6			−0.792336
$122$			7035.02i			0.472656i
$123$	−2704.67	+	4743.91i	−0.178774	+	0.313564i
$124$	−23035.7			−1.49816
$125$			21202.6i			1.35697i
$126$	24138.3	−	14287.9i	1.52043	−	0.899970i
$127$	17272.2			1.07088			0.535438	−	0.844575i	$-0.320147\pi$
$127$	17272.2			1.07088			0.535438	+	0.844575i	$0.320147\pi$
$128$		−	7443.60i		−	0.454321i
$129$	−19599.4	−	11174.3i	−1.17778	−	0.671493i
$130$	−60468.0			−3.57799
$131$			8931.88i			0.520476i	0.965545	+	0.260238i	$0.0838009\pi$
$131$			8931.88i			0.520476i	−0.965545	+	0.260238i	$0.916199\pi$
$132$	9584.71	−	16811.3i	0.550087	−	0.964836i
$133$	28633.4			1.61871
$134$			31414.8i			1.74954i
$135$	30544.2	−	497.466i	1.67595	−	0.0272958i
$136$	1450.21			0.0784066
$137$			27846.5i			1.48364i	0.670597	+	0.741822i	$0.266038\pi$
$137$			27846.5i			1.48364i	−0.670597	+	0.741822i	$0.733962\pi$
$138$	1221.21	+	696.252i	0.0641255	+	0.0365602i
$139$	−14087.1			−0.729111			−0.364555	−	0.931182i	$-0.618779\pi$
$139$	−14087.1			−0.729111			−0.364555	+	0.931182i	$0.618779\pi$
$140$		−	35600.2i		−	1.81634i
$141$	−11222.6	+	19684.2i	−0.564491	+	0.990100i
$142$	38089.6			1.88899
$143$		−	43204.2i		−	2.11278i
$144$	−12055.6	−	20367.0i	−0.581385	−	0.982205i
$145$	−14124.7			−0.671805
$146$			20197.9i			0.947546i
$147$	13257.2	+	7558.38i	0.613503	+	0.349779i
$148$	4363.75			0.199222
$149$		−	21635.1i		−	0.974512i	−0.873259	−	0.487256i	$-0.837998\pi$
$149$		−	21635.1i		−	0.974512i	0.873259	−	0.487256i	$-0.162002\pi$
$150$	27276.8	−	47842.7i	1.21230	−	2.12634i
$151$	−10716.1			−0.469985			−0.234992	−	0.971997i	$-0.575507\pi$
$151$	−10716.1			−0.469985			−0.234992	+	0.971997i	$0.575507\pi$
$152$		−	6599.73i		−	0.285653i
$153$	6852.10	−	4055.88i	0.292712	−	0.173262i
$154$	56097.5			2.36539
$155$		−	72724.5i		−	3.02703i
$156$	27678.1	+	15780.3i	1.13733	+	0.648433i
$157$	−43733.5			−1.77425			−0.887125	−	0.461529i	$-0.847301\pi$
$157$	−43733.5			−1.77425			−0.887125	+	0.461529i	$0.847301\pi$
$158$		−	22640.4i		−	0.906923i
$159$	−7848.86	+	13766.7i	−0.310465	+	0.544546i
$160$	−56355.5			−2.20139
$161$			1847.73i			0.0712833i
$162$	−31120.5	−	17077.4i	−1.18581	−	0.650718i
$163$	−29538.5			−1.11176			−0.555882	−	0.831261i	$-0.687619\pi$
$163$	−29538.5			−1.11176			−0.555882	+	0.831261i	$0.687619\pi$
$164$		−	8053.63i		−	0.299436i
$165$	53073.8	+	30259.2i	1.94945	+	1.11145i
$166$	32530.3			1.18052
$167$			24433.8i			0.876108i	0.898949	+	0.438054i	$0.144332\pi$
$167$			24433.8i			0.876108i	−0.898949	+	0.438054i	$0.855668\pi$
$168$	4209.02	−	7382.50i	0.149129	−	0.261568i
$169$	42570.3			1.49051
$170$		−	22287.4i		−	0.771192i
$171$	−18457.9	−	31183.2i	−0.631232	−	1.06642i
$172$	33273.5			1.12471
$173$			18199.7i			0.608097i	0.952656	+	0.304049i	$0.0983386\pi$
$173$			18199.7i			0.608097i	−0.952656	+	0.304049i	$0.901661\pi$
$174$	14258.8	+	8129.42i	0.470959	+	0.268510i
$175$	72387.8			2.36368
$176$		−	47332.9i		−	1.52805i
$177$	−2020.14	+	3543.27i	−0.0644815	+	0.113099i
$178$	−72164.7			−2.27764
$179$		−	36106.0i		−	1.12687i	−0.826161	−	0.563435i	$-0.809480\pi$
$179$		−	36106.0i		−	1.12687i	0.826161	−	0.563435i	$-0.190520\pi$
$180$	−38770.3	+	22948.8i	−1.19661	+	0.708297i
$181$	4609.61			0.140704			0.0703521	−	0.997522i	$-0.477588\pi$
$181$	4609.61			0.140704			0.0703521	+	0.997522i	$0.477588\pi$
$182$			92358.9i			2.78828i
$183$	10166.1	+	5796.05i	0.303566	+	0.173073i
$184$	425.885			0.0125793
$185$			13776.5i			0.402527i
$186$	−41856.3	+	73414.7i	−1.20986	+	2.12206i
$187$	15924.3			0.455383
$188$		−	33417.4i		−	0.945489i
$189$	−759.829	−	46653.3i	−0.0212712	−	1.30605i
$190$	−101428.			−2.80963
$191$			71978.1i			1.97303i	0.163671	+	0.986515i	$0.447666\pi$
$191$			71978.1i			1.97303i	−0.163671	+	0.986515i	$0.552334\pi$
$192$	20338.2	+	11595.5i	0.551708	+	0.314548i
$193$	−65292.5			−1.75287			−0.876433	−	0.481523i	$-0.840084\pi$
$193$	−65292.5			−1.75287			−0.876433	+	0.481523i	$0.840084\pi$
$194$		−	41908.3i		−	1.11352i
$195$	−49818.8	+	87380.7i	−1.31016	+	2.29798i
$196$	−22506.4			−0.585860
$197$		−	20345.6i		−	0.524249i	−0.965034	−	0.262124i	$-0.915577\pi$
$197$		−	20345.6i		−	0.524249i	0.965034	−	0.262124i	$-0.0844231\pi$
$198$	−36162.0	−	61092.9i	−0.922405	−	1.55833i
$199$	40599.6			1.02522			0.512608	−	0.858623i	$-0.328679\pi$
$199$	40599.6			1.02522			0.512608	+	0.858623i	$0.328679\pi$
$200$		−	16684.7i		−	0.417118i
$201$	45396.6	+	25882.2i	1.12365	+	0.640633i
$202$	7869.89			0.192871
$203$			21574.1i			0.523528i
$204$	−5816.33	+	10201.7i	−0.139762	+	0.245138i
$205$	25425.6			0.605010
$206$			61558.6i			1.45062i
$207$	2012.27	−	1191.10i	0.0469619	−	0.0277976i
$208$	77928.9			1.80124
$209$		−	72469.6i		−	1.65906i
$210$	−113458.	−	64686.1i	−2.57273	−	1.46681i
$211$	75004.1			1.68469			0.842345	−	0.538939i	$-0.181175\pi$
$211$	75004.1			1.68469			0.842345	+	0.538939i	$0.181175\pi$
$212$		−	23371.3i		−	0.520010i
$213$	31381.5	−	55042.2i	0.691695	−	1.21321i
$214$	−33800.5			−0.738066
$215$			105045.i			2.27248i
$216$	−10753.1	+	175.133i	−0.230477	+	0.00375372i
$217$	−111079.			−2.35892
$218$		−	45209.7i		−	0.951304i
$219$	29187.4	+	16640.8i	0.608566	+	0.346965i
$220$	−90102.1			−1.86161
$221$			26217.7i			0.536798i
$222$	7929.02	−	13907.3i	0.160884	−	0.282186i
$223$	−38212.6			−0.768418			−0.384209	−	0.923246i	$-0.625526\pi$
$223$	−38212.6			−0.768418			−0.384209	+	0.923246i	$0.625526\pi$
$224$			86077.4i			1.71551i
$225$	−46663.2	−	78833.8i	−0.921741	−	1.55721i
$226$	15871.1			0.310734
$227$		−	57636.8i		−	1.11853i	−0.828989	−	0.559265i	$-0.811083\pi$
$227$		−	57636.8i		−	1.11853i	0.828989	−	0.559265i	$-0.188917\pi$
$228$	46426.6	+	26469.4i	0.893095	+	0.509185i
$229$	18933.1			0.361036			0.180518	−	0.983572i	$-0.442223\pi$
$229$	18933.1			0.361036			0.180518	+	0.983572i	$0.442223\pi$
$230$		−	6545.20i		−	0.123728i
$231$	46217.9	−	81064.9i	0.866137	−	1.51918i
$232$	4972.62			0.0923867
$233$			12366.1i			0.227783i	0.993493	+	0.113891i	$0.0363316\pi$
$233$			12366.1i			0.227783i	−0.993493	+	0.113891i	$0.963668\pi$
$234$	100583.	−	59537.0i	1.83694	−	1.08732i
$235$	105500.			1.91036
$236$		−	6015.32i		−	0.108003i
$237$	−32717.0	−	18653.1i	−0.582475	−	0.332089i
$238$	−34041.9			−0.600979
$239$			11878.9i			0.207960i	0.994579	+	0.103980i	$0.0331578\pi$
$239$			11878.9i			0.207960i	−0.994579	+	0.103980i	$0.966842\pi$
$240$	−54579.6	+	95731.1i	−0.947563	+	1.66200i
$241$	−45059.9			−0.775811			−0.387905	−	0.921699i	$-0.626801\pi$
$241$	−45059.9			−0.775811			−0.387905	+	0.921699i	$0.626801\pi$
$242$		−	62764.8i		−	1.07173i
$243$	−50317.8	+	30901.4i	−0.852137	+	0.523319i
$244$	−17258.8			−0.289888
$245$		−	71053.4i		−	1.18373i
$246$	−25666.9	−	14633.6i	−0.424134	−	0.241813i
$247$	119314.			1.95568
$248$			25602.7i			0.416278i
$249$	26801.3	−	47008.6i	0.432271	−	0.758191i
$250$	−114716.			−1.83546
$251$			10604.9i			0.168329i	0.996452	+	0.0841646i	$0.0268221\pi$
$251$			10604.9i			0.168329i	−0.996452	+	0.0841646i	$0.973178\pi$
$252$	35052.1	+	59217.8i	0.551966	+	0.932504i
$253$	4676.51			0.0730602
$254$			93450.7i			1.44849i
$255$	−32207.0	−	18362.3i	−0.495301	−	0.282389i
$256$	81893.8			1.24960
$257$			11638.4i			0.176209i	0.996111	+	0.0881046i	$0.0280810\pi$
$257$			11638.4i			0.176209i	−0.996111	+	0.0881046i	$0.971919\pi$
$258$	60458.4	−	106042.i	0.908275	−	1.59309i
$259$	21042.2			0.313684
$260$		−	148344.i		−	2.19444i
$261$	23495.2	−	13907.2i	0.344904	−	0.204155i
$262$	−48325.8			−0.704006
$263$			3594.97i			0.0519737i	0.999662	+	0.0259869i	$0.00827280\pi$
$263$			3594.97i			0.0519737i	−0.999662	+	0.0259869i	$0.991727\pi$
$264$	−18684.7	−	10652.8i	−0.268089	−	0.152847i
$265$	73784.0			1.05068
$266$			154921.i			2.18951i
$267$	−59455.5	+	104283.i	−0.834007	+	1.46282i
$268$	−77068.8			−1.07302
$269$			32803.0i			0.453325i	0.973973	+	0.226662i	$0.0727814\pi$
$269$			32803.0i			0.453325i	−0.973973	+	0.226662i	$0.927219\pi$
$270$	2691.53	+	165259.i	0.0369209	+	2.26693i
$271$	28994.4			0.394798			0.197399	−	0.980323i	$-0.436751\pi$
$271$	28994.4			0.394798			0.197399	+	0.980323i	$0.436751\pi$
$272$			28723.2i			0.388235i
$273$	133465.	+	76093.2i	1.79078	+	1.02099i
$274$	−150663.			−2.00681
$275$		−	183210.i		−	2.42261i
$276$	−1708.09	+	2995.94i	−0.0224230	+	0.0393292i
$277$	−88957.8			−1.15938			−0.579688	−	0.814838i	$-0.696826\pi$
$277$	−88957.8			−1.15938			−0.579688	+	0.814838i	$0.696826\pi$
$278$		−	76218.3i		−	0.986211i
$279$	71604.7	+	120971.i	0.919885	+	1.55407i
$280$	−39567.3			−0.504685
$281$		−	62305.2i		−	0.789063i	−0.918882	−	0.394532i	$-0.870907\pi$
$281$		−	62305.2i		−	0.789063i	0.918882	−	0.394532i	$-0.129093\pi$
$282$	−106501.	−	60719.9i	−1.33923	−	0.763542i
$283$	−102769.			−1.28318			−0.641592	−	0.767046i	$-0.721726\pi$
$283$	−102769.			−1.28318			−0.641592	+	0.767046i	$0.721726\pi$
$284$			93443.9i			1.15855i
$285$	−83564.8	+	146570.i	−1.02881	+	1.80450i
$286$	233755.			2.85779
$287$		−	38835.0i		−	0.471476i
$288$	93742.4	−	55487.8i	1.13019	−	0.668979i
$289$	73857.6			0.884300
$290$		−	76421.5i		−	0.908698i
$291$	−60560.5	−	34527.6i	−0.715160	−	0.407738i
$292$	−49550.8			−0.581145
$293$			124891.i			1.45478i	0.686225	+	0.727389i	$0.259267\pi$
$293$			124891.i			1.45478i	−0.686225	+	0.727389i	$0.740733\pi$
$294$	−40894.5	+	71727.8i	−0.473119	+	0.829837i
$295$	18990.5			0.218219
$296$		−	4850.04i		−	0.0553556i
$297$	−118077.	+	1923.09i	−1.33860	+	0.0218015i
$298$	117057.			1.31815
$299$			7699.41i			0.0861222i
$300$	117371.	+	66917.1i	1.30412	+	0.743524i
$301$	160446.			1.77091
$302$		−	57979.4i		−	0.635712i
$303$	6483.89	−	11372.6i	0.0706237	−	0.123872i
$304$	130716.			1.41443
$305$		−	54486.4i		−	0.585718i
$306$	21944.3	+	37073.2i	0.234358	+	0.395929i
$307$	82222.6			0.872398			0.436199	−	0.899850i	$-0.356324\pi$
$307$	82222.6			0.872398			0.436199	+	0.899850i	$0.356324\pi$
$308$			137622.i			1.45073i
$309$	88956.7	+	50717.3i	0.931669	+	0.531177i
$310$	393475.			4.09443
$311$			153255.i			1.58450i	0.610195	+	0.792251i	$0.291091\pi$
$311$			153255.i			1.58450i	−0.610195	+	0.792251i	$0.708909\pi$
$312$	17538.8	−	30762.5i	0.180173	−	0.316018i
$313$	−146232.			−1.49263			−0.746316	−	0.665591i	$-0.768179\pi$
$313$	−146232.			−1.49263			−0.746316	+	0.665591i	$0.768179\pi$
$314$		−	236619.i		−	2.39989i
$315$	−186952.	+	110660.i	−1.88412	+	1.11525i
$316$	55542.9			0.556230
$317$		−	47521.9i		−	0.472907i	−0.971643	−	0.236453i	$-0.924015\pi$
$317$		−	47521.9i		−	0.472907i	0.971643	−	0.236453i	$-0.0759851\pi$
$318$	−74484.4	−	42466.1i	−0.736565	−	0.419941i
$319$	54602.8			0.536579
$320$		−	109005.i		−	1.06450i
$321$	−27847.7	+	48844.1i	−0.270259	+	0.474026i
$322$	−9997.13			−0.0964193
$323$			43977.0i			0.421522i
$324$	41895.5	−	76346.7i	0.399096	−	0.727278i
$325$	301636.			2.85573
$326$		−	159817.i		−	1.50380i
$327$	−65331.3	−	37247.7i	−0.610979	−	0.348340i
$328$	−8951.10			−0.0832010
$329$		−	161140.i		−	1.48872i
$330$	−163717.	+	287155.i	−1.50337	+	2.63687i
$331$	23464.2			0.214165			0.107083	−	0.994250i	$-0.465849\pi$
$331$	23464.2			0.214165			0.107083	+	0.994250i	$0.465849\pi$
$332$			79805.4i			0.724029i
$333$	−13564.4	−	22916.0i	−0.122324	−	0.206657i
$334$	−132199.			−1.18504
$335$		−	243308.i		−	2.16804i
$336$	146220.	+	83365.0i	1.29517	+	0.738423i
$337$	−98655.4			−0.868682			−0.434341	−	0.900748i	$-0.643019\pi$
$337$	−98655.4			−0.868682			−0.434341	+	0.900748i	$0.643019\pi$
$338$			230326.i			2.01609i
$339$	13075.9	−	22934.8i	0.113782	−	0.199570i
$340$	54677.0			0.472985
$341$			281136.i			2.41773i
$342$	168716.	−	99866.0i	1.44246	−	0.853819i
$343$	45148.4			0.383755
$344$		−	36981.3i		−	0.312511i
$345$	−9458.28	−	5392.50i	−0.0794646	−	0.0453056i
$346$	−98469.5			−0.822525
$347$			166071.i			1.37923i	0.724178	+	0.689614i	$0.242220\pi$
$347$			166071.i			1.37923i	−0.724178	+	0.689614i	$0.757780\pi$
$348$	−19943.6	+	34980.5i	−0.164682	+	0.288847i
$349$	−4808.67			−0.0394797			−0.0197399	−	0.999805i	$-0.506284\pi$
$349$	−4808.67			−0.0394797			−0.0197399	+	0.999805i	$0.506284\pi$
$350$			391653.i			3.19717i
$351$	−3166.17	−	194402.i	−0.0256992	−	1.57792i
$352$	217857.			1.75827
$353$		−	75307.1i		−	0.604347i	−0.953253	−	0.302174i	$-0.902288\pi$
$353$		−	75307.1i		−	0.604347i	0.953253	−	0.302174i	$-0.0977122\pi$
$354$	−19170.8	−	10929.9i	−0.152980	−	0.0872190i
$355$	−295005.			−2.34085
$356$		−	177039.i		−	1.39691i
$357$	−28046.6	+	49192.9i	−0.220061	+	0.385981i
$358$	195351.			1.52423
$359$		−	198922.i		−	1.54346i	−0.635953	−	0.771728i	$-0.719393\pi$
$359$		−	198922.i		−	1.54346i	0.635953	−	0.771728i	$-0.280607\pi$
$360$	25506.2	+	43090.7i	0.196807	+	0.332490i
$361$	69813.4			0.535704
$362$			24940.2i			0.190319i
$363$	−90699.7	−	51711.1i	−0.688323	−	0.392437i
$364$	−226581.			−1.71010
$365$		−	156433.i		−	1.17420i
$366$	−31359.5	+	55003.6i	−0.234103	+	0.410609i
$367$	−152393.			−1.13144			−0.565722	−	0.824596i	$-0.691402\pi$
$367$	−152393.			−1.13144			−0.565722	+	0.824596i	$0.691402\pi$
$368$			8435.19i			0.0622873i
$369$	−42293.2	+	25034.1i	−0.310611	+	0.183857i
$370$	−74537.6			−0.544467
$371$		−	112698.i		−	0.818780i
$372$	−180106.	−	102685.i	−1.30149	−	0.742026i
$373$	−116970.			−0.840733			−0.420366	−	0.907354i	$-0.638098\pi$
$373$	−116970.			−0.840733			−0.420366	+	0.907354i	$0.638098\pi$
$374$			86158.1i			0.615961i
$375$	−94513.3	+	165773.i	−0.672094	+	1.17883i
$376$	−37141.3			−0.262713
$377$			89898.1i			0.632510i
$378$	252417.	−	4111.04i	1.76659	−	0.0287719i
$379$	−185149.			−1.28897			−0.644487	−	0.764616i	$-0.722929\pi$
$379$	−185149.			−1.28897			−0.644487	+	0.764616i	$0.722929\pi$
$380$		−	248829.i		−	1.72319i
$381$	135043.	+	76992.8i	0.930298	+	0.530396i
$382$	−389436.			−2.66876
$383$		−	219154.i		−	1.49401i	−0.664821	−	0.747003i	$-0.731492\pi$
$383$		−	219154.i		−	1.49401i	0.664821	−	0.747003i	$-0.268508\pi$
$384$	33180.7	−	58198.1i	0.225021	−	0.394681i
$385$	−434477.			−2.93120
$386$		−	353264.i		−	2.37096i
$387$	−103428.	−	174734.i	−0.690583	−	1.16669i
$388$	102812.			0.682937
$389$			177651.i			1.17400i	0.809586	+	0.587002i	$0.199692\pi$
$389$			177651.i			1.17400i	−0.809586	+	0.587002i	$0.800308\pi$
$390$	−472772.	−	269544.i	−3.10830	−	1.77215i
$391$	−2837.87			−0.0185626
$392$			25014.4i			0.162787i
$393$	−39815.0	+	69834.3i	−0.257787	+	0.452151i
$394$	110079.			0.709110
$395$			175351.i			1.12386i
$396$	149877.	−	88714.8i	0.955750	−	0.565726i
$397$	202948.			1.28767			0.643834	−	0.765165i	$-0.277343\pi$
$397$	202948.			1.28767			0.643834	+	0.765165i	$0.277343\pi$
$398$			219663.i			1.38673i
$399$	223872.	+	127637.i	1.40622	+	0.801735i
$400$	330462.			2.06539
$401$			71075.9i			0.442012i	0.975272	+	0.221006i	$0.0709340\pi$
$401$			71075.9i			0.442012i	−0.975272	+	0.221006i	$0.929066\pi$
$402$	−140035.	+	245618.i	−0.866534	+	1.51987i
$403$	−462862.			−2.84998
$404$			19306.9i			0.118291i
$405$	241029.	+	132265.i	1.46946	+	0.806372i
$406$	−116726.			−0.708136
$407$		−	53256.8i		−	0.321504i
$408$	11338.5	+	6464.48i	0.0681139	+	0.0388341i
$409$	237140.			1.41762			0.708808	−	0.705402i	$-0.249233\pi$
$409$	237140.			1.41762			0.708808	+	0.705402i	$0.249233\pi$
$410$			137565.i			0.818350i
$411$	−124129.	+	217719.i	−0.734836	+	1.28888i
$412$	−151020.			−0.889690
$413$		−	29006.2i		−	0.170055i
$414$	6444.42	+	10887.4i	0.0375996	+	0.0635216i
$415$	−251948.			−1.46290
$416$			358680.i			2.07262i
$417$	−110141.	−	62795.2i	−0.633398	−	0.361122i
$418$	392096.			2.24409
$419$		−	148867.i		−	0.847950i	−0.905674	−	0.423975i	$-0.860634\pi$
$419$		−	148867.i		−	0.847950i	0.905674	−	0.423975i	$-0.139366\pi$
$420$	158692.	−	278341.i	0.899615	−	1.57790i
$421$	−205091.			−1.15713			−0.578565	−	0.815636i	$-0.696387\pi$
$421$	−205091.			−1.15713			−0.578565	+	0.815636i	$0.696387\pi$
$422$			405808.i			2.27875i
$423$	−175489.	+	103875.i	−0.980776	+	0.580539i
$424$	−25975.8			−0.144490
$425$			111178.i			0.615518i
$426$	297805.	+	169789.i	1.64102	+	0.935601i
$427$	−83222.6			−0.456442
$428$		−	82921.5i		−	0.452668i
$429$	192588.	−	337793.i	1.04644	−	1.83542i
$430$	−568346.			−3.07380
$431$		−	209347.i		−	1.12697i	−0.826126	−	0.563485i	$-0.809460\pi$
$431$		−	209347.i		−	1.12697i	0.826126	−	0.563485i	$-0.190540\pi$
$432$	−3468.74	−	212980.i	−0.0185868	−	1.14122i
$433$	207554.			1.10702			0.553511	−	0.832842i	$-0.313288\pi$
$433$	207554.			1.10702			0.553511	+	0.832842i	$0.313288\pi$
$434$		−	600993.i		−	3.19073i
$435$	−110435.	−	62962.6i	−0.583615	−	0.332739i
$436$	110911.			0.583450
$437$			12914.8i			0.0676278i
$438$	−90034.6	+	157918.i	−0.469312	+	0.823159i
$439$	87515.8			0.454106			0.227053	−	0.973882i	$-0.427091\pi$
$439$	87515.8			0.454106			0.227053	+	0.973882i	$0.427091\pi$
$440$			100143.i			0.517266i
$441$	69959.4	+	118191.i	0.359724	+	0.607725i
$442$	−141851.			−0.726084
$443$		−	262305.i		−	1.33659i	−0.743896	−	0.668296i	$-0.767024\pi$
$443$		−	262305.i		−	1.33659i	0.743896	−	0.668296i	$-0.232976\pi$
$444$	34118.2	+	19452.0i	0.173069	+	0.0986729i
$445$	558918.			2.82246
$446$		−	206749.i		−	1.03938i
$447$	96441.3	−	169155.i	0.482668	−	0.846585i
$448$	−166494.			−0.829549
$449$		−	171982.i		−	0.853080i	−0.904469	−	0.426540i	$-0.859732\pi$
$449$		−	171982.i		−	0.853080i	0.904469	−	0.426540i	$-0.140268\pi$
$450$	426529.	−	252470.i	2.10632	−	1.24677i
$451$	−98289.3			−0.483229
$452$			38935.9i			0.190578i
$453$	−83784.5	−	47768.4i	−0.408288	−	0.232779i
$454$	311843.			1.51295
$455$		−	715323.i		−	3.45525i
$456$	29419.1	−	51600.3i	0.141482	−	0.248155i
$457$	3157.29			0.0151176			0.00755879	−	0.999971i	$-0.497594\pi$
$457$	3157.29			0.0151176			0.00755879	+	0.999971i	$0.497594\pi$
$458$			102437.i			0.488345i
$459$	71653.1	−	1166.99i	0.340102	−	0.00553915i
$460$	16057.1			0.0758842
$461$			272235.i			1.28098i	0.767966	+	0.640490i	$0.221269\pi$
$461$			272235.i			1.28098i	−0.767966	+	0.640490i	$0.778731\pi$
$462$	438601.	+	250062.i	2.05487	+	1.17156i
$463$	249599.			1.16434			0.582171	−	0.813066i	$-0.302203\pi$
$463$	249599.			1.16434			0.582171	+	0.813066i	$0.302203\pi$
$464$			98489.1i			0.457459i
$465$	324178.	−	568599.i	1.49926	−	2.62966i
$466$	−66906.6			−0.308104
$467$			159468.i			0.731207i	0.930771	+	0.365604i	$0.119137\pi$
$467$			159468.i			0.731207i	−0.930771	+	0.365604i	$0.880863\pi$
$468$	146060.	+	246757.i	0.666868	+	1.12662i
$469$	−371629.			−1.68952
$470$			570804.i			2.58399i
$471$	−341932.	−	194947.i	−1.54134	−	0.878771i
$472$	−6685.65			−0.0300095
$473$		−	406081.i		−	1.81506i
$474$	100922.	−	177015.i	0.449191	−	0.787868i
$475$	505958.			2.24247
$476$		−	83513.7i		−	0.368590i
$477$	−122733.	+	72648.0i	−0.539418	+	0.319291i
$478$	−64270.5			−0.281291
$479$		−	285627.i		−	1.24488i	−0.782666	−	0.622441i	$-0.786141\pi$
$479$		−	285627.i		−	1.24488i	0.782666	−	0.622441i	$-0.213859\pi$
$480$	−440618.	−	251212.i	−1.91240	−	1.09033i
$481$	87681.9			0.378983
$482$		−	243796.i		−	1.04938i
$483$	−8236.50	+	14446.6i	−0.0353060	+	0.0619257i
$484$	153979.			0.657309
$485$			324581.i			1.37987i
$486$	−167192.	−	272244.i	−0.707852	−	1.15262i
$487$	−325973.			−1.37443			−0.687216	−	0.726453i	$-0.741167\pi$
$487$	−325973.			−1.37443			−0.687216	+	0.726453i	$0.741167\pi$
$488$			19182.0i			0.0805480i
$489$	−230948.	−	131671.i	−0.965820	−	0.550648i
$490$	384433.			1.60114
$491$			278762.i			1.15630i	0.815931	+	0.578149i	$0.196225\pi$
$491$			278762.i			1.15630i	−0.815931	+	0.578149i	$0.803775\pi$
$492$	35900.1	−	62967.6i	0.148308	−	0.260128i
$493$	−33134.8			−0.136330
$494$			645547.i			2.64529i
$495$	280075.	+	473166.i	1.14305	+	1.93109i
$496$	−507095.			−2.06123
$497$			450591.i			1.82419i
$498$	254339.	+	145008.i	1.02555	+	0.584699i
$499$	−204145.			−0.819857			−0.409928	−	0.912118i	$-0.634446\pi$
$499$	−204145.			−0.819857			−0.409928	+	0.912118i	$0.634446\pi$
$500$		−	281430.i		−	1.12572i
$501$	−108917.	+	191037.i	−0.433929	+	0.761099i
$502$	−57377.7			−0.227686
$503$			27595.1i			0.109068i	0.998512	+	0.0545339i	$0.0173673\pi$
$503$			27595.1i			0.109068i	−0.998512	+	0.0545339i	$0.982633\pi$
$504$	65816.8	−	38958.1i	0.259105	−	0.153369i
$505$	−60952.5			−0.239006
$506$			25302.2i			0.0988228i
$507$	332838.	+	189762.i	1.29484	+	0.738234i
$508$	−229259.			−0.888382
$509$		−	84040.5i		−	0.324379i	−0.986760	−	0.162190i	$-0.948144\pi$
$509$		−	84040.5i		−	0.324379i	0.986760	−	0.162190i	$-0.0518556\pi$
$510$	99349.1	−	174255.i	0.381965	−	0.669955i
$511$	−238936.			−0.915041
$512$			323988.i			1.23592i
$513$	−5310.86	−	326085.i	−0.0201804	−	1.23907i
$514$	−62969.6			−0.238344
$515$		−	476773.i		−	1.79762i
$516$	260150.	+	148321.i	0.977067	+	0.557060i
$517$	−407837.			−1.52583
$518$			113849.i			0.424296i
$519$	−81127.6	+	142295.i	−0.301185	+	0.528270i
$520$	−164875.			−0.609745
$521$			107436.i			0.395800i	0.980222	+	0.197900i	$0.0634121\pi$
$521$			107436.i			0.395800i	−0.980222	+	0.197900i	$0.936588\pi$
$522$	75244.9	+	127120.i	0.276144	+	0.466524i
$523$	−102442.			−0.374521			−0.187261	−	0.982310i	$-0.559961\pi$
$523$	−102442.			−0.374521			−0.187261	+	0.982310i	$0.559961\pi$
$524$		−	118556.i		−	0.431778i
$525$	565967.	+	322678.i	2.05340	+	1.17071i
$526$	−19450.5			−0.0703007
$527$		−	170603.i		−	0.614278i
$528$	210992.	−	370074.i	0.756830	−	1.32746i
$529$	279008.			0.997022
$530$			399207.i			1.42117i
$531$	−31589.1	+	18698.2i	−0.112034	+	0.0663147i
$532$	−380061.			−1.34286
$533$		−	161823.i		−	0.569622i
$534$	−564223.	−	321683.i	−1.97865	−	1.12810i
$535$	261786.			0.914615
$536$			85657.1i			0.298149i
$537$	160947.	−	282296.i	0.558129	−	0.978942i
$538$	−177480.			−0.613177
$539$			274676.i			0.945460i
$540$	−405424.	+	6603.04i	−1.39034	+	0.0226442i
$541$	−40329.8			−0.137794			−0.0688972	−	0.997624i	$-0.521948\pi$
$541$	−40329.8			−0.137794			−0.0688972	+	0.997624i	$0.521948\pi$
$542$			156874.i			0.534012i
$543$	36040.4	+	20547.9i	0.122233	+	0.0696896i
$544$	−132203.			−0.446729
$545$			350151.i			1.17886i
$546$	−411701.	+	722112.i	−1.38101	+	2.42225i
$547$	123440.			0.412556			0.206278	−	0.978493i	$-0.433865\pi$
$547$	123440.			0.412556			0.206278	+	0.978493i	$0.433865\pi$
$548$		−	369616.i		−	1.23081i
$549$	53647.5	+	90633.4i	0.177994	+	0.300707i
$550$	991253.			3.27687
$551$			150793.i			0.496681i
$552$	3329.80	+	1898.44i	0.0109280	+	0.00623042i
$553$	267831.			0.875810
$554$		−	481305.i		−	1.56820i
$555$	−61410.5	+	107712.i	−0.199368	+	0.349686i
$556$	186984.			0.604859
$557$		−	309624.i		−	0.997987i	−0.866606	−	0.498993i	$-0.833703\pi$
$557$		−	309624.i		−	0.997987i	0.866606	−	0.498993i	$-0.166297\pi$
$558$	−654510.	+	387416.i	−2.10207	+	1.24426i
$559$	668571.			2.13956
$560$		−	783681.i		−	2.49898i
$561$	124505.	+	70984.5i	0.395603	+	0.225547i
$562$	337102.			1.06730
$563$			501724.i			1.58288i	0.611247	+	0.791440i	$0.290668\pi$
$563$			501724.i			1.58288i	−0.611247	+	0.791440i	$0.709332\pi$
$564$	148962.	−	261275.i	0.468293	−	0.821372i
$565$	−122922.			−0.385063
$566$		−	556030.i		−	1.73566i
$567$	202022.	−	368148.i	0.628395	−	1.14513i
$568$	103857.			0.321913
$569$			187984.i			0.580627i	0.956932	+	0.290313i	$0.0937595\pi$
$569$			187984.i			0.580627i	−0.956932	+	0.290313i	$0.906240\pi$
$570$	−793016.	−	452126.i	−2.44080	−	1.39159i
$571$	404837.			1.24167			0.620837	−	0.783939i	$-0.286793\pi$
$571$	404837.			1.24167			0.620837	+	0.783939i	$0.286793\pi$
$572$			573464.i			1.75273i
$573$	−320851.	+	562764.i	−0.977225	+	1.71402i
$574$	210116.			0.637728
$575$			32649.8i			0.0987518i
$576$	107326.	+	181320.i	0.323491	+	0.546513i
$577$	285933.			0.858841			0.429421	−	0.903105i	$-0.358718\pi$
$577$	285933.			0.858841			0.429421	+	0.903105i	$0.358718\pi$
$578$			399605.i			1.19612i
$579$	−510492.	−	291050.i	−1.52276	−	0.868180i
$580$	187482.			0.557319
$581$			384826.i			1.14002i
$582$	186811.	−	327661.i	0.551515	−	0.967341i
$583$	−285232.			−0.839191
$584$			55072.6i			0.161477i
$585$	−779020.	+	461116.i	−2.27634	+	1.34741i
$586$	−675722.			−1.96776
$587$			186645.i			0.541676i	0.962625	+	0.270838i	$0.0873008\pi$
$587$			186645.i			0.541676i	−0.962625	+	0.270838i	$0.912699\pi$
$588$	−175967.	−	100325.i	−0.508952	−	0.290172i
$589$	−776394.			−2.23796
$590$			102748.i			0.295168i
$591$	90692.9	−	159073.i	0.259656	−	0.455429i
$592$	96061.1			0.274097
$593$		−	160449.i		−	0.456276i	−0.973629	−	0.228138i	$-0.926736\pi$
$593$		−	160449.i		−	0.456276i	0.973629	−	0.228138i	$-0.0732637\pi$
$594$	−10404.8	−	638853.i	−0.0294891	−	1.81062i
$595$	263655.			0.744736
$596$			287171.i			0.808440i
$597$	317429.	+	180978.i	0.890632	+	0.507781i
$598$	−41657.6			−0.116491
$599$		−	258334.i		−	0.719993i	−0.932954	−	0.359996i	$-0.882778\pi$
$599$		−	258334.i		−	0.719993i	0.932954	−	0.359996i	$-0.117222\pi$
$600$	74374.2	−	130450.i	0.206595	−	0.362361i
$601$	173281.			0.479734			0.239867	−	0.970806i	$-0.422896\pi$
$601$	173281.			0.479734			0.239867	+	0.970806i	$0.422896\pi$
$602$			868092.i			2.39537i
$603$	239562.	+	404722.i	0.658846	+	1.11307i
$604$	142239.			0.389892
$605$			486115.i			1.32809i
$606$	61531.1	+	35081.0i	0.167552	+	0.0955271i
$607$	−592777.			−1.60884			−0.804422	−	0.594058i	$-0.797525\pi$
$607$	−592777.			−1.60884			−0.804422	+	0.594058i	$0.797525\pi$
$608$			601642.i			1.62754i
$609$	−96169.1	+	168678.i	−0.259299	+	0.454803i
$610$	294798.			0.792255
$611$		−	671463.i		−	1.79862i
$612$	−90950.4	+	53835.2i	−0.242830	+	0.143735i
$613$	144770.			0.385264			0.192632	−	0.981271i	$-0.438298\pi$
$613$	144770.			0.385264			0.192632	+	0.981271i	$0.438298\pi$
$614$			444864.i			1.18002i
$615$	198791.	+	113338.i	0.525589	+	0.299656i
$616$	152958.			0.403098
$617$			57533.0i			0.151129i	0.997141	+	0.0755643i	$0.0240758\pi$
$617$			57533.0i			0.151129i	−0.997141	+	0.0755643i	$0.975924\pi$
$618$	−274405.	+	481299.i	−0.718481	+	1.26020i
$619$	349680.			0.912618			0.456309	−	0.889821i	$-0.349171\pi$
$619$	349680.			0.912618			0.456309	+	0.889821i	$0.349171\pi$
$620$			965297.i			2.51118i
$621$	21042.5	−	342.713i	0.0545650	−	0.000888685i
$622$	−829182.			−2.14323
$623$		−	853691.i		−	2.19950i
$624$	609290.	+	347378.i	1.56479	+	0.892139i
$625$	181622.			0.464952
$626$		−	791185.i		−	2.01897i
$627$	323042.	−	566607.i	0.821721	−	1.44127i
$628$	580490.			1.47189
$629$			32318.0i			0.0816852i
$630$	−598726.	−	1.01150e6i	−1.50851	−	2.54851i
$631$	152337.			0.382601			0.191300	−	0.981532i	$-0.438730\pi$
$631$	152337.			0.382601			0.191300	+	0.981532i	$0.438730\pi$
$632$		−	61732.5i		−	0.154554i
$633$	586422.	+	334340.i	1.46354	+	0.834412i
$634$	257117.			0.639664
$635$		−	723779.i		−	1.79497i
$636$	104181.	−	182730.i	0.257557	−	0.451747i
$637$	−452226.			−1.11449
$638$			295428.i			0.725788i
$639$	490715.	−	290463.i	1.20179	−	0.711360i
$640$	−311919.			−0.761521
$641$			367955.i			0.895526i	0.894152	+	0.447763i	$0.147779\pi$
$641$			367955.i			0.895526i	−0.894152	+	0.447763i	$0.852221\pi$
$642$	−264270.	−	150670.i	−0.641178	−	0.365558i
$643$	−369504.			−0.893711			−0.446856	−	0.894606i	$-0.647456\pi$
$643$	−369504.			−0.893711			−0.446856	+	0.894606i	$0.647456\pi$
$644$		−	24525.6i		−	0.0591355i
$645$	−468252.	+	821301.i	−1.12554	+	1.97416i
$646$	−237937.			−0.570160
$647$			358923.i			0.857419i	0.903442	+	0.428709i	$0.141032\pi$
$647$			358923.i			0.857419i	−0.903442	+	0.428709i	$0.858968\pi$
$648$	−84854.5	−	46564.2i	−0.202081	−	0.110892i
$649$	−73413.0			−0.174294
$650$			1.63200e6i			3.86272i
$651$	−868479.	−	495150.i	−2.04926	−	1.16835i
$652$	392075.			0.922303
$653$			415428.i			0.974247i	0.873333	+	0.487123i	$0.161954\pi$
$653$			415428.i			0.974247i	−0.873333	+	0.487123i	$0.838046\pi$
$654$	201528.	−	353474.i	0.471173	−	0.826423i
$655$	374285.			0.872408
$656$		−	177288.i		−	0.411976i
$657$	154025.	+	260213.i	0.356829	+	0.602835i
$658$	871846.			2.01367
$659$			689382.i			1.58741i	0.608303	+	0.793705i	$0.291851\pi$
$659$			689382.i			1.58741i	−0.608303	+	0.793705i	$0.708149\pi$
$660$	−704467.	−	401641.i	−1.61723	−	0.922042i
$661$	213731.			0.489175			0.244587	−	0.969627i	$-0.421347\pi$
$661$	213731.			0.489175			0.244587	+	0.969627i	$0.421347\pi$
$662$			126953.i			0.289685i
$663$	−116869.	+	204984.i	−0.265871	+	0.466331i
$664$	88698.7			0.201178
$665$		−	1.19987e6i		−	2.71325i
$666$	123987.	−	73389.9i	0.279529	−	0.165458i
$667$	−9730.77			−0.0218723
$668$		−	324318.i		−	0.726806i
$669$	−298767.	−	170338.i	−0.667545	−	0.380591i
$670$	1.31642e6			2.93254
$671$			210632.i			0.467820i
$672$	−383701.	+	673000.i	−0.849677	+	1.49031i
$673$	−807880.			−1.78368			−0.891840	−	0.452352i	$-0.850585\pi$
$673$	−807880.			−1.78368			−0.891840	+	0.452352i	$0.850585\pi$
$674$		−	533773.i		−	1.17500i
$675$	−13426.3	−	824372.i	−0.0294679	−	1.80932i
$676$	−565051.			−1.23650
$677$		−	189407.i		−	0.413256i	−0.978420	−	0.206628i	$-0.933751\pi$
$677$		−	189407.i		−	0.413256i	0.978420	−	0.206628i	$-0.0662490\pi$
$678$	124089.	+	70747.2i	0.269943	+	0.153904i
$679$	495765.			1.07532
$680$		−	60770.0i		−	0.131423i
$681$	256923.	−	450636.i	0.553999	−	0.971698i
$682$	−1.52108e6			−3.27027
$683$		−	547508.i		−	1.17368i	−0.809704	−	0.586839i	$-0.800372\pi$
$683$		−	547508.i		−	1.17368i	0.809704	−	0.586839i	$-0.199628\pi$
$684$	244998.	+	413905.i	0.523661	+	0.884685i
$685$	1.16689e6			2.48685
$686$			244275.i			0.519076i
$687$	148029.	+	84396.5i	0.313641	+	0.178818i
$688$	732462.			1.54742
$689$		−	469606.i		−	0.989225i
$690$	29176.0	−	51173.9i	0.0612813	−	0.107486i
$691$	442497.			0.926733			0.463366	−	0.886167i	$-0.346641\pi$
$691$	442497.			0.926733			0.463366	+	0.886167i	$0.346641\pi$
$692$		−	241572.i		−	0.504468i
$693$	722714.	−	427787.i	1.50487	−	0.890761i
$694$	−898527.			−1.86557
$695$			590313.i			1.22212i
$696$	38878.6	+	22166.1i	0.0802588	+	0.0457583i
$697$	59645.3			0.122775
$698$		−	26017.2i		−	0.0534011i
$699$	−55123.4	+	96684.9i	−0.112819	+	0.197881i
$700$	−960829.			−1.96088
$701$		−	468708.i		−	0.953820i	−0.878952	−	0.476910i	$-0.841757\pi$
$701$		−	468708.i		−	0.953820i	0.878952	−	0.476910i	$-0.158243\pi$
$702$	1.05181e6	−	17130.5i	2.13433	−	0.0347613i
$703$	147076.			0.297598
$704$			421387.i			0.850229i
$705$	824853.	+	470278.i	1.65958	+	0.946185i
$706$	407448.			0.817453
$707$			93098.9i			0.186254i
$708$	26814.0	−	47031.0i	0.0534928	−	0.0938248i
$709$	532060.			1.05844			0.529222	−	0.848483i	$-0.322484\pi$
$709$	532060.			1.05844			0.529222	+	0.848483i	$0.322484\pi$
$710$		−	1.59612e6i		−	3.16628i
$711$	−172651.	−	291680.i	−0.341531	−	0.576990i
$712$	−196768.			−0.388145
$713$		−	50101.2i		−	0.0985529i
$714$	−266158.	−	151746.i	−0.522087	−	0.297660i
$715$	−1.81044e6			−3.54138
$716$			479248.i			0.934834i
$717$	−52951.6	+	92875.5i	−0.103001	+	0.180660i
$718$	1.07627e6			2.08771
$719$		−	408677.i		−	0.790537i	−0.918566	−	0.395268i	$-0.870652\pi$
$719$		−	408677.i		−	0.790537i	0.918566	−	0.395268i	$-0.129348\pi$
$720$	−853466.	+	505182.i	−1.64635	+	0.974502i
$721$	−728224.			−1.40086
$722$			377725.i			0.724604i
$723$	−352302.	−	200860.i	−0.673968	−	0.384252i
$724$	−61184.9			−0.116726
$725$			381218.i			0.725266i
$726$	279782.	−	490729.i	0.530819	−	0.931041i
$727$	−235444.			−0.445471			−0.222735	−	0.974879i	$-0.571499\pi$
$727$	−235444.			−0.445471			−0.222735	+	0.974879i	$0.571499\pi$
$728$			251830.i			0.475166i
$729$	−531159.	+	17306.3i	−0.999470	+	0.0325648i
$730$	846380.			1.58825
$731$			246423.i			0.461155i
$732$	−134938.	−	76933.0i	−0.251833	−	0.143579i
$733$	342720.			0.637869			0.318934	−	0.947777i	$-0.396675\pi$
$733$	342720.			0.637869			0.318934	+	0.947777i	$0.396675\pi$
$734$		−	824520.i		−	1.53041i
$735$	316729.	−	555534.i	0.586291	−	1.02834i
$736$	−38824.3			−0.0716718
$737$			940574.i			1.73164i
$738$	−135447.	−	228827.i	−0.248688	−	0.420140i
$739$	234714.			0.429784			0.214892	−	0.976638i	$-0.431060\pi$
$739$	234714.			0.429784			0.214892	+	0.976638i	$0.431060\pi$
$740$		−	182860.i		−	0.333931i
$741$	932861.	+	531857.i	1.69895	+	0.968631i
$742$	609750.			1.10750
$743$		−	367771.i		−	0.666193i	−0.942893	−	0.333096i	$-0.891907\pi$
$743$		−	367771.i		−	0.666193i	0.942893	−	0.333096i	$-0.108093\pi$
$744$	−114127.	+	200176.i	−0.206179	+	0.361632i
$745$	−906607.			−1.63345
$746$		−	632866.i		−	1.13719i
$747$	419094.	−	248069.i	0.751052	−	0.444561i
$748$	−211369.			−0.377779
$749$		−	399851.i		−	0.712746i
$750$	−896915.	−	511363.i	−1.59452	−	0.909089i
$751$	769434.			1.36424			0.682122	−	0.731239i	$-0.261057\pi$
$751$	769434.			1.36424			0.682122	+	0.731239i	$0.261057\pi$
$752$		−	735630.i		−	1.30084i
$753$	−47272.7	+	82914.9i	−0.0833720	+	0.146232i
$754$	−486392.			−0.855547
$755$			449052.i			0.787777i
$756$	10085.5	+	619245.i	0.0176463	+	1.08348i
$757$	−311650.			−0.543845			−0.271923	−	0.962319i	$-0.587659\pi$
$757$	−311650.			−0.543845			−0.271923	+	0.962319i	$0.587659\pi$
$758$		−	1.00175e6i		−	1.74349i
$759$	36563.5	+	20846.1i	0.0634694	+	0.0361861i
$760$	−276558.			−0.478805
$761$			825994.i			1.42629i	0.701017	+	0.713144i	$0.252730\pi$
$761$			825994.i			1.42629i	−0.701017	+	0.713144i	$0.747270\pi$
$762$	−416568.	+	730648.i	−0.717424	+	1.25834i
$763$	534821.			0.918669
$764$		−	955391.i		−	1.63679i
$765$	−169959.	−	287133.i	−0.290417	−	0.490637i
$766$	1.18573e6			2.02082
$767$		−	120867.i		−	0.205455i
$768$	640290.	+	365052.i	1.08556	+	0.618917i
$769$	−441175.			−0.746033			−0.373016	−	0.927825i	$-0.621676\pi$
$769$	−441175.			−0.746033			−0.373016	+	0.927825i	$0.621676\pi$
$770$		−	2.35073e6i		−	3.96480i
$771$	−51879.8	+	90995.6i	−0.0872749	+	0.153078i
$772$	866651.			1.45415
$773$		−	550891.i		−	0.921949i	−0.887413	−	0.460975i	$-0.847500\pi$
$773$		−	550891.i		−	0.921949i	0.887413	−	0.460975i	$-0.152500\pi$
$774$	945393.	−	559595.i	1.57809	−	0.934097i
$775$	−1.96279e6			−3.26792
$776$		−	114269.i		−	0.189760i
$777$	164520.	+	93798.4i	0.272506	+	0.155365i
$778$	−961180.			−1.58798
$779$		−	271439.i		−	0.447298i
$780$	661262.	−	1.15983e6i	1.08689	−	1.90637i
$781$	1.14042e6			1.86966
$782$		−	15354.2i		−	0.0251081i
$783$	245691.	−	4001.51i	0.400743	−	0.00652680i
$784$	−495443.			−0.806049
$785$			1.83262e6i			2.97395i
$786$	−377837.	−	215418.i	−0.611589	−	0.348688i
$787$	−1.11051e6			−1.79297			−0.896484	−	0.443076i	$-0.853887\pi$
$787$	−1.11051e6			−1.79297			−0.896484	+	0.443076i	$0.853887\pi$
$788$			270054.i			0.434909i
$789$	−16025.0	+	28107.4i	−0.0257421	+	0.0451509i
$790$	−948732.			−1.52016
$791$			187751.i			0.300075i
$792$	−98600.9	−	166579.i	−0.157192	−	0.265564i
$793$	−346784.			−0.551459
$794$			1.09805e6i			1.74173i
$795$	576884.	+	328901.i	0.912754	+	0.520393i
$796$	−538892.			−0.850503
$797$			349352.i			0.549980i	0.961447	+	0.274990i	$0.0886745\pi$
$797$			349352.i			0.549980i	−0.961447	+	0.274990i	$0.911325\pi$
$798$	−690578.	+	1.21125e6i	−1.08444	+	1.90208i
$799$	247489.			0.387671
$800$			1.52100e6i			2.37657i
$801$	−929711.	+	550312.i	−1.44905	+	0.857718i
$802$	−384555.			−0.597875
$803$			604735.i			0.937851i
$804$	−602566.	−	343544.i	−0.932164	−	0.531459i
$805$	77428.1			0.119483
$806$		−	2.50431e6i		−	3.85494i
$807$	−146224.	+	256472.i	−0.224528	+	0.393815i
$808$	21458.4			0.0328681
$809$		−	396648.i		−	0.606049i	−0.952983	−	0.303024i	$-0.902004\pi$
$809$		−	396648.i		−	0.606049i	0.952983	−	0.303024i	$-0.0979964\pi$
$810$	−715619.	+	1.30408e6i	−1.09072	+	1.98763i
$811$	−907516.			−1.37979			−0.689894	−	0.723910i	$-0.742343\pi$
$811$	−907516.			−1.37979			−0.689894	+	0.723910i	$0.742343\pi$
$812$		−	286360.i		−	0.434311i
$813$	226694.	+	129246.i	0.342972	+	0.195540i
$814$	288145.			0.434873
$815$			1.23779e6i			1.86351i
$816$	−128037.	+	224574.i	−0.192290	+	0.337270i
$817$	1.12145e6			1.68010
$818$			1.28304e6i			1.91750i
$819$	704309.	+	1.18988e6i	1.05001	+	1.77392i
$820$	−337482.			−0.501907
$821$		−	640918.i		−	0.950859i	−0.879754	−	0.475429i	$-0.842293\pi$
$821$		−	640918.i		−	0.950859i	0.879754	−	0.475429i	$-0.157707\pi$
$822$	−1.17797e6	−	671599.i	−1.74337	−	0.993955i
$823$	−154146.			−0.227579			−0.113789	−	0.993505i	$-0.536299\pi$
$823$	−154146.			−0.227579			−0.113789	+	0.993505i	$0.536299\pi$
$824$			167849.i			0.247209i
$825$	816680.	−	1.43243e6i	1.19990	−	2.10458i
$826$	156937.			0.230020
$827$			250368.i			0.366073i	0.983106	+	0.183036i	$0.0585926\pi$
$827$			250368.i			0.366073i	−0.983106	+	0.183036i	$0.941407\pi$
$828$	−26709.6	+	15809.9i	−0.0389589	+	0.0230604i
$829$	−262281.			−0.381644			−0.190822	−	0.981625i	$-0.561115\pi$
$829$	−262281.			−0.381644			−0.190822	+	0.981625i	$0.561115\pi$
$830$		−	1.36316e6i		−	1.97875i
$831$	−695520.	−	396540.i	−1.00718	−	0.574229i
$832$	−693772.			−1.00224
$833$		−	166683.i		−	0.240215i
$834$	339753.	−	595916.i	0.488462	−	0.856748i
$835$	1.02388e6			1.46851
$836$			961915.i			1.37633i
$837$	20602.7	+	1.26500e6i	0.0294086	+	1.80568i
$838$	805442.			1.14695
$839$			1.23368e6i			1.75258i	0.481781	+	0.876291i	$0.339990\pi$
$839$			1.23368e6i			1.75258i	−0.481781	+	0.876291i	$0.660010\pi$
$840$	−309359.	−	176376.i	−0.438434	−	0.249966i
$841$	593665.			0.839362
$842$		−	1.10964e6i		−	1.56516i
$843$	277733.	−	487136.i	0.390816	−	0.685481i
$844$	−995555.			−1.39759
$845$		−	1.78388e6i		−	2.49835i
$846$	−562016.	−	949482.i	−0.785250	−	1.32662i
$847$	742493.			1.03496
$848$		−	514483.i		−	0.715450i
$849$	−803503.	−	458105.i	−1.11474	−	0.635550i
$850$	−601526.			−0.832562
$851$			9490.89i			0.0131053i
$852$	−416538.	+	730595.i	−0.573819	+	1.00646i
$853$	−499522.			−0.686526			−0.343263	−	0.939239i	$-0.611532\pi$
$853$	−499522.			−0.686526			−0.343263	+	0.939239i	$0.611532\pi$
$854$		−	450274.i		−	0.617393i
$855$	−1.30671e6	+	773465.i	−1.78750	+	1.05806i
$856$	−92162.0			−0.125778
$857$			1.05701e6i			1.43919i	0.694394	+	0.719595i	$0.255672\pi$
$857$			1.05701e6i			1.43919i	−0.694394	+	0.719595i	$0.744328\pi$
$858$	1.82763e6	+	1.04199e6i	2.48264	+	1.41544i
$859$	−540656.			−0.732715			−0.366357	−	0.930474i	$-0.619395\pi$
$859$	−540656.			−0.732715			−0.366357	+	0.930474i	$0.619395\pi$
$860$		−	1.39430e6i		−	1.88521i
$861$	173112.	−	303633.i	0.233518	−	0.409584i
$862$	1.13267e6			1.52436
$863$			529074.i			0.710386i	0.934793	+	0.355193i	$0.115585\pi$
$863$			529074.i			0.710386i	−0.934793	+	0.355193i	$0.884415\pi$
$864$	980272.	−	15965.4i	1.31317	−	0.0213872i
$865$	762649.			1.01928
$866$			1.12297e6i			1.49738i
$867$	577459.	+	329229.i	0.768215	+	0.437986i
$868$	1.47440e6			1.95693
$869$		−	677865.i		−	0.897643i
$870$	340658.	−	597505.i	0.450070	−	0.789410i
$871$	−1.54856e6			−2.04123
$872$		−	123271.i		−	0.162117i
$873$	−319583.	−	539911.i	−0.419330	−	0.708425i
$874$	−69875.4			−0.0914748
$875$		−	1.35707e6i		−	1.77250i
$876$	−387415.	−	220879.i	−0.504857	−	0.287836i
$877$	111.187			0.000144562			7.22809e−5	−	1.00000i	$-0.499977\pi$
$877$	111.187			0.000144562			7.22809e−5		1.00000i	$0.499977\pi$
$878$			473503.i			0.614234i
$879$	−556718.	+	976468.i	−0.720539	+	1.26381i
$880$	−1.98345e6			−2.56128
$881$		−	681518.i		−	0.878062i	−0.898472	−	0.439031i	$-0.855322\pi$
$881$		−	681518.i		−	0.878062i	0.898472	−	0.439031i	$-0.144678\pi$
$882$	−639471.	+	378514.i	−0.822022	+	0.486570i
$883$	28080.8			0.0360153			0.0180077	−	0.999838i	$-0.494268\pi$
$883$	28080.8			0.0360153			0.0180077	+	0.999838i	$0.494268\pi$
$884$		−	347997.i		−	0.445319i
$885$	148478.	+	84652.7i	0.189573	+	0.108082i
$886$	1.41920e6			1.80790
$887$			690151.i			0.877197i	0.898683	+	0.438598i	$0.144525\pi$
$887$			690151.i			0.877197i	−0.898683	+	0.438598i	$0.855475\pi$
$888$	21619.6	−	37920.2i	0.0274172	−	0.0480889i
$889$	−1.10550e6			−1.39880
$890$			3.02402e6i			3.81772i
$891$	−931762.	−	511307.i	−1.17368	−	0.644060i
$892$	507210.			0.637467
$893$		−	1.12630e6i		−	1.41237i
$894$	915212.	+	521794.i	1.14511	+	0.652866i
$895$	−1.51300e6			−1.88883
$896$			476426.i			0.593443i
$897$	−34321.1	+	60198.2i	−0.0426556	+	0.0748167i
$898$	930505.			1.15389
$899$		−	584980.i		−	0.723805i
$900$	619376.	+	1.04639e6i	0.764662	+	1.29184i
$901$	173088.			0.213215
$902$		−	531793.i		−	0.653626i
$903$	1.25446e6	+	715209.i	1.53844	+	0.877117i
$904$	43274.8			0.0529539
$905$		−	193163.i		−	0.235845i
$906$	258450.	−	453315.i	0.314863	−	0.552260i
$907$	−1.17298e6			−1.42586			−0.712930	−	0.701236i	$-0.752632\pi$
$907$	−1.17298e6			−1.42586			−0.712930	+	0.701236i	$0.752632\pi$
$908$			765033.i			0.927916i
$909$	101389.	−	60014.1i	0.122705	−	0.0726315i
$910$	3.87024e6			4.67364
$911$		−	1.38486e6i		−	1.66866i	−0.551262	−	0.834332i	$-0.685854\pi$
$911$		−	1.38486e6i		−	1.66866i	0.551262	−	0.834332i	$-0.314146\pi$
$912$	1.02201e6	+	582683.i	1.22875	+	0.700556i
$913$	973973.			1.16844
$914$			17082.5i			0.0204484i
$915$	242880.	−	426004.i	0.290101	−	0.508829i
$916$	−251305.			−0.299510
$917$		−	571683.i		−	0.679855i
$918$	6314.00	+	387678.i	0.00749237	+	0.460029i
$919$	−927791.			−1.09855			−0.549274	−	0.835642i	$-0.685096\pi$
$919$	−927791.			−1.09855			−0.549274	+	0.835642i	$0.685096\pi$
$920$		−	17846.4i		−	0.0210851i
$921$	642861.	+	366518.i	0.757876	+	0.432091i
$922$	−1.47292e6			−1.73268
$923$			1.87759e6i			2.20393i
$924$	−613467.	+	1.07600e6i	−0.718534	+	1.26029i
$925$	371820.			0.434560
$926$			1.35045e6i			1.57491i
$927$	469433.	+	793071.i	0.546278	+	0.922895i
$928$	−453312.			−0.526382
$929$			743660.i			0.861674i	0.902430	+	0.430837i	$0.141782\pi$
$929$			743660.i			0.861674i	−0.902430	+	0.430837i	$0.858218\pi$
$930$	3.07640e6	+	1.75396e6i	3.55694	+	2.02794i
$931$	−758554.			−0.875159
$932$		−	164140.i		−	0.188965i
$933$	−683151.	+	1.19823e6i	−0.784790	+	1.37650i
$934$	−862801.			−0.989046
$935$		−	667297.i		−	0.763301i
$936$	274255.	−	162337.i	0.313042	−	0.185295i
$937$	477019.			0.543321			0.271661	−	0.962393i	$-0.412427\pi$
$937$	477019.			0.543321			0.271661	+	0.962393i	$0.412427\pi$
$938$		−	2.01070e6i		−	2.28529i
$939$	−1.14332e6	−	651846.i	−1.29669	−	0.739288i
$940$	−1.40033e6			−1.58480
$941$		−	40142.2i		−	0.0453338i	−0.999743	−	0.0226669i	$-0.992784\pi$
$941$		−	40142.2i		−	0.0453338i	0.999743	−	0.0226669i	$-0.00721572\pi$
$942$	1.05476e6	−	1.85002e6i	1.18864	−	2.08485i
$943$	17516.1			0.0196977
$944$		−	132418.i		−	0.148594i
$945$	−1.95498e6	+	31840.2i	−2.18916	+	0.0356543i
$946$	2.19709e6			2.45508
$947$		−	576964.i		−	0.643352i	−0.946850	−	0.321676i	$-0.895754\pi$
$947$		−	576964.i		−	0.643352i	0.946850	−	0.321676i	$-0.104246\pi$
$948$	434265.	+	247589.i	0.483212	+	0.275496i
$949$	−995635.			−1.10552
$950$			2.73748e6i			3.03322i
$951$	211835.	−	371552.i	0.234227	−	0.410827i
$952$	−92820.2			−0.102416
$953$			1.03182e6i			1.13610i	0.822994	+	0.568050i	$0.192302\pi$
$953$			1.03182e6i			1.13610i	−0.822994	+	0.568050i	$0.807698\pi$
$954$	−393061.	−	664046.i	−0.431880	−	0.729628i
$955$	3.01620e6			3.30714
$956$		−	157673.i		−	0.172520i
$957$	426914.	+	243399.i	0.466141	+	0.265763i
$958$	1.54538e6			1.68385
$959$		−	1.78231e6i		−	1.93796i
$960$	485902.	−	852258.i	0.527238	−	0.924759i
$961$	2.08839e6			2.26134
$962$			474402.i			0.512621i
$963$	−435457.	+	257755.i	−0.469562	+	0.277942i
$964$	598095.			0.643600
$965$			2.73604e6i			2.93811i
$966$	−78163.0	−	44563.5i	−0.0837620	−	0.0477556i
$967$	1.33664e6			1.42942			0.714710	−	0.699421i	$-0.246559\pi$
$967$	1.33664e6			1.42942			0.714710	+	0.699421i	$0.246559\pi$
$968$		−	171138.i		−	0.182639i
$969$	−196033.	+	343836.i	−0.208776	+	0.366188i
$970$	−1.75614e6			−1.86645
$971$			520992.i			0.552576i	0.961075	+	0.276288i	$0.0891044\pi$
$971$			520992.i			0.552576i	−0.961075	+	0.276288i	$0.910896\pi$
$972$	667886.	−	410166.i	0.706920	−	0.434137i
$973$	901644.			0.952379
$974$		−	1.76367e6i		−	1.85909i
$975$	2.35836e6	+	1.34458e6i	2.48085	+	1.41442i
$976$	−379924.			−0.398839
$977$		−	231741.i		−	0.242781i	−0.992605	−	0.121390i	$-0.961265\pi$
$977$		−	231741.i		−	0.242781i	0.992605	−	0.121390i	$-0.0387353\pi$
$978$	712406.	−	1.24954e6i	0.744818	−	1.30639i
$979$	−2.16065e6			−2.25433
$980$			943117.i			0.982004i
$981$	−344760.	−	582445.i	−0.358244	−	0.605225i
$982$	−1.50824e6			−1.56403
$983$			184930.i			0.191382i	0.995411	+	0.0956909i	$0.0305060\pi$
$983$			184930.i			0.191382i	−0.995411	+	0.0956909i	$0.969494\pi$
$984$	−69984.6	−	39900.6i	−0.0722790	−	0.0412088i
$985$	−852569.			−0.878733
$986$		−	179276.i		−	0.184403i
$987$	718302.	−	1.25988e6i	0.737349	−	1.29329i
$988$	−1.58370e6			−1.62240
$989$			72367.6i			0.0739864i
$990$	−2.56006e6	+	1.51534e6i	−2.61204	+	1.54611i
$991$	52997.5			0.0539645			0.0269822	−	0.999636i	$-0.491410\pi$
$991$	52997.5			0.0539645			0.0269822	+	0.999636i	$0.491410\pi$
$992$		−	2.33398e6i		−	2.37178i
$993$	183456.	+	104594.i	0.186051	+	0.106074i
$994$	−2.43792e6			−2.46744
$995$		−	1.70130e6i		−	1.71844i
$996$	−355743.	+	623962.i	−0.358606	+	0.628984i
$997$	1.13206e6			1.13888			0.569441	−	0.822032i	$-0.307160\pi$
$997$	1.13206e6			1.13888			0.569441	+	0.822032i	$0.307160\pi$
$998$		−	1.10452e6i		−	1.10896i
$999$	−3902.86	−	239635.i	−0.00391068	−	0.240115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.63	yes	78
3.2	odd	2	inner	177.5.b.a.119.16	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.16	✓	78	3.2	odd	2	inner
177.5.b.a.119.63	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)

\(f(q)\)	\(=\)	\(q+5.41049i q^{2} +(7.81854 + 4.45762i) q^{3} -13.2734 q^{4} -41.9044i q^{5} +(-24.1179 + 42.3021i) q^{6} -64.0047 q^{7} +14.7525i q^{8} +(41.2592 + 69.7042i) q^{9} +O(q^{10})\)	\(q+5.41049i q^{2} +(7.81854 + 4.45762i) q^{3} -13.2734 q^{4} -41.9044i q^{5} +(-24.1179 + 42.3021i) q^{6} -64.0047 q^{7} +14.7525i q^{8} +(41.2592 + 69.7042i) q^{9} +226.723 q^{10} +161.993i q^{11} +(-103.778 - 59.1676i) q^{12} -266.705 q^{13} -346.297i q^{14} +(186.794 - 327.631i) q^{15} -292.192 q^{16} -98.3026i q^{17} +(-377.134 + 223.232i) q^{18} -447.364 q^{19} +556.211i q^{20} +(-500.424 - 285.309i) q^{21} -876.458 q^{22} -28.8687i q^{23} +(-65.7610 + 115.343i) q^{24} -1130.98 q^{25} -1443.00i q^{26} +(11.8714 + 728.903i) q^{27} +849.558 q^{28} -337.070i q^{29} +(1772.64 + 1010.65i) q^{30} +1735.49 q^{31} -1344.86i q^{32} +(-722.102 + 1266.55i) q^{33} +531.865 q^{34} +2682.08i q^{35} +(-547.648 - 925.209i) q^{36} -328.761 q^{37} -2420.46i q^{38} +(-2085.24 - 1188.87i) q^{39} +618.194 q^{40} +606.752i q^{41} +(1543.66 - 2707.54i) q^{42} -2506.79 q^{43} -2150.18i q^{44} +(2920.91 - 1728.94i) q^{45} +156.194 q^{46} +2517.63i q^{47} +(-2284.51 - 1302.48i) q^{48} +1695.61 q^{49} -6119.13i q^{50} +(438.196 - 768.583i) q^{51} +3540.06 q^{52} +1760.77i q^{53} +(-3943.72 + 64.2303i) q^{54} +6788.20 q^{55} -944.229i q^{56} +(-3497.73 - 1994.18i) q^{57} +1823.71 q^{58} +453.188i q^{59} +(-2479.38 + 4348.76i) q^{60} +1300.26 q^{61} +9389.82i q^{62} +(-2640.78 - 4461.40i) q^{63} +2601.27 q^{64} +11176.1i q^{65} +(-6852.63 - 3906.92i) q^{66} +5806.28 q^{67} +1304.80i q^{68} +(128.686 - 225.711i) q^{69} -14511.3 q^{70} -7039.96i q^{71} +(-1028.31 + 608.676i) q^{72} +3733.10 q^{73} -1778.75i q^{74} +(-8842.58 - 5041.47i) q^{75} +5938.02 q^{76} -10368.3i q^{77} +(6432.36 - 11282.2i) q^{78} -4184.54 q^{79} +12244.1i q^{80} +(-3156.36 + 5751.88i) q^{81} -3282.82 q^{82} -6012.45i q^{83} +(6642.30 + 3787.01i) q^{84} -4119.31 q^{85} -13562.9i q^{86} +(1502.53 - 2635.40i) q^{87} -2389.79 q^{88} +13337.9i q^{89} +(9354.41 + 15803.6i) q^{90} +17070.4 q^{91} +383.184i q^{92} +(13569.0 + 7736.14i) q^{93} -13621.6 q^{94} +18746.5i q^{95} +(5994.88 - 10514.8i) q^{96} -7745.75 q^{97} +9174.06i q^{98} +(-11291.6 + 6683.68i) 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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