LMFDB - Embedded newform 177.5.b.a.119.8

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			119.8
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.71

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.80672i q^{2} +(7.51401 + 4.95376i) q^{3} -30.3314 q^{4} -9.67205i q^{5} +(33.7188 - 51.1457i) q^{6} -60.1761 q^{7} +97.5501i q^{8} +(31.9206 + 74.4451i) q^{9} +O(q^{10})$	\(q-6.80672i q^{2} +(7.51401 + 4.95376i) q^{3} -30.3314 q^{4} -9.67205i q^{5} +(33.7188 - 51.1457i) q^{6} -60.1761 q^{7} +97.5501i q^{8} +(31.9206 + 74.4451i) q^{9} -65.8349 q^{10} +66.8602i q^{11} +(-227.911 - 150.255i) q^{12} -79.5991 q^{13} +409.602i q^{14} +(47.9130 - 72.6758i) q^{15} +178.693 q^{16} -76.6480i q^{17} +(506.727 - 217.274i) q^{18} -369.199 q^{19} +293.367i q^{20} +(-452.163 - 298.098i) q^{21} +455.098 q^{22} +853.775i q^{23} +(-483.240 + 732.992i) q^{24} +531.452 q^{25} +541.809i q^{26} +(-128.932 + 717.508i) q^{27} +1825.23 q^{28} +694.927i q^{29} +(-494.684 - 326.130i) q^{30} -1164.96 q^{31} +344.487i q^{32} +(-331.209 + 502.388i) q^{33} -521.721 q^{34} +582.026i q^{35} +(-968.197 - 2258.03i) q^{36} -1061.64 q^{37} +2513.04i q^{38} +(-598.108 - 394.315i) q^{39} +943.509 q^{40} -738.368i q^{41} +(-2029.07 + 3077.75i) q^{42} +1783.16 q^{43} -2027.97i q^{44} +(720.037 - 308.737i) q^{45} +5811.40 q^{46} -1018.21i q^{47} +(1342.70 + 885.202i) q^{48} +1220.16 q^{49} -3617.44i q^{50} +(379.696 - 575.934i) q^{51} +2414.36 q^{52} -3786.72i q^{53} +(4883.88 + 877.603i) q^{54} +646.675 q^{55} -5870.18i q^{56} +(-2774.17 - 1828.92i) q^{57} +4730.17 q^{58} -453.188i q^{59} +(-1453.27 + 2204.36i) q^{60} -3105.94 q^{61} +7929.55i q^{62} +(-1920.85 - 4479.81i) q^{63} +5203.92 q^{64} +769.887i q^{65} +(3419.61 + 2254.45i) q^{66} -6621.39 q^{67} +2324.84i q^{68} +(-4229.39 + 6415.27i) q^{69} +3961.69 q^{70} -2089.76i q^{71} +(-7262.13 + 3113.85i) q^{72} +1724.26 q^{73} +7226.28i q^{74} +(3993.33 + 2632.68i) q^{75} +11198.3 q^{76} -4023.38i q^{77} +(-2683.99 + 4071.16i) q^{78} -4302.81 q^{79} -1728.33i q^{80} +(-4523.15 + 4752.66i) q^{81} -5025.86 q^{82} +5199.00i q^{83} +(13714.8 + 9041.73i) q^{84} -741.343 q^{85} -12137.5i q^{86} +(-3442.50 + 5221.68i) q^{87} -6522.22 q^{88} -3690.17i q^{89} +(-2101.49 - 4901.09i) q^{90} +4789.96 q^{91} -25896.2i q^{92} +(-8753.51 - 5770.93i) q^{93} -6930.68 q^{94} +3570.91i q^{95} +(-1706.51 + 2588.48i) q^{96} -12997.5 q^{97} -8305.27i q^{98} +(-4977.41 + 2134.21i) 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 $

$2$		−	6.80672i		−	1.70168i	−0.525425	−	0.850840i	$-0.676094\pi$
$2$		−	6.80672i		−	1.70168i	0.525425	−	0.850840i	$-0.323906\pi$
$3$	7.51401	+	4.95376i	0.834890	+	0.550418i
$3$	7.51401	+	4.95376i	0.834890	+	0.550418i
$4$	−30.3314			−1.89571
$5$		−	9.67205i		−	0.386882i	−0.981112	−	0.193441i	$-0.938035\pi$
$5$		−	9.67205i		−	0.386882i	0.981112	−	0.193441i	$-0.0619648\pi$
$6$	33.7188	−	51.1457i	0.936635	−	1.42071i
$7$	−60.1761			−1.22808			−0.614041	−	0.789274i	$-0.710457\pi$
$7$	−60.1761			−1.22808			−0.614041	+	0.789274i	$0.710457\pi$
$8$			97.5501i			1.52422i
$9$	31.9206	+	74.4451i	0.394081	+	0.919076i
$10$	−65.8349			−0.658349
$11$			66.8602i			0.552563i	0.961077	+	0.276282i	$0.0891023\pi$
$11$			66.8602i			0.552563i	−0.961077	+	0.276282i	$0.910898\pi$
$12$	−227.911	−	150.255i	−1.58271	−	1.04343i
$13$	−79.5991			−0.471001			−0.235500	−	0.971874i	$-0.575673\pi$
$13$	−79.5991			−0.471001			−0.235500	+	0.971874i	$0.575673\pi$
$14$			409.602i			2.08980i
$15$	47.9130	−	72.6758i	0.212947	−	0.323004i
$16$	178.693			0.698020
$17$		−	76.6480i		−	0.265218i	−0.991168	−	0.132609i	$-0.957665\pi$
$17$		−	76.6480i		−	0.265218i	0.991168	−	0.132609i	$-0.0423355\pi$
$18$	506.727	−	217.274i	1.56397	−	0.670600i
$19$	−369.199			−1.02271			−0.511356	−	0.859369i	$-0.670857\pi$
$19$	−369.199			−1.02271			−0.511356	+	0.859369i	$0.670857\pi$
$20$			293.367i			0.733418i
$21$	−452.163	−	298.098i	−1.02531	−	0.675958i
$22$	455.098			0.940286
$23$			853.775i			1.61394i	0.590592	+	0.806970i	$0.298894\pi$
$23$			853.775i			1.61394i	−0.590592	+	0.806970i	$0.701106\pi$
$24$	−483.240	+	732.992i	−0.838957	+	1.27256i
$25$	531.452			0.850322
$26$			541.809i			0.801493i
$27$	−128.932	+	717.508i	−0.176861	+	0.984236i
$28$	1825.23			2.32809
$29$			694.927i			0.826310i	0.910661	+	0.413155i	$0.135573\pi$
$29$			694.927i			0.826310i	−0.910661	+	0.413155i	$0.864427\pi$
$30$	−494.684	−	326.130i	−0.549649	−	0.362367i
$31$	−1164.96			−1.21224			−0.606118	−	0.795375i	$-0.707274\pi$
$31$	−1164.96			−1.21224			−0.606118	+	0.795375i	$0.707274\pi$
$32$			344.487i			0.336413i
$33$	−331.209	+	502.388i	−0.304141	+	0.461329i
$34$	−521.721			−0.451316
$35$			582.026i			0.475123i
$36$	−968.197	−	2258.03i	−0.747065	−	1.74231i
$37$	−1061.64			−0.775485			−0.387742	−	0.921768i	$-0.626745\pi$
$37$	−1061.64			−0.775485			−0.387742	+	0.921768i	$0.626745\pi$
$38$			2513.04i			1.74033i
$39$	−598.108	−	394.315i	−0.393234	−	0.259247i
$40$	943.509			0.589693
$41$		−	738.368i		−	0.439243i	−0.975585	−	0.219622i	$-0.929518\pi$
$41$		−	738.368i		−	0.439243i	0.975585	−	0.219622i	$-0.0704822\pi$
$42$	−2029.07	+	3077.75i	−1.15026	+	1.74476i
$43$	1783.16			0.964394			0.482197	−	0.876063i	$-0.339839\pi$
$43$	1783.16			0.964394			0.482197	+	0.876063i	$0.339839\pi$
$44$		−	2027.97i		−	1.04750i
$45$	720.037	−	308.737i	0.355574	−	0.152463i
$46$	5811.40			2.74641
$47$		−	1018.21i		−	0.460938i	−0.973080	−	0.230469i	$-0.925974\pi$
$47$		−	1018.21i		−	0.460938i	0.973080	−	0.230469i	$-0.0740260\pi$
$48$	1342.70	+	885.202i	0.582770	+	0.384202i
$49$	1220.16			0.508187
$50$		−	3617.44i		−	1.44698i
$51$	379.696	−	575.934i	0.145981	−	0.221428i
$52$	2414.36			0.892883
$53$		−	3786.72i		−	1.34807i	−0.738700	−	0.674034i	$-0.764560\pi$
$53$		−	3786.72i		−	1.34807i	0.738700	−	0.674034i	$-0.235440\pi$
$54$	4883.88	+	877.603i	1.67485	+	0.300961i
$55$	646.675			0.213777
$56$		−	5870.18i		−	1.87187i
$57$	−2774.17	−	1828.92i	−0.853852	−	0.562919i
$58$	4730.17			1.40611
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	−1453.27	+	2204.36i	−0.403686	+	0.612323i
$61$	−3105.94			−0.834706			−0.417353	−	0.908744i	$-0.637042\pi$
$61$	−3105.94			−0.834706			−0.417353	+	0.908744i	$0.637042\pi$
$62$			7929.55i			2.06284i
$63$	−1920.85	−	4479.81i	−0.483964	−	1.12870i
$64$	5203.92			1.27049
$65$			769.887i			0.182222i
$66$	3419.61	+	2254.45i	0.785035	+	0.517550i
$67$	−6621.39			−1.47502			−0.737512	−	0.675334i	$-0.764000\pi$
$67$	−6621.39			−1.47502			−0.737512	+	0.675334i	$0.764000\pi$
$68$			2324.84i			0.502778i
$69$	−4229.39	+	6415.27i	−0.888341	+	1.34746i
$70$	3961.69			0.808507
$71$		−	2089.76i		−	0.414552i	−0.978283	−	0.207276i	$-0.933540\pi$
$71$		−	2089.76i		−	0.414552i	0.978283	−	0.207276i	$-0.0664598\pi$
$72$	−7262.13	+	3113.85i	−1.40087	+	0.600666i
$73$	1724.26			0.323562			0.161781	−	0.986827i	$-0.448276\pi$
$73$	1724.26			0.323562			0.161781	+	0.986827i	$0.448276\pi$
$74$			7226.28i			1.31963i
$75$	3993.33	+	2632.68i	0.709925	+	0.468032i
$76$	11198.3			1.93877
$77$		−	4023.38i		−	0.678594i
$78$	−2683.99	+	4071.16i	−0.441156	+	0.669158i
$79$	−4302.81			−0.689443			−0.344721	−	0.938705i	$-0.612027\pi$
$79$	−4302.81			−0.689443			−0.344721	+	0.938705i	$0.612027\pi$
$80$		−	1728.33i		−	0.270051i
$81$	−4523.15	+	4752.66i	−0.689400	+	0.724381i
$82$	−5025.86			−0.747451
$83$			5199.00i			0.754681i	0.926075	+	0.377341i	$0.123161\pi$
$83$			5199.00i			0.754681i	−0.926075	+	0.377341i	$0.876839\pi$
$84$	13714.8	+	9041.73i	1.94370	+	1.28142i
$85$	−741.343			−0.102608
$86$		−	12137.5i		−	1.64109i
$87$	−3442.50	+	5221.68i	−0.454815	+	0.689877i
$88$	−6522.22			−0.842228
$89$		−	3690.17i		−	0.465872i	−0.972492	−	0.232936i	$-0.925167\pi$
$89$		−	3690.17i		−	0.465872i	0.972492	−	0.232936i	$-0.0748333\pi$
$90$	−2101.49	−	4901.09i	−0.259443	−	0.605073i
$91$	4789.96			0.578428
$92$		−	25896.2i		−	3.05957i
$93$	−8753.51	−	5770.93i	−1.01208	−	0.667236i
$94$	−6930.68			−0.784369
$95$			3570.91i			0.395669i
$96$	−1706.51	+	2588.48i	−0.185168	+	0.280868i
$97$	−12997.5			−1.38139			−0.690695	−	0.723147i	$-0.742695\pi$
$97$	−12997.5			−1.38139			−0.690695	+	0.723147i	$0.742695\pi$
$98$		−	8305.27i		−	0.864772i
$99$	−4977.41	+	2134.21i	−0.507848	+	0.217755i
$100$	−16119.7			−1.61197
$101$			7148.94i			0.700808i	0.936599	+	0.350404i	$0.113956\pi$
$101$			7148.94i			0.700808i	−0.936599	+	0.350404i	$0.886044\pi$
$102$	−3920.22	−	2584.48i	−0.376799	−	0.248412i
$103$	4725.85			0.445456			0.222728	−	0.974881i	$-0.428504\pi$
$103$	4725.85			0.445456			0.222728	+	0.974881i	$0.428504\pi$
$104$		−	7764.90i		−	0.717909i
$105$	−2883.21	+	4373.34i	−0.261516	+	0.396675i
$106$	−25775.2			−2.29398
$107$		−	2061.82i		−	0.180088i	−0.995938	−	0.0900439i	$-0.971299\pi$
$107$		−	2061.82i		−	0.180088i	0.995938	−	0.0900439i	$-0.0287007\pi$
$108$	3910.69	−	21763.0i	0.335278	−	1.86583i
$109$	1859.91			0.156545			0.0782725	−	0.996932i	$-0.475060\pi$
$109$	1859.91			0.156545			0.0782725	+	0.996932i	$0.475060\pi$
$110$		−	4401.73i		−	0.363780i
$111$	−7977.16	−	5259.10i	−0.647444	−	0.426840i
$112$	−10753.0			−0.857226
$113$		−	15951.3i		−	1.24922i	−0.780935	−	0.624612i	$-0.785257\pi$
$113$		−	15951.3i		−	1.24922i	0.780935	−	0.624612i	$-0.214743\pi$
$114$	−12449.0	+	18883.0i	−0.957908	+	1.45298i
$115$	8257.75			0.624404
$116$		−	21078.1i		−	1.56645i
$117$	−2540.85	−	5925.77i	−0.185613	−	0.432885i
$118$	−3084.72			−0.221540
$119$			4612.37i			0.325710i
$120$	7089.53	+	4673.92i	0.492329	+	0.324577i
$121$	10170.7			0.694674
$122$			21141.3i			1.42040i
$123$	3657.69	−	5548.10i	0.241767	−	0.366719i
$124$	35334.9			2.29805
$125$		−	11185.3i		−	0.715856i
$126$	−30492.8	+	13074.7i	−1.92069	+	0.823552i
$127$	−28137.9			−1.74455			−0.872276	−	0.489014i	$-0.837357\pi$
$127$	−28137.9			−1.74455			−0.872276	+	0.489014i	$0.837357\pi$
$128$		−	29909.8i		−	1.82555i
$129$	13398.7	+	8833.36i	0.805162	+	0.530819i
$130$	5240.40			0.310083
$131$			32488.0i			1.89313i	0.322512	+	0.946565i	$0.395473\pi$
$131$			32488.0i			1.89313i	−0.322512	+	0.946565i	$0.604527\pi$
$132$	10046.0	−	15238.1i	0.576564	−	0.874549i
$133$	22217.0			1.25598
$134$			45069.9i			2.51002i
$135$	6939.77	+	1247.03i	0.380783	+	0.0684244i
$136$	7477.02			0.404251
$137$			8126.87i			0.432994i	0.976283	+	0.216497i	$0.0694632\pi$
$137$			8126.87i			0.432994i	−0.976283	+	0.216497i	$0.930537\pi$
$138$	43666.9	+	28788.3i	2.29295	+	1.51167i
$139$	−12474.3			−0.645633			−0.322816	−	0.946462i	$-0.604630\pi$
$139$	−12474.3			−0.645633			−0.322816	+	0.946462i	$0.604630\pi$
$140$		−	17653.7i		−	0.900698i
$141$	5043.98	−	7650.85i	0.253708	−	0.384832i
$142$	−14224.4			−0.705434
$143$		−	5322.01i		−	0.260258i
$144$	5703.99	+	13302.8i	0.275076	+	0.641533i
$145$	6721.36			0.319684
$146$		−	11736.6i		−	0.550599i
$147$	9168.27	+	6044.37i	0.424280	+	0.279715i
$148$	32201.0			1.47010
$149$		−	3743.91i		−	0.168637i	−0.996439	−	0.0843186i	$-0.973129\pi$
$149$		−	3743.91i		−	0.168637i	0.996439	−	0.0843186i	$-0.0268713\pi$
$150$	17919.9	−	27181.5i	0.796441	−	1.20807i
$151$	−6575.64			−0.288393			−0.144196	−	0.989549i	$-0.546060\pi$
$151$	−6575.64			−0.288393			−0.144196	+	0.989549i	$0.546060\pi$
$152$		−	36015.4i		−	1.55884i
$153$	5706.07	−	2446.65i	0.243755	−	0.104517i
$154$	−27386.0			−1.15475
$155$			11267.5i			0.468992i
$156$	18141.5	+	11960.1i	0.745459	+	0.491459i
$157$	41732.5			1.69307			0.846536	−	0.532331i	$-0.178684\pi$
$157$	41732.5			1.69307			0.846536	+	0.532331i	$0.178684\pi$
$158$			29288.0i			1.17321i
$159$	18758.5	−	28453.5i	0.742000	−	1.12549i
$160$	3331.90			0.130152
$161$		−	51376.8i		−	1.98205i
$162$	32350.0	+	30787.8i	1.23266	+	1.17314i
$163$	−596.443			−0.0224488			−0.0112244	−	0.999937i	$-0.503573\pi$
$163$	−596.443			−0.0224488			−0.0112244	+	0.999937i	$0.503573\pi$
$164$			22395.8i			0.832680i
$165$	4859.12	+	3203.47i	0.178480	+	0.117666i
$166$	35388.1			1.28423
$167$			16614.0i			0.595719i	0.954610	+	0.297859i	$0.0962726\pi$
$167$			16614.0i			0.595719i	−0.954610	+	0.297859i	$0.903727\pi$
$168$	29079.4	−	44108.6i	1.03031	−	1.56280i
$169$	−22225.0			−0.778158
$170$			5046.11i			0.174606i
$171$	−11785.0	−	27485.1i	−0.403032	−	0.939950i
$172$	−54085.9			−1.82822
$173$			42859.0i			1.43202i	0.698088	+	0.716012i	$0.254034\pi$
$173$			42859.0i			1.43202i	−0.698088	+	0.716012i	$0.745966\pi$
$174$	35542.5	+	23432.1i	1.17395	+	0.773950i
$175$	−31980.7			−1.04427
$176$			11947.5i			0.385700i
$177$	2244.98	−	3405.25i	0.0716583	−	0.108693i
$178$	−25118.0			−0.792765
$179$		−	53772.0i		−	1.67822i	−0.543959	−	0.839112i	$-0.683075\pi$
$179$		−	53772.0i		−	1.67822i	0.543959	−	0.839112i	$-0.316925\pi$
$180$	−21839.8	+	9364.44i	−0.674066	+	0.289026i
$181$	−55039.5			−1.68003			−0.840015	−	0.542563i	$-0.817454\pi$
$181$	−55039.5			−1.68003			−0.840015	+	0.542563i	$0.817454\pi$
$182$		−	32603.9i		−	0.984299i
$183$	−23338.1	−	15386.1i	−0.696887	−	0.459437i
$184$	−83285.8			−2.46000
$185$			10268.2i			0.300021i
$186$	−39281.1	+	59582.7i	−1.13542	+	1.72224i
$187$	5124.70			0.146550
$188$			30883.8i			0.873807i
$189$	7758.61	−	43176.8i	0.217200	−	1.20872i
$190$	24306.2			0.673302
$191$		−	64602.6i		−	1.77086i	−0.464776	−	0.885428i	$-0.653865\pi$
$191$		−	64602.6i		−	1.77086i	0.464776	−	0.885428i	$-0.346135\pi$
$192$	39102.3	+	25779.0i	1.06072	+	0.699299i
$193$	64886.0			1.74195			0.870976	−	0.491326i	$-0.163488\pi$
$193$	64886.0			1.74195			0.870976	+	0.491326i	$0.163488\pi$
$194$			88470.3i			2.35068i
$195$	−3813.83	+	5784.93i	−0.100298	+	0.152135i
$196$	−37009.1			−0.963378
$197$			40406.6i			1.04117i	0.853811	+	0.520583i	$0.174285\pi$
$197$			40406.6i			1.04117i	−0.853811	+	0.520583i	$0.825715\pi$
$198$	14527.0	+	33879.9i	0.370549	+	0.864194i
$199$	17926.2			0.452670			0.226335	−	0.974050i	$-0.427326\pi$
$199$	17926.2			0.452670			0.226335	+	0.974050i	$0.427326\pi$
$200$			51843.1i			1.29608i
$201$	−49753.1	−	32800.7i	−1.23148	−	0.811880i
$202$	48660.8			1.19255
$203$		−	41817.9i		−	1.01478i
$204$	−11516.7	+	17468.9i	−0.276738	+	0.419764i
$205$	−7141.53			−0.169935
$206$		−	32167.5i		−	0.758024i
$207$	−63559.4	+	27253.0i	−1.48333	+	0.636023i
$208$	−14223.8			−0.328768
$209$		−	24684.7i		−	0.565114i
$210$	29768.1	+	19625.2i	0.675014	+	0.445017i
$211$	64119.6			1.44021			0.720105	−	0.693865i	$-0.244094\pi$
$211$	64119.6			1.44021			0.720105	+	0.693865i	$0.244094\pi$
$212$			114857.i			2.55555i
$213$	10352.1	−	15702.4i	0.228177	−	0.346105i
$214$	−14034.3			−0.306452
$215$		−	17246.8i		−	0.373106i
$216$	−69993.0	−	12577.3i	−1.50019	−	0.269575i
$217$	70102.7			1.48873
$218$		−	12659.9i		−	0.266390i
$219$	12956.1	+	8541.58i	0.270139	+	0.178094i
$220$	−19614.6			−0.405260
$221$			6101.12i			0.124918i
$222$	−35797.2	+	54298.3i	−0.726346	+	1.10174i
$223$	−39719.5			−0.798719			−0.399359	−	0.916794i	$-0.630767\pi$
$223$	−39719.5			−0.798719			−0.399359	+	0.916794i	$0.630767\pi$
$224$		−	20729.9i		−	0.413143i
$225$	16964.2	+	39564.0i	0.335096	+	0.781511i
$226$	−108576.			−2.12578
$227$		−	12769.2i		−	0.247807i	−0.992294	−	0.123903i	$-0.960459\pi$
$227$		−	12769.2i		−	0.247807i	0.992294	−	0.123903i	$-0.0395413\pi$
$228$	84144.4	+	55473.9i	1.61866	+	1.06713i
$229$	79213.6			1.51053			0.755264	−	0.655421i	$-0.227509\pi$
$229$	79213.6			1.51053			0.755264	+	0.655421i	$0.227509\pi$
$230$		−	56208.2i		−	1.06254i
$231$	19930.9	−	30231.7i	0.373510	−	0.566551i
$232$	−67790.1			−1.25948
$233$			23.2998i			0.000429182i	1.00000		0.000214591i	$6.83064e-5\pi$
$233$			23.2998i			0.000429182i	−1.00000		0.000214591i	$0.999932\pi$
$234$	−40335.1	+	17294.9i	−0.736633	+	0.315853i
$235$	−9848.20			−0.178329
$236$			13745.8i			0.246801i
$237$	−32331.3	−	21315.1i	−0.575608	−	0.379481i
$238$	31395.1			0.554254
$239$			66769.5i			1.16891i	0.811425	+	0.584457i	$0.198692\pi$
$239$			66769.5i			1.16891i	−0.811425	+	0.584457i	$0.801308\pi$
$240$	8561.72	−	12986.7i	0.148641	−	0.225463i
$241$	54046.8			0.930542			0.465271	−	0.885168i	$-0.345957\pi$
$241$	54046.8			0.930542			0.465271	+	0.885168i	$0.345957\pi$
$242$		−	69229.2i		−	1.18211i
$243$	−57530.5	+	13304.9i	−0.974285	+	0.225320i
$244$	94207.7			1.58236
$245$		−	11801.4i		−	0.196608i
$246$	−37764.4	−	24896.9i	−0.624039	−	0.411410i
$247$	29387.9			0.481699
$248$		−	113642.i		−	1.84772i
$249$	−25754.6	+	39065.3i	−0.415390	+	0.630075i
$250$	−76134.9			−1.21816
$251$			6027.25i			0.0956691i	0.998855	+	0.0478345i	$0.0152320\pi$
$251$			6027.25i			0.0956691i	−0.998855	+	0.0478345i	$0.984768\pi$
$252$	58262.3	+	135879.i	0.917458	+	2.13970i
$253$	−57083.5			−0.891804
$254$			191527.i			2.96867i
$255$	−5570.46	−	3672.43i	−0.0856664	−	0.0564773i
$256$	−120325.			−1.83602
$257$			74332.0i			1.12541i	0.826659	+	0.562703i	$0.190239\pi$
$257$			74332.0i			1.12541i	−0.826659	+	0.562703i	$0.809761\pi$
$258$	60126.2	−	91201.2i	0.903284	−	1.37013i
$259$	63885.2			0.952360
$260$		−	23351.8i		−	0.345440i
$261$	−51733.9	+	22182.4i	−0.759441	+	0.325633i
$262$	221137.			3.22150
$263$			46448.8i			0.671527i	0.941946	+	0.335763i	$0.108994\pi$
$263$			46448.8i			0.671527i	−0.941946	+	0.335763i	$0.891006\pi$
$264$	−49008.0	−	32309.5i	−0.703168	−	0.463577i
$265$	−36625.4			−0.521543
$266$		−	151225.i		−	2.13727i
$267$	18280.2	−	27728.0i	0.256424	−	0.388952i
$268$	200836.			2.79623
$269$		−	36243.2i		−	0.500867i	−0.968134	−	0.250433i	$-0.919427\pi$
$269$		−	36243.2i		−	0.500867i	0.968134	−	0.250433i	$-0.0805731\pi$
$270$	8488.22	−	47237.1i	0.116436	−	0.647971i
$271$	−8415.64			−0.114590			−0.0572952	−	0.998357i	$-0.518248\pi$
$271$	−8415.64			−0.114590			−0.0572952	+	0.998357i	$0.518248\pi$
$272$		−	13696.5i		−	0.185127i
$273$	35991.8	+	23728.3i	0.482924	+	0.318377i
$274$	55317.3			0.736818
$275$			35532.9i			0.469857i
$276$	128284.	−	194584.i	1.68404	−	2.55440i
$277$	52973.6			0.690399			0.345199	−	0.938529i	$-0.387811\pi$
$277$	52973.6			0.690399			0.345199	+	0.938529i	$0.387811\pi$
$278$			84908.8i			1.09866i
$279$	−37186.2	−	86725.5i	−0.477719	−	1.11414i
$280$	−56776.7			−0.724192
$281$		−	38300.1i		−	0.485051i	−0.970145	−	0.242526i	$-0.922024\pi$
$281$		−	38300.1i		−	0.485051i	0.970145	−	0.242526i	$-0.0779759\pi$
$282$	−52077.2	−	34332.9i	−0.654862	−	0.431730i
$283$	−12441.2			−0.155342			−0.0776712	−	0.996979i	$-0.524748\pi$
$283$	−12441.2			−0.155342			−0.0776712	+	0.996979i	$0.524748\pi$
$284$			63385.3i			0.785872i
$285$	−17689.4	+	26831.9i	−0.217783	+	0.330340i
$286$	−36225.4			−0.442876
$287$			44432.0i			0.539427i
$288$	−25645.4	+	10996.2i	−0.309189	+	0.132574i
$289$	77646.1			0.929659
$290$		−	45750.4i		−	0.544000i
$291$	−97663.2	−	64386.4i	−1.15331	−	0.760341i
$292$	−52299.4			−0.613382
$293$		−	146740.i		−	1.70928i	−0.519223	−	0.854639i	$-0.673779\pi$
$293$		−	146740.i		−	1.70928i	0.519223	−	0.854639i	$-0.326221\pi$
$294$	41142.3	−	62405.9i	0.475986	−	0.721989i
$295$	−4383.25			−0.0503677
$296$		−	103563.i		−	1.18201i
$297$	−47972.7	−	8620.40i	−0.543853	−	0.0977270i
$298$	−25483.8			−0.286966
$299$		−	67959.7i		−	0.760167i
$300$	−121123.	−	79853.0i	−1.34582	−	0.887256i
$301$	−107304.			−1.18436
$302$			44758.5i			0.490752i
$303$	−35414.1	+	53717.2i	−0.385737	+	0.585097i
$304$	−65973.4			−0.713874
$305$			30040.8i			0.322933i
$306$	−16653.6	−	38839.6i	−0.177855	−	0.414794i
$307$	−38709.3			−0.410713			−0.205356	−	0.978687i	$-0.565835\pi$
$307$	−38709.3			−0.410713			−0.205356	+	0.978687i	$0.565835\pi$
$308$			122035.i			1.28642i
$309$	35510.0	+	23410.7i	0.371907	+	0.245187i
$310$	76695.0			0.798075
$311$			69420.6i			0.717741i	0.933387	+	0.358870i	$0.116838\pi$
$311$			69420.6i			0.717741i	−0.933387	+	0.358870i	$0.883162\pi$
$312$	38465.5	−	58345.5i	0.395150	−	0.599375i
$313$	90383.4			0.922572			0.461286	−	0.887252i	$-0.347388\pi$
$313$	90383.4			0.922572			0.461286	+	0.887252i	$0.347388\pi$
$314$		−	284062.i		−	2.88107i
$315$	−43329.0	+	18578.6i	−0.436674	+	0.187237i
$316$	130510.			1.30699
$317$			18279.9i			0.181910i	0.995855	+	0.0909549i	$0.0289919\pi$
$317$			18279.9i			0.181910i	−0.995855	+	0.0909549i	$0.971008\pi$
$318$	−193675.	−	127684.i	−1.91522	−	1.26265i
$319$	−46462.9			−0.456589
$320$		−	50332.5i		−	0.491529i
$321$	10213.8	−	15492.6i	0.0991234	−	0.150353i
$322$	−349707.			−3.37282
$323$			28298.4i			0.271242i
$324$	137194.	−	144155.i	1.30691	−	1.37322i
$325$	−42303.1			−0.400503
$326$			4059.82i			0.0382007i
$327$	13975.4	+	9213.55i	0.130698	+	0.0861651i
$328$	72027.8			0.669503
$329$			61272.0i			0.566070i
$330$	21805.1	−	33074.7i	0.200231	−	0.303716i
$331$	93312.0			0.851690			0.425845	−	0.904796i	$-0.359977\pi$
$331$	93312.0			0.851690			0.425845	+	0.904796i	$0.359977\pi$
$332$		−	157693.i		−	1.43066i
$333$	−33888.1	−	79033.8i	−0.305604	−	0.712729i
$334$	113087.			1.01372
$335$			64042.4i			0.570660i
$336$	−80798.5	−	53268.0i	−0.715689	−	0.471832i
$337$	153601.			1.35249			0.676247	−	0.736675i	$-0.263605\pi$
$337$	153601.			1.35249			0.676247	+	0.736675i	$0.263605\pi$
$338$			151279.i			1.32418i
$339$	79019.1	−	119859.i	0.687595	−	1.04296i
$340$	22486.0			0.194516
$341$		−	77889.4i		−	0.669837i
$342$	−187083.	+	80217.5i	−1.59949	+	0.685831i
$343$	71058.4			0.603987
$344$			173948.i			1.46995i
$345$	62048.8	+	40906.9i	0.521309	+	0.343683i
$346$	291730.			2.43685
$347$			45198.1i			0.375371i	0.982229	+	0.187686i	$0.0600986\pi$
$347$			45198.1i			0.375371i	−0.982229	+	0.187686i	$0.939901\pi$
$348$	104416.	−	158381.i	0.862200	−	1.30781i
$349$	−226920.			−1.86304			−0.931518	−	0.363695i	$-0.881515\pi$
$349$	−226920.			−1.86304			−0.931518	+	0.363695i	$0.881515\pi$
$350$			217683.i			1.77701i
$351$	10262.9	−	57113.0i	0.0833018	−	0.463576i
$352$	−23032.5			−0.185890
$353$			102234.i			0.820436i	0.911987	+	0.410218i	$0.134547\pi$
$353$			102234.i			0.820436i	−0.911987	+	0.410218i	$0.865453\pi$
$354$	−23178.6	−	15281.0i	−0.184961	−	0.121939i
$355$	−20212.2			−0.160383
$356$			111928.i			0.883161i
$357$	−22848.6	+	34657.4i	−0.179276	+	0.271932i
$358$	−366011.			−2.85580
$359$			149322.i			1.15860i	0.815114	+	0.579301i	$0.196675\pi$
$359$			149322.i			1.15860i	−0.815114	+	0.579301i	$0.803325\pi$
$360$	30117.3	+	70239.7i	0.232387	+	0.541973i
$361$	5987.10			0.0459412
$362$			374638.i			2.85887i
$363$	76422.8	+	50383.3i	0.579976	+	0.382361i
$364$	−145286.			−1.09653
$365$		−	16677.2i		−	0.125180i
$366$	−104729.	+	158856.i	−0.781814	+	1.18588i
$367$	−126266.			−0.937463			−0.468732	−	0.883341i	$-0.655289\pi$
$367$	−126266.			−0.937463			−0.468732	+	0.883341i	$0.655289\pi$
$368$			152564.i			1.12656i
$369$	54967.9	−	23569.1i	0.403698	−	0.173097i
$370$	69892.9			0.510540
$371$			227870.i			1.65554i
$372$	265507.	+	175040.i	1.91862	+	1.26489i
$373$	−56999.8			−0.409690			−0.204845	−	0.978794i	$-0.565669\pi$
$373$	−56999.8			−0.409690			−0.204845	+	0.978794i	$0.565669\pi$
$374$		−	34882.4i		−	0.249381i
$375$	55409.0	−	84046.1i	0.394020	−	0.597661i
$376$	99326.7			0.702571
$377$		−	55315.6i		−	0.389193i
$378$	−293892.	−	52810.7i	−2.05686	−	0.369605i
$379$	198960.			1.38512			0.692561	−	0.721359i	$-0.256482\pi$
$379$	198960.			1.38512			0.692561	+	0.721359i	$0.256482\pi$
$380$		−	108311.i		−	0.750076i
$381$	−211428.	−	139388.i	−1.45651	−	0.960232i
$382$	−439732.			−3.01343
$383$			173036.i			1.17961i	0.807544	+	0.589807i	$0.200796\pi$
$383$			173036.i			1.17961i	−0.807544	+	0.589807i	$0.799204\pi$
$384$	148166.	−	224743.i	1.00482	−	1.52413i
$385$	−38914.3			−0.262536
$386$		−	441661.i		−	2.96424i
$387$	56919.6	+	132748.i	0.380049	+	0.886351i
$388$	394233.			2.61872
$389$		−	13759.1i		−	0.0909265i	−0.998966	−	0.0454632i	$-0.985524\pi$
$389$		−	13759.1i		−	0.0909265i	0.998966	−	0.0454632i	$-0.0144764\pi$
$390$	39376.4	+	25959.7i	0.258885	+	0.170675i
$391$	65440.1			0.428046
$392$			119026.i			0.774589i
$393$	−160938.	+	244115.i	−1.04201	+	1.58055i
$394$	275037.			1.77173
$395$			41617.0i			0.266733i
$396$	150972.	−	64733.8i	0.962734	−	0.412801i
$397$	−308123.			−1.95499			−0.977493	−	0.210969i	$-0.932338\pi$
$397$	−308123.			−1.95499			−0.977493	+	0.210969i	$0.932338\pi$
$398$		−	122019.i		−	0.770300i
$399$	166938.	+	110057.i	1.04860	+	0.691311i
$400$	94966.7			0.593542
$401$			92117.9i			0.572869i	0.958100	+	0.286435i	$0.0924701\pi$
$401$			92117.9i			0.572869i	−0.958100	+	0.286435i	$0.907530\pi$
$402$	−223265.	+	338656.i	−1.38156	+	2.09559i
$403$	92729.8			0.570964
$404$		−	216838.i		−	1.32853i
$405$	45968.0	+	43748.2i	0.280250	+	0.266716i
$406$	−284643.			−1.72683
$407$		−	70981.4i		−	0.428505i
$408$	56182.4	+	37039.3i	0.337505	+	0.222507i
$409$	133670.			0.799072			0.399536	−	0.916717i	$-0.369171\pi$
$409$	133670.			0.799072			0.399536	+	0.916717i	$0.369171\pi$
$410$			48610.4i			0.289175i
$411$	−40258.6	+	61065.4i	−0.238328	+	0.361503i
$412$	−143342.			−0.844458
$413$			27271.0i			0.159883i
$414$	185503.	+	432631.i	1.08231	+	2.52416i
$415$	50285.0			0.291973
$416$		−	27420.9i		−	0.158451i
$417$	−93731.7	−	61794.5i	−0.539032	−	0.355367i
$418$	−168022.			−0.961642
$419$			17851.9i			0.101685i	0.998707	+	0.0508425i	$0.0161906\pi$
$419$			17851.9i			0.101685i	−0.998707	+	0.0508425i	$0.983809\pi$
$420$	87452.0	−	132650.i	0.495760	−	0.751983i
$421$	−199234.			−1.12408			−0.562042	−	0.827109i	$-0.689984\pi$
$421$	−199234.			−1.12408			−0.562042	+	0.827109i	$0.689984\pi$
$422$		−	436444.i		−	2.45078i
$423$	75800.9	−	32501.9i	0.423637	−	0.181647i
$424$	369395.			2.05475
$425$		−	40734.7i		−	0.225521i
$426$	−106882.	−	70464.1i	−0.588960	−	0.388284i
$427$	186903.			1.02509
$428$			62538.1i			0.341395i
$429$	26364.0	−	39989.6i	0.143250	−	0.217287i
$430$	−117394.			−0.634908
$431$			42353.7i			0.228001i	0.993481	+	0.114001i	$0.0363666\pi$
$431$			42353.7i			0.228001i	−0.993481	+	0.114001i	$0.963633\pi$
$432$	−23039.2	+	128214.i	−0.123453	+	0.687016i
$433$	−218337.			−1.16453			−0.582267	−	0.812997i	$-0.697834\pi$
$433$	−218337.			−1.16453			−0.582267	+	0.812997i	$0.697834\pi$
$434$		−	477169.i		−	2.53334i
$435$	50504.4	+	33296.0i	0.266901	+	0.175960i
$436$	−56413.8			−0.296765
$437$		−	315213.i		−	1.65060i
$438$	58140.2	−	88188.7i	0.303060	−	0.459690i
$439$	−77607.9			−0.402696			−0.201348	−	0.979520i	$-0.564532\pi$
$439$	−77607.9			−0.402696			−0.201348	+	0.979520i	$0.564532\pi$
$440$			63083.2i			0.325843i
$441$	38948.1	+	90834.8i	0.200267	+	0.467063i
$442$	41528.6			0.212570
$443$			106771.i			0.544057i	0.962289	+	0.272028i	$0.0876945\pi$
$443$			106771.i			0.544057i	−0.962289	+	0.272028i	$0.912306\pi$
$444$	241959.	+	159516.i	1.22737	+	0.809168i
$445$	−35691.5			−0.180237
$446$			270359.i			1.35916i
$447$	18546.4	−	28131.8i	0.0928208	−	0.140793i
$448$	−313151.			−1.56026
$449$		−	373144.i		−	1.85090i	−0.378866	−	0.925451i	$-0.623686\pi$
$449$		−	373144.i		−	1.85090i	0.378866	−	0.925451i	$-0.376314\pi$
$450$	269301.	−	115471.i	1.32988	−	0.570226i
$451$	49367.4			0.242710
$452$			483827.i			2.36817i
$453$	−49409.4	−	32574.1i	−0.240776	−	0.158736i
$454$	−86916.5			−0.421687
$455$		−	46328.7i		−	0.223783i
$456$	178412.	−	270620.i	0.858012	−	1.30146i
$457$	−11487.8			−0.0550054			−0.0275027	−	0.999622i	$-0.508755\pi$
$457$	−11487.8			−0.0550054			−0.0275027	+	0.999622i	$0.508755\pi$
$458$		−	539185.i		−	2.57043i
$459$	54995.5	+	9882.37i	0.261037	+	0.0469068i
$460$	−250469.			−1.18369
$461$			103362.i			0.486362i	0.969981	+	0.243181i	$0.0781908\pi$
$461$			103362.i			0.486362i	−0.969981	+	0.243181i	$0.921809\pi$
$462$	−205779.	−	135664.i	−0.964088	−	0.635594i
$463$	228771.			1.06719			0.533593	−	0.845742i	$-0.320842\pi$
$463$	228771.			1.06719			0.533593	+	0.845742i	$0.320842\pi$
$464$			124179.i			0.576781i
$465$	−55816.7	+	84664.4i	−0.258142	+	0.391557i
$466$	158.596			0.000730330
$467$			362034.i			1.66003i	0.557744	+	0.830013i	$0.311667\pi$
$467$			362034.i			1.66003i	−0.557744	+	0.830013i	$0.688333\pi$
$468$	77067.6	+	179737.i	0.351868	+	0.820627i
$469$	398449.			1.81145
$470$			67033.9i			0.303458i
$471$	313579.	+	206733.i	1.41353	+	0.931897i
$472$	44208.5			0.198437
$473$			119223.i			0.532889i
$474$	−145086.	+	220070.i	−0.645756	+	0.979501i
$475$	−196212.			−0.869635
$476$		−	139900.i		−	0.617453i
$477$	281903.	−	120874.i	1.23898	−	0.531248i
$478$	454481.			1.98912
$479$		−	36289.9i		−	0.158166i	−0.996868	−	0.0790832i	$-0.974801\pi$
$479$		−	36289.9i		−	0.158166i	0.996868	−	0.0790832i	$-0.0251993\pi$
$480$	25035.9	+	16505.4i	0.108663	+	0.0716381i
$481$	84505.5			0.365254
$482$		−	367882.i		−	1.58348i
$483$	254508.	−	386045.i	1.09096	−	1.65480i
$484$	−308492.			−1.31690
$485$			125712.i			0.534434i
$486$	90562.8	+	391594.i	0.383422	+	1.65792i
$487$	−147016.			−0.619880			−0.309940	−	0.950756i	$-0.600309\pi$
$487$	−147016.			−0.619880			−0.309940	+	0.950756i	$0.600309\pi$
$488$		−	302985.i		−	1.27228i
$489$	−4481.67	−	2954.63i	−0.0187423	−	0.0123562i
$490$	−80329.0			−0.334565
$491$			253813.i			1.05281i	0.850233	+	0.526406i	$0.176461\pi$
$491$			253813.i			1.05281i	−0.850233	+	0.526406i	$0.823539\pi$
$492$	−110943.	+	168282.i	−0.458321	+	0.695195i
$493$	53264.7			0.219152
$494$		−	200036.i		−	0.819697i
$495$	20642.2	+	48141.8i	0.0842454	+	0.196477i
$496$	−208170.			−0.846165
$497$			125753.i			0.509104i
$498$	265907.	+	175304.i	1.07219	+	0.706861i
$499$	−361497.			−1.45179			−0.725895	−	0.687805i	$-0.758574\pi$
$499$	−361497.			−1.45179			−0.725895	+	0.687805i	$0.758574\pi$
$500$			339265.i			1.35706i
$501$	−82301.7	+	124838.i	−0.327894	+	0.497359i
$502$	41025.8			0.162798
$503$			487472.i			1.92670i	0.268252	+	0.963349i	$0.413554\pi$
$503$			487472.i			1.92670i	−0.268252	+	0.963349i	$0.586446\pi$
$504$	437006.	−	187379.i	1.72039	−	0.737668i
$505$	69144.9			0.271130
$506$			388551.i			1.51757i
$507$	−166999.	−	110097.i	−0.649676	−	0.428312i
$508$	853462.			3.30717
$509$		−	213583.i		−	0.824389i	−0.911096	−	0.412194i	$-0.864762\pi$
$509$		−	213583.i		−	0.824389i	0.911096	−	0.412194i	$-0.135238\pi$
$510$	−24997.2	+	37916.5i	−0.0961062	+	0.145777i
$511$	−103759.			−0.397361
$512$			340462.i			1.29876i
$513$	47601.5	−	264903.i	0.180878	−	1.00659i
$514$	505957.			1.91508
$515$		−	45708.6i		−	0.172339i
$516$	−406402.	−	267929.i	−1.52636	−	1.00628i
$517$	68077.8			0.254697
$518$		−	434849.i		−	1.62061i
$519$	−212313.	+	322043.i	−0.788211	+	1.19558i
$520$	−75102.5			−0.277746
$521$			464857.i			1.71255i	0.516517	+	0.856277i	$0.327228\pi$
$521$			464857.i			1.71255i	−0.516517	+	0.856277i	$0.672772\pi$
$522$	150990.	+	352138.i	0.554123	+	1.29233i
$523$	228186.			0.834230			0.417115	−	0.908854i	$-0.363041\pi$
$523$	228186.			0.834230			0.417115	+	0.908854i	$0.363041\pi$
$524$		−	985408.i		−	3.58884i
$525$	−240303.	−	158424.i	−0.871847	−	0.574782i
$526$	316164.			1.14272
$527$			89291.8i			0.321507i
$528$	−59184.8	+	89773.2i	−0.212296	+	0.322017i
$529$	−449090.			−1.60480
$530$			249299.i			0.887499i
$531$	33737.6	−	14466.0i	0.119653	−	0.0513050i
$532$	−673872.			−2.38097
$533$			58773.4i			0.206884i
$534$	−188737.	−	124428.i	−0.661871	−	0.436352i
$535$	−19942.1			−0.0696727
$536$		−	645917.i		−	2.24826i
$537$	266373.	−	404043.i	0.923724	−	1.40113i
$538$	−246698.			−0.852315
$539$			81580.0i			0.280806i
$540$	−210493.	−	37824.4i	−0.721856	−	0.129713i
$541$	−397328.			−1.35755			−0.678773	−	0.734348i	$-0.737488\pi$
$541$	−397328.			−1.35755			−0.678773	+	0.734348i	$0.737488\pi$
$542$			57282.9i			0.194996i
$543$	−413567.	−	272652.i	−1.40264	−	0.924718i
$544$	26404.3			0.0892229
$545$		−	17989.2i		−	0.0605644i
$546$	161512.	−	244986.i	0.541776	−	0.821781i
$547$	193122.			0.645441			0.322720	−	0.946494i	$-0.395403\pi$
$547$	193122.			0.645441			0.322720	+	0.946494i	$0.395403\pi$
$548$		−	246500.i		−	0.820834i
$549$	−99143.4	−	231222.i	−0.328942	−	0.767158i
$550$	241863.			0.799546
$551$		−	256566.i		−	0.845078i
$552$	−625810.	−	412578.i	−2.05383	−	1.35403i
$553$	258926.			0.846693
$554$		−	360576.i		−	1.17484i
$555$	−50866.3	+	77155.5i	−0.165137	+	0.250484i
$556$	378362.			1.22394
$557$		−	226827.i		−	0.731112i	−0.930789	−	0.365556i	$-0.880879\pi$
$557$		−	226827.i		−	0.731112i	0.930789	−	0.365556i	$-0.119121\pi$
$558$	−590316.	+	253116.i	−1.89590	+	0.812926i
$559$	−141938.			−0.454230
$560$			104004.i			0.331645i
$561$	38507.0	+	25386.5i	0.122353	+	0.0806636i
$562$	−260698.			−0.825402
$563$			184337.i			0.581562i	0.956790	+	0.290781i	$0.0939151\pi$
$563$			184337.i			0.581562i	−0.956790	+	0.290781i	$0.906085\pi$
$564$	−152991.	+	232061.i	−0.480959	+	0.729532i
$565$	−154282.			−0.483302
$566$			84683.9i			0.264343i
$567$	272186.	−	285996.i	0.846641	−	0.889599i
$568$	203856.			0.631868
$569$		−	337265.i		−	1.04171i	−0.853645	−	0.520856i	$-0.825613\pi$
$569$		−	337265.i		−	1.04171i	0.853645	−	0.520856i	$-0.174387\pi$
$570$	182637.	+	120407.i	0.562133	+	0.370597i
$571$	571586.			1.75311			0.876556	−	0.481300i	$-0.159835\pi$
$571$	571586.			1.75311			0.876556	+	0.481300i	$0.159835\pi$
$572$			161424.i			0.493375i
$573$	320026.	−	485424.i	0.974710	−	1.47847i
$574$	302437.			0.917932
$575$			453740.i			1.37237i
$576$	166112.	+	387406.i	0.500675	+	1.16767i
$577$	−547922.			−1.64576			−0.822882	−	0.568213i	$-0.807635\pi$
$577$	−547922.			−1.64576			−0.822882	+	0.568213i	$0.807635\pi$
$578$		−	528515.i		−	1.58198i
$579$	487553.	+	321429.i	1.45434	+	0.958801i
$580$	−203869.			−0.606030
$581$		−	312855.i		−	0.926811i
$582$	−438260.	+	664766.i	−1.29386	+	1.96256i
$583$	253181.			0.744893
$584$			168202.i			0.493180i
$585$	−57314.3	+	24575.2i	−0.167476	+	0.0718101i
$586$	−998816.			−2.90864
$587$		−	547351.i		−	1.58851i	−0.607585	−	0.794255i	$-0.707862\pi$
$587$		−	547351.i		−	1.58851i	0.607585	−	0.794255i	$-0.292138\pi$
$588$	−278087.	−	183334.i	−0.804314	−	0.530260i
$589$	430102.			1.23977
$590$			29835.6i			0.0857098i
$591$	−200165.	+	303616.i	−0.573076	+	0.869259i
$592$	−189708.			−0.541304
$593$			618108.i			1.75774i	0.477060	+	0.878871i	$0.341703\pi$
$593$			618108.i			1.75774i	−0.477060	+	0.878871i	$0.658297\pi$
$594$	−58676.7	+	326537.i	−0.166300	+	0.925463i
$595$	44611.1			0.126011
$596$			113558.i			0.319688i
$597$	134698.	+	88802.0i	0.377930	+	0.249158i
$598$	−462583.			−1.29356
$599$		−	466415.i		−	1.29993i	−0.759966	−	0.649963i	$-0.774784\pi$
$599$		−	466415.i		−	1.29993i	0.759966	−	0.649963i	$-0.225216\pi$
$600$	−256818.	+	389550.i	−0.713384	+	1.08208i
$601$	−572948.			−1.58623			−0.793115	−	0.609072i	$-0.791542\pi$
$601$	−572948.			−1.58623			−0.793115	+	0.609072i	$0.791542\pi$
$602$			730387.i			2.01539i
$603$	−211358.	−	492930.i	−0.581279	−	1.35566i
$604$	199449.			0.546710
$605$		−	98371.7i		−	0.268757i
$606$	365638.	+	241054.i	0.995648	+	0.656401i
$607$	−568966.			−1.54422			−0.772110	−	0.635489i	$-0.780798\pi$
$607$	−568966.			−1.54422			−0.772110	+	0.635489i	$0.780798\pi$
$608$		−	127184.i		−	0.344054i
$609$	207156.	−	314220.i	0.558551	−	0.847227i
$610$	204479.			0.549528
$611$			81048.8i			0.217102i
$612$	−173073.	+	74210.3i	−0.462091	+	0.198135i
$613$	80594.2			0.214478			0.107239	−	0.994233i	$-0.465799\pi$
$613$	80594.2			0.214478			0.107239	+	0.994233i	$0.465799\pi$
$614$			263483.i			0.698902i
$615$	−53661.5	−	35377.4i	−0.141877	−	0.0935353i
$616$	392481.			1.03433
$617$		−	112761.i		−	0.296203i	−0.988972	−	0.148101i	$-0.952684\pi$
$617$		−	112761.i		−	0.296203i	0.988972	−	0.148101i	$-0.0473162\pi$
$618$	159350.	−	241707.i	0.417230	−	0.632867i
$619$	−308341.			−0.804729			−0.402364	−	0.915480i	$-0.631812\pi$
$619$	−308341.			−0.804729			−0.402364	+	0.915480i	$0.631812\pi$
$620$		−	341761.i		−	0.889076i
$621$	−612590.	−	110079.i	−1.58850	−	0.285444i
$622$	472527.			1.22137
$623$			222060.i			0.572129i
$624$	−106878.	−	70461.4i	−0.274485	−	0.180960i
$625$	223973.			0.573371
$626$		−	615215.i		−	1.56992i
$627$	122282.	−	185481.i	0.311048	−	0.471807i
$628$	−1.26581e6			−3.20958
$629$			81372.5i			0.205673i
$630$	126459.	+	294928.i	0.318617	+	0.743079i
$631$	303140.			0.761351			0.380676	−	0.924709i	$-0.375691\pi$
$631$	303140.			0.761351			0.380676	+	0.924709i	$0.375691\pi$
$632$		−	419740.i		−	1.05086i
$633$	481795.	+	317633.i	1.20242	+	0.792717i
$634$	124426.			0.309552
$635$			272151.i			0.674936i
$636$	−568973.	+	863034.i	−1.40662	+	2.13360i
$637$	−97123.5			−0.239357
$638$			316260.i			0.776968i
$639$	155572.	−	66706.2i	0.381004	−	0.163367i
$640$	−289289.			−0.706272
$641$		−	579703.i		−	1.41088i	−0.708770	−	0.705440i	$-0.750750\pi$
$641$		−	579703.i		−	1.41088i	0.708770	−	0.705440i	$-0.249250\pi$
$642$	−105454.	−	69522.3i	−0.255853	−	0.168676i
$643$	−193005.			−0.466816			−0.233408	−	0.972379i	$-0.574988\pi$
$643$	−193005.			−0.466816			−0.233408	+	0.972379i	$0.574988\pi$
$644$			1.55833e6i			3.75741i
$645$	85436.7	−	129593.i	0.205364	−	0.311503i
$646$	192619.			0.461567
$647$		−	426473.i		−	1.01879i	−0.860534	−	0.509393i	$-0.829870\pi$
$647$		−	426473.i		−	1.01879i	0.860534	−	0.509393i	$-0.170130\pi$
$648$	−463623.	−	441234.i	−1.10412	−	1.05080i
$649$	30300.2			0.0719376
$650$			287945.i			0.681527i
$651$	526752.	+	347272.i	1.24292	+	0.819421i
$652$	18091.0			0.0425566
$653$			315858.i			0.740741i	0.928884	+	0.370370i	$0.120769\pi$
$653$			315858.i			0.740741i	−0.928884	+	0.370370i	$0.879231\pi$
$654$	62714.1	−	95126.5i	0.146625	−	0.222406i
$655$	314226.			0.732418
$656$		−	131941.i		−	0.306600i
$657$	55039.5	+	128363.i	0.127510	+	0.297378i
$658$	417061.			0.963270
$659$			809211.i			1.86333i	0.363312	+	0.931667i	$0.381646\pi$
$659$			809211.i			1.86333i	−0.363312	+	0.931667i	$0.618354\pi$
$660$	−147384.	−	97165.9i	−0.338347	−	0.223062i
$661$	440500.			1.00819			0.504096	−	0.863648i	$-0.331826\pi$
$661$	440500.			1.00819			0.504096	+	0.863648i	$0.331826\pi$
$662$		−	635148.i		−	1.44930i
$663$	−30223.4	+	45843.8i	−0.0687570	+	0.104293i
$664$	−507163.			−1.15030
$665$		−	214883.i		−	0.485914i
$666$	−537961.	+	230667.i	−1.21284	+	0.520040i
$667$	−593311.			−1.33361
$668$		−	503926.i		−	1.12931i
$669$	−298452.	−	196761.i	−0.666842	−	0.439629i
$670$	435918.			0.971081
$671$		−	207664.i		−	0.461228i
$672$	102691.	−	155764.i	0.227401	−	0.344929i
$673$	210294.			0.464297			0.232148	−	0.972680i	$-0.425424\pi$
$673$	210294.			0.464297			0.232148	+	0.972680i	$0.425424\pi$
$674$		−	1.04552e6i		−	2.30151i
$675$	−68521.0	+	381321.i	−0.150389	+	0.836918i
$676$	674115.			1.47517
$677$		−	765156.i		−	1.66945i	−0.550670	−	0.834723i	$-0.685628\pi$
$677$		−	765156.i		−	1.66945i	0.550670	−	0.834723i	$-0.314372\pi$
$678$	−815843.	−	537861.i	−1.77479	−	1.17007i
$679$	782138.			1.69646
$680$		−	72318.1i		−	0.156397i
$681$	63255.6	−	95948.0i	0.136397	−	0.206891i
$682$	−530171.			−1.13985
$683$		−	490389.i		−	1.05123i	−0.850721	−	0.525617i	$-0.823835\pi$
$683$		−	490389.i		−	1.05123i	0.850721	−	0.525617i	$-0.176165\pi$
$684$	357458.	+	833662.i	0.764033	+	1.78188i
$685$	78603.5			0.167518
$686$		−	483675.i		−	1.02779i
$687$	595211.	+	392405.i	1.26112	+	0.831421i
$688$	318639.			0.673166
$689$			301420.i			0.634941i
$690$	278442.	−	422349.i	0.584839	−	0.887101i
$691$	616309.			1.29075			0.645375	−	0.763866i	$-0.276701\pi$
$691$	616309.			1.29075			0.645375	+	0.763866i	$0.276701\pi$
$692$		−	1.29998e6i		−	2.71471i
$693$	299521.	−	128429.i	0.623679	−	0.267421i
$694$	307651.			0.638761
$695$			120652.i			0.249784i
$696$	−509376.	−	335816.i	−1.05153	−	0.693239i
$697$	−56594.4			−0.116495
$698$			1.54458e6i			3.17029i
$699$	−115.422	+	175.075i	−0.000236229	+	0.000358319i
$700$	970019.			1.97963
$701$		−	264327.i		−	0.537905i	−0.963153	−	0.268953i	$-0.913322\pi$
$701$		−	264327.i		−	0.537905i	0.963153	−	0.268953i	$-0.0866775\pi$
$702$	−388752.	−	69856.4i	−0.788858	−	0.141753i
$703$	391956.			0.793098
$704$			347935.i			0.702025i
$705$	−73999.4	−	48785.6i	−0.148885	−	0.0981552i
$706$	695876.			1.39612
$707$		−	430195.i		−	0.860650i
$708$	−68093.5	+	103286.i	−0.135844	+	0.206052i
$709$	−581894.			−1.15758			−0.578791	−	0.815476i	$-0.696475\pi$
$709$	−581894.			−1.15758			−0.578791	+	0.815476i	$0.696475\pi$
$710$			137579.i			0.272920i
$711$	−137348.	−	320323.i	−0.271696	−	0.633650i
$712$	359977.			0.710092
$713$		−	994613.i		−	1.95648i
$714$	235903.	+	155524.i	0.462741	+	0.305071i
$715$	−51474.8			−0.100689
$716$			1.63098e6i			3.18143i
$717$	−330760.	+	501706.i	−0.643390	+	0.975913i
$718$	1.01639e6			1.97157
$719$		−	178512.i		−	0.345310i	−0.984982	−	0.172655i	$-0.944765\pi$
$719$		−	178512.i		−	0.345310i	0.984982	−	0.172655i	$-0.0552346\pi$
$720$	128666.	−	55169.2i	0.248198	−	0.106422i
$721$	−284383.			−0.547057
$722$		−	40752.5i		−	0.0781772i
$723$	406108.	+	267735.i	0.776900	+	0.512187i
$724$	1.66943e6			3.18486
$725$			369320.i			0.702630i
$726$	342945.	−	520189.i	0.650655	−	0.986933i
$727$	−211.589			−0.000400336			−0.000200168	−	1.00000i	$-0.500064\pi$
$727$	−211.589			−0.000400336			−0.000200168		1.00000i	$0.500064\pi$
$728$			467261.i			0.881652i
$729$	−498194.	−	185019.i	−0.937440	−	0.348146i
$730$	−113517.			−0.213017
$731$		−	136676.i		−	0.255775i
$732$	707877.	+	466682.i	1.32110	+	0.870961i
$733$	−534109.			−0.994081			−0.497040	−	0.867727i	$-0.665580\pi$
$733$	−534109.			−0.994081			−0.497040	+	0.867727i	$0.665580\pi$
$734$			859457.i			1.59526i
$735$	58461.4	−	88676.0i	0.108217	−	0.164146i
$736$	−294114.			−0.542951
$737$		−	442707.i		−	0.815045i
$738$	−160428.	−	374151.i	−0.294556	−	0.686964i
$739$	−361404.			−0.661765			−0.330882	−	0.943672i	$-0.607346\pi$
$739$	−361404.			−0.661765			−0.330882	+	0.943672i	$0.607346\pi$
$740$		−	311450.i		−	0.568754i
$741$	220821.	+	145581.i	0.402165	+	0.265135i
$742$	1.55105e6			2.81720
$743$			85738.0i			0.155309i	0.996980	+	0.0776543i	$0.0247430\pi$
$743$			85738.0i			0.155309i	−0.996980	+	0.0776543i	$0.975257\pi$
$744$	562954.	−	853906.i	1.01701	−	1.54264i
$745$	−36211.3			−0.0652426
$746$			387982.i			0.697162i
$747$	−387040.	+	165955.i	−0.693609	+	0.297406i
$748$	−155439.			−0.277817
$749$			124072.i			0.221163i
$750$	−572078.	−	377154.i	−1.01703	−	0.670496i
$751$	193039.			0.342267			0.171134	−	0.985248i	$-0.445257\pi$
$751$	193039.			0.342267			0.171134	+	0.985248i	$0.445257\pi$
$752$		−	181948.i		−	0.321744i
$753$	−29857.5	+	45288.8i	−0.0526579	+	0.0798731i
$754$	−376518.			−0.662281
$755$			63599.9i			0.111574i
$756$	−235330.	+	1.30961e6i	−0.411750	+	2.29139i
$757$	−849700.			−1.48277			−0.741385	−	0.671080i	$-0.765831\pi$
$757$	−849700.			−1.48277			−0.741385	+	0.671080i	$0.765831\pi$
$758$		−	1.35427e6i		−	2.35704i
$759$	−428926.	−	282778.i	−0.744558	−	0.490865i
$760$	−348343.			−0.603087
$761$		−	515391.i		−	0.889954i	−0.895542	−	0.444977i	$-0.853212\pi$
$761$		−	515391.i		−	0.889954i	0.895542	−	0.444977i	$-0.146788\pi$
$762$	−948777.	+	1.43913e6i	−1.63401	+	2.47851i
$763$	−111922.			−0.192250
$764$			1.95949e6i			3.35704i
$765$	−23664.1	−	55189.4i	−0.0404359	−	0.0943046i
$766$	1.17781e6			2.00732
$767$			36073.3i			0.0613191i
$768$	−904123.	−	596061.i	−1.53287	−	1.01057i
$769$	−437007.			−0.738985			−0.369493	−	0.929234i	$-0.620468\pi$
$769$	−437007.			−0.738985			−0.369493	+	0.929234i	$0.620468\pi$
$770$			264879.i			0.446752i
$771$	−368223.	+	558531.i	−0.619443	+	0.939590i
$772$	−1.96808e6			−3.30224
$773$			490308.i			0.820559i	0.911960	+	0.410280i	$0.134569\pi$
$773$			490308.i			0.820559i	−0.911960	+	0.410280i	$0.865431\pi$
$774$	903577.	−	387436.i	1.50829	−	0.646722i
$775$	−619119.			−1.03079
$776$		−	1.26791e6i		−	2.10554i
$777$	480034.	+	316472.i	0.795115	+	0.524195i
$778$	−93654.3			−0.154728
$779$			272605.i			0.449219i
$780$	115679.	−	175465.i	0.190136	−	0.288405i
$781$	139721.			0.229066
$782$		−	445433.i		−	0.728397i
$783$	−498615.	−	89598.2i	−0.813284	−	0.146142i
$784$	218034.			0.354725
$785$		−	403639.i		−	0.655019i
$786$	1.66162e6	+	1.09546e6i	2.68960	+	1.77317i
$787$	−404151.			−0.652521			−0.326261	−	0.945280i	$-0.605789\pi$
$787$	−404151.			−0.652521			−0.326261	+	0.945280i	$0.605789\pi$
$788$		−	1.22559e6i		−	1.97375i
$789$	−230096.	+	349017.i	−0.369620	+	0.560650i
$790$	283275.			0.453894
$791$			959889.i			1.53415i
$792$	−208193.	−	485547.i	−0.331906	−	0.774071i
$793$	247230.			0.393147
$794$			2.09731e6i			3.32676i
$795$	−275203.	−	181433.i	−0.435431	−	0.287066i
$796$	−543727.			−0.858134
$797$			1.08805e6i			1.71290i	0.516230	+	0.856450i	$0.327335\pi$
$797$			1.08805e6i			1.71290i	−0.516230	+	0.856450i	$0.672665\pi$
$798$	749130.	−	1.13630e6i	1.17639	−	1.78438i
$799$	−78043.9			−0.122249
$800$			183078.i			0.286060i
$801$	274715.	−	117792.i	0.428172	−	0.183591i
$802$	627021.			0.974840
$803$			115285.i			0.178789i
$804$	1.50908e6	+	994894.i	2.33454	+	1.53909i
$805$	−496919.			−0.766820
$806$		−	631186.i		−	0.971599i
$807$	179540.	−	272332.i	0.275686	−	0.418169i
$808$	−697380.			−1.06819
$809$			1.15016e6i			1.75737i	0.477405	+	0.878683i	$0.341577\pi$
$809$			1.15016e6i			1.75737i	−0.477405	+	0.878683i	$0.658423\pi$
$810$	297782.	−	312891.i	0.453866	−	0.476895i
$811$	789484.			1.20033			0.600166	−	0.799875i	$-0.295101\pi$
$811$	789484.			1.20033			0.600166	+	0.799875i	$0.295101\pi$
$812$			1.26840e6i			1.92373i
$813$	−63235.1	−	41689.0i	−0.0956703	−	0.0630726i
$814$	−483150.			−0.729178
$815$			5768.82i			0.00868504i
$816$	67849.0	−	102915.i	0.101897	−	0.154561i
$817$	−658343.			−0.986297
$818$		−	909852.i		−	1.35977i
$819$	152898.	+	356589.i	0.227948	+	0.531619i
$820$	216613.			0.322149
$821$		−	666524.i		−	0.988848i	−0.869221	−	0.494424i	$-0.835379\pi$
$821$		−	666524.i		−	0.988848i	0.869221	−	0.494424i	$-0.164621\pi$
$822$	415655.	+	274029.i	0.615162	+	0.405558i
$823$	439317.			0.648603			0.324301	−	0.945954i	$-0.394871\pi$
$823$	439317.			0.648603			0.324301	+	0.945954i	$0.394871\pi$
$824$			461007.i			0.678974i
$825$	−176022.	+	266995.i	−0.258618	+	0.392279i
$826$	185626.			0.272069
$827$		−	156952.i		−	0.229486i	−0.993395	−	0.114743i	$-0.963396\pi$
$827$		−	156952.i		−	0.229486i	0.993395	−	0.114743i	$-0.0366044\pi$
$828$	1.92785e6	−	826622.i	2.81198	−	1.20572i
$829$	1.00301e6			1.45948			0.729738	−	0.683727i	$-0.239642\pi$
$829$	1.00301e6			1.45948			0.729738	+	0.683727i	$0.239642\pi$
$830$		−	342276.i		−	0.496844i
$831$	398044.	+	262418.i	0.576406	+	0.380007i
$832$	−414227.			−0.598401
$833$		−	93522.7i		−	0.134780i
$834$	−420618.	+	638006.i	−0.604722	+	0.917260i
$835$	160691.			0.230473
$836$			748723.i			1.07129i
$837$	150200.	−	835867.i	0.214398	−	1.19313i
$838$	121513.			0.173035
$839$		−	668344.i		−	0.949459i	−0.880132	−	0.474730i	$-0.842546\pi$
$839$		−	668344.i		−	0.949459i	0.880132	−	0.474730i	$-0.157454\pi$
$840$	−426620.	−	281258.i	−0.604620	−	0.398608i
$841$	224358.			0.317212
$842$			1.35613e6i			1.91283i
$843$	189730.	−	287788.i	0.266981	−	0.404964i
$844$	−1.94484e6			−2.73023
$845$			214961.i			0.301055i
$846$	−221231.	−	515956.i	−0.309105	−	0.720895i
$847$	−612034.			−0.853117
$848$		−	676661.i		−	0.940978i
$849$	−93483.4	−	61630.8i	−0.129694	−	0.0855032i
$850$	−277270.			−0.383764
$851$		−	906400.i		−	1.25159i
$852$	−313995.	+	476277.i	−0.432558	+	0.656116i
$853$	−736375.			−1.01205			−0.506024	−	0.862519i	$-0.668885\pi$
$853$	−736375.			−1.01205			−0.506024	+	0.862519i	$0.668885\pi$
$854$		−	1.27220e6i		−	1.74437i
$855$	−265837.	+	113986.i	−0.363650	+	0.155926i
$856$	201131.			0.274493
$857$			110524.i			0.150486i	0.997165	+	0.0752428i	$0.0239732\pi$
$857$			110524.i			0.150486i	−0.997165	+	0.0752428i	$0.976027\pi$
$858$	−272198.	−	179452.i	−0.369752	−	0.243766i
$859$	−855963.			−1.16003			−0.580014	−	0.814606i	$-0.696953\pi$
$859$	−855963.			−1.16003			−0.580014	+	0.814606i	$0.696953\pi$
$860$			523122.i			0.707303i
$861$	−220106.	+	333863.i	−0.296910	+	0.450362i
$862$	288290.			0.387985
$863$			1.46104e6i			1.96173i	0.194685	+	0.980866i	$0.437632\pi$
$863$			1.46104e6i			1.96173i	−0.194685	+	0.980866i	$0.562368\pi$
$864$	−247172.	−	44415.4i	−0.331110	−	0.0594985i
$865$	414535.			0.554024
$866$			1.48616e6i			1.98167i
$867$	583433.	+	384640.i	0.776163	+	0.511701i
$868$	−2.12631e6			−2.82220
$869$		−	287687.i		−	0.380961i
$870$	226637.	−	343769.i	0.299427	−	0.454180i
$871$	527057.			0.694738
$872$			181435.i			0.238609i
$873$	−414887.	−	967600.i	−0.544379	−	1.26960i
$874$	−2.14557e6			−2.80879
$875$			673084.i			0.879131i
$876$	−392978.	−	259078.i	−0.512106	−	0.337616i
$877$	−1.09465e6			−1.42323			−0.711616	−	0.702568i	$-0.752037\pi$
$877$	−1.09465e6			−1.42323			−0.711616	+	0.702568i	$0.752037\pi$
$878$			528256.i			0.685259i
$879$	726913.	−	1.10260e6i	0.940816	−	1.42706i
$880$	115556.			0.149220
$881$			1.15039e6i			1.48215i	0.671421	+	0.741076i	$0.265684\pi$
$881$			1.15039e6i			1.48215i	−0.671421	+	0.741076i	$0.734316\pi$
$882$	618287.	−	265109.i	0.794791	−	0.340790i
$883$	−1.32976e6			−1.70550			−0.852749	−	0.522320i	$-0.825067\pi$
$883$	−1.32976e6			−1.70550			−0.852749	+	0.522320i	$0.825067\pi$
$884$		−	185056.i		−	0.236809i
$885$	−32935.8	−	21713.6i	−0.0420515	−	0.0277233i
$886$	726758.			0.925811
$887$			142061.i			0.180562i	0.995916	+	0.0902812i	$0.0287766\pi$
$887$			142061.i			0.180562i	−0.995916	+	0.0902812i	$0.971223\pi$
$888$	513026.	−	778173.i	0.650599	−	0.986848i
$889$	1.69323e6			2.14245
$890$			242942.i			0.306706i
$891$	−317764.	−	302419.i	−0.400266	−	0.380937i
$892$	1.20475e6			1.51414
$893$			375923.i			0.471407i
$894$	−191485.	−	126240.i	−0.239585	−	0.157951i
$895$	−520085.			−0.649274
$896$			1.79986e6i			2.24193i
$897$	336656.	−	510650.i	0.418410	−	0.634656i
$898$	−2.53989e6			−3.14964
$899$		−	809561.i		−	1.00168i
$900$	−514550.	−	1.20003e6i	−0.635246	−	1.48152i
$901$	−290245.			−0.357532
$902$		−	336030.i		−	0.413014i
$903$	−806281.	−	531557.i	−0.988806	−	0.651890i
$904$	1.55606e6			1.90409
$905$			532344.i			0.649973i
$906$	−221723.	+	336316.i	−0.270118	+	0.409724i
$907$	383329.			0.465969			0.232985	−	0.972480i	$-0.425151\pi$
$907$	383329.			0.465969			0.232985	+	0.972480i	$0.425151\pi$
$908$			387309.i			0.469771i
$909$	−532204.	+	228198.i	−0.644096	+	0.276175i
$910$	−315347.			−0.380808
$911$		−	229786.i		−	0.276876i	−0.990371	−	0.138438i	$-0.955792\pi$
$911$		−	229786.i		−	0.276876i	0.990371	−	0.138438i	$-0.0442082\pi$
$912$	−495724.	−	326816.i	−0.596006	−	0.392929i
$913$	−347606.			−0.417009
$914$			78194.4i			0.0936016i
$915$	−148815.	+	225727.i	−0.177748	+	0.269613i
$916$	−2.40266e6			−2.86353
$917$		−	1.95500e6i		−	2.32492i
$918$	67266.5	−	374339.i	0.0798203	−	0.444202i
$919$	917016.			1.08579			0.542895	−	0.839800i	$-0.317328\pi$
$919$	917016.			1.08579			0.542895	+	0.839800i	$0.317328\pi$
$920$			805544.i			0.951730i
$921$	−290862.	−	191756.i	−0.342900	−	0.226064i
$922$	703557.			0.827632
$923$			166343.i			0.195254i
$924$	−604532.	+	916971.i	−0.708068	+	1.07402i
$925$	−564210.			−0.659412
$926$		−	1.55718e6i		−	1.81601i
$927$	150852.	+	351816.i	0.175546	+	0.409408i
$928$	−239393.			−0.277982
$929$			686558.i			0.795510i	0.917492	+	0.397755i	$0.130211\pi$
$929$			686558.i			0.795510i	−0.917492	+	0.397755i	$0.869789\pi$
$930$	576287.	+	379928.i	0.666304	+	0.439274i
$931$	−450481.			−0.519730
$932$		−	706.718i		−	0.000813606i
$933$	−343893.	+	521627.i	−0.395057	+	0.599234i
$934$	2.46426e6			2.82483
$935$		−	49566.3i		−	0.0566974i
$936$	578059.	−	247860.i	0.659813	−	0.282914i
$937$	−64813.7			−0.0738223			−0.0369112	−	0.999319i	$-0.511752\pi$
$937$	−64813.7			−0.0738223			−0.0369112	+	0.999319i	$0.511752\pi$
$938$		−	2.71213e6i		−	3.08251i
$939$	679142.	+	447738.i	0.770245	+	0.507800i
$940$	298710.			0.338060
$941$		−	503266.i		−	0.568353i	−0.958772	−	0.284176i	$-0.908280\pi$
$941$		−	503266.i		−	0.568353i	0.958772	−	0.284176i	$-0.0917202\pi$
$942$	1.40717e6	−	2.13444e6i	1.58579	−	2.40537i
$943$	630399.			0.708912
$944$		−	80981.5i		−	0.0908745i
$945$	−417608.	−	75041.6i	−0.467633	−	0.0840308i
$946$	811515.			0.906806
$947$			102947.i			0.114792i	0.998351	+	0.0573962i	$0.0182798\pi$
$947$			102947.i			0.114792i	−0.998351	+	0.0573962i	$0.981720\pi$
$948$	980656.	+	646517.i	1.09119	+	0.719388i
$949$	−137250.			−0.152398
$950$			1.33556e6i			1.47984i
$951$	−90554.4	+	137356.i	−0.100126	+	0.151875i
$952$	−449938.			−0.496453
$953$		−	1.31199e6i		−	1.44459i	−0.691586	−	0.722294i	$-0.743088\pi$
$953$		−	1.31199e6i		−	1.44459i	0.691586	−	0.722294i	$-0.256912\pi$
$954$	−822758.	−	1.91884e6i	−0.904014	−	2.10834i
$955$	−624840.			−0.685112
$956$		−	2.02521e6i		−	2.21593i
$957$	−349123.	−	230166.i	−0.381201	−	0.251314i
$958$	−247015.			−0.269149
$959$		−	489043.i		−	0.531753i
$960$	249335.	−	378199.i	0.270546	−	0.410372i
$961$	433609.			0.469517
$962$		−	575206.i		−	0.621546i
$963$	153493.	−	65814.6i	0.165514	−	0.0709692i
$964$	−1.63932e6			−1.76404
$965$		−	627580.i		−	0.673930i
$966$	−2.62770e6	−	1.73237e6i	−2.81593	−	1.85646i
$967$	−1.35952e6			−1.45389			−0.726945	−	0.686696i	$-0.759060\pi$
$967$	−1.35952e6			−1.45389			−0.726945	+	0.686696i	$0.759060\pi$
$968$			992154.i			1.05884i
$969$	−140183.	+	212634.i	−0.149296	+	0.226457i
$970$	855689.			0.909436
$971$		−	1.05256e6i		−	1.11638i	−0.829715	−	0.558188i	$-0.811497\pi$
$971$		−	1.05256e6i		−	1.11638i	0.829715	−	0.558188i	$-0.188503\pi$
$972$	1.74498e6	−	403557.i	1.84697	−	0.427142i
$973$	750652.			0.792890
$974$			1.00070e6i			1.05484i
$975$	−317866.	−	209559.i	−0.334375	−	0.220444i
$976$	−555010.			−0.582642
$977$		−	1.33808e6i		−	1.40182i	−0.713249	−	0.700910i	$-0.752777\pi$
$977$		−	1.33808e6i		−	1.40182i	0.713249	−	0.700910i	$-0.247223\pi$
$978$	−20111.4	+	30505.5i	−0.0210263	+	0.0318934i
$979$	246726.			0.257424
$980$			357954.i			0.372714i
$981$	59369.4	+	138461.i	0.0616914	+	0.143877i
$982$	1.72764e6			1.79155
$983$			1.07918e6i			1.11683i	0.829562	+	0.558415i	$0.188590\pi$
$983$			1.07918e6i			1.11683i	−0.829562	+	0.558415i	$0.811410\pi$
$984$	541217.	+	356808.i	0.558961	+	0.368506i
$985$	390815.			0.402808
$986$		−	362558.i		−	0.372927i
$987$	−303527.	+	460398.i	−0.311575	+	0.472606i
$988$	−891379.			−0.913163
$989$			1.52242e6i			1.55647i
$990$	327688.	−	140506.i	0.334341	−	0.143359i
$991$	1.05967e6			1.07900			0.539501	−	0.841985i	$-0.318613\pi$
$991$	1.05967e6			1.07900			0.539501	+	0.841985i	$0.318613\pi$
$992$		−	401314.i		−	0.407813i
$993$	701147.	+	462245.i	0.711067	+	0.468785i
$994$	855967.			0.866332
$995$		−	173383.i		−	0.175130i
$996$	781174.	−	1.18491e6i	0.787461	−	1.19444i
$997$	1.06066e6			1.06706			0.533528	−	0.845782i	$-0.320866\pi$
$997$	1.06066e6			1.06706			0.533528	+	0.845782i	$0.320866\pi$
$998$			2.46061e6i			2.47048i
$999$	136879.	−	761734.i	0.137153	−	0.763260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.8	✓	78
3.2	odd	2	inner	177.5.b.a.119.71	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.8	✓	78	1.1	even	1	trivial
177.5.b.a.119.71	yes	78	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-6.80672i q^{2} +(7.51401 + 4.95376i) q^{3} -30.3314 q^{4} -9.67205i q^{5} +(33.7188 - 51.1457i) q^{6} -60.1761 q^{7} +97.5501i q^{8} +(31.9206 + 74.4451i) q^{9} +O(q^{10})\)	\(q-6.80672i q^{2} +(7.51401 + 4.95376i) q^{3} -30.3314 q^{4} -9.67205i q^{5} +(33.7188 - 51.1457i) q^{6} -60.1761 q^{7} +97.5501i q^{8} +(31.9206 + 74.4451i) q^{9} -65.8349 q^{10} +66.8602i q^{11} +(-227.911 - 150.255i) q^{12} -79.5991 q^{13} +409.602i q^{14} +(47.9130 - 72.6758i) q^{15} +178.693 q^{16} -76.6480i q^{17} +(506.727 - 217.274i) q^{18} -369.199 q^{19} +293.367i q^{20} +(-452.163 - 298.098i) q^{21} +455.098 q^{22} +853.775i q^{23} +(-483.240 + 732.992i) q^{24} +531.452 q^{25} +541.809i q^{26} +(-128.932 + 717.508i) q^{27} +1825.23 q^{28} +694.927i q^{29} +(-494.684 - 326.130i) q^{30} -1164.96 q^{31} +344.487i q^{32} +(-331.209 + 502.388i) q^{33} -521.721 q^{34} +582.026i q^{35} +(-968.197 - 2258.03i) q^{36} -1061.64 q^{37} +2513.04i q^{38} +(-598.108 - 394.315i) q^{39} +943.509 q^{40} -738.368i q^{41} +(-2029.07 + 3077.75i) q^{42} +1783.16 q^{43} -2027.97i q^{44} +(720.037 - 308.737i) q^{45} +5811.40 q^{46} -1018.21i q^{47} +(1342.70 + 885.202i) q^{48} +1220.16 q^{49} -3617.44i q^{50} +(379.696 - 575.934i) q^{51} +2414.36 q^{52} -3786.72i q^{53} +(4883.88 + 877.603i) q^{54} +646.675 q^{55} -5870.18i q^{56} +(-2774.17 - 1828.92i) q^{57} +4730.17 q^{58} -453.188i q^{59} +(-1453.27 + 2204.36i) q^{60} -3105.94 q^{61} +7929.55i q^{62} +(-1920.85 - 4479.81i) q^{63} +5203.92 q^{64} +769.887i q^{65} +(3419.61 + 2254.45i) q^{66} -6621.39 q^{67} +2324.84i q^{68} +(-4229.39 + 6415.27i) q^{69} +3961.69 q^{70} -2089.76i q^{71} +(-7262.13 + 3113.85i) q^{72} +1724.26 q^{73} +7226.28i q^{74} +(3993.33 + 2632.68i) q^{75} +11198.3 q^{76} -4023.38i q^{77} +(-2683.99 + 4071.16i) q^{78} -4302.81 q^{79} -1728.33i q^{80} +(-4523.15 + 4752.66i) q^{81} -5025.86 q^{82} +5199.00i q^{83} +(13714.8 + 9041.73i) q^{84} -741.343 q^{85} -12137.5i q^{86} +(-3442.50 + 5221.68i) q^{87} -6522.22 q^{88} -3690.17i q^{89} +(-2101.49 - 4901.09i) q^{90} +4789.96 q^{91} -25896.2i q^{92} +(-8753.51 - 5770.93i) q^{93} -6930.68 q^{94} +3570.91i q^{95} +(-1706.51 + 2588.48i) q^{96} -12997.5 q^{97} -8305.27i q^{98} +(-4977.41 + 2134.21i) 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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