LMFDB - Embedded newform 177.5.b.a.119.66

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			119.66
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.74797i q^{2} +(-1.10979 - 8.93131i) q^{3} -17.0392 q^{4} -1.93242i q^{5} +(51.3369 - 6.37903i) q^{6} -31.0983 q^{7} -5.97306i q^{8} +(-78.5367 + 19.8237i) q^{9} +O(q^{10})$	\(q+5.74797i q^{2} +(-1.10979 - 8.93131i) q^{3} -17.0392 q^{4} -1.93242i q^{5} +(51.3369 - 6.37903i) q^{6} -31.0983 q^{7} -5.97306i q^{8} +(-78.5367 + 19.8237i) q^{9} +11.1075 q^{10} +36.5780i q^{11} +(18.9098 + 152.182i) q^{12} +150.671 q^{13} -178.752i q^{14} +(-17.2590 + 2.14458i) q^{15} -238.294 q^{16} -397.713i q^{17} +(-113.946 - 451.427i) q^{18} +641.461 q^{19} +32.9268i q^{20} +(34.5125 + 277.749i) q^{21} -210.249 q^{22} -670.788i q^{23} +(-53.3473 + 6.62883i) q^{24} +621.266 q^{25} +866.051i q^{26} +(264.211 + 679.436i) q^{27} +529.889 q^{28} -1328.66i q^{29} +(-12.3270 - 99.2045i) q^{30} +747.325 q^{31} -1465.27i q^{32} +(326.690 - 40.5939i) q^{33} +2286.04 q^{34} +60.0949i q^{35} +(1338.20 - 337.780i) q^{36} +1452.82 q^{37} +3687.10i q^{38} +(-167.213 - 1345.69i) q^{39} -11.5425 q^{40} -820.955i q^{41} +(-1596.49 + 198.377i) q^{42} -2961.00 q^{43} -623.259i q^{44} +(38.3078 + 151.766i) q^{45} +3855.67 q^{46} -945.968i q^{47} +(264.455 + 2128.27i) q^{48} -1433.90 q^{49} +3571.02i q^{50} +(-3552.10 + 441.376i) q^{51} -2567.30 q^{52} +5310.33i q^{53} +(-3905.38 + 1518.68i) q^{54} +70.6841 q^{55} +185.752i q^{56} +(-711.885 - 5729.09i) q^{57} +7637.10 q^{58} +453.188i q^{59} +(294.080 - 36.5418i) q^{60} +722.307 q^{61} +4295.60i q^{62} +(2442.36 - 616.484i) q^{63} +4609.65 q^{64} -291.159i q^{65} +(233.332 + 1877.80i) q^{66} +7494.48 q^{67} +6776.69i q^{68} +(-5991.02 + 744.433i) q^{69} -345.424 q^{70} -3888.73i q^{71} +(118.408 + 469.105i) q^{72} -8396.06 q^{73} +8350.75i q^{74} +(-689.473 - 5548.72i) q^{75} -10930.0 q^{76} -1137.51i q^{77} +(7734.98 - 961.133i) q^{78} +9517.31 q^{79} +460.483i q^{80} +(5775.04 - 3113.78i) q^{81} +4718.82 q^{82} +432.863i q^{83} +(-588.064 - 4732.60i) q^{84} -768.548 q^{85} -17019.7i q^{86} +(-11866.7 + 1474.53i) q^{87} +218.483 q^{88} -6891.78i q^{89} +(-872.346 + 220.192i) q^{90} -4685.60 q^{91} +11429.7i q^{92} +(-829.372 - 6674.59i) q^{93} +5437.39 q^{94} -1239.57i q^{95} +(-13086.8 + 1626.14i) q^{96} +3927.71 q^{97} -8242.00i q^{98} +(-725.113 - 2872.72i) 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 $

$2$			5.74797i			1.43699i	0.695531	+	0.718496i	$0.255169\pi$
$2$			5.74797i			1.43699i	−0.695531	+	0.718496i	$0.744831\pi$
$3$	−1.10979	−	8.93131i	−0.123310	−	0.992368i
$3$	−1.10979	−	8.93131i	−0.123310	−	0.992368i
$4$	−17.0392			−1.06495
$5$		−	1.93242i		−	0.0772968i	−0.999253	−	0.0386484i	$-0.987695\pi$
$5$		−	1.93242i		−	0.0772968i	0.999253	−	0.0386484i	$-0.0123052\pi$
$6$	51.3369	−	6.37903i	1.42603	−	0.177195i
$7$	−31.0983			−0.634659			−0.317329	−	0.948315i	$-0.602786\pi$
$7$	−31.0983			−0.634659			−0.317329	+	0.948315i	$0.602786\pi$
$8$		−	5.97306i		−	0.0933291i
$9$	−78.5367	+	19.8237i	−0.969589	+	0.244737i
$10$	11.1075			0.111075
$11$			36.5780i			0.302298i	0.988511	+	0.151149i	$0.0482973\pi$
$11$			36.5780i			0.302298i	−0.988511	+	0.151149i	$0.951703\pi$
$12$	18.9098	+	152.182i	0.131318	+	1.05682i
$13$	150.671			0.891543			0.445772	−	0.895147i	$-0.352929\pi$
$13$	150.671			0.891543			0.445772	+	0.895147i	$0.352929\pi$
$14$		−	178.752i		−	0.912000i
$15$	−17.2590	+	2.14458i	−0.0767069	+	0.00953145i
$16$	−238.294			−0.930834
$17$		−	397.713i		−	1.37617i	−0.725631	−	0.688084i	$-0.758452\pi$
$17$		−	397.713i		−	1.37617i	0.725631	−	0.688084i	$-0.241548\pi$
$18$	−113.946	−	451.427i	−0.351686	−	1.39329i
$19$	641.461			1.77690			0.888450	−	0.458974i	$-0.151783\pi$
$19$	641.461			1.77690			0.888450	+	0.458974i	$0.151783\pi$
$20$			32.9268i			0.0823170i
$21$	34.5125	+	277.749i	0.0782596	+	0.629815i
$22$	−210.249			−0.434400
$23$		−	670.788i		−	1.26803i	−0.773320	−	0.634016i	$-0.781406\pi$
$23$		−	670.788i		−	1.26803i	0.773320	−	0.634016i	$-0.218594\pi$
$24$	−53.3473	+	6.62883i	−0.0926168	+	0.0115084i
$25$	621.266			0.994025
$26$			866.051i			1.28114i
$27$	264.211	+	679.436i	0.362429	+	0.932011i
$28$	529.889			0.675878
$29$		−	1328.66i		−	1.57986i	−0.613198	−	0.789929i	$-0.710117\pi$
$29$		−	1328.66i		−	1.57986i	0.613198	−	0.789929i	$-0.289883\pi$
$30$	−12.3270	−	99.2045i	−0.0136966	−	0.110227i
$31$	747.325			0.777653			0.388827	−	0.921311i	$-0.372880\pi$
$31$	747.325			0.777653			0.388827	+	0.921311i	$0.372880\pi$
$32$		−	1465.27i		−	1.43093i
$33$	326.690	−	40.5939i	0.299991	−	0.0372763i
$34$	2286.04			1.97754
$35$			60.0949i			0.0490571i
$36$	1338.20	−	337.780i	1.03256	−	0.260632i
$37$	1452.82			1.06123			0.530613	−	0.847614i	$-0.321962\pi$
$37$	1452.82			1.06123			0.530613	+	0.847614i	$0.321962\pi$
$38$			3687.10i			2.55339i
$39$	−167.213	−	1345.69i	−0.109936	−	0.884739i
$40$	−11.5425			−0.00721404
$41$		−	820.955i		−	0.488373i	−0.969728	−	0.244186i	$-0.921479\pi$
$41$		−	820.955i		−	0.488373i	0.969728	−	0.244186i	$-0.0785209\pi$
$42$	−1596.49	+	198.377i	−0.905040	+	0.112458i
$43$	−2961.00			−1.60141			−0.800703	−	0.599061i	$-0.795541\pi$
$43$	−2961.00			−1.60141			−0.800703	+	0.599061i	$0.795541\pi$
$44$		−	623.259i		−	0.321931i
$45$	38.3078	+	151.766i	0.0189174	+	0.0749461i
$46$	3855.67			1.82215
$47$		−	945.968i		−	0.428233i	−0.976808	−	0.214117i	$-0.931313\pi$
$47$		−	945.968i		−	0.428233i	0.976808	−	0.214117i	$-0.0686873\pi$
$48$	264.455	+	2128.27i	0.114781	+	0.923730i
$49$	−1433.90			−0.597208
$50$			3571.02i			1.42841i
$51$	−3552.10	+	441.376i	−1.36567	+	0.169695i
$52$	−2567.30			−0.949447
$53$			5310.33i			1.89047i	0.326389	+	0.945236i	$0.394168\pi$
$53$			5310.33i			1.89047i	−0.326389	+	0.945236i	$0.605832\pi$
$54$	−3905.38	+	1518.68i	−1.33929	+	0.520808i
$55$	70.6841			0.0233667
$56$			185.752i			0.0592321i
$57$	−711.885	−	5729.09i	−0.219109	−	1.76334i
$58$	7637.10			2.27024
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	294.080	−	36.5418i	0.0816888	−	0.0101505i
$61$	722.307			0.194116			0.0970581	−	0.995279i	$-0.469057\pi$
$61$	722.307			0.194116			0.0970581	+	0.995279i	$0.469057\pi$
$62$			4295.60i			1.11748i
$63$	2442.36	−	616.484i	0.615358	−	0.155325i
$64$	4609.65			1.12540
$65$		−	291.159i		−	0.0689134i
$66$	233.332	+	1877.80i	0.0535657	+	0.431085i
$67$	7494.48			1.66952			0.834761	−	0.550613i	$-0.185606\pi$
$67$	7494.48			1.66952			0.834761	+	0.550613i	$0.185606\pi$
$68$			6776.69i			1.46555i
$69$	−5991.02	+	744.433i	−1.25835	+	0.156361i
$70$	−345.424			−0.0704947
$71$		−	3888.73i		−	0.771420i	−0.922620	−	0.385710i	$-0.873957\pi$
$71$		−	3888.73i		−	0.771420i	0.922620	−	0.385710i	$-0.126043\pi$
$72$	118.408	+	469.105i	0.0228411	+	0.0904909i
$73$	−8396.06			−1.57554			−0.787771	−	0.615968i	$-0.788765\pi$
$73$	−8396.06			−1.57554			−0.787771	+	0.615968i	$0.788765\pi$
$74$			8350.75i			1.52497i
$75$	−689.473	−	5548.72i	−0.122573	−	0.986439i
$76$	−10930.0			−1.89230
$77$		−	1137.51i		−	0.191856i
$78$	7734.98	−	961.133i	1.27136	−	0.157977i
$79$	9517.31			1.52497			0.762483	−	0.647009i	$-0.223980\pi$
$79$	9517.31			1.52497			0.762483	+	0.647009i	$0.223980\pi$
$80$			460.483i			0.0719505i
$81$	5775.04	−	3113.78i	0.880207	−	0.474589i
$82$	4718.82			0.701788
$83$			432.863i			0.0628340i	0.999506	+	0.0314170i	$0.0100020\pi$
$83$			432.863i			0.0628340i	−0.999506	+	0.0314170i	$0.989998\pi$
$84$	−588.064	−	4732.60i	−0.0833424	−	0.670720i
$85$	−768.548			−0.106373
$86$		−	17019.7i		−	2.30121i
$87$	−11866.7	+	1474.53i	−1.56780	+	0.194812i
$88$	218.483			0.0282132
$89$		−	6891.78i		−	0.870064i	−0.900415	−	0.435032i	$-0.856737\pi$
$89$		−	6891.78i		−	0.870064i	0.900415	−	0.435032i	$-0.143263\pi$
$90$	−872.346	+	220.192i	−0.107697	+	0.0271842i
$91$	−4685.60			−0.565826
$92$			11429.7i			1.35039i
$93$	−829.372	−	6674.59i	−0.0958922	−	0.771719i
$94$	5437.39			0.615368
$95$		−	1239.57i		−	0.137349i
$96$	−13086.8	+	1626.14i	−1.42001	+	0.176448i
$97$	3927.71			0.417442			0.208721	−	0.977975i	$-0.433070\pi$
$97$	3927.71			0.417442			0.208721	+	0.977975i	$0.433070\pi$
$98$		−	8242.00i		−	0.858184i
$99$	−725.113	−	2872.72i	−0.0739836	−	0.293105i
$100$	−10585.8			−1.05858
$101$			9292.23i			0.910914i	0.890258	+	0.455457i	$0.150524\pi$
$101$			9292.23i			0.910914i	−0.890258	+	0.455457i	$0.849476\pi$
$102$	−2537.02	−	20417.3i	−0.243850	−	1.96245i
$103$	−8180.42			−0.771083			−0.385542	−	0.922690i	$-0.625985\pi$
$103$	−8180.42			−0.771083			−0.385542	+	0.922690i	$0.625985\pi$
$104$		−	899.966i		−	0.0832069i
$105$	536.727	−	66.6926i	0.0486827	−	0.00604922i
$106$	−30523.6			−2.71659
$107$		−	15960.5i		−	1.39406i	−0.717044	−	0.697028i	$-0.754505\pi$
$107$		−	15960.5i		−	1.39406i	0.717044	−	0.697028i	$-0.245495\pi$
$108$	−4501.93	−	11577.0i	−0.385968	−	0.992543i
$109$	−8197.01			−0.689926			−0.344963	−	0.938616i	$-0.612109\pi$
$109$	−8197.01			−0.689926			−0.344963	+	0.938616i	$0.612109\pi$
$110$			406.290i			0.0335777i
$111$	−1612.32	−	12975.6i	−0.130859	−	1.05313i
$112$	7410.52			0.590762
$113$		−	9498.83i		−	0.743897i	−0.928253	−	0.371949i	$-0.878690\pi$
$113$		−	9498.83i		−	0.743897i	0.928253	−	0.371949i	$-0.121310\pi$
$114$	32930.6	−	4091.89i	2.53390	−	0.314858i
$115$	−1296.24			−0.0980147
$116$			22639.3i			1.68247i
$117$	−11833.2	+	2986.86i	−0.864431	+	0.218194i
$118$	−2604.91			−0.187080
$119$			12368.2i			0.873397i
$120$	12.8097	+	103.089i	0.000889561	+	0.00715898i
$121$	13303.0			0.908616
$122$			4151.80i			0.278944i
$123$	−7332.20	+	911.085i	−0.484646	+	0.0602211i
$124$	−12733.8			−0.828160
$125$		−	2408.31i		−	0.154132i
$126$	3543.53	+	14038.6i	0.223200	+	0.884265i
$127$	14304.8			0.886896			0.443448	−	0.896300i	$-0.353755\pi$
$127$	14304.8			0.886896			0.443448	+	0.896300i	$0.353755\pi$
$128$			3051.76i			0.186264i
$129$	3286.08	+	26445.6i	0.197469	+	1.58918i
$130$	1673.57			0.0990281
$131$			5681.21i			0.331054i	0.986205	+	0.165527i	$0.0529324\pi$
$131$			5681.21i			0.331054i	−0.986205	+	0.165527i	$0.947068\pi$
$132$	−5566.52	+	691.685i	−0.319474	+	0.0396973i
$133$	−19948.3			−1.12772
$134$			43078.1i			2.39909i
$135$	1312.96	−	510.567i	0.0720415	−	0.0280146i
$136$	−2375.56			−0.128436
$137$		−	2593.21i		−	0.138165i	−0.997611	−	0.0690823i	$-0.977993\pi$
$137$		−	2593.21i		−	0.138165i	0.997611	−	0.0690823i	$-0.0220071\pi$
$138$	−4278.98	−	34436.2i	−0.224689	−	1.80824i
$139$	17990.6			0.931141			0.465571	−	0.885011i	$-0.345849\pi$
$139$	17990.6			0.931141			0.465571	+	0.885011i	$0.345849\pi$
$140$		−	1023.97i		−	0.0522432i
$141$	−8448.74	+	1049.82i	−0.424965	+	0.0528054i
$142$	22352.3			1.10852
$143$			5511.24i			0.269512i
$144$	18714.8	−	4723.87i	0.902527	−	0.227810i
$145$	−2567.53			−0.122118
$146$		−	48260.3i		−	2.26404i
$147$	1591.32	+	12806.6i	0.0736416	+	0.592650i
$148$	−24754.8			−1.13015
$149$			31573.3i			1.42216i	0.703112	+	0.711079i	$0.251793\pi$
$149$			31573.3i			1.42216i	−0.703112	+	0.711079i	$0.748207\pi$
$150$	31893.9	−	3963.07i	1.41751	−	0.176136i
$151$	−37926.7			−1.66338			−0.831689	−	0.555241i	$-0.812626\pi$
$151$	−37926.7			−1.66338			−0.831689	+	0.555241i	$0.812626\pi$
$152$		−	3831.48i		−	0.165836i
$153$	7884.14	+	31235.1i	0.336800	+	1.33432i
$154$	6538.40			0.275696
$155$		−	1444.15i		−	0.0601101i
$156$	2849.16	+	22929.4i	0.117076	+	0.942201i
$157$	−25795.6			−1.04652			−0.523258	−	0.852174i	$-0.675284\pi$
$157$	−25795.6			−1.04652			−0.523258	+	0.852174i	$0.675284\pi$
$158$			54705.2i			2.19136i
$159$	47428.3	−	5893.34i	1.87604	−	0.233113i
$160$	−2831.52			−0.110606
$161$			20860.4i			0.804767i
$162$	17897.9	+	33194.8i	0.681981	+	1.26485i
$163$	−20201.6			−0.760343			−0.380172	−	0.924916i	$-0.624135\pi$
$163$	−20201.6			−0.760343			−0.380172	+	0.924916i	$0.624135\pi$
$164$			13988.4i			0.520091i
$165$	−78.4444	−	631.302i	−0.00288134	−	0.0231883i
$166$	−2488.09			−0.0902920
$167$		−	22630.0i		−	0.811432i	−0.913999	−	0.405716i	$-0.867022\pi$
$167$		−	22630.0i		−	0.811432i	0.913999	−	0.405716i	$-0.132978\pi$
$168$	1659.01	−	206.145i	0.0587801	−	0.00730389i
$169$	−5859.30			−0.205151
$170$		−	4417.59i		−	0.152858i
$171$	−50378.2	+	12716.1i	−1.72286	+	0.434874i
$172$	50453.0			1.70541
$173$			16695.6i			0.557839i	0.960314	+	0.278920i	$0.0899763\pi$
$173$			16695.6i			0.557839i	−0.960314	+	0.278920i	$0.910024\pi$
$174$	−8475.56	−	68209.4i	−0.279943	−	2.25292i
$175$	−19320.3			−0.630867
$176$		−	8716.31i		−	0.281389i
$177$	4047.56	−	502.942i	0.129195	−	0.0160536i
$178$	39613.7			1.25028
$179$		−	22555.9i		−	0.703970i	−0.936006	−	0.351985i	$-0.885507\pi$
$179$		−	22555.9i		−	0.703970i	0.936006	−	0.351985i	$-0.114493\pi$
$180$	−652.732	−	2585.96i	−0.0201460	−	0.0798137i
$181$	−27550.6			−0.840958			−0.420479	−	0.907302i	$-0.638138\pi$
$181$	−27550.6			−0.840958			−0.420479	+	0.907302i	$0.638138\pi$
$182$		−	26932.7i		−	0.813087i
$183$	−801.607	−	6451.15i	−0.0239364	−	0.192635i
$184$	−4006.66			−0.118344
$185$		−	2807.45i		−	0.0820293i
$186$	38365.4	−	4767.21i	1.10895	−	0.137796i
$187$	14547.5			0.416013
$188$			16118.5i			0.456046i
$189$	−8216.51	−	21129.3i	−0.230019	−	0.591509i
$190$	7125.02			0.197369
$191$		−	35316.8i		−	0.968089i	−0.875043	−	0.484044i	$-0.839167\pi$
$191$		−	35316.8i		−	0.968089i	0.875043	−	0.484044i	$-0.160833\pi$
$192$	−5115.73	−	41170.2i	−0.138773	−	1.11681i
$193$	47333.5			1.27073			0.635366	−	0.772211i	$-0.280849\pi$
$193$	47333.5			1.27073			0.635366	+	0.772211i	$0.280849\pi$
$194$			22576.4i			0.599861i
$195$	−2600.43	+	323.125i	−0.0683875	+	0.00849770i
$196$	24432.4			0.635995
$197$			11513.5i			0.296671i	0.988937	+	0.148335i	$0.0473915\pi$
$197$			11513.5i			0.296671i	−0.988937	+	0.148335i	$0.952609\pi$
$198$	16512.3	−	4167.93i	0.421189	−	0.106314i
$199$	61848.9			1.56180			0.780901	−	0.624655i	$-0.214760\pi$
$199$	61848.9			1.56180			0.780901	+	0.624655i	$0.214760\pi$
$200$		−	3710.86i		−	0.0927714i
$201$	−8317.28	−	66935.6i	−0.205868	−	1.65678i
$202$	−53411.5			−1.30898
$203$			41319.1i			1.00267i
$204$	60524.7	−	7520.68i	1.45436	−	0.180716i
$205$	−1586.43			−0.0377496
$206$		−	47020.8i		−	1.10804i
$207$	13297.5	+	52681.5i	0.310335	+	1.22947i
$208$	−35903.9			−0.829879
$209$			23463.4i			0.537153i
$210$	383.347	+	3085.09i	0.00869268	+	0.0699567i
$211$	−15185.7			−0.341090			−0.170545	−	0.985350i	$-0.554553\pi$
$211$	−15185.7			−0.341090			−0.170545	+	0.985350i	$0.554553\pi$
$212$		−	90483.6i		−	2.01325i
$213$	−34731.5	+	4315.66i	−0.765533	+	0.0951236i
$214$	91740.7			2.00325
$215$			5721.89i			0.123784i
$216$	4058.31	−	1578.15i	0.0869837	−	0.0338252i
$217$	−23240.5			−0.493545
$218$		−	47116.2i		−	0.991419i
$219$	9317.85	+	74987.9i	0.194280	+	1.56352i
$220$	−1204.40			−0.0248843
$221$		−	59923.7i		−	1.22691i
$222$	74583.2	−	9267.56i	1.51333	−	0.188044i
$223$	4578.23			0.0920636			0.0460318	−	0.998940i	$-0.485342\pi$
$223$	4578.23			0.0920636			0.0460318	+	0.998940i	$0.485342\pi$
$224$			45567.5i			0.908153i
$225$	−48792.2	+	12315.8i	−0.963796	+	0.243275i
$226$	54599.0			1.06898
$227$		−	37276.5i		−	0.723407i	−0.932293	−	0.361704i	$-0.882195\pi$
$227$		−	37276.5i		−	0.723407i	0.932293	−	0.361704i	$-0.117805\pi$
$228$	12129.9	+	97618.8i	0.233340	+	1.87786i
$229$	15778.0			0.300871			0.150435	−	0.988620i	$-0.451932\pi$
$229$	15778.0			0.300871			0.150435	+	0.988620i	$0.451932\pi$
$230$		−	7450.78i		−	0.140846i
$231$	−10159.5	+	1262.40i	−0.190392	+	0.0236577i
$232$	−7936.17			−0.147447
$233$			48712.1i			0.897275i	0.893714	+	0.448637i	$0.148090\pi$
$233$			48712.1i			0.897275i	−0.893714	+	0.448637i	$0.851910\pi$
$234$	−17168.4	−	68016.9i	−0.313543	−	1.24218i
$235$	−1828.01			−0.0331011
$236$		−	7721.94i		−	0.138644i
$237$	−10562.2	−	85002.1i	−0.188043	−	1.51333i
$238$	−71091.9			−1.25507
$239$		−	84845.2i		−	1.48536i	−0.669647	−	0.742679i	$-0.733555\pi$
$239$		−	84845.2i		−	1.48536i	0.669647	−	0.742679i	$-0.266445\pi$
$240$	4112.72	−	511.039i	0.0714014	−	0.00887220i
$241$	−53883.0			−0.927722			−0.463861	−	0.885908i	$-0.653536\pi$
$241$	−53883.0			−0.927722			−0.463861	+	0.885908i	$0.653536\pi$
$242$			76465.5i			1.30567i
$243$	−34219.2	−	48123.1i	−0.579506	−	0.814968i
$244$	−12307.5			−0.206724
$245$			2770.89i			0.0461623i
$246$	−5236.89	−	42145.3i	−0.0865373	−	0.696432i
$247$	96649.4			1.58418
$248$		−	4463.82i		−	0.0725777i
$249$	3866.04	−	480.386i	0.0623545	−	0.00774804i
$250$	13842.9			0.221486
$251$			77001.2i			1.22222i	0.791545	+	0.611111i	$0.209277\pi$
$251$			77001.2i			1.22222i	−0.791545	+	0.611111i	$0.790723\pi$
$252$	−41615.7	+	10504.4i	−0.655324	+	0.165413i
$253$	24536.1			0.383323
$254$			82223.3i			1.27446i
$255$	852.925	+	6864.14i	0.0131169	+	0.105562i
$256$	56213.0			0.857742
$257$			33402.0i			0.505716i	0.967503	+	0.252858i	$0.0813705\pi$
$257$			33402.0i			0.505716i	−0.967503	+	0.252858i	$0.918630\pi$
$258$	−152009.	+	18888.3i	−2.28365	+	0.283761i
$259$	−45180.1			−0.673516
$260$			4961.11i			0.0733892i
$261$	26339.0	+	104349.i	0.386650	+	1.53181i
$262$	−32655.4			−0.475721
$263$		−	86858.5i		−	1.25574i	−0.778317	−	0.627871i	$-0.783926\pi$
$263$		−	86858.5i		−	1.25574i	0.778317	−	0.627871i	$-0.216074\pi$
$264$	−242.470	−	1951.34i	−0.00347896	−	0.0279979i
$265$	10261.8			0.146127
$266$		−	114662.i		−	1.62053i
$267$	−61552.6	+	7648.41i	−0.863424	+	0.107287i
$268$	−127700.			−1.77795
$269$			89268.9i			1.23366i	0.787096	+	0.616830i	$0.211583\pi$
$269$			89268.9i			1.23366i	−0.787096	+	0.616830i	$0.788417\pi$
$270$	2934.72	+	7546.83i	0.0402568	+	0.103523i
$271$	113447.			1.54474			0.772371	−	0.635172i	$-0.219071\pi$
$271$	113447.			1.54474			0.772371	+	0.635172i	$0.219071\pi$
$272$			94772.4i			1.28098i
$273$	5200.02	+	41848.6i	0.0697718	+	0.561508i
$274$	14905.7			0.198542
$275$			22724.7i			0.300492i
$276$	102082.	−	12684.5i	1.34008	−	0.166516i
$277$	−57909.5			−0.754727			−0.377364	−	0.926065i	$-0.623169\pi$
$277$	−57909.5			−0.754727			−0.377364	+	0.926065i	$0.623169\pi$
$278$			103409.i			1.33804i
$279$	−58692.5	+	14814.8i	−0.754005	+	0.190321i
$280$	358.951			0.00457845
$281$			16277.6i			0.206147i	0.994674	+	0.103073i	$0.0328677\pi$
$281$			16277.6i			0.206147i	−0.994674	+	0.103073i	$0.967132\pi$
$282$	−6034.35	−	48563.1i	−0.0758809	−	0.610672i
$283$	118418.			1.47858			0.739289	−	0.673388i	$-0.235162\pi$
$283$	118418.			1.47858			0.739289	+	0.673388i	$0.235162\pi$
$284$			66260.7i			0.821522i
$285$	−11071.0	+	1375.66i	−0.136300	+	0.0169364i
$286$	−31678.5			−0.387286
$287$			25530.3i			0.309950i
$288$	29047.2	+	115078.i	0.350202	+	1.38742i
$289$	−74654.3			−0.893839
$290$		−	14758.1i		−	0.175483i
$291$	−4358.92	−	35079.6i	−0.0514746	−	0.414256i
$292$	143062.			1.67787
$293$		−	146916.i		−	1.71133i	−0.517531	−	0.855665i	$-0.673149\pi$
$293$		−	146916.i		−	1.71133i	0.517531	−	0.855665i	$-0.326851\pi$
$294$	−73611.9	+	9146.87i	−0.851634	+	0.105822i
$295$	875.749			0.0100632
$296$		−	8677.76i		−	0.0990431i
$297$	−24852.4	+	9664.32i	−0.281745	+	0.109562i
$298$	−181483.			−2.04363
$299$		−	101068.i		−	1.13050i
$300$	11748.0	+	94545.5i	0.130534	+	1.05051i
$301$	92082.0			1.01635
$302$		−	218002.i		−	2.39026i
$303$	82991.8	−	10312.4i	0.903962	−	0.112325i
$304$	−152856.			−1.65400
$305$		−	1395.80i		−	0.0150046i
$306$	−179538.	+	45317.8i	−1.91741	+	0.483979i
$307$	7617.24			0.0808204			0.0404102	−	0.999183i	$-0.487134\pi$
$307$	7617.24			0.0808204			0.0404102	+	0.999183i	$0.487134\pi$
$308$			19382.3i			0.204317i
$309$	9078.53	+	73061.9i	0.0950821	+	0.765198i
$310$	8300.91			0.0863778
$311$			77684.8i			0.803184i	0.915819	+	0.401592i	$0.131543\pi$
$311$			77684.8i			0.803184i	−0.915819	+	0.401592i	$0.868457\pi$
$312$	−8037.88	+	998.771i	−0.0825719	+	0.0102602i
$313$	−4590.34			−0.0468551			−0.0234275	−	0.999726i	$-0.507458\pi$
$313$	−4590.34			−0.0468551			−0.0234275	+	0.999726i	$0.507458\pi$
$314$		−	148272.i		−	1.50384i
$315$	−1191.31	−	4719.66i	−0.0120061	−	0.0475652i
$316$	−162167.			−1.62401
$317$		−	12717.0i		−	0.126551i	−0.997996	−	0.0632757i	$-0.979845\pi$
$317$		−	12717.0i		−	0.126551i	0.997996	−	0.0632757i	$-0.0201548\pi$
$318$	33874.8	+	272616.i	0.334982	+	2.69586i
$319$	48599.8			0.477588
$320$		−	8907.78i		−	0.0869900i
$321$	−142549.	+	17712.8i	−1.38342	+	0.171901i
$322$	−119905.			−1.15644
$323$		−	255117.i		−	2.44531i
$324$	−98401.8	+	53056.2i	−0.937375	+	0.505413i
$325$	93606.6			0.886217
$326$		−	116118.i		−	1.09261i
$327$	9096.94	+	73210.1i	0.0850746	+	0.684661i
$328$	−4903.61			−0.0455794
$329$			29418.0i			0.271782i
$330$	3628.71	−	450.896i	0.0333214	−	0.00414046i
$331$	−84728.0			−0.773341			−0.386671	−	0.922218i	$-0.626375\pi$
$331$	−84728.0			−0.773341			−0.386671	+	0.922218i	$0.626375\pi$
$332$		−	7375.63i		−	0.0669149i
$333$	−114100.	+	28800.2i	−1.02895	+	0.259721i
$334$	130077.			1.16602
$335$		−	14482.5i		−	0.129049i
$336$	−8224.10	−	66185.7i	−0.0728467	−	0.586254i
$337$	18359.9			0.161663			0.0808317	−	0.996728i	$-0.474242\pi$
$337$	18359.9			0.161663			0.0808317	+	0.996728i	$0.474242\pi$
$338$		−	33679.1i		−	0.294800i
$339$	−84837.0	+	10541.7i	−0.738220	+	0.0917298i
$340$	13095.4			0.113282
$341$			27335.7i			0.235083i
$342$	−73092.0	−	289573.i	−0.624910	−	2.47574i
$343$	119259.			1.01368
$344$			17686.2i			0.149458i
$345$	1438.56	+	11577.2i	0.0120862	+	0.0972667i
$346$	−95965.6			−0.801611
$347$		−	68522.1i		−	0.569078i	−0.958665	−	0.284539i	$-0.908160\pi$
$347$		−	68522.1i		−	0.569078i	0.958665	−	0.284539i	$-0.0918405\pi$
$348$	202198.	−	25124.8i	1.66963	−	0.207464i
$349$	9503.69			0.0780264			0.0390132	−	0.999239i	$-0.487579\pi$
$349$	9503.69			0.0780264			0.0390132	+	0.999239i	$0.487579\pi$
$350$		−	111052.i		−	0.906551i
$351$	39808.9	+	102371.i	0.323121	+	0.830928i
$352$	53596.8			0.432567
$353$			157953.i			1.26759i	0.773501	+	0.633795i	$0.218504\pi$
$353$			157953.i			1.26759i	−0.773501	+	0.633795i	$0.781496\pi$
$354$	2890.90	+	23265.3i	0.0230688	+	0.185653i
$355$	−7514.65			−0.0596283
$356$			117430.i			0.926573i
$357$	110464.	−	13726.1i	0.866732	−	0.107698i
$358$	129651.			1.01160
$359$			43690.8i			0.339001i	0.985530	+	0.169500i	$0.0542154\pi$
$359$			43690.8i			0.339001i	−0.985530	+	0.169500i	$0.945785\pi$
$360$	906.507	−	228.814i	0.00699465	−	0.00176554i
$361$	281151.			2.15737
$362$		−	158360.i		−	1.20845i
$363$	−14763.6	−	118814.i	−0.112041	−	0.901682i
$364$	79838.7			0.602575
$365$			16224.7i			0.121784i
$366$	37081.0	−	4607.61i	0.276815	−	0.0343965i
$367$	−209462.			−1.55515			−0.777576	−	0.628789i	$-0.783551\pi$
$367$	−209462.			−1.55515			−0.777576	+	0.628789i	$0.783551\pi$
$368$			159845.i			1.18033i
$369$	16274.4	+	64475.1i	0.119523	+	0.473521i
$370$	16137.2			0.117875
$371$		−	165142.i		−	1.19980i
$372$	14131.8	+	113729.i	0.102120	+	0.821840i
$373$	12200.0			0.0876886			0.0438443	−	0.999038i	$-0.486039\pi$
$373$	12200.0			0.0876886			0.0438443	+	0.999038i	$0.486039\pi$
$374$			83618.9i			0.597807i
$375$	−21509.4	+	2672.71i	−0.152955	+	0.0190059i
$376$	−5650.32			−0.0399666
$377$		−	200190.i		−	1.40851i
$378$	121451.	−	47228.2i	0.849994	−	0.330536i
$379$	58846.1			0.409675			0.204838	−	0.978796i	$-0.434333\pi$
$379$	58846.1			0.409675			0.204838	+	0.978796i	$0.434333\pi$
$380$			21121.3i			0.146269i
$381$	−15875.2	−	127760.i	−0.109363	−	0.880128i
$382$	203000.			1.39114
$383$		−	96149.7i		−	0.655466i	−0.944770	−	0.327733i	$-0.893715\pi$
$383$		−	96149.7i		−	0.655466i	0.944770	−	0.327733i	$-0.106285\pi$
$384$	27256.2	−	3386.80i	0.184843	−	0.0229682i
$385$	−2198.15			−0.0148299
$386$			272072.i			1.82603i
$387$	232547.	−	58698.0i	1.55271	−	0.391924i
$388$	−66924.9			−0.444554
$389$		−	189303.i		−	1.25100i	−0.780222	−	0.625502i	$-0.784894\pi$
$389$		−	189303.i		−	1.25100i	0.780222	−	0.625502i	$-0.215106\pi$
$390$	−1857.31	−	14947.2i	−0.0122111	−	0.0982723i
$391$	−266781.			−1.74502
$392$			8564.75i			0.0557369i
$393$	50740.7	−	6304.94i	0.328527	−	0.0408221i
$394$	−66179.2			−0.426313
$395$		−	18391.4i		−	0.117875i
$396$	12355.3	+	48948.7i	0.0787886	+	0.312141i
$397$	−14667.4			−0.0930619			−0.0465310	−	0.998917i	$-0.514817\pi$
$397$	−14667.4			−0.0930619			−0.0465310	+	0.998917i	$0.514817\pi$
$398$			355506.i			2.24430i
$399$	22138.4	+	178165.i	0.139059	+	1.11912i
$400$	−148044.			−0.925273
$401$		−	83639.3i		−	0.520142i	−0.965590	−	0.260071i	$-0.916254\pi$
$401$		−	83639.3i		−	0.520142i	0.965590	−	0.260071i	$-0.0837459\pi$
$402$	384744.	−	47807.5i	2.38078	−	0.295831i
$403$	112600.			0.693312
$404$		−	158332.i		−	0.970075i
$405$	−6017.13	−	11159.8i	−0.0366842	−	0.0680372i
$406$	−237501.			−1.44083
$407$			53141.2i			0.320806i
$408$	2636.37	+	21216.9i	0.0158375	+	0.127456i
$409$	−87346.8			−0.522156			−0.261078	−	0.965318i	$-0.584078\pi$
$409$	−87346.8			−0.522156			−0.261078	+	0.965318i	$0.584078\pi$
$410$		−	9118.75i		−	0.0542460i
$411$	−23160.8	+	2877.92i	−0.137110	+	0.0170370i
$412$	139388.			0.821163
$413$		−	14093.4i		−	0.0826255i
$414$	−302812.	+	76433.8i	−1.76674	+	0.445948i
$415$	836.474			0.00485687
$416$		−	220774.i		−	1.27574i
$417$	−19965.7	−	160679.i	−0.114819	−	0.924035i
$418$	−134867.			−0.771885
$419$			252031.i			1.43558i	0.696261	+	0.717789i	$0.254846\pi$
$419$			252031.i			1.43558i	−0.696261	+	0.717789i	$0.745154\pi$
$420$	−9145.37	+	1136.39i	−0.0518445	+	0.00644210i
$421$	61654.8			0.347859			0.173929	−	0.984758i	$-0.444354\pi$
$421$	61654.8			0.347859			0.173929	+	0.984758i	$0.444354\pi$
$422$		−	87286.7i		−	0.490143i
$423$	18752.6	+	74293.2i	0.104805	+	0.415211i
$424$	31718.9			0.176436
$425$		−	247085.i		−	1.36795i
$426$	−24806.3	−	199635.i	−0.136692	−	1.10006i
$427$	−22462.5			−0.123198
$428$			271954.i			1.48460i
$429$	49222.6	−	6116.31i	0.267455	−	0.0332334i
$430$	−32889.3			−0.177876
$431$			278438.i			1.49890i	0.662059	+	0.749452i	$0.269683\pi$
$431$			278438.i			1.49890i	−0.662059	+	0.749452i	$0.730317\pi$
$432$	−62959.8	−	161905.i	−0.337362	−	0.867548i
$433$	−208094.			−1.10990			−0.554949	−	0.831884i	$-0.687262\pi$
$433$	−208094.			−1.10990			−0.554949	+	0.831884i	$0.687262\pi$
$434$		−	133586.i		−	0.709220i
$435$	2849.41	+	22931.4i	0.0150583	+	0.121186i
$436$	139670.			0.734735
$437$		−	430284.i		−	2.25316i
$438$	−431028.	+	53558.7i	−2.24676	+	0.279178i
$439$	110262.			0.572132			0.286066	−	0.958210i	$-0.407652\pi$
$439$	110262.			0.572132			0.286066	+	0.958210i	$0.407652\pi$
$440$		−	422.200i		−	0.00218079i
$441$	112614.	−	28425.2i	0.579047	−	0.146159i
$442$	344440.			1.76307
$443$			240587.i			1.22593i	0.790112	+	0.612963i	$0.210023\pi$
$443$			240587.i			1.22593i	−0.790112	+	0.612963i	$0.789977\pi$
$444$	27472.6	+	221093.i	0.139358	+	1.12152i
$445$	−13317.8			−0.0672532
$446$			26315.5i			0.132295i
$447$	281991.	−	35039.7i	1.41130	−	0.175366i
$448$	−143352.			−0.714247
$449$			300308.i			1.48962i	0.667279	+	0.744808i	$0.267459\pi$
$449$			300308.i			1.48962i	−0.667279	+	0.744808i	$0.732541\pi$
$450$	−70790.9	−	280456.i	−0.349584	−	1.38497i
$451$	30028.9			0.147634
$452$			161852.i			0.792212i
$453$	42090.6	+	338735.i	0.205111	+	1.65068i
$454$	214264.			1.03953
$455$			9054.55i			0.0437365i
$456$	−34220.2	+	4252.13i	−0.164571	+	0.0204492i
$457$	−196362.			−0.940213			−0.470106	−	0.882610i	$-0.655784\pi$
$457$	−196362.			−0.940213			−0.470106	+	0.882610i	$0.655784\pi$
$458$			90691.3i			0.432349i
$459$	270220.	−	105080.i	1.28260	−	0.498764i
$460$	22086.9			0.104381
$461$			236979.i			1.11509i	0.830148	+	0.557544i	$0.188256\pi$
$461$			236979.i			1.11509i	−0.830148	+	0.557544i	$0.811744\pi$
$462$	−7256.23	−	58396.5i	−0.0339960	−	0.273592i
$463$	91894.9			0.428676			0.214338	−	0.976760i	$-0.431241\pi$
$463$	91894.9			0.428676			0.214338	+	0.976760i	$0.431241\pi$
$464$			316611.i			1.47059i
$465$	−12898.1	+	1602.69i	−0.0596514	+	0.00741216i
$466$	−279996.			−1.28938
$467$		−	153481.i		−	0.703754i	−0.936046	−	0.351877i	$-0.885544\pi$
$467$		−	153481.i		−	0.703754i	0.936046	−	0.351877i	$-0.114456\pi$
$468$	201628.	−	50893.5i	0.920574	−	0.232365i
$469$	−233065.			−1.05958
$470$		−	10507.3i		−	0.0475660i
$471$	28627.6	+	230388.i	0.129046	+	1.03853i
$472$	2706.92			0.0121504
$473$		−	108308.i		−	0.484102i
$474$	488589.	−	60711.2i	2.17464	−	0.270216i
$475$	398518.			1.76628
$476$		−	210743.i		−	0.930122i
$477$	−105271.	−	417056.i	−0.462669	−	1.83298i
$478$	487688.			2.13445
$479$			89639.7i			0.390688i	0.980735	+	0.195344i	$0.0625823\pi$
$479$			89639.7i			0.390688i	−0.980735	+	0.195344i	$0.937418\pi$
$480$	3142.39	+	25289.2i	0.0136388	+	0.109762i
$481$	218897.			0.946128
$482$		−	309718.i		−	1.33313i
$483$	186310.	−	23150.6i	0.798625	−	0.0992356i
$484$	−226673.			−0.967628
$485$		−	7589.98i		−	0.0322669i
$486$	276610.	−	196691.i	1.17110	−	0.832745i
$487$	44486.3			0.187572			0.0937861	−	0.995592i	$-0.470103\pi$
$487$	44486.3			0.187572			0.0937861	+	0.995592i	$0.470103\pi$
$488$		−	4314.38i		−	0.0181167i
$489$	22419.4	+	180427.i	0.0937578	+	0.754541i
$490$	−15927.0			−0.0663348
$491$			404358.i			1.67727i	0.544695	+	0.838635i	$0.316646\pi$
$491$			404358.i			1.67727i	−0.544695	+	0.838635i	$0.683354\pi$
$492$	124935.	−	15524.1i	0.516122	−	0.0641323i
$493$	−528425.			−2.17415
$494$			555538.i			2.27646i
$495$	−5551.30	+	1401.22i	−0.0226561	+	0.00571869i
$496$	−178083.			−0.723867
$497$			120933.i			0.489588i
$498$	2761.25	+	22221.9i	0.0111339	+	0.0896029i
$499$	187410.			0.752648			0.376324	−	0.926488i	$-0.377188\pi$
$499$	187410.			0.752648			0.376324	+	0.926488i	$0.377188\pi$
$500$			41035.6i			0.164142i
$501$	−202116.	+	25114.5i	−0.805240	+	0.100058i
$502$	−442601.			−1.75632
$503$		−	203611.i		−	0.804760i	−0.915473	−	0.402380i	$-0.868183\pi$
$503$		−	203611.i		−	0.804760i	0.915473	−	0.402380i	$-0.131817\pi$
$504$	−3682.29	−	14588.3i	−0.0144963	−	0.0574308i
$505$	17956.5			0.0704107
$506$			141033.i			0.550832i
$507$	6502.58	+	52331.3i	0.0252971	+	0.203585i
$508$	−243741.			−0.944498
$509$			95695.5i			0.369365i	0.982798	+	0.184682i	$0.0591257\pi$
$509$			95695.5i			0.369365i	−0.982798	+	0.184682i	$0.940874\pi$
$510$	−39454.9	+	4902.59i	−0.151691	+	0.0188488i
$511$	261103.			0.999932
$512$			371939.i			1.41883i
$513$	169481.	+	435832.i	0.644001	+	1.65609i
$514$	−191994.			−0.726710
$515$			15808.0i			0.0596022i
$516$	−55992.1	−	450611.i	−0.210294	−	1.69240i
$517$	34601.7			0.129454
$518$		−	259694.i		−	0.967837i
$519$	149113.	−	18528.5i	0.553582	−	0.0687870i
$520$	−1739.11			−0.00643163
$521$		−	431600.i		−	1.59003i	−0.606589	−	0.795016i	$-0.707463\pi$
$521$		−	431600.i		−	1.59003i	0.606589	−	0.795016i	$-0.292537\pi$
$522$	−599793.	+	151396.i	−2.20120	+	0.555613i
$523$	507455.			1.85522			0.927608	−	0.373555i	$-0.121861\pi$
$523$	507455.			1.85522			0.927608	+	0.373555i	$0.121861\pi$
$524$		−	96803.0i		−	0.352555i
$525$	21441.4	+	172556.i	0.0777920	+	0.626052i
$526$	499260.			1.80449
$527$		−	297221.i		−	1.07018i
$528$	−77848.1	+	9673.26i	−0.279242	+	0.0346980i
$529$	−170116.			−0.607903
$530$			58984.5i			0.209984i
$531$	−8983.87	−	35591.9i	−0.0318621	−	0.126230i
$532$	339903.			1.20097
$533$		−	123694.i		−	0.435406i
$534$	−43962.8	−	353803.i	−0.154171	−	1.24073i
$535$	−30842.5			−0.107756
$536$		−	44765.0i		−	0.155815i
$537$	−201454.	+	25032.2i	−0.698597	+	0.0868063i
$538$	−513115.			−1.77276
$539$		−	52449.1i		−	0.180535i
$540$	−22371.7	+	8699.62i	−0.0767204	+	0.0298341i
$541$	113361.			0.387320			0.193660	−	0.981069i	$-0.437964\pi$
$541$	113361.			0.387320			0.193660	+	0.981069i	$0.437964\pi$
$542$			652092.i			2.21978i
$543$	30575.3	+	246063.i	0.103698	+	0.834540i
$544$	−582758.			−1.96920
$545$			15840.1i			0.0533291i
$546$	−240544.	+	29889.6i	−0.806882	+	0.100262i
$547$	−91662.3			−0.306349			−0.153174	−	0.988199i	$-0.548950\pi$
$547$	−91662.3			−0.306349			−0.153174	+	0.988199i	$0.548950\pi$
$548$			44186.2i			0.147138i
$549$	−56727.6	+	14318.8i	−0.188213	+	0.0475075i
$550$	−130621.			−0.431804
$551$		−	852284.i		−	2.80725i
$552$	4446.54	+	35784.7i	0.0145930	+	0.117441i
$553$	−295972.			−0.967833
$554$		−	332862.i		−	1.08454i
$555$	−25074.2	+	3115.68i	−0.0814033	+	0.0101150i
$556$	−306544.			−0.991616
$557$			145180.i			0.467946i	0.972243	+	0.233973i	$0.0751727\pi$
$557$			145180.i			0.467946i	−0.972243	+	0.233973i	$0.924827\pi$
$558$	−85154.8	−	337363.i	−0.273490	−	1.08350i
$559$	−446136.			−1.42772
$560$		−	14320.2i		−	0.0456640i
$561$	−16144.7	−	129929.i	−0.0512984	−	0.412838i
$562$	−93563.0			−0.296232
$563$			458837.i			1.44758i	0.690023	+	0.723788i	$0.257600\pi$
$563$			458837.i			1.44758i	−0.690023	+	0.723788i	$0.742400\pi$
$564$	143959.	−	17888.1i	0.452566	−	0.0562349i
$565$	−18355.7			−0.0575009
$566$			680663.i			2.12471i
$567$	−179594.	+	96833.2i	−0.558631	+	0.301202i
$568$	−23227.6			−0.0719959
$569$			165151.i			0.510101i	0.966928	+	0.255050i	$0.0820921\pi$
$569$			165151.i			0.510101i	−0.966928	+	0.255050i	$0.917908\pi$
$570$	−7907.26	−	63635.8i	−0.0243375	−	0.195863i
$571$	407820.			1.25082			0.625411	−	0.780295i	$-0.284931\pi$
$571$	407820.			1.25082			0.625411	+	0.780295i	$0.284931\pi$
$572$		−	93907.0i		−	0.287016i
$573$	−315426.	+	39194.2i	−0.960700	+	0.119375i
$574$	−146747.			−0.445396
$575$		−	416738.i		−	1.26045i
$576$	−362027.	+	91380.4i	−1.09118	+	0.275428i
$577$	−364230.			−1.09402			−0.547008	−	0.837127i	$-0.684233\pi$
$577$	−364230.			−1.09402			−0.547008	+	0.837127i	$0.684233\pi$
$578$		−	429111.i		−	1.28444i
$579$	−52530.2	−	422751.i	−0.156694	−	1.26104i
$580$	43748.6			0.130049
$581$		−	13461.3i		−	0.0398781i
$582$	201637.	−	25055.0i	0.595283	−	0.0739687i
$583$	−194242.			−0.571485
$584$			50150.2i			0.147044i
$585$	5771.86	+	22866.7i	0.0168657	+	0.0668177i
$586$	844468.			2.45917
$587$			467751.i			1.35750i	0.734371	+	0.678749i	$0.237477\pi$
$587$			467751.i			1.35750i	−0.734371	+	0.678749i	$0.762523\pi$
$588$	−27114.8	−	218213.i	−0.0784244	−	0.631142i
$589$	479380.			1.38181
$590$			5033.78i			0.0144607i
$591$	102831.	−	12777.5i	0.294406	−	0.0365824i
$592$	−346197.			−0.987825
$593$			8445.16i			0.0240159i	0.999928	+	0.0120079i	$0.00382234\pi$
$593$			8445.16i			0.0240159i	−0.999928	+	0.0120079i	$0.996178\pi$
$594$	−55550.2	−	142851.i	−0.157439	−	0.404865i
$595$	23900.5			0.0675108
$596$		−	537983.i		−	1.51452i
$597$	−68639.2	−	552392.i	−0.192585	−	1.54988i
$598$	580937.			1.62453
$599$			618699.i			1.72435i	0.506609	+	0.862176i	$0.330899\pi$
$599$			618699.i			1.72435i	−0.506609	+	0.862176i	$0.669101\pi$
$600$	−33142.8	+	4118.26i	−0.0920634	+	0.0114396i
$601$	−585473.			−1.62091			−0.810453	−	0.585804i	$-0.800779\pi$
$601$	−585473.			−1.62091			−0.810453	+	0.585804i	$0.800779\pi$
$602$			529285.i			1.46048i
$603$	−588592.	+	148569.i	−1.61875	+	0.408594i
$604$	646239.			1.77141
$605$		−	25707.1i		−	0.0702331i
$606$	59275.4	+	477035.i	0.161410	+	1.29899i
$607$	262153.			0.711504			0.355752	−	0.934580i	$-0.384225\pi$
$607$	262153.			0.711504			0.355752	+	0.934580i	$0.384225\pi$
$608$		−	939915.i		−	2.54262i
$609$	369034.	−	45855.4i	0.995019	−	0.123639i
$610$	8023.01			0.0215614
$611$		−	142530.i		−	0.381789i
$612$	−134339.	−	532219.i	−0.358674	−	1.42098i
$613$	−654490.			−1.74174			−0.870868	−	0.491517i	$-0.836442\pi$
$613$	−654490.			−1.74174			−0.870868	+	0.491517i	$0.836442\pi$
$614$			43783.7i			0.116138i
$615$	1760.60	+	14168.9i	0.00465490	+	0.0374616i
$616$	−6794.44			−0.0179057
$617$		−	370184.i		−	0.972406i	−0.873846	−	0.486203i	$-0.838382\pi$
$617$		−	370184.i		−	0.972406i	0.873846	−	0.486203i	$-0.161618\pi$
$618$	−419958.	+	52183.1i	−1.09958	+	0.136632i
$619$	215394.			0.562150			0.281075	−	0.959686i	$-0.409309\pi$
$619$	215394.			0.562150			0.281075	+	0.959686i	$0.409309\pi$
$620$			24607.0i			0.0640141i
$621$	455758.	−	177230.i	1.18182	−	0.459572i
$622$	−446530.			−1.15417
$623$			214322.i			0.552194i
$624$	39845.7	+	320669.i	0.102332	+	0.823546i
$625$	383637.			0.982111
$626$		−	26385.2i		−	0.0673304i
$627$	209559.	−	26039.4i	0.533054	−	0.0662362i
$628$	439535.			1.11448
$629$		−	577804.i		−	1.46042i
$630$	27128.5	−	6847.59i	0.0683509	−	0.0172527i
$631$	−547165.			−1.37423			−0.687116	−	0.726548i	$-0.741123\pi$
$631$	−547165.			−1.37423			−0.687116	+	0.726548i	$0.741123\pi$
$632$		−	56847.5i		−	0.142324i
$633$	16852.8	+	135628.i	0.0420597	+	0.338487i
$634$	73097.1			0.181853
$635$		−	27642.8i		−	0.0685542i
$636$	−808138.	+	100418.i	−1.99789	+	0.248254i
$637$	−216046.			−0.532437
$638$			279350.i			0.686290i
$639$	77089.1	+	305408.i	0.188795	+	0.747961i
$640$	5897.27			0.0143976
$641$			169274.i			0.411978i	0.978554	+	0.205989i	$0.0660410\pi$
$641$			169274.i			0.411978i	−0.978554	+	0.205989i	$0.933959\pi$
$642$	−101813.	−	819365.i	−0.247020	−	1.98796i
$643$	−169103.			−0.409006			−0.204503	−	0.978866i	$-0.565558\pi$
$643$	−169103.			−0.409006			−0.204503	+	0.978866i	$0.565558\pi$
$644$		−	355443.i		−	0.857035i
$645$	51104.0	−	6350.09i	0.122839	−	0.0152637i
$646$	1.46641e6			3.51390
$647$			75215.6i			0.179680i	0.995956	+	0.0898399i	$0.0286355\pi$
$647$			75215.6i			0.179680i	−0.995956	+	0.0898399i	$0.971364\pi$
$648$	−18598.8	−	34494.7i	−0.0442930	−	0.0821489i
$649$	−16576.7			−0.0393558
$650$			538048.i			1.27349i
$651$	25792.0	+	207568.i	0.0608589	+	0.489778i
$652$	344218.			0.809726
$653$		−	221333.i		−	0.519062i	−0.965735	−	0.259531i	$-0.916432\pi$
$653$		−	221333.i		−	0.519062i	0.965735	−	0.259531i	$-0.0835679\pi$
$654$	−420809.	+	52289.0i	−0.983853	+	0.122252i
$655$	10978.5			0.0255894
$656$			195628.i			0.454594i
$657$	659400.	−	166441.i	1.52763	−	0.385594i
$658$	−169094.			−0.390549
$659$			514765.i			1.18533i	0.805450	+	0.592664i	$0.201924\pi$
$659$			514765.i			1.18533i	−0.805450	+	0.592664i	$0.798076\pi$
$660$	1336.63	+	10756.9i	0.00306847	+	0.0246943i
$661$	483903.			1.10753			0.553765	−	0.832673i	$-0.313191\pi$
$661$	483903.			1.10753			0.553765	+	0.832673i	$0.313191\pi$
$662$		−	487014.i		−	1.11129i
$663$	−535197.	+	66502.6i	−1.21755	+	0.151290i
$664$	2585.52			0.00586424
$665$			38548.5i			0.0871695i
$666$	−165543.	−	655841.i	−0.373218	−	1.47860i
$667$	−891250.			−2.00331
$668$			385597.i			0.864133i
$669$	−5080.86	−	40889.6i	−0.0113523	−	0.0913610i
$670$	83244.9			0.185442
$671$			26420.6i			0.0586809i
$672$	406977.	−	50570.2i	0.901222	−	0.111984i
$673$	−321389.			−0.709580			−0.354790	−	0.934946i	$-0.615448\pi$
$673$	−321389.			−0.709580			−0.354790	+	0.934946i	$0.615448\pi$
$674$			105532.i			0.232309i
$675$	164145.	+	422110.i	0.360264	+	0.926443i
$676$	99837.6			0.218475
$677$		−	13310.7i		−	0.0290418i	−0.999895	−	0.0145209i	$-0.995378\pi$
$677$		−	13310.7i		−	0.0290418i	0.999895	−	0.0145209i	$-0.00462231\pi$
$678$	−60593.3	−	487641.i	−0.131815	−	1.06082i
$679$	−122145.			−0.264933
$680$			4590.58i			0.00992773i
$681$	−332928.	+	41369.0i	−0.717886	+	0.0892032i
$682$	−157125.			−0.337813
$683$			106249.i			0.227763i	0.993494	+	0.113881i	$0.0363284\pi$
$683$			106249.i			0.227763i	−0.993494	+	0.113881i	$0.963672\pi$
$684$	858403.	−	216672.i	1.83476	−	0.463118i
$685$	−5011.18			−0.0106797
$686$			685495.i			1.45665i
$687$	−17510.2	−	140918.i	−0.0371003	−	0.298575i
$688$	705587.			1.49064
$689$			800112.i			1.68544i
$690$	−66545.2	+	8268.78i	−0.139772	+	0.0173677i
$691$	239444.			0.501473			0.250737	−	0.968055i	$-0.419327\pi$
$691$	239444.			0.501473			0.250737	+	0.968055i	$0.419327\pi$
$692$		−	284478.i		−	0.594070i
$693$	22549.8	+	89336.7i	0.0469543	+	0.186022i
$694$	393863.			0.817760
$695$		−	34765.3i		−	0.0719742i
$696$	8807.46	+	70880.4i	0.0181816	+	0.146321i
$697$	−326504.			−0.672083
$698$			54627.0i			0.112123i
$699$	435063.	−	54060.1i	0.890427	−	0.110643i
$700$	329202.			0.671840
$701$			292642.i			0.595526i	0.954640	+	0.297763i	$0.0962404\pi$
$701$			292642.i			0.595526i	−0.954640	+	0.297763i	$0.903760\pi$
$702$	−588427.	+	228820.i	−1.19404	+	0.464323i
$703$	931925.			1.88569
$704$			168612.i			0.340207i
$705$	2028.70	+	16326.5i	0.00408168	+	0.0328485i
$706$	−907910.			−1.82152
$707$		−	288972.i		−	0.578119i
$708$	−68967.0	+	8569.71i	−0.137586	+	0.0170962i
$709$	116194.			0.231148			0.115574	−	0.993299i	$-0.463129\pi$
$709$	116194.			0.231148			0.115574	+	0.993299i	$0.463129\pi$
$710$		−	43194.0i		−	0.0856854i
$711$	−747458.	+	188669.i	−1.47859	+	0.373216i
$712$	−41165.0			−0.0812023
$713$		−	501297.i		−	0.986089i
$714$	78896.9	+	634944.i	0.154762	+	1.24549i
$715$	10650.0			0.0208324
$716$			384333.i			0.749691i
$717$	−757779.	+	94160.1i	−1.47402	+	0.183159i
$718$	−251133.			−0.487142
$719$		−	586921.i		−	1.13533i	−0.823260	−	0.567665i	$-0.807847\pi$
$719$		−	586921.i		−	1.13533i	0.823260	−	0.567665i	$-0.192153\pi$
$720$	−9128.49	−	36164.9i	−0.0176090	−	0.0697624i
$721$	254397.			0.489375
$722$			1.61605e6i			3.10013i
$723$	59798.7	+	481246.i	0.114397	+	0.920642i
$724$	469439.			0.895576
$725$		−	825451.i		−	1.57042i
$726$	682938.	−	84860.5i	1.29571	−	0.161002i
$727$	288584.			0.546014			0.273007	−	0.962012i	$-0.411982\pi$
$727$	288584.			0.546014			0.273007	+	0.962012i	$0.411982\pi$
$728$			27987.4i			0.0528080i
$729$	−391826.	+	359029.i	−0.737290	+	0.675576i
$730$	−93259.2			−0.175003
$731$			1.17763e6i			2.20380i
$732$	13658.7	+	109922.i	0.0254910	+	0.205146i
$733$	−907687.			−1.68938			−0.844692	−	0.535253i	$-0.820216\pi$
$733$	−907687.			−1.68938			−0.844692	+	0.535253i	$0.820216\pi$
$734$		−	1.20398e6i		−	2.23474i
$735$	24747.7	−	3075.10i	0.0458100	−	0.00569226i
$736$	−982888.			−1.81446
$737$			274133.i			0.504693i
$738$	−370601.	+	93544.6i	−0.680446	+	0.171754i
$739$	−476269.			−0.872094			−0.436047	−	0.899924i	$-0.643622\pi$
$739$	−476269.			−0.872094			−0.436047	+	0.899924i	$0.643622\pi$
$740$			47836.6i			0.0873569i
$741$	−107260.	−	863206.i	−0.195345	−	1.57209i
$742$	949233.			1.72411
$743$		−	141273.i		−	0.255906i	−0.991780	−	0.127953i	$-0.959159\pi$
$743$		−	141273.i		−	0.255906i	0.991780	−	0.127953i	$-0.0408407\pi$
$744$	−39867.7	+	4953.89i	−0.0720238	+	0.00894953i
$745$	61012.9			0.109928
$746$			70125.4i			0.126008i
$747$	−8580.96	−	33995.7i	−0.0153778	−	0.0609232i
$748$	−247878.			−0.443032
$749$			496345.i			0.884750i
$750$	−15362.7	−	123635.i	−0.0273114	−	0.219796i
$751$	−678092.			−1.20229			−0.601144	−	0.799141i	$-0.705288\pi$
$751$	−678092.			−1.20229			−0.601144	+	0.799141i	$0.705288\pi$
$752$			225418.i			0.398614i
$753$	687722.	−	85455.0i	1.21289	−	0.150712i
$754$	1.15069e6			2.02402
$755$			73290.3i			0.128574i
$756$	140002.	+	360025.i	0.244958	+	0.629926i
$757$	354843.			0.619219			0.309610	−	0.950864i	$-0.399802\pi$
$757$	354843.			0.619219			0.309610	+	0.950864i	$0.399802\pi$
$758$			338246.i			0.588700i
$759$	−27229.9	−	219140.i	−0.0472675	−	0.380398i
$760$	−7404.03			−0.0128186
$761$			242437.i			0.418629i	0.977848	+	0.209315i	$0.0671232\pi$
$761$			242437.i			0.418629i	−0.977848	+	0.209315i	$0.932877\pi$
$762$	734362.	−	91250.4i	1.26474	−	0.157154i
$763$	254913.			0.437868
$764$			601769.i			1.03096i
$765$	60359.2	−	15235.5i	0.103138	−	0.0260335i
$766$	552665.			0.941900
$767$			68282.1i			0.116069i
$768$	−62384.5	−	502056.i	−0.105768	−	0.851196i
$769$	766824.			1.29671			0.648355	−	0.761338i	$-0.275457\pi$
$769$	766824.			1.29671			0.648355	+	0.761338i	$0.275457\pi$
$770$		−	12634.9i		−	0.0213104i
$771$	298324.	−	37069.1i	0.501856	−	0.0623597i
$772$	−806524.			−1.35326
$773$			277865.i			0.465024i	0.972593	+	0.232512i	$0.0746945\pi$
$773$			277865.i			0.465024i	−0.972593	+	0.232512i	$0.925305\pi$
$774$	337395.	+	1.33667e6i	0.563192	+	2.23123i
$775$	464287.			0.773007
$776$		−	23460.4i		−	0.0389594i
$777$	50140.3	+	403518.i	0.0830511	+	0.668376i
$778$	1.08811e6			1.79768
$779$		−	526610.i		−	0.867790i
$780$	44309.2	−	5505.78i	0.0728291	−	0.00904960i
$781$	142242.			0.233199
$782$		−	1.53345e6i		−	2.50759i
$783$	902740.	−	351047.i	1.47245	−	0.572587i
$784$	341688.			0.555902
$785$			49847.9i			0.0808923i
$786$	36240.6	+	291656.i	0.0586611	+	0.472091i
$787$	32094.9			0.0518187			0.0259093	−	0.999664i	$-0.491752\pi$
$787$	32094.9			0.0518187			0.0259093	+	0.999664i	$0.491752\pi$
$788$		−	196180.i		−	0.315939i
$789$	−775760.	+	96394.4i	−1.24616	+	0.154845i
$790$	105713.			0.169385
$791$			295397.i			0.472121i
$792$	−17158.9	+	4331.14i	−0.0273552	+	0.00690482i
$793$	108831.			0.173063
$794$		−	84307.8i		−	0.133729i
$795$	−11388.4	−	91651.3i	−0.0180189	−	0.145012i
$796$	−1.05385e6			−1.66324
$797$		−	391192.i		−	0.615848i	−0.951411	−	0.307924i	$-0.900366\pi$
$797$		−	391192.i		−	0.615848i	0.951411	−	0.307924i	$-0.0996342\pi$
$798$	−1.02409e6	+	127251.i	−1.60816	+	0.199827i
$799$	−376223.			−0.589321
$800$		−	910324.i		−	1.42238i
$801$	136621.	+	541258.i	0.212937	+	0.843605i
$802$	480756.			0.747440
$803$		−	307112.i		−	0.476283i
$804$	141720.	+	1.14053e6i	0.219239	+	1.76438i
$805$	40311.0			0.0622059
$806$			647222.i			0.996284i
$807$	797289.	−	99069.5i	1.22425	−	0.152122i
$808$	55503.0			0.0850147
$809$			664544.i			1.01538i	0.861541	+	0.507688i	$0.169500\pi$
$809$			664544.i			1.01538i	−0.861541	+	0.507688i	$0.830500\pi$
$810$	64146.2	−	34586.3i	0.0977689	−	0.0527150i
$811$	113644.			0.172785			0.0863925	−	0.996261i	$-0.472466\pi$
$811$	113644.			0.172785			0.0863925	+	0.996261i	$0.472466\pi$
$812$		−	704042.i		−	1.06779i
$813$	−125902.	−	1.01323e6i	−0.190482	−	1.53295i
$814$	−305454.			−0.460996
$815$			39037.9i			0.0587721i
$816$	846442.	−	105177.i	1.27121	−	0.157958i
$817$	−1.89937e6			−2.84554
$818$		−	502067.i		−	0.750335i
$819$	367992.	−	92886.1i	0.548619	−	0.138479i
$820$	27031.4			0.0402014
$821$		−	142654.i		−	0.211639i	−0.994385	−	0.105820i	$-0.966253\pi$
$821$		−	142654.i		−	0.211639i	0.994385	−	0.105820i	$-0.0337467\pi$
$822$	−16542.2	−	133128.i	−0.0244821	−	0.197026i
$823$	−542479.			−0.800909			−0.400454	−	0.916317i	$-0.631148\pi$
$823$	−542479.			−0.800909			−0.400454	+	0.916317i	$0.631148\pi$
$824$			48862.1i			0.0719645i
$825$	202961.	−	25219.6i	0.298198	−	0.0370536i
$826$	81008.2			0.118732
$827$		−	1.06740e6i		−	1.56069i	−0.625350	−	0.780344i	$-0.715044\pi$
$827$		−	1.06740e6i		−	1.56069i	0.625350	−	0.780344i	$-0.284956\pi$
$828$	−226579.	−	897649.i	−0.330490	−	1.30932i
$829$	251080.			0.365345			0.182672	−	0.983174i	$-0.441525\pi$
$829$	251080.			0.365345			0.182672	+	0.983174i	$0.441525\pi$
$830$			4808.03i			0.00697928i
$831$	64267.2	+	517208.i	0.0930652	+	0.748967i
$832$	694540.			1.00335
$833$			570279.i			0.821859i
$834$	923581.	−	114762.i	1.32783	−	0.164994i
$835$	−43730.7			−0.0627211
$836$		−	399796.i		−	0.572040i
$837$	197451.	+	507760.i	0.281844	+	0.724782i
$838$	−1.44867e6			−2.06291
$839$		−	649983.i		−	0.923375i	−0.887043	−	0.461687i	$-0.847244\pi$
$839$		−	649983.i		−	0.923375i	0.887043	−	0.461687i	$-0.152756\pi$
$840$	−398.359	−	3205.90i	−0.000564568	−	0.00454351i
$841$	−1.05806e6			−1.49595
$842$			354390.i			0.499870i
$843$	145380.	−	18064.6i	0.204574	−	0.0254199i
$844$	258751.			0.363243
$845$			11322.6i			0.0158575i
$846$	−427035.	+	107789.i	−0.596655	+	0.150604i
$847$	−413702.			−0.576661
$848$		−	1.26542e6i		−	1.75972i
$849$	−131419.	−	1.05763e6i	−0.182323	−	1.46729i
$850$	1.42024e6			1.96573
$851$		−	974533.i		−	1.34567i
$852$	591795.	−	73535.3i	0.815252	−	0.101302i
$853$	−487566.			−0.670093			−0.335047	−	0.942202i	$-0.608752\pi$
$853$	−487566.			−0.670093			−0.335047	+	0.942202i	$0.608752\pi$
$854$		−	129114.i		−	0.177034i
$855$	24572.9	+	97351.9i	0.0336143	+	0.133172i
$856$	−95333.3			−0.130106
$857$		−	354580.i		−	0.482784i	−0.970428	−	0.241392i	$-0.922396\pi$
$857$		−	354580.i		−	0.482784i	0.970428	−	0.241392i	$-0.0776039\pi$
$858$	35156.4	+	282930.i	0.0477562	+	0.384331i
$859$	588729.			0.797865			0.398932	−	0.916980i	$-0.369381\pi$
$859$	588729.			0.797865			0.398932	+	0.916980i	$0.369381\pi$
$860$		−	97496.3i		−	0.131823i
$861$	228019.	−	28333.2i	0.307585	−	0.0382199i
$862$	−1.60045e6			−2.15391
$863$		−	839061.i		−	1.12661i	−0.826251	−	0.563303i	$-0.809531\pi$
$863$		−	839061.i		−	1.12661i	0.826251	−	0.563303i	$-0.190469\pi$
$864$	995560.	−	387141.i	1.33364	−	0.518611i
$865$	32262.8			0.0431192
$866$		−	1.19612e6i		−	1.59492i
$867$	82850.4	+	666761.i	0.110219	+	0.887017i
$868$	395999.			0.525599
$869$			348125.i			0.460994i
$870$	−131809.	+	16378.3i	−0.174143	+	0.0216387i
$871$	1.12920e6			1.48845
$872$			48961.3i			0.0643902i
$873$	−308470.	+	77861.8i	−0.404747	+	0.102164i
$874$	2.47326e6			3.23778
$875$			74894.3i			0.0978211i
$876$	−158768.	−	1.27773e6i	−0.206898	−	1.66506i
$877$	−366896.			−0.477028			−0.238514	−	0.971139i	$-0.576660\pi$
$877$	−366896.			−0.477028			−0.238514	+	0.971139i	$0.576660\pi$
$878$			633782.i			0.822149i
$879$	−1.31215e6	+	163045.i	−1.69827	+	0.211024i
$880$	−16843.6			−0.0217505
$881$			866863.i			1.11686i	0.829552	+	0.558430i	$0.188596\pi$
$881$			866863.i			1.11686i	−0.829552	+	0.558430i	$0.811404\pi$
$882$	163387.	+	647300.i	0.210030	+	0.832086i
$883$	−271282.			−0.347937			−0.173968	−	0.984751i	$-0.555659\pi$
$883$	−271282.			−0.347937			−0.173968	+	0.984751i	$0.555659\pi$
$884$			1.02105e6i			1.30660i
$885$	−971.895	−	7821.59i	−0.00124089	−	0.00998638i
$886$	−1.38289e6			−1.76165
$887$		−	1.54470e6i		−	1.96335i	−0.190574	−	0.981673i	$-0.561035\pi$
$887$		−	1.54470e6i		−	1.96335i	0.190574	−	0.981673i	$-0.438965\pi$
$888$	−77503.8	+	9630.47i	−0.0982873	+	0.0122130i
$889$	−444853.			−0.562877
$890$		−	76550.4i		−	0.0966423i
$891$	113896.	+	211240.i	0.143467	+	0.266085i
$892$	−78009.2			−0.0980429
$893$		−	606801.i		−	0.760928i
$894$	201407.	+	1.62088e6i	0.251999	+	2.02803i
$895$	−43587.4			−0.0544146
$896$		−	94904.4i		−	0.118214i
$897$	−902672.	+	112164.i	−1.12188	+	0.139402i
$898$	−1.72616e6			−2.14057
$899$		−	992941.i		−	1.22858i
$900$	831378.	−	209851.i	1.02639	−	0.259075i
$901$	2.11199e6			2.60161
$902$			172605.i			0.212149i
$903$	−102191.	−	822413.i	−0.125325	−	1.00859i
$904$	−56737.1			−0.0694272
$905$			53239.4i			0.0650033i
$906$	−1.94704e6	+	241935.i	−2.37202	+	0.294743i
$907$	554942.			0.674580			0.337290	−	0.941401i	$-0.390490\pi$
$907$	554942.			0.674580			0.337290	+	0.941401i	$0.390490\pi$
$908$			635160.i			0.770391i
$909$	−184207.	−	729782.i	−0.222935	−	0.883212i
$910$	−52045.3			−0.0628490
$911$			677023.i			0.815768i	0.913034	+	0.407884i	$0.133733\pi$
$911$			677023.i			0.815768i	−0.913034	+	0.407884i	$0.866267\pi$
$912$	169638.	+	1.36520e6i	0.203954	+	1.64138i
$913$	−15833.3			−0.0189946
$914$		−	1.12869e6i		−	1.35108i
$915$	−12466.3	+	1549.04i	−0.0148901	+	0.00185021i
$916$	−268843.			−0.320412
$917$		−	176676.i		−	0.210106i
$918$	603997.	+	1.55322e6i	0.716720	+	1.84309i
$919$	−263620.			−0.312139			−0.156069	−	0.987746i	$-0.549882\pi$
$919$	−263620.			−0.312139			−0.156069	+	0.987746i	$0.549882\pi$
$920$			7742.55i			0.00914762i
$921$	−8453.52	−	68031.9i	−0.00996594	−	0.0802036i
$922$	−1.36215e6			−1.60237
$923$		−	585918.i		−	0.687754i
$924$	173109.	−	21510.2i	0.202757	−	0.0251942i
$925$	902586.			1.05488
$926$			528209.i			0.616005i
$927$	642464.	−	162166.i	0.747634	−	0.188713i
$928$	−1.94685e6			−2.26067
$929$			160769.i			0.186282i	0.995653	+	0.0931408i	$0.0296907\pi$
$929$			160769.i			0.186282i	−0.995653	+	0.0931408i	$0.970309\pi$
$930$	−9212.24	−	74138.0i	−0.0106512	−	0.0857186i
$931$	−919789.			−1.06118
$932$		−	830014.i		−	0.955550i
$933$	693827.	−	86213.6i	0.797054	−	0.0990404i
$934$	882204.			1.01129
$935$		−	28112.0i		−	0.0321564i
$936$	17840.7	+	70680.4i	0.0203638	+	0.0806765i
$937$	−1.70649e6			−1.94368			−0.971839	−	0.235644i	$-0.924280\pi$
$937$	−1.70649e6			−1.94368			−0.971839	+	0.235644i	$0.924280\pi$
$938$		−	1.33965e6i		−	1.52260i
$939$	5094.31	+	40997.8i	0.00577768	+	0.0464975i
$940$	31147.7			0.0352509
$941$			394940.i			0.446018i	0.974816	+	0.223009i	$0.0715879\pi$
$941$			394940.i			0.446018i	−0.974816	+	0.223009i	$0.928412\pi$
$942$	−1.32427e6	+	164551.i	−1.49236	+	0.185438i
$943$	−550687.			−0.619272
$944$		−	107992.i		−	0.121184i
$945$	−40830.7	+	15877.7i	−0.0457218	+	0.0177797i
$946$	622549.			0.695651
$947$			558825.i			0.623126i	0.950226	+	0.311563i	$0.100852\pi$
$947$			558825.i			0.623126i	−0.950226	+	0.311563i	$0.899148\pi$
$948$	179971.	+	1.44836e6i	0.200256	+	1.61161i
$949$	−1.26504e6			−1.40466
$950$			2.29067e6i			2.53814i
$951$	−113580.	+	14113.2i	−0.125586	+	0.0156050i
$952$	73875.9			0.0815133
$953$			460301.i			0.506823i	0.967359	+	0.253412i	$0.0815527\pi$
$953$			460301.i			0.506823i	−0.967359	+	0.253412i	$0.918447\pi$
$954$	2.39723e6	−	605092.i	2.63398	−	0.664852i
$955$	−68247.0			−0.0748301
$956$			1.44569e6i			1.58183i
$957$	−53935.5	−	434060.i	−0.0588912	−	0.473943i
$958$	−515246.			−0.561415
$959$			80644.5i			0.0876874i
$960$	−79558.2	+	9885.74i	−0.0863261	+	0.0107267i
$961$	−365026.			−0.395255
$962$			1.25821e6i			1.35958i
$963$	316397.	+	1.25349e6i	0.341177	+	1.35166i
$964$	918122.			0.987975
$965$		−	91468.2i		−	0.0982236i
$966$	133069.	+	1.07091e6i	0.142601	+	1.14762i
$967$	789597.			0.844408			0.422204	−	0.906501i	$-0.361257\pi$
$967$	789597.			0.844408			0.422204	+	0.906501i	$0.361257\pi$
$968$		−	79459.9i		−	0.0848003i
$969$	−2.27853e6	+	283126.i	−2.42665	+	0.301531i
$970$	43627.0			0.0463673
$971$		−	1.38642e6i		−	1.47047i	−0.677815	−	0.735233i	$-0.737073\pi$
$971$		−	1.38642e6i		−	1.47047i	0.677815	−	0.735233i	$-0.262927\pi$
$972$	583067.	+	819977.i	0.617143	+	0.867898i
$973$	−559476.			−0.590957
$974$			255706.i			0.269540i
$975$	−103883.	−	836030.i	−0.109279	−	0.879453i
$976$	−172121.			−0.180690
$977$		−	1.02010e6i		−	1.06870i	−0.845264	−	0.534348i	$-0.820557\pi$
$977$		−	1.02010e6i		−	1.06870i	0.845264	−	0.534348i	$-0.179443\pi$
$978$	−1.03709e6	+	128866.i	−1.08427	+	0.134729i
$979$	252088.			0.263019
$980$		−	47213.6i		−	0.0491604i
$981$	643767.	−	162495.i	0.668945	−	0.168851i
$982$	−2.32424e6			−2.41022
$983$		−	319388.i		−	0.330530i	−0.986249	−	0.165265i	$-0.947152\pi$
$983$		−	319388.i		−	0.330530i	0.986249	−	0.165265i	$-0.0528479\pi$
$984$	5441.97	+	43795.7i	0.00562038	+	0.0452315i
$985$	22248.9			0.0229317
$986$		−	3.03737e6i		−	3.12424i
$987$	262741.	−	32647.7i	0.269708	−	0.0335134i
$988$	−1.64682e6			−1.68707
$989$			1.98620e6i			2.03063i
$990$	−8054.19	−	31908.7i	−0.00821772	−	0.0325566i
$991$	−1.62654e6			−1.65621			−0.828107	−	0.560571i	$-0.810582\pi$
$991$	−1.62654e6			−1.65621			−0.828107	+	0.560571i	$0.810582\pi$
$992$		−	1.09504e6i		−	1.11277i
$993$	94030.1	+	756733.i	0.0953605	+	0.767439i
$994$	−695118.			−0.703535
$995$		−	119518.i		−	0.120722i
$996$	−65874.1	+	8185.38i	−0.0664042	+	0.00825126i
$997$	−393492.			−0.395864			−0.197932	−	0.980216i	$-0.563423\pi$
$997$	−393492.			−0.395864			−0.197932	+	0.980216i	$0.563423\pi$
$998$			1.07723e6i			1.08155i
$999$	383850.	+	987097.i	0.384619	+	0.989074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.66	yes	78
3.2	odd	2	inner	177.5.b.a.119.13	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.13	✓	78	3.2	odd	2	inner
177.5.b.a.119.66	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)

\(f(q)\)	\(=\)	\(q+5.74797i q^{2} +(-1.10979 - 8.93131i) q^{3} -17.0392 q^{4} -1.93242i q^{5} +(51.3369 - 6.37903i) q^{6} -31.0983 q^{7} -5.97306i q^{8} +(-78.5367 + 19.8237i) q^{9} +O(q^{10})\)	\(q+5.74797i q^{2} +(-1.10979 - 8.93131i) q^{3} -17.0392 q^{4} -1.93242i q^{5} +(51.3369 - 6.37903i) q^{6} -31.0983 q^{7} -5.97306i q^{8} +(-78.5367 + 19.8237i) q^{9} +11.1075 q^{10} +36.5780i q^{11} +(18.9098 + 152.182i) q^{12} +150.671 q^{13} -178.752i q^{14} +(-17.2590 + 2.14458i) q^{15} -238.294 q^{16} -397.713i q^{17} +(-113.946 - 451.427i) q^{18} +641.461 q^{19} +32.9268i q^{20} +(34.5125 + 277.749i) q^{21} -210.249 q^{22} -670.788i q^{23} +(-53.3473 + 6.62883i) q^{24} +621.266 q^{25} +866.051i q^{26} +(264.211 + 679.436i) q^{27} +529.889 q^{28} -1328.66i q^{29} +(-12.3270 - 99.2045i) q^{30} +747.325 q^{31} -1465.27i q^{32} +(326.690 - 40.5939i) q^{33} +2286.04 q^{34} +60.0949i q^{35} +(1338.20 - 337.780i) q^{36} +1452.82 q^{37} +3687.10i q^{38} +(-167.213 - 1345.69i) q^{39} -11.5425 q^{40} -820.955i q^{41} +(-1596.49 + 198.377i) q^{42} -2961.00 q^{43} -623.259i q^{44} +(38.3078 + 151.766i) q^{45} +3855.67 q^{46} -945.968i q^{47} +(264.455 + 2128.27i) q^{48} -1433.90 q^{49} +3571.02i q^{50} +(-3552.10 + 441.376i) q^{51} -2567.30 q^{52} +5310.33i q^{53} +(-3905.38 + 1518.68i) q^{54} +70.6841 q^{55} +185.752i q^{56} +(-711.885 - 5729.09i) q^{57} +7637.10 q^{58} +453.188i q^{59} +(294.080 - 36.5418i) q^{60} +722.307 q^{61} +4295.60i q^{62} +(2442.36 - 616.484i) q^{63} +4609.65 q^{64} -291.159i q^{65} +(233.332 + 1877.80i) q^{66} +7494.48 q^{67} +6776.69i q^{68} +(-5991.02 + 744.433i) q^{69} -345.424 q^{70} -3888.73i q^{71} +(118.408 + 469.105i) q^{72} -8396.06 q^{73} +8350.75i q^{74} +(-689.473 - 5548.72i) q^{75} -10930.0 q^{76} -1137.51i q^{77} +(7734.98 - 961.133i) q^{78} +9517.31 q^{79} +460.483i q^{80} +(5775.04 - 3113.78i) q^{81} +4718.82 q^{82} +432.863i q^{83} +(-588.064 - 4732.60i) q^{84} -768.548 q^{85} -17019.7i q^{86} +(-11866.7 + 1474.53i) q^{87} +218.483 q^{88} -6891.78i q^{89} +(-872.346 + 220.192i) q^{90} -4685.60 q^{91} +11429.7i q^{92} +(-829.372 - 6674.59i) q^{93} +5437.39 q^{94} -1239.57i q^{95} +(-13086.8 + 1626.14i) q^{96} +3927.71 q^{97} -8242.00i q^{98} +(-725.113 - 2872.72i) 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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