LMFDB - Embedded newform 177.5.b.a.119.62

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			119.62
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.25412i q^{2} +(4.74448 + 7.64787i) q^{3} -11.6058 q^{4} +7.04330i q^{5} +(-40.1829 + 24.9281i) q^{6} +35.8552 q^{7} +23.0875i q^{8} +(-35.9798 + 72.5703i) q^{9} +O(q^{10})$	\(q+5.25412i q^{2} +(4.74448 + 7.64787i) q^{3} -11.6058 q^{4} +7.04330i q^{5} +(-40.1829 + 24.9281i) q^{6} +35.8552 q^{7} +23.0875i q^{8} +(-35.9798 + 72.5703i) q^{9} -37.0064 q^{10} +53.7614i q^{11} +(-55.0636 - 88.7598i) q^{12} +72.1398 q^{13} +188.388i q^{14} +(-53.8662 + 33.4168i) q^{15} -306.998 q^{16} +83.3038i q^{17} +(-381.294 - 189.042i) q^{18} -387.051 q^{19} -81.7433i q^{20} +(170.114 + 274.216i) q^{21} -282.469 q^{22} -137.560i q^{23} +(-176.570 + 109.538i) q^{24} +575.392 q^{25} +379.032i q^{26} +(-725.714 + 69.1399i) q^{27} -416.129 q^{28} -105.343i q^{29} +(-175.576 - 283.020i) q^{30} -942.385 q^{31} -1243.61i q^{32} +(-411.160 + 255.070i) q^{33} -437.689 q^{34} +252.539i q^{35} +(417.575 - 842.239i) q^{36} +2041.28 q^{37} -2033.61i q^{38} +(342.266 + 551.716i) q^{39} -162.612 q^{40} +119.053i q^{41} +(-1440.76 + 893.802i) q^{42} +3203.63 q^{43} -623.946i q^{44} +(-511.134 - 253.416i) q^{45} +722.756 q^{46} -1973.51i q^{47} +(-1456.55 - 2347.88i) q^{48} -1115.41 q^{49} +3023.18i q^{50} +(-637.097 + 395.233i) q^{51} -837.242 q^{52} -1181.07i q^{53} +(-363.269 - 3812.99i) q^{54} -378.658 q^{55} +827.808i q^{56} +(-1836.36 - 2960.11i) q^{57} +553.483 q^{58} +453.188i q^{59} +(625.162 - 387.829i) q^{60} -3111.42 q^{61} -4951.41i q^{62} +(-1290.06 + 2602.02i) q^{63} +1622.09 q^{64} +508.102i q^{65} +(-1340.17 - 2160.29i) q^{66} +4166.52 q^{67} -966.810i q^{68} +(1052.04 - 652.650i) q^{69} -1326.87 q^{70} +1448.75i q^{71} +(-1675.47 - 830.685i) q^{72} -2159.42 q^{73} +10725.2i q^{74} +(2729.94 + 4400.52i) q^{75} +4492.04 q^{76} +1927.63i q^{77} +(-2898.78 + 1798.31i) q^{78} +2141.63 q^{79} -2162.28i q^{80} +(-3971.91 - 5222.13i) q^{81} -625.522 q^{82} +4416.32i q^{83} +(-1974.32 - 3182.50i) q^{84} -586.733 q^{85} +16832.3i q^{86} +(805.646 - 499.796i) q^{87} -1241.22 q^{88} +13821.0i q^{89} +(1331.48 - 2685.56i) q^{90} +2586.59 q^{91} +1596.50i q^{92} +(-4471.13 - 7207.24i) q^{93} +10369.1 q^{94} -2726.11i q^{95} +(9510.93 - 5900.26i) q^{96} +10753.5 q^{97} -5860.48i q^{98} +(-3901.48 - 1934.32i) 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 $

$2$			5.25412i			1.31353i	0.754095	+	0.656766i	$0.228076\pi$
$2$			5.25412i			1.31353i	−0.754095	+	0.656766i	$0.771924\pi$
$3$	4.74448	+	7.64787i	0.527165	+	0.849763i
$3$	4.74448	+	7.64787i	0.527165	+	0.849763i
$4$	−11.6058			−0.725364
$5$			7.04330i			0.281732i	0.990029	+	0.140866i	$0.0449886\pi$
$5$			7.04330i			0.281732i	−0.990029	+	0.140866i	$0.955011\pi$
$6$	−40.1829	+	24.9281i	−1.11619	+	0.692447i
$7$	35.8552			0.731738			0.365869	−	0.930666i	$-0.380772\pi$
$7$	35.8552			0.731738			0.365869	+	0.930666i	$0.380772\pi$
$8$			23.0875i			0.360743i
$9$	−35.9798	+	72.5703i	−0.444195	+	0.895930i
$10$	−37.0064			−0.370064
$11$			53.7614i			0.444309i	0.975011	+	0.222155i	$0.0713090\pi$
$11$			53.7614i			0.444309i	−0.975011	+	0.222155i	$0.928691\pi$
$12$	−55.0636	−	88.7598i	−0.382386	−	0.616388i
$13$	72.1398			0.426863			0.213431	−	0.976958i	$-0.431536\pi$
$13$	72.1398			0.426863			0.213431	+	0.976958i	$0.431536\pi$
$14$			188.388i			0.961161i
$15$	−53.8662	+	33.4168i	−0.239405	+	0.148519i
$16$	−306.998			−1.19921
$17$			83.3038i			0.288248i	0.989560	+	0.144124i	$0.0460365\pi$
$17$			83.3038i			0.288248i	−0.989560	+	0.144124i	$0.953964\pi$
$18$	−381.294	−	189.042i	−1.17683	−	0.583464i
$19$	−387.051			−1.07216			−0.536081	−	0.844166i	$-0.680096\pi$
$19$	−387.051			−1.07216			−0.536081	+	0.844166i	$0.680096\pi$
$20$		−	81.7433i		−	0.204358i
$21$	170.114	+	274.216i	0.385747	+	0.621804i
$22$	−282.469			−0.583614
$23$		−	137.560i		−	0.260037i	−0.991512	−	0.130019i	$-0.958496\pi$
$23$		−	137.560i		−	0.260037i	0.991512	−	0.130019i	$-0.0415037\pi$
$24$	−176.570	+	109.538i	−0.306546	+	0.190171i
$25$	575.392			0.920627
$26$			379.032i			0.560698i
$27$	−725.714	+	69.1399i	−0.995492	+	0.0948421i
$28$	−416.129			−0.530777
$29$		−	105.343i		−	0.125259i	−0.998037	−	0.0626293i	$-0.980051\pi$
$29$		−	105.343i		−	0.125259i	0.998037	−	0.0626293i	$-0.0199486\pi$
$30$	−175.576	−	283.020i	−0.195084	−	0.314466i
$31$	−942.385			−0.980630			−0.490315	−	0.871545i	$-0.663118\pi$
$31$	−942.385			−0.980630			−0.490315	+	0.871545i	$0.663118\pi$
$32$		−	1243.61i		−	1.21446i
$33$	−411.160	+	255.070i	−0.377558	+	0.234224i
$34$	−437.689			−0.378623
$35$			252.539i			0.206154i
$36$	417.575	−	842.239i	0.322203	−	0.649876i
$37$	2041.28			1.49108			0.745538	−	0.666463i	$-0.232193\pi$
$37$	2041.28			1.49108			0.745538	+	0.666463i	$0.232193\pi$
$38$		−	2033.61i		−	1.40832i
$39$	342.266	+	551.716i	0.225027	+	0.362732i
$40$	−162.612			−0.101633
$41$			119.053i			0.0708230i	0.999373	+	0.0354115i	$0.0112742\pi$
$41$			119.053i			0.0708230i	−0.999373	+	0.0354115i	$0.988726\pi$
$42$	−1440.76	+	893.802i	−0.816760	+	0.506690i
$43$	3203.63			1.73263			0.866315	−	0.499498i	$-0.166482\pi$
$43$	3203.63			1.73263			0.866315	+	0.499498i	$0.166482\pi$
$44$		−	623.946i		−	0.322286i
$45$	−511.134	−	253.416i	−0.252412	−	0.125144i
$46$	722.756			0.341567
$47$		−	1973.51i		−	0.893396i	−0.894685	−	0.446698i	$-0.852600\pi$
$47$		−	1973.51i		−	0.893396i	0.894685	−	0.446698i	$-0.147400\pi$
$48$	−1456.55	−	2347.88i	−0.632182	−	1.01905i
$49$	−1115.41			−0.464559
$50$			3023.18i			1.20927i
$51$	−637.097	+	395.233i	−0.244943	+	0.151954i
$52$	−837.242			−0.309631
$53$		−	1181.07i		−	0.420461i	−0.977652	−	0.210230i	$-0.932579\pi$
$53$		−	1181.07i		−	0.420461i	0.977652	−	0.210230i	$-0.0674214\pi$
$54$	−363.269	−	3812.99i	−0.124578	−	1.30761i
$55$	−378.658			−0.125176
$56$			827.808i			0.263969i
$57$	−1836.36	−	2960.11i	−0.565206	−	0.911085i
$58$	553.483			0.164531
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	625.162	−	387.829i	0.173656	−	0.107730i
$61$	−3111.42			−0.836179			−0.418090	−	0.908406i	$-0.637300\pi$
$61$	−3111.42			−0.836179			−0.418090	+	0.908406i	$0.637300\pi$
$62$		−	4951.41i		−	1.28809i
$63$	−1290.06	+	2602.02i	−0.325035	+	0.655587i
$64$	1622.09			0.396018
$65$			508.102i			0.120261i
$66$	−1340.17	−	2160.29i	−0.307661	−	0.495934i
$67$	4166.52			0.928162			0.464081	−	0.885793i	$-0.346385\pi$
$67$	4166.52			0.928162			0.464081	+	0.885793i	$0.346385\pi$
$68$		−	966.810i		−	0.209085i
$69$	1052.04	−	652.650i	0.220970	−	0.137083i
$70$	−1326.87			−0.270790
$71$			1448.75i			0.287393i	0.989622	+	0.143696i	$0.0458989\pi$
$71$			1448.75i			0.287393i	−0.989622	+	0.143696i	$0.954101\pi$
$72$	−1675.47	−	830.685i	−0.323200	−	0.160240i
$73$	−2159.42			−0.405220			−0.202610	−	0.979260i	$-0.564942\pi$
$73$	−2159.42			−0.405220			−0.202610	+	0.979260i	$0.564942\pi$
$74$			10725.2i			1.95858i
$75$	2729.94	+	4400.52i	0.485322	+	0.782315i
$76$	4492.04			0.777709
$77$			1927.63i			0.325118i
$78$	−2898.78	+	1798.31i	−0.476460	+	0.295580i
$79$	2141.63			0.343155			0.171578	−	0.985171i	$-0.445114\pi$
$79$	2141.63			0.343155			0.171578	+	0.985171i	$0.445114\pi$
$80$		−	2162.28i		−	0.337856i
$81$	−3971.91	−	5222.13i	−0.605382	−	0.795935i
$82$	−625.522			−0.0930282
$83$			4416.32i			0.641068i	0.947237	+	0.320534i	$0.103862\pi$
$83$			4416.32i			0.641068i	−0.947237	+	0.320534i	$0.896138\pi$
$84$	−1974.32	−	3182.50i	−0.279807	−	0.451035i
$85$	−586.733			−0.0812088
$86$			16832.3i			2.27586i
$87$	805.646	−	499.796i	0.106440	−	0.0660319i
$88$	−1241.22			−0.160281
$89$			13821.0i			1.74485i	0.488749	+	0.872425i	$0.337453\pi$
$89$			13821.0i			1.74485i	−0.488749	+	0.872425i	$0.662547\pi$
$90$	1331.48	−	2685.56i	0.164380	−	0.331551i
$91$	2586.59			0.312352
$92$			1596.50i			0.188622i
$93$	−4471.13	−	7207.24i	−0.516953	−	0.833303i
$94$	10369.1			1.17350
$95$		−	2726.11i		−	0.302062i
$96$	9510.93	−	5900.26i	1.03200	−	0.640219i
$97$	10753.5			1.14290			0.571448	−	0.820638i	$-0.306382\pi$
$97$	10753.5			1.14290			0.571448	+	0.820638i	$0.306382\pi$
$98$		−	5860.48i		−	0.610212i
$99$	−3901.48	−	1934.32i	−0.398070	−	0.197360i
$100$	−6677.90			−0.667790
$101$			6746.90i			0.661396i	0.943737	+	0.330698i	$0.107284\pi$
$101$			6746.90i			0.661396i	−0.943737	+	0.330698i	$0.892716\pi$
$102$	−2076.61	−	3347.38i	−0.199597	−	0.321740i
$103$	4079.24			0.384508			0.192254	−	0.981345i	$-0.438420\pi$
$103$	4079.24			0.384508			0.192254	+	0.981345i	$0.438420\pi$
$104$			1665.53i			0.153988i
$105$	−1931.38	+	1198.16i	−0.175182	+	0.108677i
$106$	6205.51			0.552288
$107$			10692.5i			0.933926i	0.884277	+	0.466963i	$0.154652\pi$
$107$			10692.5i			0.933926i	−0.884277	+	0.466963i	$0.845348\pi$
$108$	8422.51	−	802.425i	0.722095	−	0.0687950i
$109$	−3718.61			−0.312988			−0.156494	−	0.987679i	$-0.550019\pi$
$109$	−3718.61			−0.312988			−0.156494	+	0.987679i	$0.550019\pi$
$110$		−	1989.51i		−	0.164423i
$111$	9684.83	+	15611.5i	0.786043	+	1.26706i
$112$	−11007.5			−0.877509
$113$			12359.6i			0.967936i	0.875086	+	0.483968i	$0.160805\pi$
$113$			12359.6i			0.967936i	−0.875086	+	0.483968i	$0.839195\pi$
$114$	15552.8	−	9648.44i	1.19674	−	0.742416i
$115$	968.874			0.0732608
$116$			1222.59i			0.0908582i
$117$	−2595.58	+	5235.21i	−0.189610	+	0.382439i
$118$	−2381.10			−0.171007
$119$			2986.87i			0.210922i
$120$	−771.511	−	1243.64i	−0.0535772	−	0.0863637i
$121$	11750.7			0.802589
$122$		−	16347.8i		−	1.09835i
$123$	−910.505	+	564.847i	−0.0601828	+	0.0373354i
$124$	10937.2			0.711314
$125$			8454.72i			0.541102i
$126$	−13671.4	−	6778.15i	−0.861133	−	0.426943i
$127$	6349.54			0.393672			0.196836	−	0.980436i	$-0.436933\pi$
$127$	6349.54			0.393672			0.196836	+	0.980436i	$0.436933\pi$
$128$		−	11375.0i		−	0.694276i
$129$	15199.6	+	24501.0i	0.913381	+	1.47233i
$130$	−2669.63			−0.157966
$131$			14041.4i			0.818216i	0.912486	+	0.409108i	$0.134160\pi$
$131$			14041.4i			0.818216i	−0.912486	+	0.409108i	$0.865840\pi$
$132$	4771.86	−	2960.30i	0.273867	−	0.169898i
$133$	−13877.8			−0.784543
$134$			21891.4i			1.21917i
$135$	−486.972	−	5111.42i	−0.0267200	−	0.280462i
$136$	−1923.28			−0.103984
$137$		−	13528.0i		−	0.720765i	−0.932805	−	0.360383i	$-0.882646\pi$
$137$		−	13528.0i		−	0.720765i	0.932805	−	0.360383i	$-0.117354\pi$
$138$	3429.10	+	5527.55i	0.180062	+	0.290251i
$139$	2624.62			0.135843			0.0679214	−	0.997691i	$-0.478363\pi$
$139$	2624.62			0.135843			0.0679214	+	0.997691i	$0.478363\pi$
$140$		−	2930.92i		−	0.149537i
$141$	15093.2	−	9363.29i	0.759175	−	0.470967i
$142$	−7611.89			−0.377499
$143$			3878.34i			0.189659i
$144$	11045.7	−	22279.0i	0.532684	−	1.07441i
$145$	741.959			0.0352894
$146$		−	11345.8i		−	0.532269i
$147$	−5292.02	−	8530.48i	−0.244899	−	0.394765i
$148$	−23690.8			−1.08157
$149$		−	27527.8i		−	1.23994i	−0.784627	−	0.619968i	$-0.787146\pi$
$149$		−	27527.8i		−	1.23994i	0.784627	−	0.619968i	$-0.212854\pi$
$150$	−23120.9	+	14343.4i	−1.02760	+	0.637486i
$151$	−17919.6			−0.785915			−0.392958	−	0.919557i	$-0.628548\pi$
$151$	−17919.6			−0.785915			−0.392958	+	0.919557i	$0.628548\pi$
$152$		−	8936.05i		−	0.386775i
$153$	−6045.39	−	2997.25i	−0.258250	−	0.128039i
$154$	−10128.0			−0.427053
$155$		−	6637.50i		−	0.276275i
$156$	−3972.28	−	6403.12i	−0.163227	−	0.263113i
$157$	−18785.5			−0.762118			−0.381059	−	0.924551i	$-0.624441\pi$
$157$	−18785.5			−0.762118			−0.381059	+	0.924551i	$0.624441\pi$
$158$			11252.4i			0.450745i
$159$	9032.70	−	5603.58i	0.357292	−	0.221652i
$160$	8759.08			0.342152
$161$		−	4932.23i		−	0.190279i
$162$	27437.7	−	20868.9i	1.04549	−	0.795188i
$163$	29203.1			1.09914			0.549570	−	0.835447i	$-0.314791\pi$
$163$	29203.1			1.09914			0.549570	+	0.835447i	$0.314791\pi$
$164$		−	1381.71i		−	0.0513725i
$165$	−1796.53	−	2895.92i	−0.0659884	−	0.106370i
$166$	−23203.9			−0.842063
$167$		−	14056.6i		−	0.504018i	−0.967725	−	0.252009i	$-0.918909\pi$
$167$		−	14056.6i		−	0.504018i	0.967725	−	0.252009i	$-0.0810913\pi$
$168$	−6330.97	+	3927.52i	−0.224311	+	0.139155i
$169$	−23356.8			−0.817788
$170$		−	3082.77i		−	0.106670i
$171$	13926.0	−	28088.4i	0.476249	−	0.960583i
$172$	−37180.8			−1.25679
$173$		−	10847.8i		−	0.362452i	−0.983441	−	0.181226i	$-0.941993\pi$
$173$		−	10847.8i		−	0.362452i	0.983441	−	0.181226i	$-0.0580066\pi$
$174$	2625.99	+	4232.96i	0.0867350	+	0.139813i
$175$	20630.8			0.673658
$176$		−	16504.6i		−	0.532821i
$177$	−3465.92	+	2150.14i	−0.110630	+	0.0686310i
$178$	−72617.0			−2.29191
$179$			17664.8i			0.551317i	0.961256	+	0.275659i	$0.0888960\pi$
$179$			17664.8i			0.551317i	−0.961256	+	0.275659i	$0.911104\pi$
$180$	5932.14	+	2941.11i	0.183091	+	0.0907749i
$181$	53290.1			1.62663			0.813316	−	0.581823i	$-0.197660\pi$
$181$	53290.1			1.62663			0.813316	+	0.581823i	$0.197660\pi$
$182$			13590.2i			0.410284i
$183$	−14762.1	−	23795.8i	−0.440804	−	0.710554i
$184$	3175.92			0.0938066
$185$			14377.4i			0.420084i
$186$	37867.7	−	23491.9i	1.09457	−	0.679034i
$187$	−4478.53			−0.128071
$188$			22904.2i			0.648037i
$189$	−26020.6	+	2479.02i	−0.728440	+	0.0693996i
$190$	14323.3			0.396768
$191$		−	45052.3i		−	1.23495i	−0.786589	−	0.617476i	$-0.788155\pi$
$191$		−	45052.3i		−	1.23495i	0.786589	−	0.617476i	$-0.211845\pi$
$192$	7695.97	+	12405.5i	0.208767	+	0.336521i
$193$	46146.6			1.23887			0.619434	−	0.785048i	$-0.287362\pi$
$193$	46146.6			1.23887			0.619434	+	0.785048i	$0.287362\pi$
$194$			56500.3i			1.50123i
$195$	−3885.90	+	2410.68i	−0.102193	+	0.0633973i
$196$	12945.2			0.336974
$197$			46937.7i			1.20945i	0.796433	+	0.604727i	$0.206718\pi$
$197$			46937.7i			1.20945i	−0.796433	+	0.604727i	$0.793282\pi$
$198$	10163.2	−	20498.9i	0.259238	−	0.522877i
$199$	2813.95			0.0710575			0.0355288	−	0.999369i	$-0.488688\pi$
$199$	2813.95			0.0710575			0.0355288	+	0.999369i	$0.488688\pi$
$200$			13284.4i			0.332110i
$201$	19768.0	+	31865.0i	0.489294	+	0.788718i
$202$	−35449.1			−0.868764
$203$		−	3777.08i		−	0.0916566i
$204$	7394.03	−	4587.01i	0.177673	−	0.110222i
$205$	−838.528			−0.0199531
$206$			21432.8i			0.505063i
$207$	9982.76	+	4949.37i	0.232975	+	0.115507i
$208$	−22146.8			−0.511899
$209$		−	20808.4i		−	0.476372i
$210$	−6295.31	−	10147.7i	−0.142751	−	0.230107i
$211$	−15688.9			−0.352392			−0.176196	−	0.984355i	$-0.556379\pi$
$211$	−15688.9			−0.352392			−0.176196	+	0.984355i	$0.556379\pi$
$212$			13707.3i			0.304987i
$213$	−11079.8	+	6873.55i	−0.244216	+	0.151503i
$214$	−56179.8			−1.22674
$215$			22564.1i			0.488137i
$216$	−1596.27	−	16754.9i	−0.0342136	−	0.359117i
$217$	−33789.4			−0.717565
$218$		−	19538.0i		−	0.411119i
$219$	−10245.3	−	16514.9i	−0.213617	−	0.344341i
$220$	4394.63			0.0907982
$221$			6009.52i			0.123043i
$222$	−82024.6	+	50885.3i	−1.66433	+	1.03249i
$223$	13217.8			0.265797			0.132898	−	0.991130i	$-0.457572\pi$
$223$	13217.8			0.265797			0.132898	+	0.991130i	$0.457572\pi$
$224$		−	44589.7i		−	0.888666i
$225$	−20702.5	+	41756.4i	−0.408938	+	0.824818i
$226$	−64938.7			−1.27141
$227$		−	74384.0i		−	1.44354i	−0.692135	−	0.721768i	$-0.743330\pi$
$227$		−	74384.0i		−	1.44354i	0.692135	−	0.721768i	$-0.256670\pi$
$228$	21312.4	+	34354.6i	0.409980	+	0.660868i
$229$	−23594.8			−0.449930			−0.224965	−	0.974367i	$-0.572227\pi$
$229$	−23594.8			−0.449930			−0.224965	+	0.974367i	$0.572227\pi$
$230$			5090.59i			0.0962304i
$231$	−14742.2	+	9145.58i	−0.276273	+	0.171391i
$232$	2432.10			0.0451862
$233$		−	37798.5i		−	0.696246i	−0.937449	−	0.348123i	$-0.886819\pi$
$233$		−	37798.5i		−	0.696246i	0.937449	−	0.348123i	$-0.113181\pi$
$234$	−27506.5	−	13637.5i	−0.502346	−	0.249059i
$235$	13900.0			0.251698
$236$		−	5259.62i		−	0.0944344i
$237$	10160.9	+	16378.9i	0.180899	+	0.291601i
$238$	−15693.4			−0.277053
$239$		−	64531.0i		−	1.12972i	−0.825185	−	0.564862i	$-0.808929\pi$
$239$		−	64531.0i		−	1.12972i	0.825185	−	0.564862i	$-0.191071\pi$
$240$	16536.8	−	10258.9i	0.287097	−	0.178106i
$241$	55960.1			0.963483			0.481742	−	0.876313i	$-0.340004\pi$
$241$	55960.1			0.963483			0.481742	+	0.876313i	$0.340004\pi$
$242$			61739.7i			1.05423i
$243$	21093.5	−	55152.9i	0.357221	−	0.934020i
$244$	36110.6			0.606534
$245$		−	7856.13i		−	0.130881i
$246$	−2967.78	−	4783.91i	−0.0490412	−	0.0790519i
$247$	−27921.8			−0.457666
$248$		−	21757.4i		−	0.353755i
$249$	−33775.4	+	20953.1i	−0.544756	+	0.337948i
$250$	−44422.1			−0.710754
$251$			65007.8i			1.03185i	0.856633	+	0.515927i	$0.172552\pi$
$251$			65007.8i			1.03185i	−0.856633	+	0.515927i	$0.827448\pi$
$252$	14972.2	−	30198.6i	0.235768	−	0.475539i
$253$	7395.41			0.115537
$254$			33361.3i			0.517101i
$255$	−2783.74	−	4487.26i	−0.0428104	−	0.0690082i
$256$	85719.2			1.30797
$257$			88880.8i			1.34568i	0.739788	+	0.672840i	$0.234926\pi$
$257$			88880.8i			1.34568i	−0.739788	+	0.672840i	$0.765074\pi$
$258$	−128731.	+	79860.5i	−1.93395	+	1.19975i
$259$	73190.6			1.09108
$260$		−	5896.94i		−	0.0872329i
$261$	7644.74	+	3790.20i	0.112223	+	0.0556393i
$262$	−73775.3			−1.07475
$263$		−	31758.9i		−	0.459149i	−0.973291	−	0.229574i	$-0.926267\pi$
$263$		−	31758.9i		−	0.459149i	0.973291	−	0.229574i	$-0.0737334\pi$
$264$	−5888.94	−	9492.68i	−0.0844946	−	0.136201i
$265$	8318.65			0.118457
$266$		−	72915.6i		−	1.03052i
$267$	−105701.	+	65573.2i	−1.48271	+	0.919823i
$268$	−48355.9			−0.673256
$269$		−	27028.4i		−	0.373521i	−0.982405	−	0.186761i	$-0.940201\pi$
$269$		−	27028.4i		−	0.373521i	0.982405	−	0.186761i	$-0.0597989\pi$
$270$	26856.0	−	2558.61i	0.368395	−	0.0350976i
$271$	101687.			1.38461			0.692304	−	0.721606i	$-0.256596\pi$
$271$	101687.			1.38461			0.692304	+	0.721606i	$0.256596\pi$
$272$		−	25574.1i		−	0.345671i
$273$	12272.0	+	19781.9i	0.164661	+	0.265425i
$274$	71078.0			0.946748
$275$			30933.9i			0.409043i
$276$	−12209.8	+	7574.54i	−0.160284	+	0.0994348i
$277$	80803.4			1.05310			0.526551	−	0.850144i	$-0.323485\pi$
$277$	80803.4			1.05310			0.526551	+	0.850144i	$0.323485\pi$
$278$			13790.1i			0.178434i
$279$	33906.8	−	68389.2i	0.435591	−	0.878576i
$280$	−5830.49			−0.0743685
$281$		−	1181.63i		−	0.0149647i	−0.999972	−	0.00748236i	$-0.997618\pi$
$281$		−	1181.63i		−	0.0149647i	0.999972	−	0.00748236i	$-0.00238173\pi$
$282$	49195.9	+	79301.3i	0.618629	+	0.997200i
$283$	108188.			1.35085			0.675425	−	0.737429i	$-0.263960\pi$
$283$	108188.			1.35085			0.675425	+	0.737429i	$0.263960\pi$
$284$		−	16813.9i		−	0.208464i
$285$	20849.0	−	12934.0i	0.256682	−	0.159237i
$286$	−20377.3			−0.249123
$287$			4268.68i			0.0518239i
$288$	90248.9	+	44744.7i	1.08807	+	0.539456i
$289$	76581.5			0.916913
$290$			3898.34i			0.0463537i
$291$	51019.9	+	82241.5i	0.602495	+	0.971192i
$292$	25061.8			0.293932
$293$		−	39113.3i		−	0.455606i	−0.973707	−	0.227803i	$-0.926846\pi$
$293$		−	39113.3i		−	0.455606i	0.973707	−	0.227803i	$-0.0731542\pi$
$294$	44820.2	−	27804.9i	0.518536	−	0.321682i
$295$	−3191.93			−0.0366784
$296$			47128.2i			0.537895i
$297$	−3717.06	−	39015.4i	−0.0421392	−	0.442306i
$298$	144635.			1.62869
$299$		−	9923.54i		−	0.111000i
$300$	−31683.2	−	51071.7i	−0.352035	−	0.567463i
$301$	114867.			1.26783
$302$		−	94152.1i		−	1.03232i
$303$	−51599.4	+	32010.5i	−0.562030	+	0.348664i
$304$	118824.			1.28575
$305$		−	21914.7i		−	0.235578i
$306$	15747.9	−	31763.2i	0.168183	−	0.339220i
$307$	−19295.0			−0.204724			−0.102362	−	0.994747i	$-0.532640\pi$
$307$	−19295.0			−0.204724			−0.102362	+	0.994747i	$0.532640\pi$
$308$		−	22371.7i		−	0.235829i
$309$	19353.9	+	31197.5i	0.202699	+	0.326740i
$310$	34874.2			0.362895
$311$		−	158346.i		−	1.63714i	−0.574406	−	0.818571i	$-0.694767\pi$
$311$		−	158346.i		−	1.63714i	0.574406	−	0.818571i	$-0.305233\pi$
$312$	−12737.8	+	7902.08i	−0.130853	+	0.0811768i
$313$	−80665.2			−0.823375			−0.411687	−	0.911325i	$-0.635060\pi$
$313$	−80665.2			−0.823375			−0.411687	+	0.911325i	$0.635060\pi$
$314$		−	98701.1i		−	1.00107i
$315$	−18326.8	−	9086.29i	−0.184700	−	0.0915726i
$316$	−24855.4			−0.248913
$317$		−	7574.70i		−	0.0753784i	−0.999290	−	0.0376892i	$-0.988000\pi$
$317$		−	7574.70i		−	0.0753784i	0.999290	−	0.0376892i	$-0.0119997\pi$
$318$	29441.9	+	47458.9i	0.291147	+	0.469314i
$319$	5663.37			0.0556536
$320$			11424.9i			0.111571i
$321$	−81775.0	+	50730.5i	−0.793616	+	0.492333i
$322$	25914.6			0.249938
$323$		−	32242.8i		−	0.309049i
$324$	46097.3	+	60607.2i	0.439122	+	0.577343i
$325$	41508.7			0.392982
$326$			153437.i			1.44376i
$327$	−17642.9	−	28439.4i	−0.164996	−	0.265965i
$328$	−2748.65			−0.0255489
$329$		−	70760.6i		−	0.653732i
$330$	15215.5	−	9439.21i	0.139720	−	0.0866778i
$331$	17348.1			0.158342			0.0791708	−	0.996861i	$-0.474773\pi$
$331$	17348.1			0.158342			0.0791708	+	0.996861i	$0.474773\pi$
$332$		−	51255.0i		−	0.465008i
$333$	−73445.0	+	148137.i	−0.662329	+	1.33590i
$334$	73854.9			0.662043
$335$			29346.0i			0.261493i
$336$	−52224.7	−	84183.7i	−0.462592	−	0.745675i
$337$	−58282.4			−0.513189			−0.256595	−	0.966519i	$-0.582601\pi$
$337$	−58282.4			−0.513189			−0.256595	+	0.966519i	$0.582601\pi$
$338$		−	122720.i		−	1.07419i
$339$	−94524.4	+	58639.7i	−0.822516	+	0.510261i
$340$	6809.52			0.0589059
$341$		−	50664.0i		−	0.435703i
$342$	147580.	+	73169.0i	1.26176	+	0.625568i
$343$	−126081.			−1.07167
$344$			73964.0i			0.625034i
$345$	4596.81	+	7409.82i	0.0386205	+	0.0622543i
$346$	56995.8			0.476092
$347$		−	51313.4i		−	0.426160i	−0.977035	−	0.213080i	$-0.931651\pi$
$347$		−	51313.4i		−	0.426160i	0.977035	−	0.213080i	$-0.0683494\pi$
$348$	−9350.19	+	5800.54i	−0.0772079	+	0.0478972i
$349$	−127375.			−1.04576			−0.522882	−	0.852405i	$-0.675143\pi$
$349$	−127375.			−1.04576			−0.522882	+	0.852405i	$0.675143\pi$
$350$			108397.i			0.884871i
$351$	−52352.9	+	4987.74i	−0.424939	+	0.0404845i
$352$	66858.0			0.539595
$353$			55186.9i			0.442881i	0.975174	+	0.221440i	$0.0710758\pi$
$353$			55186.9i			0.442881i	−0.975174	+	0.221440i	$0.928924\pi$
$354$	−11297.1	−	18210.4i	−0.0901489	−	0.145316i
$355$	−10203.9			−0.0809677
$356$		−	160404.i		−	1.26565i
$357$	−22843.2	+	14171.2i	−0.179234	+	0.111191i
$358$	−92812.9			−0.724173
$359$		−	53361.3i		−	0.414035i	−0.978337	−	0.207018i	$-0.933624\pi$
$359$		−	53361.3i		−	0.414035i	0.978337	−	0.207018i	$-0.0663757\pi$
$360$	5850.76	−	11800.8i	0.0451447	−	0.0910558i
$361$	19487.3			0.149533
$362$			279993.i			2.13663i
$363$	55751.0	+	89867.9i	0.423097	+	0.682011i
$364$	−30019.5			−0.226569
$365$		−	15209.4i		−	0.114163i
$366$	125026.	−	77561.8i	0.933335	−	0.579010i
$367$	−133555.			−0.991584			−0.495792	−	0.868441i	$-0.665122\pi$
$367$	−133555.			−0.991584			−0.495792	+	0.868441i	$0.665122\pi$
$368$			42230.6i			0.311840i
$369$	−8639.75	−	4283.52i	−0.0634524	−	0.0314592i
$370$	−75540.4			−0.551793
$371$		−	42347.6i		−	0.307667i
$372$	51891.2	+	83646.0i	0.374979	+	0.604448i
$373$	17826.7			0.128131			0.0640653	−	0.997946i	$-0.479593\pi$
$373$	17826.7			0.128131			0.0640653	+	0.997946i	$0.479593\pi$
$374$		−	23530.8i		−	0.168226i
$375$	−64660.6	+	40113.2i	−0.459808	+	0.285250i
$376$	45563.5			0.322286
$377$		−	7599.39i		−	0.0534683i
$378$	−13025.1	−	136716.i	−0.0911585	−	0.956829i
$379$	−272993.			−1.90052			−0.950261	−	0.311456i	$-0.899183\pi$
$379$	−272993.			−1.90052			−0.950261	+	0.311456i	$0.899183\pi$
$380$			31638.8i			0.219105i
$381$	30125.3	+	48560.5i	0.207530	+	0.334528i
$382$	236710.			1.62215
$383$			142000.i			0.968032i	0.875059	+	0.484016i	$0.160822\pi$
$383$			142000.i			0.968032i	−0.875059	+	0.484016i	$0.839178\pi$
$384$	86994.7	−	53968.6i	0.589971	−	0.365998i
$385$	−13576.8			−0.0915961
$386$			242460.i			1.62729i
$387$	−115266.	+	232489.i	−0.769626	+	1.55232i
$388$	−124803.			−0.829016
$389$		−	213755.i		−	1.41259i	−0.707916	−	0.706297i	$-0.750364\pi$
$389$		−	213755.i		−	1.41259i	0.707916	−	0.706297i	$-0.249636\pi$
$390$	−12666.0	−	20417.0i	−0.0832743	−	0.134234i
$391$	11459.3			0.0749554
$392$		−	25752.0i		−	0.167586i
$393$	−107387.	+	66619.1i	−0.695289	+	0.431334i
$394$	−246617.			−1.58866
$395$			15084.1i			0.0966777i
$396$	45280.0	+	22449.4i	0.288746	+	0.143158i
$397$	153201.			0.972032			0.486016	−	0.873950i	$-0.338450\pi$
$397$	153201.			0.972032			0.486016	+	0.873950i	$0.338450\pi$
$398$			14784.8i			0.0933363i
$399$	−65842.9	−	106135.i	−0.413583	−	0.666676i
$400$	−176644.			−1.10403
$401$			127864.i			0.795171i	0.917565	+	0.397585i	$0.130152\pi$
$401$			127864.i			0.795171i	−0.917565	+	0.397585i	$0.869848\pi$
$402$	−167423.	+	103863.i	−1.03601	+	0.642703i
$403$	−67983.5			−0.418594
$404$		−	78303.3i		−	0.479753i
$405$	36781.0	−	27975.3i	0.224240	−	0.170555i
$406$	19845.2			0.120394
$407$			109742.i			0.662499i
$408$	−9124.96	−	14709.0i	−0.0548164	−	0.0883614i
$409$	−38312.6			−0.229031			−0.114516	−	0.993421i	$-0.536532\pi$
$409$	−38312.6			−0.229031			−0.114516	+	0.993421i	$0.536532\pi$
$410$		−	4405.73i		−	0.0262090i
$411$	103461.	−	64183.6i	0.612480	−	0.379962i
$412$	−47343.0			−0.278908
$413$			16249.1i			0.0952642i
$414$	−26004.6	+	52450.7i	−0.151722	+	0.306020i
$415$	−31105.4			−0.180609
$416$		−	89713.5i		−	0.518407i
$417$	12452.5	+	20072.8i	0.0716115	+	0.115434i
$418$	109330.			0.625729
$419$		−	242130.i		−	1.37918i	−0.724201	−	0.689589i	$-0.757791\pi$
$419$		−	242130.i		−	1.37918i	0.724201	−	0.689589i	$-0.242209\pi$
$420$	22415.3	−	13905.7i	0.127071	−	0.0788305i
$421$	−278724.			−1.57257			−0.786285	−	0.617863i	$-0.787998\pi$
$421$	−278724.			−1.57257			−0.786285	+	0.617863i	$0.787998\pi$
$422$		−	82431.2i		−	0.462878i
$423$	143218.	+	71006.5i	0.800420	+	0.396842i
$424$	27268.1			0.151678
$425$			47932.3i			0.265369i
$426$	−36114.5	−	58214.8i	−0.199004	−	0.320785i
$427$	−111561.			−0.611864
$428$		−	124096.i		−	0.677437i
$429$	−29661.0	+	18400.7i	−0.161165	+	0.0999816i
$430$	−118555.			−0.641183
$431$			189524.i			1.02025i	0.860099	+	0.510127i	$0.170402\pi$
$431$			189524.i			1.02025i	−0.860099	+	0.510127i	$0.829598\pi$
$432$	222793.	−	21225.8i	1.19381	−	0.113736i
$433$	−117183.			−0.625012			−0.312506	−	0.949916i	$-0.601168\pi$
$433$	−117183.			−0.625012			−0.312506	+	0.949916i	$0.601168\pi$
$434$		−	177534.i		−	0.942543i
$435$	3520.21	+	5674.40i	0.0186033	+	0.0299876i
$436$	43157.5			0.227030
$437$			53242.6i			0.278803i
$438$	86771.5	−	53830.1i	0.452302	−	0.280593i
$439$	−340406.			−1.76632			−0.883158	−	0.469075i	$-0.844587\pi$
$439$	−340406.			−1.76632			−0.883158	+	0.469075i	$0.844587\pi$
$440$		−	8742.27i		−	0.0451563i
$441$	40132.1	−	80945.4i	0.206355	−	0.416212i
$442$	−31574.8			−0.161620
$443$		−	114277.i		−	0.582307i	−0.956676	−	0.291154i	$-0.905961\pi$
$443$		−	114277.i		−	0.582307i	0.956676	−	0.291154i	$-0.0940391\pi$
$444$	−112400.	−	181184.i	−0.570167	−	0.919081i
$445$	−97345.0			−0.491580
$446$			69448.0i			0.349132i
$447$	210529.	−	130605.i	1.05365	−	0.653650i
$448$	58160.3			0.289782
$449$		−	336617.i		−	1.66972i	−0.550462	−	0.834860i	$-0.685548\pi$
$449$		−	336617.i		−	1.66972i	0.550462	−	0.834860i	$-0.314452\pi$
$450$	−219393.	−	108773.i	−1.08342	−	0.537153i
$451$	−6400.48			−0.0314673
$452$		−	143443.i		−	0.702106i
$453$	−85019.4	−	137047.i	−0.414307	−	0.667842i
$454$	390823.			1.89613
$455$			18218.1i			0.0879995i
$456$	68341.7	−	42396.9i	0.328667	−	0.203894i
$457$	131255.			0.628469			0.314234	−	0.949345i	$-0.398252\pi$
$457$	131255.			0.628469			0.314234	+	0.949345i	$0.398252\pi$
$458$		−	123970.i		−	0.590997i
$459$	−5759.61	−	60454.7i	−0.0273381	−	0.286949i
$460$	−11244.6			−0.0531408
$461$			210787.i			0.991841i	0.868368	+	0.495920i	$0.165169\pi$
$461$			210787.i			0.991841i	−0.868368	+	0.495920i	$0.834831\pi$
$462$	−48052.0	−	77457.5i	−0.225127	−	0.362894i
$463$	−4070.47			−0.0189882			−0.00949408	−	0.999955i	$-0.503022\pi$
$463$	−4070.47			−0.0189882			−0.00949408	+	0.999955i	$0.503022\pi$
$464$			32340.0i			0.150212i
$465$	50762.7	−	31491.5i	0.234768	−	0.145642i
$466$	198598.			0.914541
$467$			131302.i			0.602057i	0.953615	+	0.301029i	$0.0973299\pi$
$467$			131302.i			0.602057i	−0.953615	+	0.301029i	$0.902670\pi$
$468$	30123.8	−	60759.0i	0.137537	−	0.277408i
$469$	149391.			0.679172
$470$			73032.5i			0.330613i
$471$	−89127.2	−	143669.i	−0.401762	−	0.647620i
$472$	−10463.0			−0.0469647
$473$			172232.i			0.769824i
$474$	−86056.9	+	53386.8i	−0.383027	+	0.237617i
$475$	−222706.			−0.987062
$476$		−	34665.1i		−	0.152996i
$477$	85710.9	+	42494.8i	0.376703	+	0.186767i
$478$	339054.			1.48393
$479$		−	229631.i		−	1.00083i	−0.865786	−	0.500415i	$-0.833181\pi$
$479$		−	229631.i		−	1.00083i	0.865786	−	0.500415i	$-0.166819\pi$
$480$	41557.3	+	66988.3i	0.180370	+	0.290748i
$481$	147258.			0.636485
$482$			294021.i			1.26557i
$483$	37721.1	−	23400.9i	0.161692	−	0.100309i
$484$	−136377.			−0.582170
$485$			75740.2i			0.321990i
$486$	289780.	+	110828.i	1.22686	+	0.469221i
$487$	−325.460			−0.00137227			−0.000686136	−	1.00000i	$-0.500218\pi$
$487$	−325.460			−0.00137227			−0.000686136		1.00000i	$0.500218\pi$
$488$		−	71835.1i		−	0.301646i
$489$	138553.	+	223341.i	0.579428	+	0.934009i
$490$	41277.1			0.171916
$491$		−	428306.i		−	1.77661i	−0.459257	−	0.888304i	$-0.651884\pi$
$491$		−	428306.i		−	1.77661i	0.459257	−	0.888304i	$-0.348116\pi$
$492$	10567.2	−	6555.51i	0.0436544	−	0.0270817i
$493$	8775.44			0.0361056
$494$		−	146704.i		−	0.601159i
$495$	13624.0	−	27479.3i	0.0556026	−	0.112149i
$496$	289310.			1.17598
$497$			51945.1i			0.210296i
$498$	−110090.	−	177460.i	−0.443906	−	0.715554i
$499$	−209527.			−0.841471			−0.420735	−	0.907183i	$-0.638228\pi$
$499$	−209527.			−0.841471			−0.420735	+	0.907183i	$0.638228\pi$
$500$		−	98124.0i		−	0.392496i
$501$	107503.	−	66691.1i	0.428296	−	0.265700i
$502$	−341559.			−1.35537
$503$			328979.i			1.30026i	0.759821	+	0.650132i	$0.225287\pi$
$503$			328979.i			1.30026i	−0.759821	+	0.650132i	$0.774713\pi$
$504$	−60074.3	−	29784.4i	−0.236498	−	0.117254i
$505$	−47520.4			−0.186336
$506$			38856.4i			0.151762i
$507$	−110816.	−	178630.i	−0.431109	−	0.694926i
$508$	−73691.7			−0.285556
$509$		−	361912.i		−	1.39691i	−0.715655	−	0.698454i	$-0.753872\pi$
$509$		−	361912.i		−	1.39691i	0.715655	−	0.698454i	$-0.246128\pi$
$510$	23576.6	−	14626.1i	0.0906444	−	0.0562328i
$511$	−77426.2			−0.296515
$512$			268379.i			1.02379i
$513$	280888.	−	26760.6i	1.06733	−	0.101686i
$514$	−466991.			−1.76759
$515$			28731.3i			0.108328i
$516$	−176404.	−	284354.i	−0.662534	−	1.06797i
$517$	106099.			0.396944
$518$			384552.i			1.43316i
$519$	82962.8	−	51467.3i	0.307998	−	0.191072i
$520$	−11730.8			−0.0433832
$521$			268878.i			0.990559i	0.868734	+	0.495280i	$0.164934\pi$
$521$			268878.i			0.990559i	−0.868734	+	0.495280i	$0.835066\pi$
$522$	−19914.2	+	40166.4i	−0.0730839	+	0.147408i
$523$	25969.9			0.0949439			0.0474719	−	0.998873i	$-0.484884\pi$
$523$	25969.9			0.0949439			0.0474719	+	0.998873i	$0.484884\pi$
$524$		−	162962.i		−	0.593504i
$525$	97882.4	+	157782.i	0.355129	+	0.572450i
$526$	166865.			0.603106
$527$		−	78504.3i		−	0.282665i
$528$	126225.	−	78306.0i	0.452771	−	0.280884i
$529$	260918.			0.932381
$530$			43707.2i			0.155597i
$531$	−32888.0	−	16305.6i	−0.116640	−	0.0578293i
$532$	161063.			0.569079
$533$			8588.49i			0.0302317i
$534$	−344530.	−	555365.i	−1.20822	−	1.94758i
$535$	−75310.6			−0.263117
$536$			96194.7i			0.334828i
$537$	−135098.	+	83810.1i	−0.468489	+	0.290635i
$538$	142010.			0.490632
$539$		−	59965.8i		−	0.206408i
$540$	5651.72	+	59322.2i	0.0193817	+	0.203437i
$541$	88195.2			0.301335			0.150668	−	0.988584i	$-0.451858\pi$
$541$	88195.2			0.301335			0.150668	+	0.988584i	$0.451858\pi$
$542$			534276.i			1.81873i
$543$	252834.	+	407555.i	0.857502	+	1.38225i
$544$	103597.			0.350066
$545$		−	26191.2i		−	0.0881786i
$546$	−103936.	+	64478.7i	−0.348644	+	0.216287i
$547$	−553062.			−1.84841			−0.924206	−	0.381894i	$-0.875272\pi$
$547$	−553062.			−1.84841			−0.924206	+	0.381894i	$0.875272\pi$
$548$			157004.i			0.522817i
$549$	111948.	−	225797.i	0.371427	−	0.749158i
$550$	−162531.			−0.537291
$551$			40772.9i			0.134298i
$552$	15068.1	+	24289.0i	0.0494515	+	0.0797134i
$553$	76788.6			0.251100
$554$			424551.i			1.38328i
$555$	−109956.	+	68213.1i	−0.356972	+	0.221453i
$556$	−30460.9			−0.0985356
$557$		−	460127.i		−	1.48309i	−0.670903	−	0.741545i	$-0.734094\pi$
$557$		−	460127.i		−	1.48309i	0.670903	−	0.741545i	$-0.265906\pi$
$558$	359326.	+	178151.i	1.15404	+	0.572162i
$559$	231109.			0.739595
$560$		−	77528.9i		−	0.247222i
$561$	−21248.3	−	34251.2i	−0.0675147	−	0.108830i
$562$	6208.43			0.0196566
$563$		−	596909.i		−	1.88318i	−0.336763	−	0.941589i	$-0.609332\pi$
$563$		−	596909.i		−	1.88318i	0.336763	−	0.941589i	$-0.390668\pi$
$564$	−175169.	+	108669.i	−0.550678	+	0.341622i
$565$	−87052.1			−0.272698
$566$			568434.i			1.77438i
$567$	−142414.	−	187241.i	−0.442981	−	0.582417i
$568$	−33448.0			−0.103675
$569$			303832.i			0.938444i	0.883080	+	0.469222i	$0.155466\pi$
$569$			303832.i			0.938444i	−0.883080	+	0.469222i	$0.844534\pi$
$570$	67956.8	+	109543.i	0.209162	+	0.337159i
$571$	49273.8			0.151128			0.0755638	−	0.997141i	$-0.475924\pi$
$571$	49273.8			0.151128			0.0755638	+	0.997141i	$0.475924\pi$
$572$		−	45011.3i		−	0.137572i
$573$	344554.	−	213750.i	1.04942	−	0.651023i
$574$	−22428.2			−0.0680723
$575$		−	79150.8i		−	0.239398i
$576$	−58362.4	+	117716.i	−0.175909	+	0.354804i
$577$	220702.			0.662909			0.331455	−	0.943471i	$-0.392461\pi$
$577$	220702.			0.662909			0.331455	+	0.943471i	$0.392461\pi$
$578$			402369.i			1.20439i
$579$	218942.	+	352923.i	0.653088	+	1.05275i
$580$	−8611.04			−0.0255976
$581$			158348.i			0.469094i
$582$	−432107.	+	268065.i	−1.27569	+	0.791396i
$583$	63496.2			0.186815
$584$		−	49855.6i		−	0.146180i
$585$	−36873.1	−	18281.4i	−0.107745	−	0.0534193i
$586$	205506.			0.598453
$587$		−	158765.i		−	0.460764i	−0.973100	−	0.230382i	$-0.926002\pi$
$587$		−	158765.i		−	0.460764i	0.973100	−	0.230382i	$-0.0739976\pi$
$588$	61418.3	+	99003.2i	0.177641	+	0.286348i
$589$	364751.			1.05139
$590$		−	16770.8i		−	0.0481782i
$591$	−358973.	+	222695.i	−1.02775	+	0.637582i
$592$	−626670.			−1.78811
$593$			16441.0i			0.0467540i	0.999727	+	0.0233770i	$0.00744180\pi$
$593$			16441.0i			0.0467540i	−0.999727	+	0.0233770i	$0.992558\pi$
$594$	204992.	−	19529.9i	0.580983	−	0.0553512i
$595$	−21037.4			−0.0594236
$596$			319483.i			0.899405i
$597$	13350.7	+	21520.7i	0.0374590	+	0.0603821i
$598$	52139.5			0.145802
$599$		−	233718.i		−	0.651385i	−0.945476	−	0.325693i	$-0.894403\pi$
$599$		−	233718.i		−	0.651385i	0.945476	−	0.325693i	$-0.105597\pi$
$600$	−101597.	+	63027.5i	−0.282214	+	0.175076i
$601$	−164717.			−0.456026			−0.228013	−	0.973658i	$-0.573223\pi$
$601$	−164717.			−0.456026			−0.228013	+	0.973658i	$0.573223\pi$
$602$			603525.i			1.66534i
$603$	−149911.	+	302366.i	−0.412285	+	0.831569i
$604$	207972.			0.570075
$605$			82763.7i			0.226115i
$606$	−168187.	−	271110.i	−0.457982	−	0.738244i
$607$	−270098.			−0.733068			−0.366534	−	0.930405i	$-0.619456\pi$
$607$	−270098.			−0.733068			−0.366534	+	0.930405i	$0.619456\pi$
$608$			481338.i			1.30210i
$609$	28886.6	−	17920.3i	0.0778864	−	0.0483181i
$610$	115142.			0.309439
$611$		−	142369.i		−	0.381357i
$612$	70161.7	+	34785.6i	0.187326	+	0.0928746i
$613$	448318.			1.19307			0.596534	−	0.802588i	$-0.296544\pi$
$613$	448318.			1.19307			0.596534	+	0.802588i	$0.296544\pi$
$614$		−	101378.i		−	0.268911i
$615$	−3978.38	−	6412.96i	−0.0105186	−	0.0169554i
$616$	−44504.1			−0.117284
$617$			716557.i			1.88226i	0.338040	+	0.941132i	$0.390236\pi$
$617$			716557.i			1.88226i	−0.338040	+	0.941132i	$0.609764\pi$
$618$	−163916.	+	101688.i	−0.429184	+	0.266251i
$619$	47548.8			0.124096			0.0620481	−	0.998073i	$-0.480237\pi$
$619$	47548.8			0.124096			0.0620481	+	0.998073i	$0.480237\pi$
$620$			77033.7i			0.200400i
$621$	9510.87	+	99829.1i	0.0246625	+	0.258865i
$622$	831969.			2.15044
$623$			495553.i			1.27677i
$624$	−105075.	−	169376.i	−0.269855	−	0.434993i
$625$	300071.			0.768182
$626$		−	423825.i		−	1.08153i
$627$	159140.	−	98725.1i	0.404803	−	0.251126i
$628$	218021.			0.552813
$629$			170047.i			0.429800i
$630$	47740.5	−	96291.4i	0.120283	−	0.242609i
$631$	−118486.			−0.297583			−0.148791	−	0.988869i	$-0.547538\pi$
$631$	−118486.			−0.297583			−0.148791	+	0.988869i	$0.547538\pi$
$632$			49445.0i			0.123791i
$633$	−74435.5	−	119986.i	−0.185769	−	0.299450i
$634$	39798.4			0.0990118
$635$			44721.7i			0.110910i
$636$	−104832.	+	65034.2i	−0.259167	+	0.160778i
$637$	−80465.2			−0.198303
$638$			29756.0i			0.0731027i
$639$	−105136.	−	52125.6i	−0.257484	−	0.127658i
$640$	80117.7			0.195600
$641$		−	464057.i		−	1.12942i	−0.825290	−	0.564709i	$-0.808988\pi$
$641$		−	464057.i		−	1.12942i	0.825290	−	0.564709i	$-0.191012\pi$
$642$	−266544.	−	429656.i	−0.646694	−	1.04244i
$643$	671136.			1.62326			0.811630	−	0.584171i	$-0.198580\pi$
$643$	671136.			1.62326			0.811630	+	0.584171i	$0.198580\pi$
$644$			57242.6i			0.138022i
$645$	−172568.	+	107055.i	−0.414801	+	0.257329i
$646$	169408.			0.405946
$647$		−	163162.i		−	0.389773i	−0.980826	−	0.194886i	$-0.937566\pi$
$647$		−	163162.i		−	0.389773i	0.980826	−	0.194886i	$-0.0624338\pi$
$648$	120566.	−	91701.6i	0.287128	−	0.218387i
$649$	−24364.0			−0.0578441
$650$			218092.i			0.516193i
$651$	−160313.	−	258417.i	−0.378275	−	0.609760i
$652$	−338926.			−0.797277
$653$		−	696228.i		−	1.63277i	−0.577507	−	0.816385i	$-0.695975\pi$
$653$		−	696228.i		−	1.63277i	0.577507	−	0.816385i	$-0.304025\pi$
$654$	149424.	−	92697.8i	0.349354	−	0.216727i
$655$	−98897.7			−0.230517
$656$		−	36549.2i		−	0.0849317i
$657$	77695.3	−	156710.i	0.179997	−	0.363048i
$658$	371785.			0.858697
$659$		−	337529.i		−	0.777213i	−0.921404	−	0.388607i	$-0.872957\pi$
$659$		−	337529.i		−	0.777213i	0.921404	−	0.388607i	$-0.127043\pi$
$660$	20850.3	+	33609.6i	0.0478656	+	0.0771570i
$661$	766349.			1.75398			0.876988	−	0.480513i	$-0.159550\pi$
$661$	766349.			1.75398			0.876988	+	0.480513i	$0.159550\pi$
$662$			91148.8i			0.207987i
$663$	−45960.0	+	28512.1i	−0.104557	+	0.0648637i
$664$	−101962.			−0.231261
$665$		−	97745.3i		−	0.221031i
$666$	−778328.	−	385889.i	−1.75475	−	0.869989i
$667$	−14490.9			−0.0325719
$668$			163138.i			0.365597i
$669$	62711.7	+	101088.i	0.140119	+	0.225864i
$670$	−154188.			−0.343479
$671$		−	167275.i		−	0.371522i
$672$	341016.	−	211555.i	0.755156	−	0.468473i
$673$	−91779.6			−0.202636			−0.101318	−	0.994854i	$-0.532306\pi$
$673$	−91779.6			−0.202636			−0.101318	+	0.994854i	$0.532306\pi$
$674$		−	306223.i		−	0.674090i
$675$	−417570.	+	39782.5i	−0.916477	+	0.0873142i
$676$	271076.			0.593194
$677$			665195.i			1.45135i	0.688039	+	0.725674i	$0.258472\pi$
$677$			665195.i			1.45135i	−0.688039	+	0.725674i	$0.741528\pi$
$678$	−308101.	−	496643.i	−0.670244	−	1.08040i
$679$	385569.			0.836302
$680$		−	13546.2i		−	0.0292955i
$681$	568879.	−	352913.i	1.22666	−	0.760981i
$682$	266195.			0.572309
$683$		−	919287.i		−	1.97065i	−0.170688	−	0.985325i	$-0.554599\pi$
$683$		−	919287.i		−	1.97065i	0.170688	−	0.985325i	$-0.445401\pi$
$684$	−161623.	+	325989.i	−0.345454	+	0.696773i
$685$	95282.0			0.203063
$686$		−	662447.i		−	1.40768i
$687$	−111945.	−	180450.i	−0.237187	−	0.382334i
$688$	−983509.			−2.07779
$689$		−	85202.5i		−	0.179479i
$690$	−38932.1	+	24152.2i	−0.0817730	+	0.0507292i
$691$	−431736.			−0.904194			−0.452097	−	0.891969i	$-0.649324\pi$
$691$	−431736.			−0.904194			−0.452097	+	0.891969i	$0.649324\pi$
$692$			125898.i			0.262910i
$693$	−139888.	−	69355.6i	−0.291283	−	0.144416i
$694$	269607.			0.559774
$695$			18486.0i			0.0382713i
$696$	11539.1	+	18600.4i	0.0238205	+	0.0383975i
$697$	−9917.60			−0.0204146
$698$		−	669244.i		−	1.37364i
$699$	289078.	−	179334.i	0.591645	−	0.367036i
$700$	−239437.			−0.488648
$701$			792305.i			1.61234i	0.591684	+	0.806170i	$0.298463\pi$
$701$			792305.i			1.61234i	−0.591684	+	0.806170i	$0.701537\pi$
$702$	−26206.2	−	275069.i	−0.0531777	−	0.558170i
$703$	−790080.			−1.59868
$704$			87205.8i			0.175954i
$705$	65948.4	+	106306.i	0.132686	+	0.213884i
$706$	−289959.			−0.581738
$707$			241911.i			0.483969i
$708$	40224.9	−	24954.2i	0.0802469	−	0.0497825i
$709$	313982.			0.624616			0.312308	−	0.949981i	$-0.398898\pi$
$709$	313982.			0.624616			0.312308	+	0.949981i	$0.398898\pi$
$710$		−	53612.8i		−	0.106354i
$711$	−77055.5	+	155419.i	−0.152428	+	0.307443i
$712$	−319092.			−0.629442
$713$			129634.i			0.255000i
$714$	−74457.1	−	120021.i	−0.146053	−	0.235430i
$715$	−27316.3			−0.0534330
$716$		−	205014.i		−	0.399906i
$717$	493525.	−	306166.i	0.959999	−	0.595551i
$718$	280367.			0.543848
$719$		−	169678.i		−	0.328223i	−0.986442	−	0.164111i	$-0.947524\pi$
$719$		−	169678.i		−	0.328223i	0.986442	−	0.164111i	$-0.0524757\pi$
$720$	156917.	+	77798.3i	0.302695	+	0.150074i
$721$	146262.			0.281359
$722$			102389.i			0.196417i
$723$	265502.	+	427975.i	0.507914	+	0.818733i
$724$	−618475.			−1.17990
$725$		−	60613.3i		−	0.115317i
$726$	−472177.	+	292923.i	−0.895843	+	0.555751i
$727$	6078.79			0.0115013			0.00575067	−	0.999983i	$-0.498169\pi$
$727$	6078.79			0.0115013			0.00575067	+	0.999983i	$0.498169\pi$
$728$			59717.9i			0.112679i
$729$	521880.	−	100352.i	0.982010	−	0.188829i
$730$	79912.1			0.149957
$731$			266875.i			0.499428i
$732$	171326.	+	276169.i	0.319743	+	0.515411i
$733$	924119.			1.71997			0.859983	−	0.510323i	$-0.170474\pi$
$733$	924119.			1.71997			0.859983	+	0.510323i	$0.170474\pi$
$734$		−	701717.i		−	1.30248i
$735$	60082.7	−	37273.3i	0.111218	−	0.0689958i
$736$	−171070.			−0.315805
$737$			223998.i			0.412391i
$738$	22506.1	−	45394.3i	0.0413227	−	0.0833468i
$739$	91156.8			0.166917			0.0834585	−	0.996511i	$-0.473403\pi$
$739$	91156.8			0.166917			0.0834585	+	0.996511i	$0.473403\pi$
$740$		−	166861.i		−	0.304714i
$741$	−132474.	−	213542.i	−0.241266	−	0.388908i
$742$	222500.			0.404131
$743$			268211.i			0.485846i	0.970046	+	0.242923i	$0.0781063\pi$
$743$			268211.i			0.485846i	−0.970046	+	0.242923i	$0.921894\pi$
$744$	166397.	−	103227.i	0.300608	−	0.186487i
$745$	193886.			0.349329
$746$			93663.7i			0.168304i
$747$	−320494.	−	158898.i	−0.574352	−	0.284759i
$748$	51977.1			0.0928984
$749$			383382.i			0.683390i
$750$	−210760.	−	339735.i	−0.374684	−	0.603973i
$751$	2579.41			0.00457342			0.00228671	−	0.999997i	$-0.499272\pi$
$751$	2579.41			0.00457342			0.00228671	+	0.999997i	$0.499272\pi$
$752$			605864.i			1.07137i
$753$	−497171.	+	308428.i	−0.876831	+	0.543956i
$754$	39928.2			0.0702322
$755$		−	126213.i		−	0.221417i
$756$	301991.	−	28771.1i	0.528384	−	0.0503400i
$757$	−403700.			−0.704478			−0.352239	−	0.935910i	$-0.614579\pi$
$757$	−403700.			−0.704478			−0.352239	+	0.935910i	$0.614579\pi$
$758$		−	1.43434e6i		−	2.49639i
$759$	35087.4	+	56559.1i	0.0609070	+	0.0981791i
$760$	62939.2			0.108967
$761$			68694.9i			0.118619i	0.998240	+	0.0593096i	$0.0188899\pi$
$761$			68694.9i			0.118619i	−0.998240	+	0.0593096i	$0.981110\pi$
$762$	−255143.	+	158282.i	−0.439413	+	0.272597i
$763$	−133331.			−0.229025
$764$			522869.i			0.895791i
$765$	21110.5	−	42579.4i	0.0360725	−	0.0727574i
$766$	−746084.			−1.27154
$767$			32692.9i			0.0555728i
$768$	406693.	+	655569.i	0.689516	+	1.11147i
$769$	−904654.			−1.52978			−0.764891	−	0.644160i	$-0.777207\pi$
$769$	−904654.			−1.52978			−0.764891	+	0.644160i	$0.777207\pi$
$770$		−	71334.4i		−	0.120314i
$771$	−679748.	+	421693.i	−1.14351	+	0.709394i
$772$	−535570.			−0.898631
$773$			54079.3i			0.0905049i	0.998976	+	0.0452525i	$0.0144092\pi$
$773$			54079.3i			0.0905049i	−0.998976	+	0.0452525i	$0.985591\pi$
$774$	−1.22152e6	−	605622.i	−2.03901	−	1.01093i
$775$	−542241.			−0.902795
$776$			248272.i			0.412292i
$777$	347251.	+	559752.i	0.575178	+	0.927158i
$778$	1.12310e6			1.85549
$779$		−	46079.7i		−	0.0759338i
$780$	45099.1	−	27977.9i	0.0741273	−	0.0459861i
$781$	−77886.7			−0.127691
$782$			60208.4i			0.0984562i
$783$	7283.37	+	76448.6i	0.0118798	+	0.124694i
$784$	342427.			0.557104
$785$		−	132312.i		−	0.214713i
$786$	−350025.	−	564223.i	−0.566571	−	0.913284i
$787$	−123407.			−0.199246			−0.0996228	−	0.995025i	$-0.531764\pi$
$787$	−123407.			−0.199246			−0.0996228	+	0.995025i	$0.531764\pi$
$788$		−	544751.i		−	0.877295i
$789$	242888.	−	150679.i	0.390168	−	0.242047i
$790$	−79254.0			−0.126989
$791$			443155.i			0.708276i
$792$	44658.8	−	90075.6i	0.0711962	−	0.143601i
$793$	−224457.			−0.356934
$794$			804937.i			1.27679i
$795$	39467.7	+	63620.0i	0.0624464	+	0.100661i
$796$	−32658.2			−0.0515426
$797$		−	37001.6i		−	0.0582511i	−0.999576	−	0.0291256i	$-0.990728\pi$
$797$		−	37001.6i		−	0.0582511i	0.999576	−	0.0291256i	$-0.00927226\pi$
$798$	557649.	−	345947.i	0.875699	−	0.543254i
$799$	164401.			0.257520
$800$		−	715561.i		−	1.11806i
$801$	−1.00299e6	−	497275.i	−1.56326	−	0.775053i
$802$	−671815.			−1.04448
$803$		−	116093.i		−	0.180043i
$804$	−229424.	−	369820.i	−0.354917	−	0.572108i
$805$	34739.2			0.0536078
$806$		−	357194.i		−	0.549837i
$807$	206709.	−	128236.i	0.317405	−	0.196907i
$808$	−155769.			−0.238594
$809$		−	758733.i		−	1.15929i	−0.814869	−	0.579645i	$-0.803191\pi$
$809$		−	758733.i		−	1.15929i	0.814869	−	0.579645i	$-0.196809\pi$
$810$	146986.	+	193252.i	0.224030	+	0.294547i
$811$	253096.			0.384808			0.192404	−	0.981316i	$-0.438372\pi$
$811$	253096.			0.384808			0.192404	+	0.981316i	$0.438372\pi$
$812$			43836.1i			0.0664844i
$813$	482452.	+	777689.i	0.729916	+	1.17659i
$814$	−576600.			−0.870213
$815$			205686.i			0.309663i
$816$	195587.	−	121336.i	0.293738	−	0.182225i
$817$	−1.23997e6			−1.85766
$818$		−	201299.i		−	0.300840i
$819$	−93064.9	+	187709.i	−0.138745	+	0.279846i
$820$	9731.82			0.0144733
$821$			248987.i			0.369394i	0.982796	+	0.184697i	$0.0591303\pi$
$821$			248987.i			0.369394i	−0.982796	+	0.184697i	$0.940870\pi$
$822$	337228.	+	543596.i	0.499092	+	0.804511i
$823$	−816985.			−1.20619			−0.603093	−	0.797671i	$-0.706065\pi$
$823$	−816985.			−1.20619			−0.603093	+	0.797671i	$0.706065\pi$
$824$			94179.6i			0.138708i
$825$	−236578.	+	146765.i	−0.347590	+	0.215633i
$826$	−85374.9			−0.125133
$827$			772154.i			1.12900i	0.825434	+	0.564499i	$0.190931\pi$
$827$			772154.i			1.12900i	−0.825434	+	0.564499i	$0.809069\pi$
$828$	−115858.	−	57441.6i	−0.168992	−	0.0837849i
$829$	−1.13250e6			−1.64789			−0.823946	−	0.566668i	$-0.808232\pi$
$829$	−1.13250e6			−1.64789			−0.823946	+	0.566668i	$0.808232\pi$
$830$		−	163432.i		−	0.237236i
$831$	383370.	+	617974.i	0.555158	+	0.894887i
$832$	117017.			0.169045
$833$		−	92917.5i		−	0.133908i
$834$	−105465.	+	65426.8i	−0.151627	+	0.0940640i
$835$	99004.5			0.141998
$836$			241499.i			0.345543i
$837$	683902.	−	65156.4i	0.976210	−	0.0930050i
$838$	1.27218e6			1.81159
$839$			774960.i			1.10092i	0.834862	+	0.550460i	$0.185547\pi$
$839$			774960.i			1.10092i	−0.834862	+	0.550460i	$0.814453\pi$
$840$	−27662.7	−	44590.9i	−0.0392045	−	0.0631957i
$841$	696184.			0.984310
$842$		−	1.46445e6i		−	2.06562i
$843$	9036.95	−	5606.22i	0.0127165	−	0.00788887i
$844$	182082.			0.255613
$845$		−	164509.i		−	0.230397i
$846$	−373077.	+	752487.i	−0.521264	+	1.05138i
$847$	421324.			0.587285
$848$			362587.i			0.504221i
$849$	513297.	+	827409.i	0.712120	+	1.14790i
$850$	−251842.			−0.348571
$851$		−	280799.i		−	0.387736i
$852$	128591.	−	79773.2i	0.177145	−	0.109895i
$853$	−362277.			−0.497901			−0.248950	−	0.968516i	$-0.580086\pi$
$853$	−362277.			−0.497901			−0.248950	+	0.968516i	$0.580086\pi$
$854$		−	586154.i		−	0.803703i
$855$	197835.	+	98085.0i	0.270627	+	0.134175i
$856$	−246864.			−0.336907
$857$		−	949058.i		−	1.29220i	−0.763251	−	0.646102i	$-0.776398\pi$
$857$		−	949058.i		−	1.29220i	0.763251	−	0.646102i	$-0.223602\pi$
$858$	−96679.6	−	155843.i	−0.131329	−	0.211696i
$859$	−1.08543e6			−1.47101			−0.735505	−	0.677520i	$-0.763055\pi$
$859$	−1.08543e6			−1.47101			−0.735505	+	0.677520i	$0.763055\pi$
$860$		−	261875.i		−	0.354077i
$861$	−32646.3	+	20252.7i	−0.0440380	+	0.0273197i
$862$	−995781.			−1.34014
$863$		−	484952.i		−	0.651144i	−0.945517	−	0.325572i	$-0.894443\pi$
$863$		−	484952.i		−	0.651144i	0.945517	−	0.325572i	$-0.105557\pi$
$864$	85982.7	+	902502.i	0.115182	+	1.20898i
$865$	76404.5			0.102114
$866$		−	615693.i		−	0.820972i
$867$	363339.	+	585685.i	0.483364	+	0.779159i
$868$	392154.			0.520496
$869$			115137.i			0.152467i
$870$	−29814.0	+	18495.6i	−0.0393896	+	0.0244360i
$871$	300572.			0.396198
$872$		−	85853.4i		−	0.112908i
$873$	−386909.	+	780386.i	−0.507669	+	1.02396i
$874$	−279743.			−0.366216
$875$			303145.i			0.395945i
$876$	118905.	+	191669.i	0.154950	+	0.249772i
$877$	531862.			0.691511			0.345756	−	0.938325i	$-0.387623\pi$
$877$	531862.			0.691511			0.345756	+	0.938325i	$0.387623\pi$
$878$		−	1.78854e6i		−	2.32011i
$879$	299133.	−	185572.i	0.387157	−	0.240179i
$880$	116247.			0.150112
$881$			1.32814e6i			1.71117i	0.517664	+	0.855584i	$0.326802\pi$
$881$			1.32814e6i			1.71117i	−0.517664	+	0.855584i	$0.673198\pi$
$882$	425297.	+	210859.i	0.546708	+	0.271053i
$883$	−187714.			−0.240755			−0.120377	−	0.992728i	$-0.538410\pi$
$883$	−187714.			−0.240755			−0.120377	+	0.992728i	$0.538410\pi$
$884$		−	69745.5i		−	0.0892507i
$885$	−15144.1	−	24411.5i	−0.0193355	−	0.0311679i
$886$	600427.			0.764879
$887$		−	1.22289e6i		−	1.55432i	−0.629301	−	0.777161i	$-0.716659\pi$
$887$		−	1.22289e6i		−	1.55432i	0.629301	−	0.777161i	$-0.283341\pi$
$888$	−360430.	+	223599.i	−0.457083	+	0.283559i
$889$	227664.			0.288065
$890$		−	511463.i		−	0.645705i
$891$	280749.	−	213535.i	0.353641	−	0.268977i
$892$	−153404.			−0.192800
$893$			763849.i			0.957866i
$894$	686216.	+	1.10615e6i	0.858590	+	1.38400i
$895$	−124418.			−0.155324
$896$		−	407854.i		−	0.508029i
$897$	75893.9	−	47082.0i	0.0943240	−	0.0585154i
$898$	1.76863e6			2.19323
$899$			99273.3i			0.122832i
$900$	240269.	−	484617.i	0.296629	−	0.598293i
$901$	98388.0			0.121197
$902$		−	33628.9i		−	0.0413333i
$903$	544984.	+	878487.i	0.668356	+	1.07736i
$904$	−285352.			−0.349176
$905$			375338.i			0.458274i
$906$	720063.	−	446703.i	0.877231	−	0.544205i
$907$	1.07626e6			1.30828			0.654140	−	0.756374i	$-0.273031\pi$
$907$	1.07626e6			1.30828			0.654140	+	0.756374i	$0.273031\pi$
$908$			863287.i			1.04709i
$909$	−489625.	−	242752.i	−0.592565	−	0.293789i
$910$	−95720.1			−0.115590
$911$			184327.i			0.222102i	0.993815	+	0.111051i	$0.0354217\pi$
$911$			184327.i			0.222102i	−0.993815	+	0.111051i	$0.964578\pi$
$912$	563757.	+	908749.i	0.677802	+	1.09258i
$913$	−237428.			−0.284832
$914$			689631.i			0.825514i
$915$	167601.	−	103974.i	0.200186	−	0.124189i
$916$	273837.			0.326363
$917$			503457.i			0.598720i
$918$	317637.	−	30261.7i	0.376917	−	0.0359094i
$919$	−814252.			−0.964113			−0.482057	−	0.876140i	$-0.660110\pi$
$919$	−814252.			−0.964113			−0.482057	+	0.876140i	$0.660110\pi$
$920$			22368.9i			0.0264283i
$921$	−91544.8	−	147566.i	−0.107923	−	0.173967i
$922$	−1.10750e6			−1.30281
$923$			104512.i			0.122677i
$924$	171096.	−	106142.i	0.200399	−	0.124321i
$925$	1.17454e6			1.37273
$926$		−	21386.8i		−	0.0249415i
$927$	−146770.	+	296032.i	−0.170796	+	0.344492i
$928$	−131005.			−0.152121
$929$			269110.i			0.311816i	0.987772	+	0.155908i	$0.0498304\pi$
$929$			269110.i			0.311816i	−0.987772	+	0.155908i	$0.950170\pi$
$930$	165460.	+	266714.i	0.191306	+	0.308375i
$931$	431719.			0.498083
$932$			438683.i			0.505032i
$933$	1.21101e6	−	751269.i	1.39118	−	0.863043i
$934$	−689877.			−0.790821
$935$		−	31543.6i		−	0.0360818i
$936$	−120868.	−	59925.4i	−0.137962	−	0.0684005i
$937$	−512738.			−0.584005			−0.292002	−	0.956418i	$-0.594322\pi$
$937$	−512738.			−0.584005			−0.292002	+	0.956418i	$0.594322\pi$
$938$			784921.i			0.892114i
$939$	−382714.	−	616917.i	−0.434054	−	0.699673i
$940$	−161321.			−0.182573
$941$		−	247461.i		−	0.279465i	−0.990189	−	0.139732i	$-0.955376\pi$
$941$		−	247461.i		−	0.279465i	0.990189	−	0.139732i	$-0.0446242\pi$
$942$	754853.	−	468286.i	0.850669	−	0.527727i
$943$	16377.0			0.0184166
$944$		−	139128.i		−	0.156124i
$945$	−17460.5	−	183271.i	−0.0195521	−	0.205225i
$946$	−904928.			−1.01119
$947$		−	1.23441e6i		−	1.37645i	−0.725499	−	0.688223i	$-0.758391\pi$
$947$		−	1.23441e6i		−	1.37645i	0.725499	−	0.688223i	$-0.241609\pi$
$948$	−117926.	−	190091.i	−0.131218	−	0.211517i
$949$	−155780.			−0.172973
$950$		−	1.17012e6i		−	1.29654i
$951$	57930.3	−	35938.0i	0.0640538	−	0.0397368i
$952$	−68959.5			−0.0760887
$953$			1.79496e6i			1.97637i	0.153265	+	0.988185i	$0.451021\pi$
$953$			1.79496e6i			1.97637i	−0.153265	+	0.988185i	$0.548979\pi$
$954$	−223273.	+	450336.i	−0.245324	+	0.494812i
$955$	317317.			0.347925
$956$			748936.i			0.819462i
$957$	26869.7	+	43312.7i	0.0293386	+	0.0472924i
$958$	1.20651e6			1.31462
$959$		−	485051.i		−	0.527412i
$960$	−87375.8	+	54205.0i	−0.0948088	+	0.0588162i
$961$	−35430.9			−0.0383651
$962$			773711.i			0.836043i
$963$	−775960.	−	384715.i	−0.836733	−	0.414845i
$964$	−649463.			−0.698876
$965$			325024.i			0.349029i
$966$	122951.	+	198191.i	0.131758	+	0.212388i
$967$	1.37711e6			1.47271			0.736354	−	0.676596i	$-0.236546\pi$
$967$	1.37711e6			1.47271			0.736354	+	0.676596i	$0.236546\pi$
$968$			271295.i			0.289528i
$969$	246589.	−	152975.i	0.262619	−	0.162920i
$970$	−397948.			−0.422944
$971$		−	426671.i		−	0.452538i	−0.974065	−	0.226269i	$-0.927347\pi$
$971$		−	426671.i		−	0.452538i	0.974065	−	0.226269i	$-0.0726528\pi$
$972$	−244808.	+	640096.i	−0.259115	+	0.677505i
$973$	94106.2			0.0994015
$974$		−	1710.01i		−	0.00180252i
$975$	196937.	+	317453.i	0.207166	+	0.333941i
$976$	955201.			1.00276
$977$		−	1.71172e6i		−	1.79326i	−0.442777	−	0.896632i	$-0.646007\pi$
$977$		−	1.71172e6i		−	1.79326i	0.442777	−	0.896632i	$-0.353993\pi$
$978$	−1.17346e6	+	727977.i	−1.22685	+	0.761097i
$979$	−743034.			−0.775253
$980$			91176.9i			0.0949364i
$981$	133795.	−	269861.i	0.139028	−	0.280415i
$982$	2.25037e6			2.33363
$983$		−	1.83564e6i		−	1.89968i	−0.312741	−	0.949839i	$-0.601247\pi$
$983$		−	1.83564e6i		−	1.89968i	0.312741	−	0.949839i	$-0.398753\pi$
$984$	−13040.9	−	21021.3i	−0.0134685	−	0.0217105i
$985$	−330596.			−0.340742
$986$			46107.2i			0.0474259i
$987$	541168.	−	335722.i	0.555517	−	0.344624i
$988$	324055.			0.331975
$989$		−	440691.i		−	0.450549i
$990$	144380.	+	71582.3i	0.147311	+	0.0730357i
$991$	1.33828e6			1.36269			0.681347	−	0.731961i	$-0.261395\pi$
$991$	1.33828e6			1.36269			0.681347	+	0.731961i	$0.261395\pi$
$992$			1.17196e6i			1.19093i
$993$	82307.5	+	132676.i	0.0834720	+	0.134553i
$994$	−272926.			−0.276231
$995$			19819.5i			0.0200192i
$996$	391992.	−	243179.i	0.395147	−	0.245136i
$997$	968948.			0.974788			0.487394	−	0.873182i	$-0.337947\pi$
$997$	968948.			0.974788			0.487394	+	0.873182i	$0.337947\pi$
$998$		−	1.10088e6i		−	1.10530i
$999$	−1.48139e6	+	141134.i	−1.48435	+	0.141417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.62	yes	78
3.2	odd	2	inner	177.5.b.a.119.17	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.17	✓	78	3.2	odd	2	inner
177.5.b.a.119.62	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)

\(f(q)\)	\(=\)	\(q+5.25412i q^{2} +(4.74448 + 7.64787i) q^{3} -11.6058 q^{4} +7.04330i q^{5} +(-40.1829 + 24.9281i) q^{6} +35.8552 q^{7} +23.0875i q^{8} +(-35.9798 + 72.5703i) q^{9} +O(q^{10})\)	\(q+5.25412i q^{2} +(4.74448 + 7.64787i) q^{3} -11.6058 q^{4} +7.04330i q^{5} +(-40.1829 + 24.9281i) q^{6} +35.8552 q^{7} +23.0875i q^{8} +(-35.9798 + 72.5703i) q^{9} -37.0064 q^{10} +53.7614i q^{11} +(-55.0636 - 88.7598i) q^{12} +72.1398 q^{13} +188.388i q^{14} +(-53.8662 + 33.4168i) q^{15} -306.998 q^{16} +83.3038i q^{17} +(-381.294 - 189.042i) q^{18} -387.051 q^{19} -81.7433i q^{20} +(170.114 + 274.216i) q^{21} -282.469 q^{22} -137.560i q^{23} +(-176.570 + 109.538i) q^{24} +575.392 q^{25} +379.032i q^{26} +(-725.714 + 69.1399i) q^{27} -416.129 q^{28} -105.343i q^{29} +(-175.576 - 283.020i) q^{30} -942.385 q^{31} -1243.61i q^{32} +(-411.160 + 255.070i) q^{33} -437.689 q^{34} +252.539i q^{35} +(417.575 - 842.239i) q^{36} +2041.28 q^{37} -2033.61i q^{38} +(342.266 + 551.716i) q^{39} -162.612 q^{40} +119.053i q^{41} +(-1440.76 + 893.802i) q^{42} +3203.63 q^{43} -623.946i q^{44} +(-511.134 - 253.416i) q^{45} +722.756 q^{46} -1973.51i q^{47} +(-1456.55 - 2347.88i) q^{48} -1115.41 q^{49} +3023.18i q^{50} +(-637.097 + 395.233i) q^{51} -837.242 q^{52} -1181.07i q^{53} +(-363.269 - 3812.99i) q^{54} -378.658 q^{55} +827.808i q^{56} +(-1836.36 - 2960.11i) q^{57} +553.483 q^{58} +453.188i q^{59} +(625.162 - 387.829i) q^{60} -3111.42 q^{61} -4951.41i q^{62} +(-1290.06 + 2602.02i) q^{63} +1622.09 q^{64} +508.102i q^{65} +(-1340.17 - 2160.29i) q^{66} +4166.52 q^{67} -966.810i q^{68} +(1052.04 - 652.650i) q^{69} -1326.87 q^{70} +1448.75i q^{71} +(-1675.47 - 830.685i) q^{72} -2159.42 q^{73} +10725.2i q^{74} +(2729.94 + 4400.52i) q^{75} +4492.04 q^{76} +1927.63i q^{77} +(-2898.78 + 1798.31i) q^{78} +2141.63 q^{79} -2162.28i q^{80} +(-3971.91 - 5222.13i) q^{81} -625.522 q^{82} +4416.32i q^{83} +(-1974.32 - 3182.50i) q^{84} -586.733 q^{85} +16832.3i q^{86} +(805.646 - 499.796i) q^{87} -1241.22 q^{88} +13821.0i q^{89} +(1331.48 - 2685.56i) q^{90} +2586.59 q^{91} +1596.50i q^{92} +(-4471.13 - 7207.24i) q^{93} +10369.1 q^{94} -2726.11i q^{95} +(9510.93 - 5900.26i) q^{96} +10753.5 q^{97} -5860.48i q^{98} +(-3901.48 - 1934.32i) 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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