LMFDB - Embedded newform 177.5.b.a.119.69

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			119.69
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.42743i q^{2} +(2.05646 - 8.76190i) q^{3} -25.3118 q^{4} +39.0573i q^{5} +(56.3165 + 13.2178i) q^{6} +65.2885 q^{7} -59.8512i q^{8} +(-72.5419 - 36.0371i) q^{9} +O(q^{10})$	\(q+6.42743i q^{2} +(2.05646 - 8.76190i) q^{3} -25.3118 q^{4} +39.0573i q^{5} +(56.3165 + 13.2178i) q^{6} +65.2885 q^{7} -59.8512i q^{8} +(-72.5419 - 36.0371i) q^{9} -251.038 q^{10} -5.09361i q^{11} +(-52.0529 + 221.780i) q^{12} +300.078 q^{13} +419.637i q^{14} +(342.216 + 80.3200i) q^{15} -20.3001 q^{16} +418.344i q^{17} +(231.626 - 466.258i) q^{18} -156.757 q^{19} -988.613i q^{20} +(134.263 - 572.051i) q^{21} +32.7388 q^{22} -238.716i q^{23} +(-524.410 - 123.082i) q^{24} -900.474 q^{25} +1928.73i q^{26} +(-464.933 + 561.496i) q^{27} -1652.57 q^{28} +1294.15i q^{29} +(-516.251 + 2199.57i) q^{30} -398.653 q^{31} -1088.10i q^{32} +(-44.6297 - 10.4748i) q^{33} -2688.88 q^{34} +2549.99i q^{35} +(1836.17 + 912.165i) q^{36} -2417.21 q^{37} -1007.54i q^{38} +(617.099 - 2629.25i) q^{39} +2337.63 q^{40} -3.98886i q^{41} +(3676.82 + 862.968i) q^{42} +159.503 q^{43} +128.929i q^{44} +(1407.51 - 2833.29i) q^{45} +1534.33 q^{46} +1473.68i q^{47} +(-41.7465 + 177.868i) q^{48} +1861.58 q^{49} -5787.73i q^{50} +(3665.49 + 860.309i) q^{51} -7595.52 q^{52} -3452.21i q^{53} +(-3608.98 - 2988.33i) q^{54} +198.943 q^{55} -3907.59i q^{56} +(-322.365 + 1373.49i) q^{57} -8318.04 q^{58} -453.188i q^{59} +(-8662.13 - 2033.05i) q^{60} +3005.69 q^{61} -2562.31i q^{62} +(-4736.15 - 2352.81i) q^{63} +6668.86 q^{64} +11720.2i q^{65} +(67.3262 - 286.854i) q^{66} +8611.05 q^{67} -10589.1i q^{68} +(-2091.60 - 490.910i) q^{69} -16389.9 q^{70} +8909.51i q^{71} +(-2156.86 + 4341.72i) q^{72} -879.765 q^{73} -15536.4i q^{74} +(-1851.79 + 7889.87i) q^{75} +3967.81 q^{76} -332.554i q^{77} +(16899.3 + 3966.36i) q^{78} +3607.80 q^{79} -792.869i q^{80} +(3963.66 + 5228.40i) q^{81} +25.6381 q^{82} -315.278i q^{83} +(-3398.45 + 14479.7i) q^{84} -16339.4 q^{85} +1025.19i q^{86} +(11339.2 + 2661.37i) q^{87} -304.859 q^{88} -12623.1i q^{89} +(18210.8 + 9046.68i) q^{90} +19591.6 q^{91} +6042.33i q^{92} +(-819.815 + 3492.96i) q^{93} -9471.97 q^{94} -6122.50i q^{95} +(-9533.80 - 2237.63i) q^{96} +449.576 q^{97} +11965.2i q^{98} +(-183.559 + 369.500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			6.42743i			1.60686i	0.595401	+	0.803429i	$0.296993\pi$
$2$			6.42743i			1.60686i	−0.595401	+	0.803429i	$0.703007\pi$
$3$	2.05646	−	8.76190i	0.228496	−	0.973545i
$3$	2.05646	−	8.76190i	0.228496	−	0.973545i
$4$	−25.3118			−1.58199
$5$			39.0573i			1.56229i	0.624348	+	0.781146i	$0.285365\pi$
$5$			39.0573i			1.56229i	−0.624348	+	0.781146i	$0.714635\pi$
$6$	56.3165	+	13.2178i	1.56435	+	0.367160i
$7$	65.2885			1.33242			0.666209	−	0.745765i	$-0.267916\pi$
$7$	65.2885			1.33242			0.666209	+	0.745765i	$0.267916\pi$
$8$		−	59.8512i		−	0.935175i
$9$	−72.5419	−	36.0371i	−0.895579	−	0.444902i
$10$	−251.038			−2.51038
$11$		−	5.09361i		−	0.0420960i	−0.999778	−	0.0210480i	$-0.993300\pi$
$11$		−	5.09361i		−	0.0420960i	0.999778	−	0.0210480i	$-0.00670028\pi$
$12$	−52.0529	+	221.780i	−0.361478	+	1.54014i
$13$	300.078			1.77561			0.887804	−	0.460222i	$-0.152230\pi$
$13$	300.078			1.77561			0.887804	+	0.460222i	$0.152230\pi$
$14$			419.637i			2.14100i
$15$	342.216	+	80.3200i	1.52096	+	0.356978i
$16$	−20.3001			−0.0792974
$17$			418.344i			1.44756i	0.690032	+	0.723779i	$0.257596\pi$
$17$			418.344i			1.44756i	−0.690032	+	0.723779i	$0.742404\pi$
$18$	231.626	−	466.258i	0.714894	−	1.43907i
$19$	−156.757			−0.434230			−0.217115	−	0.976146i	$-0.569665\pi$
$19$	−156.757			−0.434230			−0.217115	+	0.976146i	$0.569665\pi$
$20$		−	988.613i		−	2.47153i
$21$	134.263	−	572.051i	0.304452	−	1.29717i
$22$	32.7388			0.0676422
$23$		−	238.716i		−	0.451258i	−0.974213	−	0.225629i	$-0.927556\pi$
$23$		−	238.716i		−	0.451258i	0.974213	−	0.225629i	$-0.0724438\pi$
$24$	−524.410	−	123.082i	−0.910435	−	0.213684i
$25$	−900.474			−1.44076
$26$			1928.73i			2.85315i
$27$	−464.933	+	561.496i	−0.637769	+	0.770228i
$28$	−1652.57			−2.10787
$29$			1294.15i			1.53882i	0.638755	+	0.769410i	$0.279450\pi$
$29$			1294.15i			1.53882i	−0.638755	+	0.769410i	$0.720550\pi$
$30$	−516.251	+	2199.57i	−0.573612	+	2.44397i
$31$	−398.653			−0.414831			−0.207416	−	0.978253i	$-0.566505\pi$
$31$	−398.653			−0.414831			−0.207416	+	0.978253i	$0.566505\pi$
$32$		−	1088.10i		−	1.06259i
$33$	−44.6297	−	10.4748i	−0.0409823	−	0.00961876i
$34$	−2688.88			−2.32602
$35$			2549.99i			2.08163i
$36$	1836.17	+	912.165i	1.41680	+	0.703831i
$37$	−2417.21			−1.76568			−0.882838	−	0.469678i	$-0.844370\pi$
$37$	−2417.21			−1.76568			−0.882838	+	0.469678i	$0.844370\pi$
$38$		−	1007.54i		−	0.697745i
$39$	617.099	−	2629.25i	0.405719	−	1.72863i
$40$	2337.63			1.46102
$41$		−	3.98886i		−	0.00237291i	−0.999999	−	0.00118645i	$-0.999622\pi$
$41$		−	3.98886i		−	0.00237291i	0.999999	−	0.00118645i	$-0.000377660\pi$
$42$	3676.82	+	862.968i	2.08436	+	0.489211i
$43$	159.503			0.0862642			0.0431321	−	0.999069i	$-0.486266\pi$
$43$	159.503			0.0862642			0.0431321	+	0.999069i	$0.486266\pi$
$44$			128.929i			0.0665954i
$45$	1407.51	−	2833.29i	0.695067	−	1.39916i
$46$	1534.33			0.725108
$47$			1473.68i			0.667125i	0.942728	+	0.333563i	$0.108251\pi$
$47$			1473.68i			0.667125i	−0.942728	+	0.333563i	$0.891749\pi$
$48$	−41.7465	+	177.868i	−0.0181191	+	0.0771996i
$49$	1861.58			0.775337
$50$		−	5787.73i		−	2.31509i
$51$	3665.49	+	860.309i	1.40926	+	0.330761i
$52$	−7595.52			−2.80899
$53$		−	3452.21i		−	1.22898i	−0.788924	−	0.614491i	$-0.789361\pi$
$53$		−	3452.21i		−	1.22898i	0.788924	−	0.614491i	$-0.210639\pi$
$54$	−3608.98	−	2988.33i	−1.23765	−	1.02480i
$55$	198.943			0.0657662
$56$		−	3907.59i		−	1.24604i
$57$	−322.365	+	1373.49i	−0.0992197	+	0.422742i
$58$	−8318.04			−2.47266
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	−8662.13	−	2033.05i	−2.40615	−	0.564735i
$61$	3005.69			0.807763			0.403882	−	0.914811i	$-0.367661\pi$
$61$	3005.69			0.807763			0.403882	+	0.914811i	$0.367661\pi$
$62$		−	2562.31i		−	0.666574i
$63$	−4736.15	−	2352.81i	−1.19329	−	0.592796i
$64$	6668.86			1.62814
$65$			11720.2i			2.77402i
$66$	67.3262	−	286.854i	0.0154560	−	0.0658527i
$67$	8611.05			1.91825			0.959127	−	0.282974i	$-0.0913212\pi$
$67$	8611.05			1.91825			0.959127	+	0.282974i	$0.0913212\pi$
$68$		−	10589.1i		−	2.29002i
$69$	−2091.60	−	490.910i	−0.439320	−	0.103111i
$70$	−16389.9			−3.34488
$71$			8909.51i			1.76741i	0.468045	+	0.883705i	$0.344959\pi$
$71$			8909.51i			1.76741i	−0.468045	+	0.883705i	$0.655041\pi$
$72$	−2156.86	+	4341.72i	−0.416061	+	0.837523i
$73$	−879.765			−0.165090			−0.0825451	−	0.996587i	$-0.526305\pi$
$73$	−879.765			−0.165090			−0.0825451	+	0.996587i	$0.526305\pi$
$74$		−	15536.4i		−	2.83719i
$75$	−1851.79	+	7889.87i	−0.329208	+	1.40264i
$76$	3967.81			0.686947
$77$		−	332.554i		−	0.0560894i
$78$	16899.3	+	3966.36i	2.77767	+	0.651933i
$79$	3607.80			0.578081			0.289040	−	0.957317i	$-0.406664\pi$
$79$	3607.80			0.578081			0.289040	+	0.957317i	$0.406664\pi$
$80$		−	792.869i		−	0.123886i
$81$	3963.66	+	5228.40i	0.604124	+	0.796890i
$82$	25.6381			0.00381293
$83$		−	315.278i		−	0.0457654i	−0.999738	−	0.0228827i	$-0.992716\pi$
$83$		−	315.278i		−	0.0457654i	0.999738	−	0.0228827i	$-0.00728442\pi$
$84$	−3398.45	+	14479.7i	−0.481640	+	2.05211i
$85$	−16339.4			−2.26151
$86$			1025.19i			0.138614i
$87$	11339.2	+	2661.37i	1.49811	+	0.351614i
$88$	−304.859			−0.0393671
$89$		−	12623.1i		−	1.59363i	−0.604225	−	0.796814i	$-0.706517\pi$
$89$		−	12623.1i		−	1.59363i	0.604225	−	0.796814i	$-0.293483\pi$
$90$	18210.8	+	9046.68i	2.24825	+	1.11687i
$91$	19591.6			2.36585
$92$			6042.33i			0.713886i
$93$	−819.815	+	3492.96i	−0.0947872	+	0.403857i
$94$	−9471.97			−1.07198
$95$		−	6122.50i		−	0.678394i
$96$	−9533.80	−	2237.63i	−1.03448	−	0.242799i
$97$	449.576			0.0477815			0.0238907	−	0.999715i	$-0.492395\pi$
$97$	449.576			0.0477815			0.0238907	+	0.999715i	$0.492395\pi$
$98$			11965.2i			1.24586i
$99$	−183.559	+	369.500i	−0.0187286	+	0.0377003i
$100$	22792.7			2.27927
$101$			4754.47i			0.466079i	0.972467	+	0.233039i	$0.0748671\pi$
$101$			4754.47i			0.466079i	−0.972467	+	0.233039i	$0.925133\pi$
$102$	−5529.58	+	23559.7i	−0.531486	+	2.26448i
$103$	−10711.2			−1.00963			−0.504816	−	0.863227i	$-0.668440\pi$
$103$	−10711.2			−1.00963			−0.504816	+	0.863227i	$0.668440\pi$
$104$		−	17960.0i		−	1.66050i
$105$	22342.8	+	5243.97i	2.02656	+	0.475643i
$106$	22188.9			1.97480
$107$			3010.10i			0.262914i	0.991322	+	0.131457i	$0.0419656\pi$
$107$			3010.10i			0.262914i	−0.991322	+	0.131457i	$0.958034\pi$
$108$	11768.3	−	14212.5i	1.00894	−	1.21849i
$109$	−450.138			−0.0378872			−0.0189436	−	0.999821i	$-0.506030\pi$
$109$	−450.138			−0.0378872			−0.0189436	+	0.999821i	$0.506030\pi$
$110$			1278.69i			0.105677i
$111$	−4970.90	+	21179.4i	−0.403450	+	1.71896i
$112$	−1325.36			−0.105657
$113$		−	13280.6i		−	1.04007i	−0.854146	−	0.520034i	$-0.825919\pi$
$113$		−	13280.6i		−	1.04007i	0.854146	−	0.520034i	$-0.174081\pi$
$114$	−8828.00	−	2071.98i	−0.679286	−	0.159432i
$115$	9323.60			0.704998
$116$		−	32757.3i		−	2.43440i
$117$	−21768.2	−	10813.9i	−1.59020	−	0.789972i
$118$	2912.83			0.209195
$119$			27313.0i			1.92875i
$120$	4807.25	−	20482.1i	0.333837	−	1.42237i
$121$	14615.1			0.998228
$122$			19318.8i			1.29796i
$123$	−34.9500	−	8.20295i	−0.00231013	−	0.000542200i
$124$	10090.6			0.656259
$125$		−	10759.3i		−	0.688594i
$126$	15122.5	−	30441.3i	0.952538	−	1.91744i
$127$	29458.7			1.82644			0.913222	−	0.407462i	$-0.133586\pi$
$127$	29458.7			1.82644			0.913222	+	0.407462i	$0.133586\pi$
$128$			25454.1i			1.55359i
$129$	328.011	−	1397.55i	0.0197110	−	0.0839821i
$130$	−75330.9			−4.45745
$131$		−	4752.97i		−	0.276963i	−0.990365	−	0.138482i	$-0.955778\pi$
$131$		−	4752.97i		−	0.276963i	0.990365	−	0.138482i	$-0.0442222\pi$
$132$	1129.66	+	265.137i	0.0648336	+	0.0152168i
$133$	−10234.4			−0.578575
$134$			55346.9i			3.08236i
$135$	−21930.5	−	18159.0i	−1.20332	−	0.996381i
$136$	25038.4			1.35372
$137$		−	9420.01i		−	0.501892i	−0.968001	−	0.250946i	$-0.919258\pi$
$137$		−	9420.01i		−	0.501892i	0.968001	−	0.250946i	$-0.0807417\pi$
$138$	3155.29	−	13443.6i	0.165684	−	0.705925i
$139$	8893.09			0.460281			0.230140	−	0.973157i	$-0.426081\pi$
$139$	8893.09			0.460281			0.230140	+	0.973157i	$0.426081\pi$
$140$		−	64545.0i		−	3.29311i
$141$	12912.2	+	3030.57i	0.649476	+	0.152435i
$142$	−57265.3			−2.83997
$143$		−	1528.48i		−	0.0747459i
$144$	1472.61	+	731.557i	0.0710171	+	0.0352796i
$145$	−50545.9			−2.40409
$146$		−	5654.63i		−	0.265276i
$147$	3828.28	−	16311.0i	0.177161	−	0.754825i
$148$	61184.0			2.79328
$149$		−	698.090i		−	0.0314441i	−0.999876	−	0.0157220i	$-0.994995\pi$
$149$		−	698.090i		−	0.0314441i	0.999876	−	0.0157220i	$-0.00500468\pi$
$150$	−50711.6	−	11902.3i	−2.25385	−	0.528990i
$151$	11188.7			0.490711			0.245355	−	0.969433i	$-0.421095\pi$
$151$	11188.7			0.490711			0.245355	+	0.969433i	$0.421095\pi$
$152$			9382.09i			0.406081i
$153$	15075.9	−	30347.5i	0.644021	−	1.29640i
$154$	2137.47			0.0901277
$155$		−	15570.3i		−	0.648088i
$156$	−15619.9	+	66551.2i	−0.641844	+	2.73468i
$157$	−15221.6			−0.617534			−0.308767	−	0.951138i	$-0.599916\pi$
$157$	−15221.6			−0.617534			−0.308767	+	0.951138i	$0.599916\pi$
$158$			23188.9i			0.928893i
$159$	−30248.0	−	7099.35i	−1.19647	−	0.280818i
$160$	42498.1			1.66008
$161$		−	15585.4i		−	0.601265i
$162$	−33605.2	+	25476.1i	−1.28049	+	0.970741i
$163$	15804.3			0.594838			0.297419	−	0.954747i	$-0.403874\pi$
$163$	15804.3			0.594838			0.297419	+	0.954747i	$0.403874\pi$
$164$			100.965i			0.00375392i
$165$	409.119	−	1743.12i	0.0150273	−	0.0640264i
$166$	2026.43			0.0735384
$167$		−	5741.63i		−	0.205875i	−0.994688	−	0.102937i	$-0.967176\pi$
$167$		−	5741.63i		−	0.205875i	0.994688	−	0.102937i	$-0.0328241\pi$
$168$	−34238.0	−	8035.82i	−1.21308	−	0.284716i
$169$	61485.6			2.15278
$170$		−	105020.i		−	3.63392i
$171$	11371.4	+	5649.06i	0.388887	+	0.193190i
$172$	−4037.30			−0.136469
$173$		−	55335.1i		−	1.84888i	−0.381331	−	0.924439i	$-0.624534\pi$
$173$		−	55335.1i		−	1.84888i	0.381331	−	0.924439i	$-0.375466\pi$
$174$	−17105.8	+	72881.9i	−0.564994	+	2.40725i
$175$	−58790.6			−1.91969
$176$			103.401i			0.00333810i
$177$	−3970.79	−	931.964i	−0.126745	−	0.0297476i
$178$	81134.2			2.56073
$179$			32249.6i			1.00651i	0.864137	+	0.503256i	$0.167865\pi$
$179$			32249.6i			1.00651i	−0.864137	+	0.503256i	$0.832135\pi$
$180$	−35626.7	+	71715.8i	−1.09959	+	2.21345i
$181$	−12535.0			−0.382621			−0.191310	−	0.981530i	$-0.561274\pi$
$181$	−12535.0			−0.382621			−0.191310	+	0.981530i	$0.561274\pi$
$182$			125924.i			3.80158i
$183$	6181.09	−	26335.5i	0.184571	−	0.786394i
$184$	−14287.4			−0.422006
$185$		−	94409.7i		−	2.75850i
$186$	−22450.7	−	5269.30i	−0.648940	−	0.152310i
$187$	2130.88			0.0609363
$188$		−	37301.5i		−	1.05539i
$189$	−30354.8	+	36659.2i	−0.849774	+	1.02627i
$190$	39352.0			1.09008
$191$			35056.0i			0.960939i	0.877012	+	0.480469i	$0.159534\pi$
$191$			35056.0i			0.960939i	−0.877012	+	0.480469i	$0.840466\pi$
$192$	13714.3	−	58431.9i	0.372024	−	1.58507i
$193$	17556.0			0.471314			0.235657	−	0.971836i	$-0.424276\pi$
$193$	17556.0			0.471314			0.235657	+	0.971836i	$0.424276\pi$
$194$			2889.62i			0.0767780i
$195$	102691.	+	24102.2i	2.70063	+	0.633852i
$196$	−47120.1			−1.22657
$197$		−	30322.4i		−	0.781323i	−0.920534	−	0.390662i	$-0.872246\pi$
$197$		−	30322.4i		−	0.781323i	0.920534	−	0.390662i	$-0.127754\pi$
$198$	−2374.94	−	1179.81i	−0.0605789	−	0.0300942i
$199$	−46440.1			−1.17270			−0.586351	−	0.810057i	$-0.699436\pi$
$199$	−46440.1			−1.17270			−0.586351	+	0.810057i	$0.699436\pi$
$200$			53894.5i			1.34736i
$201$	17708.3	−	75449.2i	0.438314	−	1.86751i
$202$	−30559.0			−0.748922
$203$			84492.9i			2.05035i
$204$	−92780.3	−	21776.0i	−2.22944	−	0.523261i
$205$	155.794			0.00370718
$206$		−	68845.4i		−	1.62234i
$207$	−8602.62	+	17316.9i	−0.200766	+	0.404138i
$208$	−6091.61			−0.140801
$209$			798.459i			0.0182793i
$210$	−33705.2	+	143607.i	−0.764291	+	3.25639i
$211$	55667.4			1.25036			0.625182	−	0.780479i	$-0.285025\pi$
$211$	55667.4			1.25036			0.625182	+	0.780479i	$0.285025\pi$
$212$			87381.9i			1.94424i
$213$	78064.3	+	18322.1i	1.72065	+	0.403846i
$214$	−19347.2			−0.422466
$215$			6229.74i			0.134770i
$216$	33606.2	+	27826.8i	0.720298	+	0.596425i
$217$	−26027.4			−0.552728
$218$		−	2893.23i		−	0.0608793i
$219$	−1809.21	+	7708.42i	−0.0377224	+	0.160723i
$220$	−5035.61			−0.104041
$221$			125536.i			2.57029i
$222$	−136129.	−	31950.1i	−2.76213	−	0.648286i
$223$	−35180.5			−0.707444			−0.353722	−	0.935351i	$-0.615084\pi$
$223$	−35180.5			−0.707444			−0.353722	+	0.935351i	$0.615084\pi$
$224$		−	71040.2i		−	1.41582i
$225$	65322.1	+	32450.5i	1.29031	+	0.640997i
$226$	85360.2			1.67124
$227$		−	22820.8i		−	0.442874i	−0.975175	−	0.221437i	$-0.928925\pi$
$227$		−	22820.8i		−	0.442874i	0.975175	−	0.221437i	$-0.0710747\pi$
$228$	8159.65	−	34765.5i	0.156965	−	0.668774i
$229$	43335.1			0.826359			0.413180	−	0.910650i	$-0.364418\pi$
$229$	43335.1			0.826359			0.413180	+	0.910650i	$0.364418\pi$
$230$			59926.7i			1.13283i
$231$	−2913.81	−	683.885i	−0.0546055	−	0.0128162i
$232$	77456.3			1.43907
$233$		−	57288.7i		−	1.05525i	−0.849476	−	0.527627i	$-0.823082\pi$
$233$		−	57288.7i		−	1.05525i	0.849476	−	0.527627i	$-0.176918\pi$
$234$	69505.7	−	139914.i	1.26937	−	2.55522i
$235$	−57558.0			−1.04224
$236$			11471.0i			0.205958i
$237$	7419.31	−	31611.2i	0.132089	−	0.562787i
$238$	−175553.			−3.09923
$239$		−	16376.2i		−	0.286693i	−0.989673	−	0.143346i	$-0.954214\pi$
$239$		−	16376.2i		−	0.286693i	0.989673	−	0.143346i	$-0.0457863\pi$
$240$	−6947.04	−	1630.51i	−0.120608	−	0.0283074i
$241$	−49424.5			−0.850958			−0.425479	−	0.904968i	$-0.639894\pi$
$241$	−49424.5			−0.850958			−0.425479	+	0.904968i	$0.639894\pi$
$242$			93937.2i			1.60401i
$243$	53961.8	−	23977.2i	0.913848	−	0.406056i
$244$	−76079.5			−1.27787
$245$			72708.5i			1.21130i
$246$	52.7239	−	224.639i	0.000871239	−	0.00371206i
$247$	−47039.2			−0.771021
$248$			23859.8i			0.387940i
$249$	−2762.43	−	648.357i	−0.0445547	−	0.0104572i
$250$	69154.5			1.10647
$251$		−	41797.4i		−	0.663440i	−0.943378	−	0.331720i	$-0.892371\pi$
$251$		−	41797.4i		−	0.663440i	0.943378	−	0.331720i	$-0.107629\pi$
$252$	119881.	+	59553.8i	1.88777	+	0.937797i
$253$	−1215.93			−0.0189962
$254$			189344.i			2.93484i
$255$	−33601.4	+	143164.i	−0.516746	+	2.20168i
$256$	−56902.6			−0.868264
$257$			126533.i			1.91574i	0.287207	+	0.957868i	$0.407273\pi$
$257$			126533.i			1.91574i	−0.287207	+	0.957868i	$0.592727\pi$
$258$	8982.62	+	2108.27i	0.134947	+	0.0316728i
$259$	−157816.			−2.35262
$260$		−	296661.i		−	4.38847i
$261$	46637.3	−	93879.9i	0.684624	−	1.37814i
$262$	30549.4			0.445041
$263$		−	87556.5i		−	1.26583i	−0.774219	−	0.632917i	$-0.781857\pi$
$263$		−	87556.5i		−	1.26583i	0.774219	−	0.632917i	$-0.218143\pi$
$264$	−626.931	+	2671.14i	−0.00899522	+	0.0383256i
$265$	134834.			1.92003
$266$		−	65781.0i		−	0.929688i
$267$	−110603.	−	25959.0i	−1.55147	−	0.364137i
$268$	−217961.			−3.03466
$269$		−	60072.7i		−	0.830181i	−0.909780	−	0.415091i	$-0.863750\pi$
$269$		−	60072.7i		−	0.830181i	0.909780	−	0.415091i	$-0.136250\pi$
$270$	116716.	−	140957.i	1.60104	−	1.93357i
$271$	92136.8			1.25457			0.627285	−	0.778790i	$-0.284166\pi$
$271$	92136.8			1.25457			0.627285	+	0.778790i	$0.284166\pi$
$272$		−	8492.44i		−	0.114788i
$273$	40289.4	−	171660.i	0.540587	−	2.30326i
$274$	60546.5			0.806469
$275$			4586.66i			0.0606501i
$276$	52942.4	+	12425.8i	0.695000	+	0.163120i
$277$	−8973.13			−0.116946			−0.0584728	−	0.998289i	$-0.518623\pi$
$277$	−8973.13			−0.116946			−0.0584728	+	0.998289i	$0.518623\pi$
$278$			57159.7i			0.739606i
$279$	28919.0	+	14366.3i	0.371514	+	0.184559i
$280$	152620.			1.94668
$281$		−	3227.90i		−	0.0408796i	−0.999791	−	0.0204398i	$-0.993493\pi$
$281$		−	3227.90i		−	0.0408796i	0.999791	−	0.0204398i	$-0.00650665\pi$
$282$	−19478.8	+	82992.5i	−0.244942	+	1.04362i
$283$	−61147.6			−0.763496			−0.381748	−	0.924266i	$-0.624678\pi$
$283$	−61147.6			−0.763496			−0.381748	+	0.924266i	$0.624678\pi$
$284$		−	225516.i		−	2.79602i
$285$	−53644.8	−	12590.7i	−0.660447	−	0.155010i
$286$	9824.19			0.120106
$287$		−	260.427i		−	0.00316171i
$288$	−39211.8	+	78932.6i	−0.472751	+	0.951638i
$289$	−91490.7			−1.09542
$290$		−	324880.i		−	3.86303i
$291$	924.537	−	3939.14i	0.0109179	−	0.0465174i
$292$	22268.5			0.261171
$293$			12342.0i			0.143764i	0.997413	+	0.0718819i	$0.0229005\pi$
$293$			12342.0i			0.143764i	−0.997413	+	0.0718819i	$0.977100\pi$
$294$	104838.	+	24606.0i	1.21290	+	0.284673i
$295$	17700.3			0.203393
$296$			144673.i			1.65122i
$297$	2860.04	+	2368.19i	0.0324235	+	0.0268475i
$298$	4486.92			0.0505261
$299$		−	71633.2i		−	0.801258i
$300$	46872.3	−	199707.i	0.520803	−	2.21897i
$301$	10413.7			0.114940
$302$			71914.6i			0.788502i
$303$	41658.2	+	9777.40i	0.453749	+	0.106497i
$304$	3182.19			0.0344333
$305$			117394.i			1.26196i
$306$	195056.	+	96899.3i	2.08313	+	1.03485i
$307$	159734.			1.69481			0.847404	−	0.530948i	$-0.178164\pi$
$307$	159734.			1.69481			0.847404	+	0.530948i	$0.178164\pi$
$308$			8417.56i			0.0887329i
$309$	−22027.2	+	93850.4i	−0.230697	+	0.982923i
$310$	100077.			1.04138
$311$			80684.0i			0.834193i	0.908862	+	0.417096i	$0.136952\pi$
$311$			80684.0i			0.834193i	−0.908862	+	0.417096i	$0.863048\pi$
$312$	−157364.	−	36934.1i	−1.61657	−	0.379418i
$313$	153894.			1.57085			0.785424	−	0.618958i	$-0.212445\pi$
$313$	153894.			1.57085			0.785424	+	0.618958i	$0.212445\pi$
$314$		−	97835.7i		−	0.992289i
$315$	91894.3	−	184981.i	0.926120	−	1.86426i
$316$	−91320.1			−0.914518
$317$			3629.96i			0.0361230i	0.999837	+	0.0180615i	$0.00574946\pi$
$317$			3629.96i			0.0361230i	−0.999837	+	0.0180615i	$0.994251\pi$
$318$	45630.6	−	194417.i	0.451234	−	1.92256i
$319$	6591.89			0.0647781
$320$			260468.i			2.54363i
$321$	26374.2	+	6190.17i	0.255959	+	0.0600748i
$322$	100174.			0.966147
$323$		−	65578.3i		−	0.628572i
$324$	−100327.	−	132340.i	−0.955718	−	1.26067i
$325$	−270212.			−2.55822
$326$			101581.i			0.955820i
$327$	−925.692	+	3944.06i	−0.00865707	+	0.0368849i
$328$	−238.738			−0.00221909
$329$			96214.3i			0.888889i
$330$	11203.8	+	2629.58i	0.102881	+	0.0241468i
$331$	−125930.			−1.14941			−0.574703	−	0.818362i	$-0.694883\pi$
$331$	−125930.			−1.14941			−0.574703	+	0.818362i	$0.694883\pi$
$332$			7980.26i			0.0724004i
$333$	175349.	+	87109.2i	1.58130	+	0.785553i
$334$	36903.9			0.330811
$335$			336324.i			2.99688i
$336$	−2725.56	+	11612.7i	−0.0241423	+	0.102862i
$337$	32949.8			0.290130			0.145065	−	0.989422i	$-0.453661\pi$
$337$	32949.8			0.290130			0.145065	+	0.989422i	$0.453661\pi$
$338$			395194.i			3.45921i
$339$	−116364.	−	27311.1i	−1.01255	−	0.237651i
$340$	413580.			3.57768
$341$			2030.58i			0.0174627i
$342$	−36308.9	+	73089.2i	−0.310428	+	0.624886i
$343$	−35217.7			−0.299345
$344$		−	9546.42i		−	0.0806721i
$345$	19173.6	−	81692.4i	0.161089	−	0.686347i
$346$	355662.			2.97088
$347$		−	156870.i		−	1.30281i	−0.758731	−	0.651404i	$-0.774180\pi$
$347$		−	156870.i		−	1.30281i	0.758731	−	0.651404i	$-0.225820\pi$
$348$	−287016.	−	67364.1i	−2.37000	−	0.556250i
$349$	−179198.			−1.47123			−0.735617	−	0.677397i	$-0.763108\pi$
$349$	−179198.			−1.47123			−0.735617	+	0.677397i	$0.763108\pi$
$350$		−	377872.i		−	3.08467i
$351$	−139516.	+	168492.i	−1.13243	+	1.36762i
$352$	−5542.34			−0.0447309
$353$			181513.i			1.45666i	0.685228	+	0.728329i	$0.259703\pi$
$353$			181513.i			1.45666i	−0.685228	+	0.728329i	$0.740297\pi$
$354$	5990.13	−	25521.9i	0.0478002	−	0.203661i
$355$	−347982.			−2.76121
$356$			319514.i			2.52110i
$357$	239314.	+	56168.3i	1.87773	+	0.440712i
$358$	−207282.			−1.61732
$359$		−	153380.i		−	1.19009i	−0.803691	−	0.595047i	$-0.797134\pi$
$359$		−	153380.i		−	1.19009i	0.803691	−	0.595047i	$-0.202866\pi$
$360$	−169576.	−	84241.3i	−1.30846	−	0.650010i
$361$	−105748.			−0.811445
$362$		−	80568.0i		−	0.614817i
$363$	30055.3	−	128056.i	0.228091	−	0.971820i
$364$	−495900.			−3.74275
$365$		−	34361.3i		−	0.257919i
$366$	169270.	+	39728.5i	1.26362	+	0.296579i
$367$	161326.			1.19776			0.598882	−	0.800837i	$-0.295612\pi$
$367$	161326.			1.19776			0.598882	+	0.800837i	$0.295612\pi$
$368$			4845.96i			0.0357836i
$369$	−143.747	+	289.360i	−0.00105571	+	0.00212513i
$370$	606812.			4.43252
$371$		−	225390.i		−	1.63752i
$372$	20751.0	−	88413.2i	0.149952	−	0.638897i
$373$	−230153.			−1.65424			−0.827119	−	0.562026i	$-0.810022\pi$
$373$	−230153.			−1.65424			−0.827119	+	0.562026i	$0.810022\pi$
$374$			13696.1i			0.0979160i
$375$	−94271.7	−	22126.1i	−0.670377	−	0.157341i
$376$	88201.5			0.623879
$377$			388345.i			2.73234i
$378$	−235625.	−	195103.i	−1.64906	−	1.36547i
$379$	174446.			1.21446			0.607229	−	0.794527i	$-0.292281\pi$
$379$	174446.			1.21446			0.607229	+	0.794527i	$0.292281\pi$
$380$			154972.i			1.07321i
$381$	60580.8	−	258115.i	0.417335	−	1.77813i
$382$	−225320.			−1.54409
$383$			60968.8i			0.415633i	0.978168	+	0.207816i	$0.0666357\pi$
$383$			60968.8i			0.415633i	−0.978168	+	0.207816i	$0.933364\pi$
$384$	223026.	+	52345.4i	1.51249	+	0.354990i
$385$	12988.7			0.0876281
$386$			112840.i			0.757334i
$387$	−11570.6	−	5748.00i	−0.0772564	−	0.0383791i
$388$	−11379.6			−0.0755898
$389$			213555.i			1.41127i	0.708576	+	0.705634i	$0.249338\pi$
$389$			213555.i			1.41127i	−0.708576	+	0.705634i	$0.750662\pi$
$390$	−154915.	+	660042.i	−1.01851	+	4.33953i
$391$	99865.3			0.653222
$392$		−	111418.i		−	0.725075i
$393$	−41645.0	−	9774.31i	−0.269636	−	0.0632850i
$394$	194895.			1.25548
$395$			140911.i			0.903131i
$396$	4646.21	−	9352.73i	0.0296284	−	0.0596414i
$397$	−63337.5			−0.401864			−0.200932	−	0.979605i	$-0.564397\pi$
$397$	−63337.5			−0.401864			−0.200932	+	0.979605i	$0.564397\pi$
$398$		−	298491.i		−	1.88436i
$399$	−21046.7	+	89673.0i	−0.132202	+	0.563269i
$400$	18279.7			0.114248
$401$		−	159759.i		−	0.993519i	−0.867888	−	0.496759i	$-0.834523\pi$
$401$		−	159759.i		−	0.993519i	0.867888	−	0.496759i	$-0.165477\pi$
$402$	484944.	+	113819.i	3.00082	+	0.704307i
$403$	−119627.			−0.736577
$404$		−	120344.i		−	0.737332i
$405$	−204207.	+	154810.i	−1.24498	+	0.943819i
$406$	−543072.			−3.29462
$407$			12312.3i			0.0743278i
$408$	51490.6	−	219384.i	0.309319	−	1.31791i
$409$	61661.2			0.368608			0.184304	−	0.982869i	$-0.440997\pi$
$409$	61661.2			0.368608			0.184304	+	0.982869i	$0.440997\pi$
$410$			1001.36i			0.00595691i
$411$	−82537.2	−	19371.9i	−0.488614	−	0.114680i
$412$	271120.			1.59723
$413$		−	29587.9i		−	0.173466i
$414$	−111303.	−	55292.7i	−0.649392	−	0.322602i
$415$	12313.9			0.0714989
$416$		−	326514.i		−	1.88675i
$417$	18288.3	−	77920.4i	0.105172	−	0.448104i
$418$	−5132.04			−0.0293723
$419$		−	272793.i		−	1.55384i	−0.629602	−	0.776918i	$-0.716782\pi$
$419$		−	272793.i		−	1.55384i	0.629602	−	0.776918i	$-0.283218\pi$
$420$	−565537.	−	132734.i	−3.20599	−	0.752463i
$421$	153748.			0.867451			0.433726	−	0.901045i	$-0.357199\pi$
$421$	153748.			0.867451			0.433726	+	0.901045i	$0.357199\pi$
$422$			357799.i			2.00916i
$423$	53107.1	−	106904.i	0.296806	−	0.597463i
$424$	−206619.			−1.14931
$425$		−	376708.i		−	2.08558i
$426$	−117764.	+	501753.i	−0.648923	+	2.76484i
$427$	196237.			1.07628
$428$		−	76191.3i		−	0.415928i
$429$	−13392.4	−	3143.26i	−0.0727685	−	0.0170791i
$430$	−40041.2			−0.216556
$431$			439.621i			0.00236659i	0.999999	+	0.00118330i	$0.000376655\pi$
$431$			439.621i			0.00236659i	−0.999999	+	0.00118330i	$0.999623\pi$
$432$	9438.21	−	11398.4i	0.0505734	−	0.0610771i
$433$	48241.5			0.257303			0.128652	−	0.991690i	$-0.458935\pi$
$433$	48241.5			0.257303			0.128652	+	0.991690i	$0.458935\pi$
$434$		−	167289.i		−	0.888155i
$435$	−103946.	+	442879.i	−0.549324	+	2.34049i
$436$	11393.8			0.0599372
$437$			37420.3i			0.195950i
$438$	−49545.3	−	11628.5i	−0.258258	−	0.0606146i
$439$	276969.			1.43715			0.718574	−	0.695450i	$-0.244795\pi$
$439$	276969.			1.43715			0.718574	+	0.695450i	$0.244795\pi$
$440$		−	11907.0i		−	0.0615029i
$441$	−135043.	−	67086.0i	−0.694375	−	0.344949i
$442$	−806872.			−4.13009
$443$		−	102282.i		−	0.521186i	−0.965449	−	0.260593i	$-0.916082\pi$
$443$		−	102282.i		−	0.521186i	0.965449	−	0.260593i	$-0.0839181\pi$
$444$	125823.	−	536089.i	0.638254	−	2.71938i
$445$	493025.			2.48971
$446$		−	226120.i		−	1.13676i
$447$	−6116.59	−	1435.60i	−0.0306122	−	0.00718484i
$448$	435400.			2.16936
$449$			165328.i			0.820074i	0.912069	+	0.410037i	$0.134484\pi$
$449$			165328.i			0.820074i	−0.912069	+	0.410037i	$0.865516\pi$
$450$	−208573.	+	419853.i	−1.02999	+	2.07335i
$451$	−20.3177			−9.98899e−5
$452$			336157.i			1.64538i
$453$	23009.2	−	98034.3i	0.112125	−	0.477729i
$454$	146679.			0.711635
$455$			765196.i			3.69615i
$456$	82205.0	+	19293.9i	0.395338	+	0.0927878i
$457$	157950.			0.756289			0.378145	−	0.925747i	$-0.376562\pi$
$457$	157950.			0.756289			0.378145	+	0.925747i	$0.376562\pi$
$458$			278533.i			1.32784i
$459$	−234899.	−	194502.i	−1.11495	−	0.923206i
$460$	−235997.			−1.11530
$461$		−	134676.i		−	0.633708i	−0.948474	−	0.316854i	$-0.897373\pi$
$461$		−	134676.i		−	0.633708i	0.948474	−	0.316854i	$-0.102627\pi$
$462$	4395.63	−	18728.3i	0.0205938	−	0.0877433i
$463$	−131341.			−0.612688			−0.306344	−	0.951921i	$-0.599106\pi$
$463$	−131341.			−0.612688			−0.306344	+	0.951921i	$0.599106\pi$
$464$		−	26271.4i		−	0.122024i
$465$	−136426.	−	32019.8i	−0.630942	−	0.148085i
$466$	368219.			1.69564
$467$			181133.i			0.830545i	0.909697	+	0.415273i	$0.136314\pi$
$467$			181133.i			0.830545i	−0.909697	+	0.415273i	$0.863686\pi$
$468$	550993.	+	273720.i	2.51568	+	1.24973i
$469$	562202.			2.55592
$470$		−	369950.i		−	1.67474i
$471$	−31302.7	+	133370.i	−0.141104	+	0.601197i
$472$	−27123.8			−0.121749
$473$		−	812.444i		−	0.00363137i
$474$	203179.	+	47687.1i	0.904319	+	0.212248i
$475$	141156.			0.625620
$476$		−	691343.i		−	3.05126i
$477$	−124408.	+	250430.i	−0.546777	+	1.10065i
$478$	105257.			0.460675
$479$			4491.28i			0.0195749i	0.999952	+	0.00978744i	$0.00311549\pi$
$479$			4491.28i			0.0195749i	−0.999952	+	0.00978744i	$0.996885\pi$
$480$	87395.9	−	372365.i	0.379323	−	1.61617i
$481$	−725351.			−3.13515
$482$		−	317672.i		−	1.36737i
$483$	−136558.	−	32050.8i	−0.585358	−	0.137387i
$484$	−369934.			−1.57919
$485$			17559.2i			0.0746487i
$486$	154112.	+	346836.i	0.652473	+	1.46842i
$487$	−195876.			−0.825893			−0.412946	−	0.910755i	$-0.635500\pi$
$487$	−195876.			−0.825893			−0.412946	+	0.910755i	$0.635500\pi$
$488$		−	179894.i		−	0.755400i
$489$	32500.9	−	138475.i	0.135918	−	0.579102i
$490$	−467328.			−1.94639
$491$		−	52346.0i		−	0.217131i	−0.994089	−	0.108565i	$-0.965374\pi$
$491$		−	52346.0i		−	0.217131i	0.994089	−	0.108565i	$-0.0346256\pi$
$492$	884.649	+	207.632i	0.00365461	+	0.000857756i
$493$	−541399.			−2.22753
$494$		−	302341.i		−	1.23892i
$495$	−14431.7	−	7169.32i	−0.0588988	−	0.0292595i
$496$	8092.70			0.0328950
$497$			581688.i			2.35493i
$498$	4167.27	−	17755.3i	0.0168032	−	0.0715930i
$499$	−182646.			−0.733516			−0.366758	−	0.930316i	$-0.619532\pi$
$499$	−182646.			−0.733516			−0.366758	+	0.930316i	$0.619532\pi$
$500$			272337.i			1.08935i
$501$	−50307.6	−	11807.5i	−0.200428	−	0.0470415i
$502$	268650.			1.06605
$503$		−	111201.i		−	0.439515i	−0.975555	−	0.219757i	$-0.929473\pi$
$503$		−	111201.i		−	0.439515i	0.975555	−	0.219757i	$-0.0705265\pi$
$504$	−140818.	+	283464.i	−0.554368	+	1.11593i
$505$	−185697.			−0.728151
$506$		−	7815.27i		−	0.0305241i
$507$	126443.	−	538731.i	0.491902	−	2.09583i
$508$	−745655.			−2.88942
$509$			161633.i			0.623872i	0.950103	+	0.311936i	$0.100977\pi$
$509$			161633.i			0.623872i	−0.950103	+	0.311936i	$0.899023\pi$
$510$	−920178.	−	215970.i	−3.53778	−	0.830336i
$511$	−57438.5			−0.219969
$512$			41528.3i			0.158418i
$513$	72881.5	−	88018.4i	0.276938	−	0.334456i
$514$	−813279.			−3.07832
$515$		−	418350.i		−	1.57734i
$516$	−8302.57	+	35374.5i	−0.0311826	+	0.132859i
$517$	7506.35			0.0280833
$518$		−	1.01435e6i		−	3.78032i
$519$	−484840.	−	113795.i	−1.79997	−	0.422461i
$520$	701470.			2.59419
$521$		−	230594.i		−	0.849517i	−0.905307	−	0.424759i	$-0.860359\pi$
$521$		−	230594.i		−	0.849517i	0.905307	−	0.424759i	$-0.139641\pi$
$522$	603407.	+	299758.i	2.21447	+	1.10009i
$523$	451661.			1.65123			0.825617	−	0.564231i	$-0.190827\pi$
$523$	451661.			1.65123			0.825617	+	0.564231i	$0.190827\pi$
$524$			120306.i			0.438153i
$525$	−120901.	+	515117.i	−0.438642	+	1.86891i
$526$	562763.			2.03402
$527$		−	166774.i		−	0.600492i
$528$	905.989	+	212.640i	0.00324979	+	0.000762742i
$529$	222856.			0.796366
$530$			866637.i			3.08522i
$531$	−16331.6	+	32875.1i	−0.0579213	+	0.116594i
$532$	259052.			0.915300
$533$		−	1196.97i		−	0.00421336i
$534$	166850.	−	710890.i	0.585117	−	2.49299i
$535$	−117567.			−0.410749
$536$		−	515381.i		−	1.79390i
$537$	282568.	+	66320.2i	0.979884	+	0.229984i
$538$	386113.			1.33398
$539$		−	9482.18i		−	0.0326385i
$540$	555102.	+	459639.i	1.90364	+	1.57627i
$541$	218146.			0.745336			0.372668	−	0.927965i	$-0.378443\pi$
$541$	218146.			0.745336			0.372668	+	0.927965i	$0.378443\pi$
$542$			592203.i			2.01591i
$543$	−25777.8	+	109831.i	−0.0874273	+	0.372498i
$544$	455199.			1.53817
$545$		−	17581.2i		−	0.0591909i
$546$	1.10333e6	+	258957.i	3.70101	+	0.868647i
$547$	−90378.8			−0.302059			−0.151030	−	0.988529i	$-0.548259\pi$
$547$	−90378.8			−0.302059			−0.151030	+	0.988529i	$0.548259\pi$
$548$			238438.i			0.793988i
$549$	−218038.	−	108316.i	−0.723416	−	0.359376i
$550$	−29480.5			−0.0974561
$551$		−	202867.i		−	0.668201i
$552$	−29381.6	+	125185.i	−0.0964266	+	0.410841i
$553$	235548.			0.770245
$554$		−	57674.1i		−	0.187915i
$555$	−827209.	−	194150.i	−2.68553	−	0.630307i
$556$	−225100.			−0.728160
$557$		−	525332.i		−	1.69326i	−0.532184	−	0.846629i	$-0.678628\pi$
$557$		−	525332.i		−	1.69326i	0.532184	−	0.846629i	$-0.321372\pi$
$558$	−92338.2	+	185875.i	−0.296560	+	0.596970i
$559$	47863.1			0.153171
$560$		−	51765.2i		−	0.165068i
$561$	4382.08	−	18670.6i	0.0139237	−	0.0593242i
$562$	20747.1			0.0656878
$563$			531031.i			1.67534i	0.546177	+	0.837670i	$0.316083\pi$
$563$			531031.i			1.67534i	−0.546177	+	0.837670i	$0.683917\pi$
$564$	−326833.	−	76709.3i	−1.02747	−	0.241151i
$565$	518705.			1.62489
$566$		−	393022.i		−	1.22683i
$567$	258781.	+	341354.i	0.804945	+	1.06179i
$568$	533245.			1.65284
$569$		−	71552.4i		−	0.221004i	−0.993876	−	0.110502i	$-0.964754\pi$
$569$		−	71552.4i		−	0.221004i	0.993876	−	0.110502i	$-0.0352458\pi$
$570$	80925.9	−	344798.i	0.249079	−	1.06124i
$571$	−197853.			−0.606836			−0.303418	−	0.952858i	$-0.598128\pi$
$571$	−197853.			−0.606836			−0.303418	+	0.952858i	$0.598128\pi$
$572$			38688.6i			0.118247i
$573$	307157.	+	72091.4i	0.935517	+	0.219571i
$574$	1673.87			0.00508041
$575$			214957.i			0.650154i
$576$	−483772.	−	240326.i	−1.45813	−	0.724363i
$577$	231477.			0.695273			0.347637	−	0.937629i	$-0.386984\pi$
$577$	231477.			0.695273			0.347637	+	0.937629i	$0.386984\pi$
$578$		−	588050.i		−	1.76019i
$579$	36103.2	−	153824.i	0.107693	−	0.458845i
$580$	1.27941e6			3.80324
$581$		−	20584.0i		−	0.0609786i
$582$	25318.6	+	5942.39i	0.0747468	+	0.0175435i
$583$	−17584.2			−0.0517352
$584$			52655.0i			0.154388i
$585$	422363.	−	850208.i	1.23417	−	2.48435i
$586$	−79327.2			−0.231008
$587$			540008.i			1.56720i	0.621266	+	0.783600i	$0.286619\pi$
$587$			540008.i			1.56720i	−0.621266	+	0.783600i	$0.713381\pi$
$588$	−96900.8	+	412862.i	−0.280267	+	1.19413i
$589$	62491.6			0.180132
$590$			113767.i			0.326824i
$591$	−265682.	−	62356.9i	−0.760653	−	0.178529i
$592$	49069.7			0.140013
$593$			40828.0i			0.116104i	0.998314	+	0.0580522i	$0.0184890\pi$
$593$			40828.0i			0.116104i	−0.998314	+	0.0580522i	$0.981511\pi$
$594$	−15221.4	+	18382.7i	−0.0431401	+	0.0520999i
$595$	−1.06677e6			−3.01327
$596$			17669.9i			0.0497442i
$597$	−95502.5	+	406904.i	−0.267958	+	1.14168i
$598$	460418.			1.28751
$599$			74599.9i			0.207914i	0.994582	+	0.103957i	$0.0331505\pi$
$599$			74599.9i			0.207914i	−0.994582	+	0.103957i	$0.966850\pi$
$600$	472218.	+	110832.i	1.31172	+	0.307867i
$601$	273202.			0.756370			0.378185	−	0.925730i	$-0.376548\pi$
$601$	273202.			0.756370			0.378185	+	0.925730i	$0.376548\pi$
$602$			66933.1i			0.184692i
$603$	−624662.	−	310317.i	−1.71795	−	0.853436i
$604$	−283207.			−0.776300
$605$			570825.i			1.55952i
$606$	−62843.5	+	267755.i	−0.171126	+	0.729109i
$607$	−159647.			−0.433296			−0.216648	−	0.976250i	$-0.569512\pi$
$607$	−159647.			−0.433296			−0.216648	+	0.976250i	$0.569512\pi$
$608$			170567.i			0.461410i
$609$	740319.	+	173757.i	1.99611	+	0.468497i
$610$	−754542.			−2.02779
$611$			442218.i			1.18455i
$612$	−381599.	+	768150.i	−1.01884	+	2.05090i
$613$	615909.			1.63906			0.819531	−	0.573035i	$-0.194234\pi$
$613$	615909.			1.63906			0.819531	+	0.573035i	$0.194234\pi$
$614$			1.02668e6i			2.72332i
$615$	320.385	−	1365.05i	0.000847076	−	0.00360911i
$616$	−19903.8			−0.0524534
$617$		−	695853.i		−	1.82788i	−0.405852	−	0.913939i	$-0.633025\pi$
$617$		−	695853.i		−	1.82788i	0.405852	−	0.913939i	$-0.366975\pi$
$618$	−603217.	−	141578.i	−1.57942	−	0.370697i
$619$	−38457.6			−0.100369			−0.0501847	−	0.998740i	$-0.515981\pi$
$619$	−38457.6			−0.100369			−0.0501847	+	0.998740i	$0.515981\pi$
$620$			394113.i			1.02527i
$621$	134038.	+	110987.i	0.347572	+	0.287798i
$622$	−518591.			−1.34043
$623$		−	824144.i		−	2.12338i
$624$	−12527.2	+	53374.1i	−0.0321725	+	0.137076i
$625$	−142568.			−0.364974
$626$			989146.i			2.52413i
$627$	6996.02	+	1642.00i	0.0177957	+	0.00417675i
$628$	385287.			0.976933
$629$		−	1.01123e6i		−	2.55592i
$630$	1.18895e6	+	590644.i	2.99560	+	1.48814i
$631$	−647361.			−1.62588			−0.812939	−	0.582349i	$-0.802134\pi$
$631$	−647361.			−1.62588			−0.812939	+	0.582349i	$0.802134\pi$
$632$		−	215931.i		−	0.540606i
$633$	114478.	−	487753.i	0.285703	−	1.21729i
$634$	−23331.3			−0.0580445
$635$			1.15058e6i			2.85344i
$636$	765631.	+	179698.i	1.89280	+	0.444251i
$637$	558619.			1.37669
$638$			42368.9i			0.104089i
$639$	321073.	−	646313.i	0.786324	−	1.58286i
$640$	−994169.			−2.42717
$641$			104411.i			0.254116i	0.991895	+	0.127058i	$0.0405534\pi$
$641$			104411.i			0.254116i	−0.991895	+	0.127058i	$0.959447\pi$
$642$	−39786.9	+	169519.i	−0.0965317	+	0.411289i
$643$	36891.7			0.0892290			0.0446145	−	0.999004i	$-0.485794\pi$
$643$	36891.7			0.0892290			0.0446145	+	0.999004i	$0.485794\pi$
$644$			394495.i			0.951195i
$645$	54584.4	+	12811.2i	0.131205	+	0.0307944i
$646$	421500.			1.01003
$647$		−	100450.i		−	0.239961i	−0.992776	−	0.119980i	$-0.961717\pi$
$647$		−	100450.i		−	0.239961i	0.992776	−	0.119980i	$-0.0382831\pi$
$648$	312926.	−	237230.i	0.745232	−	0.564962i
$649$	−2308.36			−0.00548043
$650$		−	1.73677e6i		−	4.11070i
$651$	−53524.5	+	228050.i	−0.126296	+	0.538106i
$652$	−400035.			−0.941028
$653$		−	30923.0i		−	0.0725195i	−0.999342	−	0.0362597i	$-0.988456\pi$
$653$		−	30923.0i		−	0.0725195i	0.999342	−	0.0362597i	$-0.0115444\pi$
$654$	−25350.2	−	5949.82i	−0.0592687	−	0.0139107i
$655$	185638.			0.432698
$656$			80.9744i			0.000188166i
$657$	63819.9	+	31704.2i	0.147851	+	0.0734490i
$658$	−618410.			−1.42832
$659$		−	543752.i		−	1.25208i	−0.779793	−	0.626038i	$-0.784676\pi$
$659$		−	543752.i		−	1.25208i	0.779793	−	0.626038i	$-0.215324\pi$
$660$	−10355.5	+	44121.5i	−0.0237731	+	0.101289i
$661$	−653369.			−1.49539			−0.747697	−	0.664040i	$-0.768840\pi$
$661$	−653369.			−1.49539			−0.747697	+	0.664040i	$0.768840\pi$
$662$		−	809407.i		−	1.84693i
$663$	1.09993e6	+	258160.i	2.50230	+	0.587302i
$664$	−18869.8			−0.0427986
$665$		−	399729.i		−	0.903904i
$666$	−559888.	+	1.12704e6i	−1.26227	+	2.54093i
$667$	308933.			0.694406
$668$			145331.i			0.325691i
$669$	−72347.4	+	308248.i	−0.161648	+	0.688728i
$670$	−2.16170e6			−4.81555
$671$		−	15309.8i		−	0.0340036i
$672$	−622447.	−	146092.i	−1.37836	−	0.323509i
$673$	554612.			1.22450			0.612251	−	0.790664i	$-0.290264\pi$
$673$	554612.			1.22450			0.612251	+	0.790664i	$0.290264\pi$
$674$			211782.i			0.466197i
$675$	418660.	−	505613.i	0.918870	−	1.10971i
$676$	−1.55631e6			−3.40568
$677$		−	303181.i		−	0.661492i	−0.943720	−	0.330746i	$-0.892700\pi$
$677$		−	303181.i		−	0.661492i	0.943720	−	0.330746i	$-0.107300\pi$
$678$	175540.	−	747918.i	0.381872	−	1.62703i
$679$	29352.1			0.0636649
$680$			977932.i			2.11491i
$681$	−199954.	−	46930.2i	−0.431157	−	0.101195i
$682$	−13051.4			−0.0280601
$683$			336072.i			0.720428i	0.932870	+	0.360214i	$0.117296\pi$
$683$			336072.i			0.720428i	−0.932870	+	0.360214i	$0.882704\pi$
$684$	−287832.	−	142988.i	−0.615215	−	0.305624i
$685$	367920.			0.784102
$686$		−	226359.i		−	0.481005i
$687$	89117.1	−	379698.i	0.188820	−	0.804498i
$688$	−3237.92			−0.00684053
$689$		−	1.03593e6i		−	2.18219i
$690$	525072.	+	123237.i	1.10286	+	0.258847i
$691$	117111.			0.245269			0.122635	−	0.992452i	$-0.460866\pi$
$691$	117111.			0.245269			0.122635	+	0.992452i	$0.460866\pi$
$692$			1.40063e6i			2.92491i
$693$	−11984.3	+	24124.1i	−0.0249543	+	0.0502325i
$694$	1.00827e6			2.09343
$695$			347340.i			0.719094i
$696$	159286.	−	678665.i	0.328821	−	1.40100i
$697$	1668.72			0.00343492
$698$		−	1.15178e6i		−	2.36406i
$699$	−501958.	−	117812.i	−1.02734	−	0.241121i
$700$	1.48810e6			3.03693
$701$			148746.i			0.302698i	0.988480	+	0.151349i	$0.0483618\pi$
$701$			148746.i			0.302698i	−0.988480	+	0.151349i	$0.951638\pi$
$702$	−1.08297e6	−	896730.i	−2.19757	−	1.81965i
$703$	378914.			0.766709
$704$		−	33968.6i		−	0.0685381i
$705$	−118366.	+	504317.i	−0.238149	+	1.01467i
$706$	−1.16666e6			−2.34064
$707$			310412.i			0.621012i
$708$	100508.	+	23589.7i	0.200509	+	0.0470605i
$709$	142329.			0.283141			0.141570	−	0.989928i	$-0.454785\pi$
$709$	142329.			0.283141			0.141570	+	0.989928i	$0.454785\pi$
$710$		−	2.23663e6i		−	4.43687i
$711$	−261717.	−	130015.i	−0.517717	−	0.257189i
$712$	−755509.			−1.49032
$713$			95164.7i			0.187196i
$714$	−361018.	+	1.53818e6i	−0.708161	+	3.01724i
$715$	59698.3			0.116775
$716$		−	816298.i		−	1.59229i
$717$	−143487.	−	33677.0i	−0.279108	−	0.0655082i
$718$	985842.			1.91231
$719$		−	108893.i		−	0.210641i	−0.994438	−	0.105321i	$-0.966413\pi$
$719$		−	108893.i		−	0.210641i	0.994438	−	0.105321i	$-0.0335869\pi$
$720$	−28572.7	+	57516.2i	−0.0551170	+	0.110949i
$721$	−699317.			−1.34525
$722$		−	679689.i		−	1.30388i
$723$	−101640.	+	433052.i	−0.194440	+	0.828445i
$724$	317285.			0.605302
$725$		−	1.16535e6i		−	2.21707i
$726$	823069.	+	193179.i	1.56158	+	0.366510i
$727$	499824.			0.945688			0.472844	−	0.881146i	$-0.343227\pi$
$727$	499824.			0.945688			0.472844	+	0.881146i	$0.343227\pi$
$728$		−	1.17258e6i		−	2.21248i
$729$	−99115.1	−	522117.i	−0.186503	−	0.982454i
$730$	220855.			0.414439
$731$			66726.9i			0.124872i
$732$	−156455.	+	666601.i	−0.291989	+	1.24407i
$733$	−154763.			−0.288044			−0.144022	−	0.989574i	$-0.546004\pi$
$733$	−154763.			−0.288044			−0.144022	+	0.989574i	$0.546004\pi$
$734$			1.03691e6i			1.92464i
$735$	637064.	+	149522.i	1.17926	+	0.276778i
$736$	−259746.			−0.479505
$737$		−	43861.3i		−	0.0807508i
$738$	−1859.84	−	923.923i	−0.00341478	−	0.00169638i
$739$	−589.545			−0.00107951			−0.000539757	−	1.00000i	$-0.500172\pi$
$739$	−589.545			−0.00107951			−0.000539757		1.00000i	$0.500172\pi$
$740$			2.38968e6i			4.36392i
$741$	−96734.5	+	412153.i	−0.176175	+	0.750624i
$742$	1.44868e6			2.63126
$743$			684478.i			1.23989i	0.784647	+	0.619943i	$0.212844\pi$
$743$			684478.i			1.23989i	−0.784647	+	0.619943i	$0.787156\pi$
$744$	209058.	+	49066.9i	0.377677	+	0.0886427i
$745$	27265.5			0.0491248
$746$		−	1.47929e6i		−	2.65813i
$747$	−11361.7	+	22870.8i	−0.0203611	+	0.0409865i
$748$	−53936.5			−0.0964006
$749$			196525.i			0.350311i
$750$	142214.	−	605925.i	0.252824	−	1.07720i
$751$	−700854.			−1.24265			−0.621323	−	0.783554i	$-0.713405\pi$
$751$	−700854.			−1.24265			−0.621323	+	0.783554i	$0.713405\pi$
$752$		−	29915.9i		−	0.0529013i
$753$	−366225.	−	85954.8i	−0.645889	−	0.151593i
$754$	−2.49606e6			−4.39048
$755$			437001.i			0.766634i
$756$	768335.	−	927913.i	1.34433	−	1.62354i
$757$	219518.			0.383070			0.191535	−	0.981486i	$-0.438653\pi$
$757$	219518.			0.383070			0.191535	+	0.981486i	$0.438653\pi$
$758$			1.12124e6i			1.95146i
$759$	−2500.51	+	10653.8i	−0.00434055	+	0.0184936i
$760$	−366439.			−0.634417
$761$			480822.i			0.830262i	0.909762	+	0.415131i	$0.136264\pi$
$761$			480822.i			0.830262i	−0.909762	+	0.415131i	$0.863736\pi$
$762$	1.65901e6	+	389379.i	2.85719	+	0.670598i
$763$	−29388.8			−0.0504816
$764$		−	887332.i		−	1.52020i
$765$	1.18529e6	+	588824.i	2.02536	+	1.00615i
$766$	−391873.			−0.667863
$767$		−	135991.i		−	0.231164i
$768$	−117018.	+	498575.i	−0.198395	+	0.845294i
$769$	−719489.			−1.21667			−0.608333	−	0.793682i	$-0.708162\pi$
$769$	−719489.			−1.21667			−0.608333	+	0.793682i	$0.708162\pi$
$770$			83483.7i			0.140806i
$771$	1.10867e6	+	260210.i	1.86506	+	0.437738i
$772$	−444374.			−0.745614
$773$			35961.4i			0.0601835i	0.999547	+	0.0300918i	$0.00957995\pi$
$773$			35961.4i			0.0601835i	−0.999547	+	0.0300918i	$0.990420\pi$
$774$	36944.9	−	74369.3i	0.0616698	−	0.124140i
$775$	358976.			0.597671
$776$		−	26907.7i		−	0.0446840i
$777$	−324543.	+	1.38277e6i	−0.537564	+	2.29038i
$778$	−1.37261e6			−2.26771
$779$			625.282i			0.00103039i
$780$	−2.59931e6	−	610072.i	−4.27237	−	1.00275i
$781$	45381.6			0.0744008
$782$			641877.i			1.04964i
$783$	−726659.	−	601692.i	−1.18524	−	0.981411i
$784$	−37790.4			−0.0614822
$785$		−	594515.i		−	0.964769i
$786$	62823.7	−	267671.i	0.101690	−	0.433267i
$787$	−1.11851e6			−1.80588			−0.902942	−	0.429763i	$-0.858597\pi$
$787$	−1.11851e6			−1.80588			−0.902942	+	0.429763i	$0.858597\pi$
$788$			767515.i			1.23605i
$789$	−767162.	−	180057.i	−1.23235	−	0.289238i
$790$	−905695.			−1.45120
$791$		−	867071.i		−	1.38580i
$792$	22115.0	+	10986.2i	0.0352563	+	0.0175145i
$793$	901939.			1.43427
$794$		−	407097.i		−	0.645739i
$795$	277282.	−	1.18140e6i	0.438719	−	1.86924i
$796$	1.17549e6			1.85520
$797$			21405.7i			0.0336986i	0.999858	+	0.0168493i	$0.00536356\pi$
$797$			21405.7i			0.0336986i	−0.999858	+	0.0168493i	$0.994636\pi$
$798$	−576367.	−	135276.i	−0.905093	−	0.212430i
$799$	−616505.			−0.965702
$800$			979803.i			1.53094i
$801$	−454900.	+	915705.i	−0.709008	+	1.42722i
$802$	1.02684e6			1.59644
$803$			4481.18i			0.00694963i
$804$	−448230.	+	1.90976e6i	−0.693408	+	2.95438i
$805$	608723.			0.939351
$806$		−	768892.i		−	1.18357i
$807$	−526351.	−	123537.i	−0.808218	−	0.189693i
$808$	284561.			0.435865
$809$			875549.i			1.33778i	0.743363	+	0.668888i	$0.233230\pi$
$809$			875549.i			1.33778i	−0.743363	+	0.668888i	$0.766770\pi$
$810$	−995029.	−	1.31253e6i	−1.51658	−	2.00050i
$811$	−513565.			−0.780825			−0.390413	−	0.920640i	$-0.627668\pi$
$811$	−513565.			−0.780825			−0.390413	+	0.920640i	$0.627668\pi$
$812$		−	2.13867e6i		−	3.24364i
$813$	189476.	−	807294.i	0.286664	−	1.22138i
$814$	−79136.6			−0.119434
$815$			617272.i			0.929311i
$816$	−74409.9	−	17464.4i	−0.111751	−	0.0262285i
$817$	−25003.1			−0.0374585
$818$			396323.i			0.592301i
$819$	−1.42121e6	−	706024.i	−2.11881	−	1.05257i
$820$	−3943.44			−0.00586472
$821$			1.05924e6i			1.57148i	0.618558	+	0.785739i	$0.287717\pi$
$821$			1.05924e6i			1.57148i	−0.618558	+	0.785739i	$0.712283\pi$
$822$	124512.	−	530502.i	0.184275	−	0.785134i
$823$	235946.			0.348348			0.174174	−	0.984715i	$-0.444275\pi$
$823$	235946.			0.348348			0.174174	+	0.984715i	$0.444275\pi$
$824$			641078.i			0.944183i
$825$	40187.9	+	9432.31i	0.0590456	+	0.0138583i
$826$	190174.			0.278735
$827$		−	113402.i		−	0.165809i	−0.996557	−	0.0829046i	$-0.973580\pi$
$827$		−	113402.i		−	0.165809i	0.996557	−	0.0829046i	$-0.0264197\pi$
$828$	217748.	−	438323.i	0.317610	−	0.639342i
$829$	−1.05464e6			−1.53460			−0.767301	−	0.641287i	$-0.778401\pi$
$829$	−1.05464e6			−1.53460			−0.767301	+	0.641287i	$0.778401\pi$
$830$			79146.7i			0.114889i
$831$	−18452.9	+	78621.7i	−0.0267216	+	0.113852i
$832$	2.00118e6			2.89094
$833$			778782.i			1.12234i
$834$	500828.	+	117547.i	0.720039	+	0.168997i
$835$	224253.			0.321636
$836$		−	20210.5i		−	0.0289177i
$837$	185347.	−	223842.i	0.264566	−	0.319515i
$838$	1.75336e6			2.49679
$839$			695640.i			0.988236i	0.869395	+	0.494118i	$0.164509\pi$
$839$			695640.i			0.988236i	−0.869395	+	0.494118i	$0.835491\pi$
$840$	313858.	−	1.33724e6i	0.444810	−	1.89519i
$841$	−967537.			−1.36797
$842$			988204.i			1.39387i
$843$	−28282.5	−	6638.06i	−0.0397982	−	0.00934084i
$844$	−1.40905e6			−1.97806
$845$			2.40146e6i			3.36327i
$846$	687115.	+	341342.i	0.960038	+	0.476924i
$847$	954194.			1.33006
$848$			70080.4i			0.0974551i
$849$	−125748.	+	535770.i	−0.174456	+	0.743298i
$850$	2.42126e6			3.35123
$851$			577026.i			0.796776i
$852$	−1.97595e6	−	463766.i	−2.72206	−	0.638880i
$853$	−82659.8			−0.113605			−0.0568024	−	0.998385i	$-0.518090\pi$
$853$	−82659.8			−0.113605			−0.0568024	+	0.998385i	$0.518090\pi$
$854$			1.26130e6i			1.72943i
$855$	−220637.	+	444138.i	−0.301819	+	0.607555i
$856$	180158.			0.245871
$857$		−	1.25026e6i		−	1.70231i	−0.524911	−	0.851157i	$-0.675901\pi$
$857$		−	1.25026e6i		−	1.70231i	0.524911	−	0.851157i	$-0.324099\pi$
$858$	20203.1	−	86078.6i	0.0274437	−	0.116929i
$859$	240395.			0.325791			0.162895	−	0.986643i	$-0.447917\pi$
$859$	240395.			0.325791			0.162895	+	0.986643i	$0.447917\pi$
$860$		−	157686.i		−	0.213205i
$861$	−2281.83	−	535.558i	−0.00307806	−	0.000722437i
$862$	−2825.63			−0.00380278
$863$			429109.i			0.576164i	0.957606	+	0.288082i	$0.0930176\pi$
$863$			429109.i			0.576164i	−0.957606	+	0.288082i	$0.906982\pi$
$864$	610962.	+	505892.i	0.818440	+	0.677689i
$865$	2.16124e6			2.88849
$866$			310069.i			0.413449i
$867$	−188147.	+	801633.i	−0.250300	+	1.06644i
$868$	658802.			0.874411
$869$		−	18376.7i		−	0.0243349i
$870$	−2.84657e6	−	668105.i	−3.76083	−	0.882686i
$871$	2.58398e6			3.40607
$872$			26941.3i			0.0354311i
$873$	−32613.1	−	16201.4i	−0.0427921	−	0.0212581i
$874$	−240517.			−0.314863
$875$		−	702457.i		−	0.917494i
$876$	45794.3	−	195114.i	0.0596765	−	0.254262i
$877$	−582531.			−0.757391			−0.378695	−	0.925521i	$-0.623627\pi$
$877$	−582531.			−0.757391			−0.378695	+	0.925521i	$0.623627\pi$
$878$			1.78020e6i			2.30929i
$879$	108139.	+	25380.8i	0.139960	+	0.0328495i
$880$	−4038.56			−0.00521509
$881$		−	510525.i		−	0.657757i	−0.944372	−	0.328879i	$-0.893329\pi$
$881$		−	510525.i		−	0.657757i	0.944372	−	0.328879i	$-0.106671\pi$
$882$	431191.	−	867978.i	0.554284	−	1.11576i
$883$	148655.			0.190659			0.0953295	−	0.995446i	$-0.469610\pi$
$883$	148655.			0.190659			0.0953295	+	0.995446i	$0.469610\pi$
$884$		−	3.17754e6i		−	4.06618i
$885$	36400.0	−	155088.i	0.0464745	−	0.198012i
$886$	657412.			0.837472
$887$			156155.i			0.198477i	0.995064	+	0.0992385i	$0.0316407\pi$
$887$			156155.i			0.198477i	−0.995064	+	0.0992385i	$0.968359\pi$
$888$	1.26761e6	+	297515.i	1.60753	+	0.377296i
$889$	1.92331e6			2.43359
$890$			3.16888e6i			4.00061i
$891$	26631.4	−	20189.3i	0.0335459	−	0.0254312i
$892$	890482.			1.11917
$893$		−	231009.i		−	0.289686i
$894$	9227.19	−	39314.0i	0.0115450	−	0.0491894i
$895$	−1.25958e6			−1.57247
$896$			1.66186e6i			2.07004i
$897$	−627644.	−	147311.i	−0.780060	−	0.183084i
$898$	−1.06263e6			−1.31774
$899$		−	515915.i		−	0.638350i
$900$	−1.65342e6	−	821381.i	−2.04126	−	1.01405i
$901$	1.44421e6			1.77902
$902$		−	130.591i		−	0.000160509i
$903$	21415.3	−	91243.6i	0.0262633	−	0.111899i
$904$	−794861.			−0.972645
$905$		−	489585.i		−	0.597765i
$906$	630108.	+	147890.i	0.767642	+	0.180170i
$907$	−404644.			−0.491879			−0.245939	−	0.969285i	$-0.579096\pi$
$907$	−404644.			−0.491879			−0.245939	+	0.969285i	$0.579096\pi$
$908$			577637.i			0.700622i
$909$	171337.	−	344898.i	0.207359	−	0.417410i
$910$	−4.91824e6			−5.93919
$911$		−	1.06424e6i		−	1.28234i	−0.767400	−	0.641169i	$-0.778450\pi$
$911$		−	1.06424e6i		−	1.28234i	0.767400	−	0.641169i	$-0.221550\pi$
$912$	6544.05	−	27882.0i	0.00786787	−	0.0335223i
$913$	−1605.90			−0.00192654
$914$			1.01521e6i			1.21525i
$915$	1.02860e6	+	241417.i	1.22858	+	0.288353i
$916$	−1.09689e6			−1.30729
$917$		−	310314.i		−	0.369031i
$918$	1.25015e6	−	1.50979e6i	1.48346	−	1.79156i
$919$	947081.			1.12139			0.560694	−	0.828023i	$-0.310534\pi$
$919$	947081.			1.12139			0.560694	+	0.828023i	$0.310534\pi$
$920$		−	558028.i		−	0.659296i
$921$	328487.	−	1.39957e6i	0.387257	−	1.64997i
$922$	865623.			1.01828
$923$			2.67355e6i			3.13823i
$924$	73753.8	+	17310.4i	0.0863854	+	0.0202751i
$925$	2.17663e6			2.54391
$926$		−	844188.i		−	0.984503i
$927$	777010.	+	386000.i	0.904206	+	0.449188i
$928$	1.40816e6			1.63514
$929$		−	541272.i		−	0.627168i	−0.949560	−	0.313584i	$-0.898470\pi$
$929$		−	541272.i		−	0.627168i	0.949560	−	0.313584i	$-0.101530\pi$
$930$	205805.	−	876865.i	0.237952	−	1.01383i
$931$	−291816.			−0.336674
$932$			1.45008e6i			1.66940i
$933$	706945.	+	165924.i	0.812124	+	0.190610i
$934$	−1.16422e6			−1.33457
$935$			83226.5i			0.0952004i
$936$	−647226.	+	1.30285e6i	−0.738762	+	1.48711i
$937$	253689.			0.288950			0.144475	−	0.989508i	$-0.453851\pi$
$937$	253689.			0.288950			0.144475	+	0.989508i	$0.453851\pi$
$938$			3.61351e6i			4.10699i
$939$	316478.	−	1.34841e6i	0.358933	−	1.52929i
$940$	1.45690e6			1.64882
$941$			730771.i			0.825281i	0.910894	+	0.412640i	$0.135393\pi$
$941$			730771.i			0.825281i	−0.910894	+	0.412640i	$0.864607\pi$
$942$	−857227.	−	201196.i	−0.966038	−	0.226734i
$943$	−952.204			−0.00107080
$944$			9199.77i			0.0103236i
$945$	−1.43181e6	−	1.18558e6i	−1.60333	−	1.32760i
$946$	5221.92			0.00583510
$947$		−	898725.i		−	1.00214i	−0.865408	−	0.501068i	$-0.832940\pi$
$947$		−	898725.i		−	1.00214i	0.865408	−	0.501068i	$-0.167060\pi$
$948$	−187796.	+	800138.i	−0.208964	+	0.890324i
$949$	−263998.			−0.293135
$950$			907267.i			1.00528i
$951$	31805.4	+	7464.88i	0.0351673	+	0.00825395i
$952$	1.63472e6			1.80372
$953$		−	274721.i		−	0.302486i	−0.988497	−	0.151243i	$-0.951672\pi$
$953$		−	274721.i		−	0.302486i	0.988497	−	0.151243i	$-0.0483277\pi$
$954$	−1.60962e6	−	799621.i	−1.76859	−	0.878593i
$955$	−1.36919e6			−1.50127
$956$			414511.i			0.453545i
$957$	13556.0	−	57757.5i	0.0148015	−	0.0630644i
$958$	−28867.4			−0.0314540
$959$		−	615018.i		−	0.668730i
$960$	2.28219e6	+	535643.i	2.47634	+	0.581210i
$961$	−764597.			−0.827915
$962$		−	4.66214e6i		−	5.03773i
$963$	108475.	−	218359.i	0.116971	−	0.235460i
$964$	1.25102e6			1.34621
$965$			685689.i			0.736330i
$966$	206004.	−	877714.i	0.220761	−	0.940587i
$967$	−940443.			−1.00573			−0.502863	−	0.864366i	$-0.667720\pi$
$967$	−940443.			−1.00573			−0.502863	+	0.864366i	$0.667720\pi$
$968$		−	874729.i		−	0.933518i
$969$	−574591.	−	134859.i	−0.611943	−	0.143626i
$970$	−112861.			−0.119950
$971$		−	1.01286e6i		−	1.07426i	−0.843500	−	0.537130i	$-0.819509\pi$
$971$		−	1.01286e6i		−	1.07426i	0.843500	−	0.537130i	$-0.180491\pi$
$972$	−1.36587e6	+	606906.i	−1.44570	+	0.642376i
$973$	580616.			0.613286
$974$		−	1.25898e6i		−	1.32709i
$975$	−555681.	+	2.36757e6i	−0.584543	+	2.49054i
$976$	−61015.8			−0.0640535
$977$		−	1.66073e6i		−	1.73985i	−0.493187	−	0.869923i	$-0.664168\pi$
$977$		−	1.66073e6i		−	1.73985i	0.493187	−	0.869923i	$-0.335832\pi$
$978$	890040.	+	208897.i	0.930533	+	0.218401i
$979$	−64297.3			−0.0670853
$980$		−	1.84038e6i		−	1.91627i
$981$	32653.8	+	16221.6i	0.0339310	+	0.0168561i
$982$	336450.			0.348898
$983$		−	37469.1i		−	0.0387763i	−0.999812	−	0.0193881i	$-0.993828\pi$
$983$		−	37469.1i		−	0.0387763i	0.999812	−	0.0193881i	$-0.00617182\pi$
$984$	−490.956	+	2091.80i	−0.000507052	+	0.00216038i
$985$	1.18431e6			1.22066
$986$		−	3.47980e6i		−	3.57932i
$987$	843020.	+	197861.i	0.865374	+	0.203108i
$988$	1.19065e6			1.21975
$989$		−	38075.8i		−	0.0389274i
$990$	46080.3	−	92758.7i	0.0470159	−	0.0946420i
$991$	−1.06310e6			−1.08250			−0.541249	−	0.840862i	$-0.682048\pi$
$991$	−1.06310e6			−1.08250			−0.541249	+	0.840862i	$0.682048\pi$
$992$			433773.i			0.440797i
$993$	−258971.	+	1.10339e6i	−0.262635	+	1.11900i
$994$	−3.73876e6			−3.78403
$995$		−	1.81383e6i		−	1.83210i
$996$	69922.3	+	16411.1i	0.0704850	+	0.0165432i
$997$	−1.31515e6			−1.32308			−0.661541	−	0.749909i	$-0.730097\pi$
$997$	−1.31515e6			−1.32308			−0.661541	+	0.749909i	$0.730097\pi$
$998$		−	1.17395e6i		−	1.17865i
$999$	1.12384e6	−	1.35725e6i	1.12609	−	1.35997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.69	yes	78
3.2	odd	2	inner	177.5.b.a.119.10	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.10	✓	78	3.2	odd	2	inner
177.5.b.a.119.69	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)

\(f(q)\)	\(=\)	\(q+6.42743i q^{2} +(2.05646 - 8.76190i) q^{3} -25.3118 q^{4} +39.0573i q^{5} +(56.3165 + 13.2178i) q^{6} +65.2885 q^{7} -59.8512i q^{8} +(-72.5419 - 36.0371i) q^{9} +O(q^{10})\)	\(q+6.42743i q^{2} +(2.05646 - 8.76190i) q^{3} -25.3118 q^{4} +39.0573i q^{5} +(56.3165 + 13.2178i) q^{6} +65.2885 q^{7} -59.8512i q^{8} +(-72.5419 - 36.0371i) q^{9} -251.038 q^{10} -5.09361i q^{11} +(-52.0529 + 221.780i) q^{12} +300.078 q^{13} +419.637i q^{14} +(342.216 + 80.3200i) q^{15} -20.3001 q^{16} +418.344i q^{17} +(231.626 - 466.258i) q^{18} -156.757 q^{19} -988.613i q^{20} +(134.263 - 572.051i) q^{21} +32.7388 q^{22} -238.716i q^{23} +(-524.410 - 123.082i) q^{24} -900.474 q^{25} +1928.73i q^{26} +(-464.933 + 561.496i) q^{27} -1652.57 q^{28} +1294.15i q^{29} +(-516.251 + 2199.57i) q^{30} -398.653 q^{31} -1088.10i q^{32} +(-44.6297 - 10.4748i) q^{33} -2688.88 q^{34} +2549.99i q^{35} +(1836.17 + 912.165i) q^{36} -2417.21 q^{37} -1007.54i q^{38} +(617.099 - 2629.25i) q^{39} +2337.63 q^{40} -3.98886i q^{41} +(3676.82 + 862.968i) q^{42} +159.503 q^{43} +128.929i q^{44} +(1407.51 - 2833.29i) q^{45} +1534.33 q^{46} +1473.68i q^{47} +(-41.7465 + 177.868i) q^{48} +1861.58 q^{49} -5787.73i q^{50} +(3665.49 + 860.309i) q^{51} -7595.52 q^{52} -3452.21i q^{53} +(-3608.98 - 2988.33i) q^{54} +198.943 q^{55} -3907.59i q^{56} +(-322.365 + 1373.49i) q^{57} -8318.04 q^{58} -453.188i q^{59} +(-8662.13 - 2033.05i) q^{60} +3005.69 q^{61} -2562.31i q^{62} +(-4736.15 - 2352.81i) q^{63} +6668.86 q^{64} +11720.2i q^{65} +(67.3262 - 286.854i) q^{66} +8611.05 q^{67} -10589.1i q^{68} +(-2091.60 - 490.910i) q^{69} -16389.9 q^{70} +8909.51i q^{71} +(-2156.86 + 4341.72i) q^{72} -879.765 q^{73} -15536.4i q^{74} +(-1851.79 + 7889.87i) q^{75} +3967.81 q^{76} -332.554i q^{77} +(16899.3 + 3966.36i) q^{78} +3607.80 q^{79} -792.869i q^{80} +(3963.66 + 5228.40i) q^{81} +25.6381 q^{82} -315.278i q^{83} +(-3398.45 + 14479.7i) q^{84} -16339.4 q^{85} +1025.19i q^{86} +(11339.2 + 2661.37i) q^{87} -304.859 q^{88} -12623.1i q^{89} +(18210.8 + 9046.68i) q^{90} +19591.6 q^{91} +6042.33i q^{92} +(-819.815 + 3492.96i) q^{93} -9471.97 q^{94} -6122.50i q^{95} +(-9533.80 - 2237.63i) q^{96} +449.576 q^{97} +11965.2i q^{98} +(-183.559 + 369.500i) 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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